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Under the difficult circumstance due to the COVID-19 pandemic, a number of academic conferences have been cancelled or postponed including Lattice 2020, the primary annual conference in the lattice field theory. As a consequence, researchers, especially our young colleagues, have lost the opportunity to present their research. Through this all online conference, which is held on Aug 4-7, 2020, we aim to address this situation by creating an opportunity to present to an international audience.
The structure of this symposium follows the parallel session format of the annual lattice conference. We choose the timezone which is most convenient for Asia-Pacific participants: 2:00pm-5:40pm in Japan and Korea, 1:00pm-4:40pm in China, etc. The parallel sessions are all on-line.
The subjects are also those of the annual lattice conference, and everyone who would like to participate and give a talk is welcome.
The subjects of the talk include
in Lattice Field Theory.
Please register and submit an abstract through the registration page. Deadline for abstract submission is Friday, July 17, 2020. The registration is free of charge. The connection information will be sent to the participants before the event.
[New July 14, 2020] To further recognise our most outstanding early-career colleagues, we are pleased to announce the "Best Presentation Awards" sponsored through generous support from the Asian Nuclear Physics Association (ANPhA). The awards will recognise outstanding research by graduate students and early-career post-doctoral research associates within 5 years of the award of their PhD, relative to opportunity. Awards will be announced broadly to our community following the on-line conference via lattice-news.
[New July 22, 2020] A preliminary program is available.
Optionally, the speakers can submit a contributed paper to arXiv mentioning the proceedings of APLAT 2020. Details will be posted later.
This symposium is co-hosted by KEK Theory Center and sponsored by Asian Nuclear Physics Association (ANPhA).
Organizers: Yasumichi Aoki (RIKEN R-CCS), Xu Feng (Peking U.), Shoji Hashimoto (KEK, chair), Takashi Kaneko (KEK), Weonjong Lee (Seoul National U), Derek Leinweber (U. of Adelaide), C.J. David Lin (National Chiao Tung U.), Jun Nishimura (KEK)
A variation of the Domain Wall operator with an additional parameter α will be introduced. The conditioning of the new Domain Wall operator depends on α, whereas the corresponding 4D propagator does not. The new and the conventional Domain Wall operator agree for α = 1. By tuning α, speed ups of the linear system solvers of around 20% could be achieved.
We compare two of different methods for coarsening domain wall fermions and discuss progress towards a multigrid method for DWF with the ability to set up and solve during gauge configuration generation.
We present a multiple right-hand side (rhs) implementation of the Adaptive Aggregation-based Domain Decomposition Multigrid method (DD$\alpha$AMG) using twisted mass fermions.
Our implementation extends the strong scaling region of DD$\alpha$AMG and simplifies vectorization, which would otherwise require using vector extensions. This multiple rhs implementation is thus better suited to take advantage of current and emerging HPC trends, which involve increasing core counts per node and more diverse CPU architectures, such as ARM, Intel Xeon, and AMD Epyc.
In this talk, we will describe our implementation strategy and show preliminary scaling results. Moreover, we will show preliminary results obtained using Block Krylov solvers as complementary preconditioners within DD$\alpha$AMG, as provided by the Fast Accurate Block Linear krylOv Solver (Fabulous) library.
We report our recent extension of Bridge++, a general-purpose code set for numerical simulations of lattice gauge theories, to the latest vector processor, NEC SX-Aurora TSUBASA. The Bridge++ project aims at developing a readable, extensible, and portable workbench with sufficiently high performance. Based on the code set we investigate fast algorithms for parallel numerical calculations, and code optimization techniques. While the major target of the code set has been cluster systems with scalar processors, we are now extending it to various architectures such as GPUs and processors with wide SIMD registers. In this talk, we introduce our framework for accommodating these platforms, and present the optimization for the vector processor.
QPACE 4 is the latest member of the QCD PArallel Compute Engine (QPACE) series, which was deployed in Regensburg in June 2020. It features 64 Fujitsu A64FX model FX700 CPUs interconnected by InfiniBand EDR. The A64FX is the first CPU supporting the Arm Scalable Vector Extension (SVE). In this contribution we discuss the implementation of SVE in the Grid Lattice QCD framework and show Grid benchmarks on QPACE 4.
I summarize recent work (arXiv:2003.10974) providing a generalization of finite-volume scattering formalism for non-identical pions in isosymmetric QCD. The result allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As an example, I present a toy implementation for I(πππ) = 0, focusing on the quantum numbers of the ω and h1 resonances.
We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles. The simplification is afforded by using time-ordered perturbation theory (TOPT) and a three-particle quasilocal K matrix that is not fully symmetrized to organize the relevant diagrams in an intuitive manner, ultimately leading to a new form of the quantization condition. This form can then be related algebraically to both the standard quantization condition, which uses a fully symmetric three-particle K matrix, and the quantization condition based on extending unitary representations of the three-particle amplitude to finite volume. It should also allow a more straightforward generalization of the quantization condition to nondegenerate particles, and perhaps also to more than three particles.
We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume three-particle scattering amplitude. Combined with earlier work, this shows the equivalence of the relativistic effective field theory approach of Refs. [1, 2] and the “finite-volume unitarity” approach of Refs. [3, 32]. It also provides a generalization of the latter approach to arbitrary angular momentum of two-particle subsystems.
Hamiltonian effective field theory (HEFT) is an approach which allows for the extraction of hadron finite-volume energy spectra from scattering observables such as phase shifts and inelasticities. As an alternative to Luscher's method, HEFT easily generalises to systems with multiple coupled channels and multiple bare states. HEFT also allows for the extraction of eigenvectors from the Hamiltonian, providing new insight into the composition of finite-volume eigenstates and their dependence on the lattice volume. In this presentation we’ll explore renormalisation in HEFT using pion-nucleon scattering data in the Delta resonance channel. By examining the composition of the Delta resonance and its dependence on the regulator parameter, connections with alternative renormalisation schemes are made.
In this talk, we show the recent status of the rho resonance study in the HAL QCD method.
We investigate the I=1 two-pion potential at $m_{\pi} \approx 411$ MeV by using a new calculation strategy, namely the combination of three techniques: the one-end trick, the sequential propagator, and covariant approximation averaging (CAA).
Thanks to the new strategy, we determine the non-local I=1 two-pion potential at the next-leading-order of the derivative expansion for the first time and obtain the pole of the S-matrix corresponding to the rho resonance.
As regards the resonance parameters, our resonance mass is consistent with the previous study using the finite-volume method, but slightly larger decay width and coupling are obtained. We discuss possible origins of this difference.
Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilaton-like state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain y_m=1+gamma^*= 1.47(5) suggesting that N_f=10 lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4+6 mass-split system exhibits near-conformal dynamics with a relatively light 0^++ isosinglet scalar.
Near-conformal systems are favored candidates to describe composite Higgs or composite dark matter particles. Their finite temperature phase structure may provide new insights into the dynamics. It is particularly important to determine the order of the phase transition. Many-flavor near-conformal systems might exhibit a first-order phase transition with a possibly large latent heat. This could have important phenomenological implications, e.g. the existence of primordial gravitational waves. In our study, we focus on a mass-split system with four light and six heavy flavors.
Starting with the phase structure of the mass-degenerate system, we continue to explore the mass-split system for different ratios of light flavor over heavy flavor masses.
With non-perturbative lattice calculations we investigate the finite-temperature confinement transition of a composite dark matter model. We focus on the regime in which this early-universe transition is first order and would generate a stochastic background of gravitational waves. Future searches for stochastic gravitational waves will provide a new way to discover or constrain composite dark matter, in addition to direct-detection and collider experiments. As a first step to enabling this phenomenology, we determine how heavy the dark fermions need to be in order to produce a first-order stealth dark matter confinement transition.
The thermal transition in QCD has been studied in detail using the staggered-quark formulation. Here we report on progress using Nf=2+1 flavours of Wilson fermions, employing anisotropic, fixed-scale lattice simulations. Observables are compared for two values of the pion mass, focusing on chiral properties: the chiral condensate and its susceptibility, quark number susceptibilities, and the onset of parity doubling in the light and strange baryonic sector. For the pseudo-critical temperature obtained from the chiral condensate, we combine our results with those from twisted-mass fermions and extrapolate to the physical point - without a continuum extrapolation -, yielding T_pc=159(6) MeV.
We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range between (approximately) 58 MeV and (approximately) 163 MeV. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$~MeV.
We will present results on the Dirac eigenvalue spectrum as well as its relation to the axial U(1) and SU(2)xSU(2) symmetries at a high temperature in (2+1)-flavor QCD. The simulations are carried out using the highly improved staggered quarks (HISQ) action on Nτ = 8, 12 and 16 lattices with the aspect ratio Nσ /Nτ in a range of [4,9] and 4-5 pion masses ranging from 160 MeV to 55 MeV at a single temperature of ∼ 200 MeV.
We propose new way of heavy ion collisions experiment data analysis. We analyze physical parameters of fireball created in RHIC experiment based on Grand Canonical Distribution and different Lattice QCD data available at the moment. Our results on chemical potential are in agreement with previous model estimations and do not depend on Lattice setup. At same time, we found possible T(V) states of fireball and estimated the most probable temperature and volume of fireball as function of collision energy.
The chiral symmetry restoration of QCD, with two light flavours in the chiral limit, is expected to be a phase transition belonging to the universality class of 3d O(N) models. The imprint of the criticality should be observed in the thermodynamic observables if we move close enough to the chiral limit. We discuss results of conserved charge fluctuations and Polyakov loop, which we propose to behave as energy-like observables with respect to the chiral phase transition, towards the chiral limit. Calculations have been performed on 2+1 flavour HISQ ensembles with pion masses starting from 160 MeV down to 55 MeV.
Chirality of HYP-smeared staggered quarks and its matrix elements on Dirac eigenspace are studied. We introduce a new chirality operator and a new shift operator, and show that chiral Ward identities relate them. Leakage is defined as matrix elements between two eigenstates of the staggered Dirac operator, which represents the transition matrix from one eigenstate to the other. Numerical evidence of Ward identities on leakage patterns for the chirality and shift operators is presented. We also show that approximate conservation of taste symmetry appears as a characteristic of leakage patterns of the chirality, which allows us to distinguish would-be zero modes from non-zero modes. The amount of the unphysical leakages indicates the size of the taste symmetry breaking.
We study chirality of staggered quarks on the Dirac eigenvalue spectrum using machine learning technique. As a result of theoretical research, we expect a characteristic pattern, we call leakage pattern, in the matrix elements of the chirality operator sandwiched between two eigenstates of staggered Dirac operator. Machine learning analysis gives 98.7(34)% accuracy per a single normal gauge configuration for classifying non-zero mode quartets in Dirac eigenvalue spectrum. It confirms that the leakage pattern is universal on normal gauge configurations. We choose the multi-layer perceptron (MLP) method which is one of the deep learning models. It happens to give the best performance in our study. The model's prediction is compared with other models', such as XGboost. Numerical study is done using HYP staggered quarks on the $20^4$ lattice in quenched QCD.
The supercomputer Fugaku is a new supercomputer in Kobe, Japan, co-developed by RIKEN with Fujitsu, and the top system of the latest June 2020 TOP500 supercomputers. I will introduce the supercomputer Fugaku and a Lattcie QCD simulation library, QCD Wide SIMD library (QWS) for Fugaku. I will also present some tuning methods for Fugaku, QWS performance on Fugaku, and tentative benchmark results on full system of Fugaku.
As parallel systems become massive, the neighboring communication in lattice QCD becomes more and more important.
In this talk, I will focus on the implementation of neighboring communication in QCD Wide SIMD library (QWS) for the supercomputer Fugaku.
We adopt the double buffering algorithm and implement it on top of a wrapper library to call the uTofu API, which is a low level interface for the TofuD interconnect.
The wrapper part is independent from the other part of QWS and can be used from the other applications. As an example, we use it in solving 2-dimensional Poisson equation.
Lattice QCD is one of the major scientific work-loads on supercomputer installations. Most of the computer time is spent in an iterative solver of a large, sparse set of linear equations. One of the simplest examples of such an iterative solver is the conjugate gradient algorithm. In this talk, we present an optimized implementation of this algorithm in the context of Lattice QCD for Xilinx Alveo U280 accelerator cards. We compare its performance with that obtained on a CPU architecture and highlight the advantages of an FPGA-based implementation.
The most computational cost in typical lattice QCD simulation is doing the invertion to obtain the propagator. While it is a huge waste to free the propagators in RAM after the contraction. This work explores a field selection algorithm for the correlation functions. The field selection algorithm constructs the correlation function by selecting point on the lattice. It is found that almost the same precision can be obtained at three point function and two point function with about 1/100 point of full lattice. The field selection algorithm has a huge advantage to save the propagators on disk and also to accelerate the complex contraction.
The origin of the low-lying nature of the Roper resonance has been the subject of significant interest for many years, including several investigations using lattice QCD. It has been claimed that chiral symmetry plays an important role in our understanding of this resonance. We present results from our systematic examination of the potential role of chiral symmetry in the low-lying nucleon spectrum through the direct comparison of the clover and overlap fermion actions. After a brief summary of the background motivation, we specify the computational details of the study and outline our comparison methodologies. We do not find any strong evidence supporting the claim that chiral symmetry plays a significant role in understanding the Roper resonance on the lattice.
We study I = 0 quarkonium resonances decaying into pairs of heavy-light mesons using static-static-light-light potentials from lattice QCD. To this end, we solve a coupled channel Schrödinger equation with one confined quarkonium channel and two channels with a heavy-light meson pair to compute phase shifts and t-matrix poles for the lightest decay channel. Finally, we discuss our results in the context of corresponding experimental results.
We investigate meson-baryon interactions in the HAL QCD method with all-to-all propagators using the stochastic estimations. We mainly report the analysis of the S-wave kaon-nucleon interactions at $m_{\pi} \approx 570$ MeV. Since there are no quark-antiquark creation/annihilation processes in this system, all-to-all propagators merely play a role in increasing statistics. In addition, we present the preliminary results for the P-wave pion-nucleon interaction in the $I=3/2$ channel using the $\Delta$ source operator on a small volume at $m_{\pi} \approx 870$ MeV, which has a bound state corresponding to the $\Delta$(1232) state.
We explore the quark composition of bottomonium bound states and resonances with I = 0 and L = 0 using lattice QCD static potentials from a previous study of string breaking and the Born-Oppenheimer approximation. We also compare the relative importance of meson-meson and diquark-antidiquark creation operators for the lattice QCD static potential relevant for b-bar b-bar u d tetraquarks with I = 0.
We report our estimation for the Isgur-Wise form factors for the inclusive semileptonic $B \to X_c \ell\nu$ on 2+1-flavor lattice QCD.
The M\"obius domain-wall fermion action is used for light, strange, charm and bottom quarks. The structure function receives contributions from various exclusive modes, including the dominant S-wave states $D^{(*)}_s$ as well as the P-wave states $D_s^{**}$. In this work, we identify and separate these contributions in the lattice data, from
which we put some constraints on the $B_s \to D_s^{**}\ell\nu$ form factors. Our work takes into account the structure functions for the cases of zero-recoil and non-zero recoil.
Layered systems such as graphene have become an important area of investigation. Within the broader programme of investigating critical phenomena in such systems, we look at different mass configurations for domain wall fermions and overlap fermions in 2+1D. The equivalence between formulations is reviewed, and formulations for the condensate and susceptibility are given. Locality of fermion operators is required for the recovery of U(2) symmetry and is demonstrated with numerical experiments. Further aspects are also considered.
A correct non perturbative treatment of gauge theories requires physical particles to be described by gauge invariant operators. It is then appropriate to use composite operators made of elementary gauge dependant fields as physical observables.
We present the first lattice calculation of the scattering amplitude of Goldstone bosons in the singlet channel relevant to test the viability of a composite Higgs scenario beyond the Standard Model. In such a framework, the scattering of the underlying Goldstone bosons controls the properties of the Higgs boson. The Higgs boson properties are constrained by the Standard Model and experimentally measured by the CERN experiments and therefore provide stringent tests of models of new physics.
In this work we focus on a SU(2) gauge theory with 2 flavours of Dirac fermions in the fundamental representation, a minimal UV completion of a composite Higgs model. We calculate the scattering amplitude near threshold of two of two Goldstone bosons in the singlet channel. The first principle prediction sheds light on the viability of the model.
Using complex Langevin dynamics, we probe the possibility of dynamical breaking of supersymmetry in a class of low-dimensional N=2 supersymmetric quantum field theories with complex potentials. We conclude that complex Langevin dynamics can reliably predict the nonperturbative breaking of supersymmetry in cases where Monte Carlo methods are unreliable.
We report the progress in the lattice studies of Sp(4) gauge theory coupled to fermions in the antisymmetric representation. Such a theory containing three Dirac flavors has a direct relevance to the phenomenological model building for certain types of composite Higgs and top partial compositeness. We formulate the lattice action with the standard plaquette and the Wilson-Dirac fermions. Our primary interests are in the mass spectra and the decay constants of (flavored) spin-0 and spin-1 mesons. In the quenched setup we measure these quantities at several values of the lattice spacing and valence fermion mass, and extrapolate the results to the continuum and the massless limits. Towards the dynamical calculations we also present some preliminary results by focusing on the finite volume effects and the mass dependence at finite lattice spacing.
Hadronic matter is known to change its behaviour during a crossover at finite temperature. One part of this crossover is the chiral transition, whose properties are well studied. The other part involves the fate of hadronic bound states and single quarks, the transition of which is less clear. We study two-flavor QCD for temperatures starting from 190 MeV and quark masses down to lighter-than-physical quarks using chirally symmetric domain-wall fermions. Adopting a novel approach to fit lattice data we get new results for screening masses, which allow for a more detailed comparison to perturbative calculations. The lattice data favors a cut instead of a single pole for the propagation of hadronic excitations above Tc. Key features of previous studies, including chiral spin and SU(4) symmetry, are reproduced.
We will present results on the second order fluctuations of net baryon number, electric charge and strangeness as well as correlations among these conserved charges in (2+1)-flavor lattice QCD in the presence of a background magnetic field.
Simulations are performed using the tree level improved gauge action and the highly improved staggered quark
(HISQ) action with a fixed scale approach ($a$=0.117 fm). The light quark mass is set to be 1/10 of the physical strange quark mass and the corresponding pion mass is about 220 MeV at vanishing magnetic field. At zero temperature the simulations are performed on $32^3\times96$ lattices while at nonzero temperature on $32^3\times N_\tau$ lattices having six values of $N_\tau$ varying from 16 to 6 corresponding to temperature ranging from 105 MeV to 280 MeV. The magnetic field strength $eB$ is simulated with about 15 different values up to 3.5 GeV$^2$ at each temperature. Chiral condensates and disconnected susceptibilities as a function of $eB$ are also discussed.
We study the pressure anisotropy in anisotropic finite-size systems in SU(3) Yang-Mills theory at nonzero temperature. Lattice simulations are performed on lattices with anisotropic spatial volumes with periodic boundary conditions. The energy-momentum tensor defined through the gradient flow is used for the analysis of the stress tensor on the lattice. We find that a clear finite-size effect in the pressure anisotropy is observed only at a significantly shorter spatial extent compared with the free scalar theory, even when accounting for a rather large mass in the latter.
In this report we present our first results on lattice study of QCD equation of state in external magnetic field and at finite baryon density. The simulations are performed with $N_f = 2+1$ rooted staggered quarks at physical quark masses. Finite baryon density is implemented through the lattice simulations at imaginary chemical potential. The results for the equation of state are expanded in imaginary chemical potential up to $O(\mu_B^6)$ and analytically continued to the real domain. A significant influence of the magnetic field on QCD equation of state is observed.
The chiral susceptibility, or the first derivative of the chiral condensate, is used as a probe for QCD phase transition. It is well-known that the chiral condensate is an order parameter of SU(2)_L x SU(2)_R symmetry breaking. However, the condensate also breaks the axial U(1) symmetry, which is usually not paid attention as it is already broken by anomaly. In this talk, we would like to show a surprising numerical result by JLQCD collaboration that the chiral susceptibility is dominated by the axial U(1) anomaly at high temperature. Namely, the chiral susceptibility is probing the temperature dependence of anomaly, rather than that of SU(2)_L x SU(2)_R.
There exists a long standing discrepancy of around 3.5 sigma between experimental measurements and standard model calculations of the magnetic moment of the muon. Current experiments aim to reduce the experimental uncertainty by a factor of 4, and Standard Model calculations must also be improved by a similar order. The largest uncertainty in the Standard Model calculation comes from the QCD contribution, in particular the leading order hadronic vacuum polarisation (HVP). To calculate the HVP contribution, we use lattice gauge theories which allows us to study QCD at low energies. In order to better understand this quantity, we investigate the effect of QED corrections to the leading order HVP term by including QED in our lattice calculations, and investigate flavour breaking effects. This is done using fully dynamical QCD+QED gauge configurations generated by the QCDSF collaboration and a novel method of quark turning.
Understanding the tension between the Standard Model prediction and the experimental results on the anomalous magnetic moment of the muon (a_\mu) has been an active research field over the past two decades. The theoretical uncertainty mainly comes from the hadronic contributions, among which the hadronic light-by-light scattering ($a_\mu^{hlbl}$) process plays an important role. We investigate this contribution on the lattice with a position-space approach. In our setup, we treat separately the QED part in the continuum and infinite volume and the QCD part on the lattice, which helps to avoid finite-size effects due to the photon in finite-volume. However, noticeable finite-size effects due to long-distance physics still persist in our approach. In our recent work [arXiv:2006.16224], we have performed computations of $a_\mu^{hlbl}$ on the lattice with $N_f=3$ ensembles having degenerate light and strange quark masses. Our results have satisfactory statistical errors and allow us to concentrate on our strategy to control the finite-size effects using the pion-exchange contribution. The extension of our setup to include non flavor-symmetric ensembles does not require much effort, thanks to the pre-computed single-propagator trace in position space shared among other Mainz projects. Our work in progress toward the physical point will be briefly reported, with focus on the Wick-contraction topologies that vanish at the flavor-symmetric point.
The leading finite-volume corrections to the HVP contribution to the muonic (g-2) are related to the forward Compton amplitude of the pion in a completely model-independent fashion. The developed formalism is able to capture a few leading contributions, up to errors of order exp(-wML) where w~1.93 and M is the pion mass. By using models and chiPT for the forward Compton tensor, the finite-volume corrections are estimated for typical interesting volumes.
We use a method to calculate the hadron's charge radius without model-dependent momentum extrapolations. The method does not require the additional quark propagator inversions on the twisted boundary conditions or the computation of the momentum derivatives of quark propagators and thus is easy to implement. We apply this method to the calculation of pion charge radius ⟨r^2⟩. For comparison, we also determine ⟨r^2⟩ with the traditional approach of computing the slope of the form factors. The new method produces results consistent with those from the traditional method and with statistical errors 1.5-1.9 times smaller. For the four gauge ensembles at the physical pion masses, the statistical errors of ⟨r^2⟩ range from 2.1% to 4.6% by using ≲50 configurations. For the ensemble at m_π≈340 MeV, the statistical uncertainty is even reduced to a sub-percent level.
For the first time the openQD code was used to generate fully dynamical Nf=1+2+1 QCD+QED configurations with C boundary conditions and degenerate down and strange quarks at an unphysical value of the electromagnetic coupling alpha~0.04. In this talk, technical details about the generation, will be presented. In particular the stability of the algorithm, diagnostic observables and neutral and charged meson masses will be discussed. Furthermore the chosen tuning strategy will be shortly presented.
The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-N limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.
The type IIB matrix model was proposed as a nonperturbative formulation of superstring theory. In particular, interesting results such as the emergence of (3+1)D exponentially expanding space-time have been obtained from the Lorentzian version of the model. Recently the complex Langevin simulation of the bosonic model has been performed to avoid the previously used approximation in overcoming the sign problem. In this talk, we include the effects of fermions in this simulation to discuss their impact on the (3+1)D space-time structure.
In a recent work, we describe and quantify a method for setting up a lattice for quantum field theory in AdS2 based on the triangle group, which enables maximally symmetric tilings of hyperbolic space. Here we extend this lattice setup to the AdS3 cylinder via Hamiltonian methods, enabling us to study dynamical systems. We verify basic properties of this discretized Euclidean AdS3 space with the continuum, such as propagators and the four-point function. For the latter, using a ``conformal center of mass frame" we are able to make the kinematic variables of the configuration conformal, providing a convenient framework for further study.
The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In the previous work, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. There, an approximation was used to avoid the sign problem, however. In this talk, we report our results obtained by using the complex Langevin method to overcome the sign problem instead of using the approximation. In particular, we discuss the space-time structure in the large-N limit based on our results obtained for large matrix size.
The Casimir effect is a quantum phenomenon rooted in the fact that vacuum fluctuations of quantum fields are affected by physical objects and boundaries. As the energy spectrum of vacuum fluctuations depends on distances between (and geometries of) physical bodies, the quantum vacuum exerts a small but experimentally detectable force on neutral objects. Usually, the associated Casimir energy is calculated for free or weakly coupled quantum fields. Recent studies of the Casimir effect in non-perturbative regimes within lattice gauge field theory are reviewed in the present talk. We discuss vacuum restructuring in finite geometries: the influence of the Casimir boundaries on the chiral and deconfining phase transitions and the mass-scales.
We present an update on our previous studies [1] of pure U(1) lattice gauge theory with a sign problem due to a complex coupling \beta. To that end a novel simulation method is employed:
Configuration space is rewritten as a union of linear submanifolds in complexified space. These submanifolds are the tangent spaces of the Lefschetz thimble decomposition. Therefore the sign problem is drastically reduced.
Tangent spaces are infinite spaces, so we specify boundaries for them, such that homotopy to real field space is in the end ensured.
The Monte Carlo simulation is set up on the tangent space corresponding to the global minimum of the action.
The other spaces are taken into account by linear mappings to them, so we can monitor their respective contributions one by one. The relative weights are computed via reweighting.
We discuss simulation results including the scaling of the sign problem with the number of tangent spaces. In particular, promising results are obtained for the beta_I / beta_R > 1 region which is relevant in the context of quantum real-time simulations.
[1] J. M. Pawlowski, M. Scherzer, C. Schmidt, F. P. G. Ziegler, F. Ziesché, „Simulating gauge theories on Lefschetz thimbles“, , 37th International Symposium on Lattice Field Theory, arXiv:2001.09767 [hep-lat]
Monte Carlo simulation of gauge theories with a theta term is known to be extremely difficult due to the sign problem. We consider the complex Langevin method (CLM), which is one of the approaches to overcome this problem. As a first step, we apply the method to 2D U(1) gauge theory with a theta term, which can be solved analytically. We find that naive implementation of the method fails because of the topological nature of the theta term. In order to circumvent this problem, we introduce a puncture on the torus. We find that the CLM works and reproduces the exact results for the punctured model even at large theta. We also prove that the punctured model is equivalent to the infinite volume limit of the original model inside the fundamental domain of theta.
The Monte Carlo simulation of the gauge theory with a theta term is difficult due to the sign problem. We use the complex Langevin method to overcome the problem. In our previous work on two-dimensional U(1) gauge theory with a theta term, we were able to reproduce the exact solution by introducing a puncture on the torus. We also proved that the effect of the puncture disappears in the infinite volume limit as long as |θ|<π. In this study, we extend this method to four-dimensional SU(2) gauge theory. Recently the analytic study of 't Hooft anomaly matching condition predicted two possible phase structures around θ=π for this theory. We discuss the possibility of investigating the phase structure by the complex Langevin simulation.
We explore the phase diagram of the 2+1-dimensional Gross-Neveu model in the limit of infinite flavors, which shares certain properties with QCD, and the existence of an inhomogeneous phase using lattice field theory. Numerical results are presented, which include the phase boundaries in the $\mu$-$T$ plane as well as the structure of the chiral condensate in the inhomogeneous phase.
We provide evidence for partial deconfinement by using lattice Monte Carlo simulations of some bosonic matrix models.
Partial deconfinement is the phenomenon that coexists the confined and deconfined phases in the system, in particular of several large-N gauge theories, at finite temperature.
By appropriately fixing the gauge, we observe that only submatrices deconfine in the analysis of the gauged-Gaussian matrix model and the Yang-Mills matrix model.
We also discuss the applications to QCD.
We present the first realistic lattice QCD calculation of the γW-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of the γW loop is calculated using a lattice QCD simulation, complemented by the perturbative QCD result at high momenta. Using the pion semileptonic decay as an example, we demonstrate the feasibility of the method. By using domain wall fermions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axial γW-box correction to the semileptonic pion decay, □γWVA|π=2.830(11)stat(26)sys×10−3, with the total uncertainty controlled at the level of ∼1%. This study sheds light on the first-principles computation of the γW-box correction to the neutron decay, which plays a decisive role in the determination of |Vud|.
Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, then π−π− → ee and π− → π+ee (or equivalently π−e+ → π+e−) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to the π
− → π+ee transition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constant gππv(mρ) =−10.89(28)stat(74)sys, which is close to gππv(mρ) = −11.96(31)stat determined from the crossed channel π−π− → ee decay.
In this talk I will briefly review our recent lattice calculations for matrix elements contributing to the mass and width differences of neutral $B$ mesons [arXiv:1907.01025, arXiv:1910.00970]. The calculations were done using the MILC ensembles generated with 4-flavours of sea quarks utilizing the highly improved staggered quark action. An improved nonrelativistic quark action was used for the bottom quark. Consequences of these calculations include determinations of the CKM matrix elements $|V_{td}|$ and $|V_{ts}|$, predictions for the rare branching fractions $B_{d,s} \to \mu^+ \mu^-$, and an improved Standard Model determinations for $\Delta \Gamma_s$.
We are presenting our ongoing Lattice QCD study on $B-\bar{B}$ mixing. Comparing a variety of different methods, we are extracting bag parameters $B_{B_{s}}$ and $B_{B_{d}}$ on several RBC/UKQCD and JLQCD ensembles with 2+1 dynamical-flavour domain wall fermions, including physical-pion-mass ensembles. We are simulating a range of heavy quark masses on each ensemble from below the charm quark mass towards (but still below) the bottom quark mass. The plan for this study is to perform a full continuum limit allowing us to get an independent determination of the CKM matrix elements $|V_{ts}|$ and $|V{td}|$, which will help to test whether the CKM matrix is indeed unitary.
The 't Hooft limit of QCD, also referred to as large Nc limit, constitutes a simplification of the theory that preserves most of its non-perturbative properties, including confinement and spontaneous chiral symmetry breaking. It also leads to some definite predictions such as a non-existing Delta I=1/2 rule in the K-> pi pi isospin decay amplitudes. Many phenomenological approaches to hadron physics employ approximations inspired by this limit, even for quantities such as the former, where the large Nc prediction is off. In this talk, I will present our recent lattice results for some relevant observables for light meson physics, such as meson mases and decay constants, nonleptonic kaon decay amplitudes, and scattering amplitudes.
Tempered Lefschetz thimble method (TLTM) [Fukuma-Umeda(1703.00861)] is an algorithm towards solving the numerical sign problem. There, the integration region is deformed into the complex space following the antiholomorphic gradient flow equation, and the system is parallel-tempered using the flow time as a tempering parameter so as to solve both sign and ergodicity problems simultaneously. In this talk, I explain the basics of the algorithm, and discuss its application to various models, including the Thirring model, the Hubbard model away from half filling, and the theta vacuum with finite theta. An application to a chiral matrix model (a toy model of finite density QCD) will be discussed by Nobuyuki Matsumoto in his talk.
Monte Carlo simulations of finite density QCD is plagued by the sign problem. The tempered Lefschetz thimble method (TLTM) [Fukuma-Umeda(1703.00861)] is a promising algorithm towards solving the sign problem, where the integration region is deformed into the complex space and the system is parallel-tempered with the flow time so as to solve both sign and ergodicity problems simultaneously. In this talk, we apply the TLTM to a chiral random matrix model, which models finite density QCD in the large N limit. We show that the TLTM correctly reproduces exact results for small N and discuss the scaling of the computational cost as N increases [Fukuma-NM-Umeda(in preparation)]. We also explain how to implement HMC algorithm to the TLTM [Fukuma-NM-Umeda(1912.13303)].
Statistical modeling plays a key role in lattice field theory calculations. Examples including extracting masses from correlation functions or taking the chiral-continuum limit of a matrix element. We discuss the method of model averaging, a way to account for uncertainty due to model variations, from the perspective of Bayesian statistics. Statistical formulas are derived for model-averaged expectation values and for estimating the required model probability weights. In addition, we reframe the common problem of data subset selection (e.g. choice of minimum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a universal alternative to hand tuning of fit ranges.
We present a synergistic approach between machine learning and histogram reweighting to discover and study phase transitions in physical systems. We treat the output of a neural network, designed for phase classification, as an observable in a statistical system enabling its extrapolation over continuous ranges in parameter space using histogram reweighting. The approach, which leads to quantitative results and overcomes the need to understand the studied system in detail, is applied to the two-dimensional Ising model by training a convolutional neural network to separate its symmetric and broken-symmetry phases. We further demonstrate that the Ising-trained neural network is sufficient to predict the phase transition in q-state Potts models and the $\phi^4$ scalar field theory under a change of order, universality class or the presence of continuous or discrete degrees of freedom. Finally, we present calculations of critical exponents and the critical coupling for the Ising model and the $\phi^4$ scalar field theory using a finite size scaling analysis on quantities derived entirely from the neural network implementation and their histogram-reweighted extrapolations.
The quantum link Hamiltonian was introduced two decades ago as an alternative to Wilson’s Euclidean lattice QCD with gauge fields represented by bi-linearfermion/anti-fermion operators, and later generalized as D-theory. Recasting as a Hamiltonian in Minkowski space for real time evolution, D-theory leads naturally to quantum algorithms. We investigate the simplest toy model of U(1) compact QED on triangular 2+1D lattice and construct gauge invariant kernels via the Suzuki-Trotter expansions which are realized as a quantum circuit capable of being tested on the Noisy Intermediate Scale Quantum (NISQ) devices. We demonstrate the performance of our algorithm on the existing hardware called IBM-Q with error mitigation. Furthermore, we also explore the similarity of our model to the Z2 gauge theory. Since its simplest example without dynamics, so-called toric code, can be leveraged as the quantum error correcting code, we may find a clue to an efficient scalable error correction/detection algorithm specifically for our model based on the relation between U(1) and Z2.
Due to the existence of sign problem in the Lattice QCD simulation with finite chemical potential, the traditional Monte-Carlo simulations on classical supercomputers are confronted with significant difficulties on achieving high precision. On the other hand, with the fast development of quantum computers, it might be possible to provide the ultimate solution to sign problem in the future. However, constrained by the nature of NISQ quantum hardware in the current days, quantum noise is one of the main barriers which prevent the realistic applications of quantum computers. Here I will introduce an optimization algorithm, which is run on current quantum devices and has been applied to a 1+1 dimension lattice gauge theory. I will also talk about a method to mitigate the quantum noise in an efficient way, which has been tested on IBM-Q quantum hardwares.
We will present the current status of nucleon structure studies with physical light quarks (m_pi = 135 MeV) in a large spatial extent of about 10 fm. Our calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared O(a) improved Wilson fermions and Iwasaki gauge action at beta=1.82 corresponding to the lattice spacing of 0.084 fm. In this talk, we mainly focus on the quark momentum and helicity fractions, which are regarded as bench marks on lattice calculations of parton distribution functions. In addition, we will also present the preliminary result of the axial charge with another PACS10 ensemble generated at the finer lattice spacing, so as to estimate the systematic uncertainties due to the lattice discretization error.
The hadronic form factors at large momentum transfers often suffer from substantial excited state contributions and poor signal-to-noise ratios. Using the Feynman-Hellmann theorem allows for calculations of the hadronic form factors which only rely on two-point functions this allows access to higher momenta while still controlling the excited state contributions. We will present results from our study of the electromagnetic form factors of the nucleons up to approximately (9 \textrm{ GeV}^2). The calculations are performed using (N_{f} = 2+1) flavour, (\mathcal{O}(a))-improved Wilson fermions on lattices with spacing (a=0.074 \textrm{ fm}) and three different pion masses of (466 \textrm{ MeV}), (360 \textrm{ MeV}) and (310 \textrm{ MeV}).
In this talk we present the first lattice QCD calculation of unpolarized and helicity generalized parton distributions (GPDs) for the proton. We use the quasi-distribution approach, which relies on computations of correlation functions that, for sufficiently fast moving hadrons, can be matched to light-cone distributions using perturbation theory. The calculations are performed on an ensemble of $N_f= 2 + 1 + 1$ maximally twisted mass fermions with a clover improvement, at pion mass $m_\pi=270$ MeV and lattice spacing $a=0.093$ fm. The proton is boosted up to 1.67 GeV to check momentum convergence. We are able to extract the $x$-dependence of GPDs, that is mostly unknown so far, with controlled statistical uncertainties. We also present other directions we explore, such as the extraction of the twist-3 parton distribution function $g_T(x)$ and the test of the Wandura-Wilczek approximation.
We will present the first calculation of the nucleon vector and axial-vector charges with a single 2+1+1 flavors Highly Improved Staggered Quarks (HISQ) ensemble generated by the MILC collaboration and a matching valence action. We will focus on the theoretical foundation of staggered baryons and outline the methods to calculate physical observables with staggered valence quarks.
Current status of LHP+RBC joint nucleon structure calculations using RBC+UKQCD 2+1-flavor domain-wall fermions lattice-QCD ensembles is summarized.
We extract structure functions corresponding to the first moment of the gluon GPDs from the matrix elements of the gluon energy momentum tensor on a clover ensemble with m_{\pi} = 450 MeV. We present the various GFFs for states of different spins with a focus on the D-terms. We then compare extracted physical quantities like the pressure and shear forces between the different hadrons.
We present our results for the semileptonic formfactors of exclusive $B_s \to K \ell \nu$ and $B_s \to D_s \ell \nu$ decays. The calculation is based on RBC/UKQCD's set of 2+1 dynamical flavour gauge field ensembles spanning three lattice spacings. We use domain wall fermions for the valence up/down, strange and charm quarks whilst the bottom quark is simulated using the relativistic heavy quark action. After presenting the extrapolation to zero lattice spacing and physical quark masses we show our complete error budget and kinematic extrapolations over the entire $q^2$ range.
Using our results we predict ratios which serve as tests of lepton flavour universality. These form factors can be combined with experimental data (where available) to extract the CKM matrix elements $V_{ub}$ and $V_{cb}$, complimentary to extractions from $B \to \pi \ell \nu$ and $B \to D \ell \nu$.
We present our (HPQCD) latest lattice QCD calculation of the scalar and the vector form factors for the D → Klν semi-leptonic decay over a full range of q^2 including q^2 = 0. This calculation has been performed on the N_f=2+1+1 MILC HISQ ensembles with the physical and heavier than physical light quark masses.This calculation allows us to precisely determine the central CKM matrix element, V_{cs} in the Standard Model, by comparing the lattice QCD results for the form factors and the experimental decay rate.
We report on our calculation of the B->D(*)\ell\nu form factors in 2+1 flavor relativistic lattice QCD. Our simulations are carried out by employing the M\""obius domain-wall quark action at lattice cut-offs a^{-1} \sim 2.4, 3.6 and 4.5 GeV with the bottom quark masses up to 0.7 a^{-1}. We discuss the extrapolation of the form factors to the continuum limit and physical quark masses.
We present the results of HPQCD's recent calculation of the $B_c \rightarrow J/\psi$ semileptonic form factors and $R(J/\psi)$ for the first time from lattice QCD using the heavy-HISQ method. We also extend these results to angular observables which we compute in the standard model and in several new physics scenarios.
"D → Klν and B → Kl + l − are important heavy to strange semileptonic decay processes, giving us direct comparison with experiment, and access to CKM
matrix elements and potential new physics. We can calculate form factors for
both of these processes in lattice QCD and connect them together by determining heavy to strange form factors for heavy quark masses ranging from c to b. We can also explore the connection to form factors with different light quark masses. Using the HISQ action on N f = 2 + 1 + 1, we demonstrate how D → K calculations can be extended up towards the b by a study of heavy-strange to η_s form factors, including tests of the dependence on heavy quark mass, comparing to HQET expectations. We also give preliminary D → K and B → K results, for the latter including results for the tensor form factor with an accurately renormalised tensor current."
The desire for additional determinations of the CKM matrix element $V_{ub}$ and a long-standing 2-3$\sigma$ discrepancy between results from inclusive $B\to X_u$ and exclusive $B\to\pi$ processes motivate the study of $B\to\pi$ semileptonic form factors on the lattice. The status of our preliminary $B\to\pi\ell\nu$ results will be discussed by highlighting updates to our analysis. The analysis is carried out on a subset of the RBC/UKQCD 2+1f Iwasaki gauge action ensembles, with $b$ quarks simulated using the Columbia formulation of the relativistic heavy quark action, and the light valence-quarks simulated with domain wall fermions. The final results of this project will provide updates to the 2015 RBC/UKQCD $B\to\pi\ell\nu$ result.
We show the heavy quark diffusion coefficient calculated on the lattice. The coefficient is obtained from the color-electric correlators via Kubo formula. The correlators are measured at 1.5$T_c$ on different large isotropic lattices in the quenched approximation under gradient flow. After continuum extrapolation we also extrapolate the continuum correlators back to zero flow time. The extrapolated correlators are then fitted using theoretically motivated model spectral functions. By taking the slope of the spectral function at vanishing frequency we obtain the heavy quark diffusion coefficient. In this talk we will also compare our results with those from other lattice studies.
We present results of chiral condensates, masses and decay constants of neutral pseudo scalar mesons in (2+1)-flavor QCD in the presence of external magnetic fields at zero temperature. We discuss the validity of Gell-Mann-Oakes-Renner relation in a wide region of magnetic field strength $eB$ up to around 3.5 GeV$^2$. The simulations were performed on $32^3\times96$ lattices using the Highly Improved Staggered Quarks (HISQ) action with a single lattice cutoff $a$=0.117 fm and $m_\pi\approx$ 220 MeV. Sixteen values of $eB$ along the $z$ direction up to around 3.5 GeV$^2$ have been applied in the simulation.
We report on our recent results of the shear viscosity $\eta$ of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. The point of our investigation consists in utilization of the inherent scale invariance of CYM, and thereby the possible lattice-spacing dependence of the numerical results was circumvented. Thus the dependence of the shear viscosity $\eta(g,T)$ on the coupling $g$ and temperature $T$ is represented by a scaling function $f_\eta(g^2T)$ as $\eta(g,T)=Tf_\eta(g^2T)$ due to the scaling-invariant property of the CYM. The explicit functional form of $f_\eta(g^2T)$ is successfully determined from the calculated shear viscosity: It turns out that $\eta(g,T)$ of the CYM field is proportional to $1/g^{1.10-1.88}$ at weak coupling, which has a weaker dependence
on $g$ than that in the leading-order perturbation theory but consistent with that of the ""anomalous viscosity"" $\eta\propto 1/g^{1.5}$ under the strong disordered field.
The obtained shear viscosity is also found to be roughly consistent with that estimated through the analysis of the anisotropy of the pressure of the CYM dynamics in the expanding geometry with recourse to a hydrodynamic equation.
We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method (C(t,τ)) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate that the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of C(t,τ) only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed.
This talk is based on
https://arxiv.org/abs/2004.02426
In this report we present the results of lattice study of how rotation influences confinement/deconfinement transition in SU(3) gluodynamics. To conduct this study we pass to the reference frame which rotates with the system under consideration. In this reference frame rotation is accounted for by the external gravitational field. We calculate the Polyakov loop, its susceptibility
and determine the critical temperature of the confinement/deconfinement transition for various angular velocities. We find that rotation leads to rise of the critical temperature.
We have recently performed a determination of the charm quark mass on Nf = 2+1 CLS ensembles of non-perturbatively improved Wilson fermions. I will present the preliminary results of this analysis for the renormalization-group invariant charm quark mass and the ratio m_c/m_s on these ensembles. The extrapolation to the chiral and continuum limits is performed using 5 lattice spacings ranging roughly from 0.09 down to 0.04 fm and pion masses from 420 MeV to 130 MeV. The spatial extent of the ensembles is generally at least 4 / M_\pi. In my talk, I will discuss the various analysis strategies we considered, including the fitting procedure, corrections for the correlations in the data, and the chiral-continuum extrapolation.
In this talk, we present a lattice determination of the coupling constant $\alpha_s$ in $N_f=3$ QCD for renormalization scales $\mu\in(1,2)$ GeV.
The computation has been performed on ensembles generated by the Coordinated Lattice Simulations (CLS) consortium, with tree-level Symanzik-improved gauge action and Wilson O(a)-improved fermions. Our approach is based on the study of current-current correlation functions in position space and allows to determine $\alpha_s$ (or alternatively the $\Lambda$ parameter) with a competitive precision.
The decomposition of energy and momentum in the hadron in terms of quark and gluon constituents is of fundamental importance to hadron structure, and with the ongoing development of the future Electron-Ion Collider, there is tremendous interest in imaging the transverse distributions of these constituents. This program will be strengthened by complimentary studies in Lattice QCD, where a renormalisation of the lattice operators is necessary to connect the calculated distributions to the corresponding phenomenological quantities reported in a familiar renormalisation scheme, such as MS-bar. In such a renormalisation scheme, the quark and gluon operators mix under renormalisation. In literature it has been common to obtain the off-diagonal renormalisation factors through perturbation theory. However, for consistency, a fully non-perturbative renormalisation scheme that computes all components of the renormalisation matrix is desired. We will demonstrate an RI-MOM renormalisation scheme that includes mixed quark and gluon amputated vertex functions, to directly compute the mixing renormalisation factors. The method utilised exploits Feynman-Hellmann techniques to overcome troublesome statistical noise associated with singlet operators. The current demonstration is performed in the quenched approximation, with a straightforward generalisation to the dynamical case to be considered in near-future work.
We propose a method to compute a spectral sum appearing in the QCD sum rule from lattice correlators.
This spectral sum corresponds to the Borel transform of the vacuum polarization, which widely appears in the phenomenological study.
We discuss how to compute it from two-point correlation functions on the lattice.
We measure it for three lattice spacing and confirm that the method gives results consistent with operator product expansion.
The range of energy scales normally accessible by large-volume lattice computations is typically fairly limited
($1/a simeq 1-4$ GeV) and potentially insufficient to reproduce high-energy perturbative results.
In order to match lattice results with more phenomenologically amenable schemes, such as the $\bar{MS}$ scheme, we must evolve the non-perturbative results to higher energies where matching with perturbation theory is possible.
We thereupon present a method to determine both the renormalization constants and anomalous dimensions for local operators by studying ratios and double ratios of correlation functions both in continuum perturbation theory and on the lattice. In particular, we employ the Yang-Mills
(Wilson) gradient flow to parametrize the renormalization scale.
This has two major benefits. On the lattice, the introduction of the flow time fixes the energy scale, which permits a continuum limit free from power divergences in the lattice spacing due to operator mixing.
Further, while the gradient flow slightly complicates perturbation theory, it has been shown that all gauge fields in the bulk are intrinsically renormalized.
Focusing on massless fermion bilinears, we study correlation functions at positive flow time at leading and next-to-leading order in perturbation theory with $\bar{MS}$ subtraction. Through renormalization group equations, it is possible to match these correlators to lattice data at the hadronic scale,
with the goal of identifying an energy regime within which both agree.
We present numerical results for 3d $\phi^4$ field theory on the $R\times S^2$ manifold in radial quantization using the quantum extension of the finite element method (QFE). The Monte Carlo study supports the QFE ansatz that once counterterms cancel effects from geometric defects in the UV, one reaches the nonperturbative conformal fixed point of the 3d Ising CFT. We demonstrate that including the Ricci curvature term for an improved lattice action drastically accelerates the approach to the continuum limit, opening the way for high precision calculation of scaling dimensions, OPE couplings, and the central charge.
When the realizations of QFT on quantum computer are discussed, the Kogut-Susskind formulation of lattice Hamiltonian is a popular option. We provide alternative formulations and discuss the pros and cons.
We perform a digital quantum simulation of the Schwinger model with the theta term, which is practically inaccessible by standard lattice Monte Carlo simulations. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit.
The efficient digitization required for the quantum simulations of QCD can be obtained by approximating continuous SU(3) gluon fields by discrete subgroups. In this talk, we discuss on-going efforts to develop this program of digitization: deriving improved discrete group lattice actions, classical simulations for quantifying systematic errors, and implementable circuits for digital quantum computers.
We discuss continuous symmetries identities using the tensor formulation of lattice spin and gauge models. We show that the symmetries are encoded in the selection rules of the tensor. This allows truncations that preserve the symmetries exactly. We present the tensorial expression of the transfer matrix for Abelian gauge theories and explain how gauge fixing and Gauss's law relate.
We propose redefinitions of the electric quantum numbers such that Gauss's law is always satisfied even when the time evolution is implemented on NISQ devices. We discuss ways to minimize the number of degrees of freedom.
We briefly discuss practical implementations for a Z2 gauge theory.
This follows arXiv:2003.10986 (Phys. Rev. D in press) and Phys. Rev. D 100, 014506
The magnetic polarisability is a fundamental property of hadrons, which provides insight into their structure in the low-energy regime. The pion magnetic polarisability is calculated using lattice QCD in the presence of background magnetic fields. The results presented are facilitated by the introduction of a new magnetic-field dependent quark-propagator eigenmode projector and the use of the background-field corrected clover fermion action. The magnetic polarisabilities are calculated in a relativistic formalism, and the excellent signal-to-noise property of pion correlation functions facilitates precise values.
Signal-to-noise problem and excited states contamination, inter alia, make studies of the QCD string breaking phenomenon a challenging task in lattice QCD. The static quark potentials produced for these studies can be combined with the Born Oppenheimer approximation to give an important insight into I=0 quarkonium resonances. Precise determination of various lattice potentials are also needed for better understanding of the bound states and hybrid mesons recently observed at LHC and other experiments. In this talk, we present preliminary results on the Wilson loop correlators and compare smeared and unsmeared static potentials for two flavour QCD with improved Wilson fermions. The systematic errors are reduced by solving the generalised eigenvalue problem.
The low-lying spectrum of charmed baryons is calculated in lattice QCD on the $32^3 \times 64$, $N_f = 2 + 1$ PACS-CS gauge configurations at the almost physical pion mass of 156 $MeV/c^2$. By employing a set of interpolating operators with different Dirac structures and quark-field smearings for the variational analysis, we extract the ground and first few excited states of the spin-1/2 and spin-3/2, singly-, doubly-, and triply-charmed baryons.
The properties of low-lying charmonium mesons offer points of high precision comparison between lattice QCD and experiment, if discretisation effects set by the charm quark mass can be controlled. Using $n_f=2+1+1$ configurations with the HISQ action, developed by the HPQCD collaboration to have very small discretisation errors, we achieve precision at or below the 1% level for a range of quantities. These include the hyperfine splitting, the $J/\psi$ vector (and tensor) decay constants and the charm connected hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon. For the last of these we are able to obtain a result with a 0.3% uncertainty. At this level of precision it is necessary to understand leading electromagnetic effects which we do through the inclusion of quenched QED. One such effect that must be accounted for is the electromagnetic effect on the tuning of the charm mass in our calculations. The meson mass shift from QED may be separated into contributions from the quark self energy and the physical contribution from the Coulomb potential. We extract the Coulomb potential contribution and compare with expectations from potential models.
Mixing in the $\Sigma^0$--$\Lambda^0$ system is a direct consequence of broken isospin symmetry and is a measure of both isospin-symmetry breaking as well as general SU(3)-flavour symmetry breaking. In this talk we present a novel scheme for calculating the extent of the physical $\Sigma^0$--$\Lambda^0$ mixing using simulations in lattice QCD+QED and discuss some of its features and initial results.
Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Phys. Rev. D101 014509 (2020), we quantify the volume effects for various 1 + 1D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of presentday Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the finite-volume system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes.
In their seminal publication of 1990, Maiani and Testa showed that Euclidean correlators are contaminated by off-shell contributions, limiting a direct extraction of amplitudes away from threshold. In this presentation, we revisit and extend this work, and explore the connection with recent developments on the inverse problem in Lattice QCD.
We review developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which non-perturbatively map spectra and matrix elements to their corresponding infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in the limiting cases of perturbative interactions and systems forming a bound state. Additionally, we study model-independent properties of their corresponding infinite-volume amplitudes, allowing us to rigorously define form-factors of resonating systems and amplitudes useful for BSM physics.
Using a non-relativistic EFT, we derive a general relativistic expression for the energy shift in finite volume. This includes the N-particle ground state, and the first two- and three-particle excited states. In addition, we probe the N particle energy shift formula in complex phi^4 theory. We investigate different fit models, that include relativistic effects, exponentially suppressed corrections and perturbation-theory inspired ansätze. We discuss the challenges to reliably obtain the three-body scattering amplitude.
Recently, many studies of quantum field theory with quantum computers have reported. Quantum calculation can only treat unitary evolution, so thermal physics is one of difficulty of it because one needs to produce mixed states within allowed operations. Towards resolving the problem, we attempt to investigate thermal physics with thermal pure quantum(TPQ) state formalism. TPQ state formalism enables us to calculate the thermal average without mixed states. In the talk, we report progress on the application of TPQ state formalism to quantum field theory.
On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of the charmed and light vector mesons including D/D, Ds/Ds, phi and K. The lattice size is 48^396, which corresponds to a spatial extension of ~5.5 fm with the lattice spacing a~0.114 fm. For the valence quarks we use overlap fermions at several mass points close to their physical values. The results are then interpolated/extrapolated to the physical point.
The rare decay J/ψ→3γ, analog to Ortho-positronium decaying to 3γ in quantum electrodynamics, can provide a high precision test for the non-perturbative quantum chromodynamics. Such a decay process was first observed by CLEO collaboration in 2008 and then by BESIII in 2013. However, the relevant theoretical researches are very limited due to the dominant non-perturbative effects. We propose to use lattice QCD to study this problem. To this end, a new method has been proposed, that only the correlation functions directly related to the physical decay width are computed with all polarizations of the initial and final states summed over, to avoid the complicated decomposition for the matrix element. Using this new method, we present the first lattice result for this rare decay. Such a new method has also been applied for the decay ηc→2γ, and we obtain a lattice result that is consistent with the experimental one within two standard deviations for the first time. In the work of three-photon decay, we also put forward a scheme to analyze the Dalitz plot of the corresponding process based on the lattice data which can provide direct information for the relevant experiments.
A new scheme for color confinement in QCD due to violation of non-Abelian Bianchi identity (VNABI) is proposed and numerical results in pure SU2 and SU3 QCD supporting the scheme are shown.
Understanding the color confinement mechanism is not yet solved in QCD. The dual Meissner effect is one of the most promising pictures as the color confinement mechanism. Recently the dual Meissner picture due to violation of the non-Abelian Bianchi identities was proposed. In this talk, we show numerical results based on that picture in pure SU(3) gauge theory, especially almost perfect Abelian dominance and monopole dominance for the static q-qbar potential without gauge fixing.
Quark confinement is still an unsolved problem. The dual Meissner effect is one of the ideas of this mechanism. In this picture, it is considered that the color flux tube between quarks is caused by the condensation of monopole in the QCD vacuum. However, how to define monopole in QCD is a difficult problem. Recently, it was shown the violation of non-Abelian Bianchi identity is equal to Abelian-like monopole currents. In this talk, we show numerical results of the dual Meissner effect due to these monopole currents.
An analysis of the lattice Landau gauge gluon and ghost propagators for pure Yang-Mills is performed using Padé approximants to compute their analytical structure. The gluon propagator is described by a pair of complex conjugate poles and a branch cut along the negative side of the Euclidean momenta. The ghost propagator revels a simple pole at zero momenta and the method identifies a branch cut that does not start at the origin. We discuss the implications of our finds and compare them to the published literature.
We investigate the two-flavour Schwinger model in the canonical formulation with fixed fermion number.
We use Wilson fermions on the lattice and present a formalism which describes the Dirac operator with dimensionally reduced canonical operators.
These reduced operators allow the direct examination of different meson sectors and the determination of the energy spectrum in
each of the sectors. Using Lüscher's finite-volume mass-shift formula we discuss the 1-meson mass as well as the effective 3-meson coupling.
From the 2-meson energies we determine the scattering phase shifts and compare the 3-meson energies in the finite volume to various
predictions based on scattering theory.
We search for possibly existent bound states in the heavy-light tetraquark channels with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $ using lattice NRQCD for the heavy quarks. We use different gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrix, we perform additionally a Lüscher analysis to extrapolate our results to infinite volume.
We compute hybrid static potentials in SU(2) lattice gauge theory using a multilevel algorithm and three different small lattice spacings. The resulting static potentials, which are valid for quark-antiquark separations as small as 0.05 fm, are important e.g. when computing masses of heavy hybrid mesons in the Born-Oppenheimer approximation. We also discuss and exclude possible systematic errors from topological freezing, the finite lattice volume and glueball decays.
Recent studies by HAL QCD collaboration have been successful in calculating hadron interactions from the first principles of QCD. In this talk, we apply the Laplacian Heaviside (LapH) smearing for the two nucleon source operator to enhance overlap with the low-energy elastic states and calculate the s-wave nuclear force. Our potential with the LapH smeared source has similar structure and comparable statistical errors to that with the standard wall source operator. This will be an important step towards future extension to the P-wave nuclear forces.
The glueballs in the SU(N) Yang-Mills theory are theoretically the most natural among composite dark matter scenarios.
In this work, we evaluate the interglueball potential in SU(N) lattice gauge theories using the HALQCD method and derive the glueball dark matter scattering cross section, and then constrain the scale parameter of the gauge theory from the observational data.
The Heavy quark Operator Product Expansion (HOPE) method allows one to extract information about light-cone matrix elements via local, instant form matrix elements. When applied to the calculation of the pion's light cone distribution amplitude, it allows (in principle) the full x dependence of the distribution amplitude to be determined. In practice, finite statistics and finite momenta mean that only a finite number of moments may be extracted. In this talk, I explain the HOPE method, and show how boosting the hadronic state leads to enhanced sensitivity to the moments. I also discuss some kinematical tricks which enable us to extract information about the second moment at much low momenta than would be naively expected.
The moments of the pion light-cone distribution amplitude (LCDA) can be extracted by comparison with the operator product expansion of the pion hadronic tensor with an artificially heavy intermediate quark. We perform a preliminary lattice calculation of this hadronic tensor in the quenched approximation at multiple lattice spacings and use it to extract the continuum limit of the second moment of the pion LCDA. Our results are in agreement with other lattice calculations of the second moment, illustrating the potential of this method.
We present a detailed study of the nucleon unpolarized parton distribution function (PDF) using the approach of parton pseudo-distribution functions. We use this method to extract PDFs from the lattice results obtained using simulations with the
light quark mass fixed to its physical value. Then, the physical Ioffe time distributions are obtained from the nucleon matrix elements extracted from lattice simulations through a matching procedure. We reconstruct the PDF using different approaches. Using a direct Fourier transform of Ioffe-time data poses an inverse problem, due to the ill-defined inverse equation. We use two advanced reconstruction techniques to tackle this problem: the Backus-Gilbert method and fitting data to a suitable function as implied by global fitting in phenomenology. We fit the real and imaginary parts of Ioffe-time data to the cosine and sine Fourier transform of $x^a(1-x)^b$ type function, respectively. We find good agreement with PDFs from global fits and it is further improved by quantifying several systematic effects.
We present a high-statistics lattice QCD determination of the valence parton distribution function (PDF) of pion, with a mass of 300 MeV, using two very fine lattice spacings of a = 0.06 fm and 0.04 fm. Our analysis use both RI-MOM and ratio-based schemes to renormalize the equal-time bi-local quark-bilinear matrix elements of pions boosted up to 2.4 GeV momenta. We reconstruct the x-dependent PDF, as well as infer the first few even moments of the PDF using the 1-loop perturbative LaMET framework. This talk is based on arXiv: 2007.06590.
We present a Lattice QCD investigation of the pion electromagnetic form factor based on gauge configurations generated by Extended Twisted Mass Collaboration with N_f = 2+1+1 dynamical quark flavors. The calculation is carried out at two different lattice spacing values directly at the physical point. Employing Wilson clover twisted mass fermions at maximal twist guarantees O(a) improved results. We present a preliminary continuum extrapolation of the form factor and compare to the experiment. In addition, we provide an estimate of the pion charge radius.
Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum of massless particles (either bosons or fermions). The current may be produced either in an unbounded curved spacetime or in flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is proportional to the beta-function associated with the renormalization of electric charge. We investigate the electric current density induced by the magnetic field in the vicinity of a Dirichlet boundary in lattice scalar QED. We show that the electric current, generated by this "conformal magnetic effect at the edge" (CMEE), is well described by the conformal anomaly in the symmetry--unbroken phase. In the symmetry--broken phase, the anomalous current becomes the usual Meissner current generated by the superconducting condensate.
We investigate Casimir energy for free fermions on the lattice.
The Casimir energy of fermion fields can be defined with the lattice regularization.
The continuum extrapolation of our results reproduces the Casimir energy known in continuum theory.
We also show the lattice effect for the Casimir energy.
The lattice effect is important as an artifact that should be well-understood in order to perform reliable lattice simulations with a small volume in particle physics.
On the other hand, the lattice effects can appear in materials such as topological insulators in condensed matter physics, and it can be detected in experiments.
We discuss a typical behavior near the phase-transition of the domain-wall fermion.
We study the defects that can be defined within the framework of lattice gauge theories, in the presence of anisotropic couplings and try to identify their target space avatars. These are relevant for describing topological insulators.
We suggest that in Yang-Mills theories the ratio R of the mass of the tensor glueball over the mass of the scalar glueball is a universal quantity that depends only on the dimensionality of the space. To support this conjecture, we compute numerically R for Sp(2N) gauge theories for N = 1, 2, 3, 4 in d=4 Euclidean dimensions on a lattice and we analyse our results together with previous lattice studies of other Yang-Mills theories, in both d=4 and d=3. We then compare our findings to various analytic models in which R can be computed explicitly in the large N limit.. Finally, we show that a constant R might emerge in a context in which scale invariance is broken, giving rise to a light dilaton state that can be interpreted as the lowest-lying scalar glueball. Our results provide further insights towards our understanding of confinement in QCD
Tensor network is an attractive approach to field theory with
negative sign problem. The complex \phi^4 theory at finite density is a test bed for numerical algorithms to verify their effectiveness.
The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm. We find a clear signal of the Silver Blaze phenomenon on a large volume of V=1024^4, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.
The need to reach high hadron momentum is key to calculations of Parton Distribution Functions and other measures of hadron structure within lattice QCD. Meanwhile, the distillation framework provides a valuable means both of more fully sampling the lattice, and of controlling the contribution of excited states. In this talk, we extend the distillation framework through the implementation of the so-called momentum-smearing method, and show that it allows a major improvement in the determination of the energies of the nucleon in motion. We then apply the method to the extraction of the Nucleon Charges between nucleons at non-zero momentum.
In this talk, we highlight our group's recent developments on computing the Compton amplitude in a lattice approach. We briefly discuss how to access the Compton amplitude directly via the second-order Feynman-Hellmann theorem. As an application, we compute the nucleon Compton tensor across a range of photon momenta at an unphysical quark mass. This enables us to study the $Q^2$ dependence of the low moments of the nucleon structure functions in a lattice calculation for the first time. We discuss possible further applications of this approach.
An understanding of the partonic structure of hadrons is an essential ingredient in making precise predictions and measurements of hadronic cross-sections and various Standard, and Beyond Standard, Model parameters. Several encouraging proposals have been developed in the past decade that relate lattice calculable quantities with PDFs via frameworks akin to QCD factorization. We report results of one such LQCD formalism, wherein the pion valence quark distribution is extracted through a short-distance collinear factorization of space-like separated vector and axial-vector current correlations. A simultaneous fit of such matrix elements computed on four distinct gauge ensembles, including systematic lattice corrections, yields a physical Ioffe-time distribution (ITD). The pion valence PDF extracted from this ITD is found to be consistent with experiment across the entire Bjorken-$x$ region, and offers tantalizing clues to its large-$x$ behavior. We further demonstrate the recently derived one-loop matching coefficient that is central to this work has a well-controlled behavior in Ioffe-time.
The light-cone definition of Parton Distribution Functions (PDFs) does not allow for a direct ab initio determination employing methods of Lattice QCD simulations that naturally take place in Euclidean spacetime. In this presentation we focus on pseudo-PDFs where the starting point is the equal time hadronic matrix element with the quark and anti-quark fields separated by a finite distance. We focus on Ioffe-time distributions, which are functions of the Ioffe-time ν, and can be understood as the Fourier transforms of parton distribution functions with respect to the momentum fraction variable x. We present lattice results for the case of the nucleon and the pion, we discuss several lattice systematics and we also perform a comparison with the pertinent phenomenological determinations
We report on our computation of the pseudoscalar-photon transition form factors from twisted mass lattice QCD for three pseudoscalar states, i.e. the neutral pion and the eta and eta' mesons, to determine the corresponding light pseudoscalar pole contributions in the dispersive analysis of hadronic light by light scattering in the muon g-2.
The neutral pion transition form factor is computed directly at the physical point.
While the eta and eta' transition form factors are more numerically challenging than the one for the neutral pion, we present first results for the eta and eta' 3-point amplitude and explore methods for extracting the transition form factors.
We perform a first calculation for the unpolarized parton distribution function of the $\Delta^+$ baryon using lattice QCD simulations within the framework of Large Momentum Effective Theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions are utilized with a pion mass of 270 MeV and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentum $P_3$ with values $\{0.42,0.83,1.25\}$ GeV, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function of $\Delta^+$ is obtained using a non-perturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute the $\overline{d}(x)-\overline{u}(x)$ asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.
The generalization of Lattice Field Theory targeting in curved Riemann manifolds referred to as Quantum Finite Elements (QFE) requires geometrical tools.
A brief outline for the construction of a Simplicial Complex and
its Delaunay dual, the construction Finite Element of lattice action based on
the elegant Discrete Exterior Calculus (DEC) is given. The focus in on spheres and hyperbolic manifolds suited to radial quantization of conformal field theory and
the AdS/CFT correspondence respectively. The formalism aims to construct simlicial
actons for scalar, Dirac and non-Abelian fields.
Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah-Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, which makes the physical roles of edge/bulk modes unclear and the causality of the total theory doubtful. In this talk, we consider a special case where the Dirac operator is in a real representation and its eta invariant becomes the mod-two type APS index. We propose a physicist-friendly reformulation of the mod-two index using domain-wall fermion formalism, which naturally describes how the global anomaly is canceled between edge and bulk.
Recently, in the context of the resurgence program, it was conjectured that the perturbative ambiguity caused by the IR renormalon is canceled against the semi-classical object called bion. This conjecture requires the circle compactification with the $Z_N$ twisted boundary condition, in which the bion solution is found. Contrary to this conjecture, we find that there is no IR renormalon in circle-compactified theories. We then argue that the bion cancels the perturbative ambiguity caused by the proliferation of Feynman diagrams, which are significantly affected by the compactification. These observations are helpful in giving a unified understanding on the resurgence structure.
Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange interactions. In this work we study in detail the properties of such a system which was proposed a long time ago. In particular, dependence of the constraints on lattice geometry and fermion multiplicity is further elaborated and is now classified for all two dimensional, rectangular lattices with arbitrary sizes. For few small systems the constraints are solved analytically and the complete spectra of reduced spin hamiltonias are shown to agree with the original fermionic ones. The equivalence is also extended to fermions in an external Wegner Z2 field. It is also illustrated by an explicit calculation for a particular configuration of Wegner variables.
This talk is about a bosonization procedure based on Clifford algebra-valued degrees of freedom, valid for spaces of any dimension. Its interpretation in terms of lattice Z_2 gauge theory will be presented. Brief comparison with other bosonization proposals will be given.
Despite the success of quantum chromodynamics (QCD) in describing the strong nuclear force, a clear picture of how this theory gives rise to the distinctive properties of confinement and dynamical chiral symmetry breaking at low energy is yet to be found. One of the more promising models used to explain these phenomena in recent times is known as the centre vortex model. In this work we explore the properties of the gluon propagator in the context of this model, adding to the already substantial body of evidence supporting the importance of centre vortices in QCD. We also present novel visualisation techniques that have been devised to allow for detailed hands-on exploration of the centre-vortex structure of the QCD vacuum. These techniques provide new insight into the behaviour of centre vortices in low-energy lattice QCD.
We study ""shifted"" double-winding Wilson loop average in SU(N) lattice Yang-Mills theory by using both strong coupling expansions and numerical simulations.
We evaluate its average by changing the distance of a transverse direction.
From this result, we discuss how interactions between the two color flux tubes change, when the distance $R$ is varied.
At the last lattice conference, we have proposed to investigate the massive Yang-Mills model, namely, Yang-Mills theory with a gauge-invariant gluon mass term, in order to clarify the mechanism of quark confinement in the Yang-Mills theory with massgap. The gluon mass term simulates the dynamically generated mass to be extracted in the low-energy effective theory of the Yang-Mills theory and plays the role of a new probe to study the phase structure and confinement mechanism.
In this talk, we first review the massive Yang-Mills model, whose gauge-invariant gluon mass term is deduced from a specific gauge-scalar model with a single radially-fixed scalar field under a suitable constraint called the reduction condition, and why such a gauge-scalar model is constructed without breaking the gauge symmetry through the gauge-independent description of the Brout-Englert-Higgs mechanism which does not rely on the spontaneous breaking of gauge symmetry. Then, we discuss how the numerical simulations for the proposed massive Yang-Mills theory can be performed by taking into account he reduction condition in the complementary gauge-scalar model on a lattice.
The phase structure of QCD at finite density is expected to be revealed by the complex Langevin method (CLM), which is a promising approach to overcome the sign problem. In particular, we discuss the possibility of investigating the color superconductivity (CSC) on the lattice by the CLM. Towards that end, we predict the parameter region in which CSC occurs in lattice perturbation theory based on the gap equation. Our perturbative calculations are justified by considering a small spatial volume due to the asymptotic freedom. Most notably, we can predict the explicit form of the Cooper pairs without imposing any ansatz.
In a recent work we investigated the existence of inhomogeneous chiral phases (i.e., a phase where the chiral condensate has a spatial dependence) in the 1+1-dimensional Gross-Neveu model at finite number of fermion flavors. In the present work we continue this investigation by studying the formation of baryons, their spatial distribution and their relation to the inhomogeneous chiral condensate.
Replica evolution of classical field is proposed as an approximate simulator of real-time quantum field dynamics at finite temperatures. We consider $N$ classical field configurations $(\phi_{\tx},\pi_{\tx} (\tau=0,1,\cdots N-1)$, dubbed as replicas, which interact with each other via the $\tau$-derivative terms and evolve with the classical equation of motion. The $\tau$-derivative terms in the Hamiltonian, $\xi^2 \sum_x (\phi_{x+\hat{\tau}}-\phi_x)^2/2$, correspond to the kinetic part of the Euclidean action in the imaginary time formalism of the finite temperature quantum field theory by regarding the replica index $\tau$ as the imaginary time index.Thus the replica evolution is technically the same as the molecular dynamics part of the hybrid Monte-Carlo sampling. The partition function of replicas at temperature $\xi$ is proven to be proportional to that in quantum field theory at temperature $T=\xi/N$. At the same time, the time dependence of the replica-index average of field variables is described by the classical equation of motion when the fluctuations are small. We examine the statistical and dynamical properties of the $\phi^4$ theory in the 4+1 spacetime dimensions. We note that the Rayleigh-Jeans divergence in the classical field can be removed in replica evolution with $N \geq 2$ by including the mass counterterm. We also find that the thermal mass obtained from the unequal time correlation function at zero momentum grows as a function of the coupling as in the perturbative estimate in the small coupling region. Hence the replica evolution, the classical field theory with improved quantum statistical property, would be a candidate to represent the real-time evolution of quantum field.