Gauge Action Research Articles

Scale setting and hadronic properties in the light quark sector with ( 2+1 )-flavor Wilson fermions at the physical point

We report scale setting and hadronic properties for our new lattice QCD gauge configuration set (HAL-conf-2023). We employ (2+1)-flavor nonperturbatively improved Wilson fermions with stout smearing and the Iwasaki gauge action on a 964 lattice, and generate configurations of 8000 trajectories at the physical point. We show the basic properties of the configurations such as the plaquette value, topological charge distribution and their autocorrelation times. The scale setting is performed by detailed analyses of the Ω baryon mass. We calculate the physical results of quark masses, decay constants of pseudoscalar mesons and single hadron spectra in light quark sector. The masses of the stable hadrons are found to agree with the experimental values within a subpercent level. Published by the American Physical Society 2024

Tensor renormalization group study of (1 + 1)-dimensional U(1) gauge-Higgs model at θ = π with Lüscher’s admissibility condition

We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a θ term, where the U(1) gauge action is constructed with Lüscher’s admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find the first-order phase transition with sufficiently large Higgs mass at θ = π, where the ℤ2 charge conjugation symmetry is spontaneously broken. On the other hand, the symmetry is restored with a sufficiently small mass. We determine the critical endpoint as a function of the Higgs mass parameter and show the critical behavior is in the two-dimensional Ising universality class.

Non-perturbative renormalisation and improvement of non-singlet tensor currents in Nf = 3 QCD

Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form.Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm cT derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.

D and Ds decay constants in Nf = 2 + 1 QCD with Wilson fermions

We present results for the leptonic decay constants of the D and Ds mesons from Nf = 2 + 1 lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range a = 0.098 fm down to a = 0.039 fm, with pion masses varying from around 420 MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain fDs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {f}_{{\ extrm{D}}_{\ extrm{s}}} $$\\end{document} = 246.8(1.3) MeV, fD = 208.4(1.5) MeV and fDs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {f}_{{\ extrm{D}}_{\ extrm{s}}} $$\\end{document}/fD = 1.1842(36), where the precision of our results is mostly limited by the determination of the scale.

Transverse-momentum-dependent wave functions of the pion from lattice QCD

We present a lattice QCD calculation of the transverse-momentum-dependent wave function (TMDWF) of the pion using large-momentum effective theory. Numerical simulations are based on one ensemble with 2+1+1 flavors of highly improved staggered quarks with lattice spacing a=0.121 fm from the MILC collaboration, and one with 2+1 flavor clover fermions and tree-level Symanzik gauge action generated by the CLS collaboration with a=0.098 fm. As a key ingredient, the soft function is first obtained by incorporating the one-loop perturbative contributions and a proper normalization. Based on this and the equal-time quasi-TMDWF simulated on the lattice, we extract the TMDWF. The results for both lattice ensembles are compatible and a comparison with a phenomenological parametrization is made. Our studies provide a first attempt of calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization. Published by the American Physical Society 2024

A comparative lattice analysis of SU(2) dark glueballs* *Supported in part by the Natural Science Foundation of China (12125503, 12335003), and the Natural Science Foundation of Shandong Province, China (ZR2022ZD26)

We study the mass and scattering cross section of glueballs as dark matter candidates using lattice simulations. We employ both naive and improved gauge actions in dimensions with several β values, and we adopt both the traditional Monte Carlo method and flow-based model based on machine learning techniques to generate lattice configurations. The mass of a dark scalar glueball with and the Nambu-Bethe-Salpeter wave function are calculated. Using a coupling constant of as an illustration, we compare the dark glueball mass calculated from the configurations generated from the two methods. While consistent results can be achieved, the two methods demonstrate distinct advantages. Using the Runge-Kutta method, we extract the glueball interaction potential and two-body scattering cross section. From the observational constraints, we obtain the lower bound of the mass of scalar glueballs as candidates of dark matter.

Nucleon form factors in Nf=2+1 lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (GE), magnetic (GM), axial (FA), induced pseudoscalar (FP), and pseudoscalar (GP) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding (10 fm)3]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling gA. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on gA is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a) improvement of the axial-vector current. Published by the American Physical Society 2024

Identifying topological structures with adjoint mode filtering

We present new investigations on the Adjoint Filtering Method (AFM), a proposal for filtering gauge configurations by using adjoint zero modes. This method relies on the existence of the Supersymmetric Zero Mode (SZM), whose density follows the gauge action density for classical configurations. We review how a similar construction on the lattice is implemented based on the overlap operator and test the method against smooth configurations showing a remarkable agreement with the expected densities even when pairs of fractionals instanton/anti-instantons are present and noise is added. Then we explore the application of the method to Monte Carlo generated configurations based on SU(2) gauge group. The tuning of the parameters and quantitative results are explicitly shown for a T3 × R lattice. We show explicit examples comparing the AFM to the density obtained from the Gradient Flow. The agreement is remarkable for some specific configurations containing fractional instantons with the advantage that the AFM does not modify the underlying structures.

Null Hamiltonian Yang–Mills theory: Soft Symmetries and Memory as Superselection

AbstractSoft symmetries for Yang–Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar–Streubel phase space, which is the result of a partial symplectic reduction. The associated momentum map is the electromagnetic memory in the Abelian theory, or a nonlinear, gauge-equivariant, generalisation thereof in the non-Abelian case. This result follows from an application of Hamiltonian reduction by stages, enabled by the existence of a natural normal subgroup of the gauge group on a null codimension-1 submanifold with boundaries. The first stage is coisotropic reduction of the Gauss constraint, and it yields a symplectic extension of the Ashtekar–Streubel phase space (up to a covering). Hamiltonian reduction of the residual gauge action leads to the fully reduced phase space of the theory. This is a Poisson manifold, whose symplectic leaves, called superselection sectors, are labelled by the (gauge classes of the generalised) electric flux across the boundary. In this framework, the Ashtekar–Streubel phase space arises as an intermediate reduction stage that enforces the superselection of the electric flux at only one of the two boundary components. These results provide a natural, purely Hamiltonian, explanation of the existence of soft symmetries as a byproduct of partial symplectic reduction, as well as a motivation for the expected decomposition of the quantum Hilbert space of states into irreducible representations labelled by the Casimirs of the Poisson structure on the reduced phase space.

Corrigendum to “Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz–Krieger algebras”

In the given proofs of Theorem 1.5 in the author’s article "K. Matsumoto, Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz–Krieger algebras", Proc. Amer. Math. Soc. 145 (2017), pp. 1131–1140, there are two places that the matrices are needed to be primitive. The statement of Theorem 1.5 and its proof are corrected.

Simple purely infinite $C^*$-algebras associated with normal subshifts

We will introduce the notion of normal subshift. A subshift ( \Lambda , \sigma ) is said to be normal if it satisfies a certain synchronizing property called \lambda -synchronizing and is infinite as a set. There are many normal subshifts such as irreducible infinite sofic shifts, Dyck shifts, and \beta -shifts whose associated C^* -algebras are simple and purely infinite. Eventual conjugacy of one-sided normal subshifts and topological conjugacy of two-sided normal subshifts are characterized in terms of the associated C^* -algebras and the associated stabilized C^* -algebras with their diagonals and gauge actions, respectively.

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, $I=0$ and $I=2$, using lattice QCD is presented. M\"obius domain wall fermions on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used for the lattice computations which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of $L=4.63$ and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states, two pions with a non-zero relative momentum as well as two pions at rest. Our results for phase shifts for both $I=0$ and $I=2$ channels are consistent with and the Roy Equation and chiral perturbation theory, though at this preliminary stage our errors for $I=0$ are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying $K\to\pi\pi$ decay, on physical-mass ensembles using GEVP.

Self-learning Monte Carlo for non-Abelian gauge theory with dynamical fermions

In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm for non-Abelian gauge theory with dynamical fermions in four dimensions to resolve the autocorrelation problem in lattice QCD. We perform simulations with the dynamical staggered fermions and plaquette gauge action by both in the hybrid Monte-Carlo (HMC) and SLMC for zero and finite temperature to examine the validity of SLMC. We confirm that SLMC can reduce autocorrelation time in non-Abelian gauge theory and reproduce results from HMC. For finite temperature runs, we confirm that SLMC reproduces correct results with HMC, including higher-order moments of the Polyakov loop and the chiral condensate. Besides, our finite temperature calculations indicate that four flavor ${\mathrm{QC}}_{2}\mathrm{D}$ with $\stackrel{^}{m}=0.5$ is likely in the crossover regime in the Colombia plot.

Muon g-2 with overlap valence fermions

We present a lattice calculation of the leading order (LO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment for the connected light and strange quarks, $a^{\rm W}_{{\rm con}, l/s}$ in the widely used window $t_0=0.4~\mathrm{fm}$, $t_1=1.0~\mathrm{fm}$, $\Delta=0.15~\mathrm{fm}$, and also of $a^{\rm S}_{{\rm con}, l/s}$ in the short distance region. We use overlap fermions on 4 physical-point ensembles. Two 2+1 flavor RBC/UKQCD ensembles use domain wall fermions (DWF) and Iwasaki gauge actions at $a = 0.084$ and 0.114 fm, and two 2+1+1 flavor MILC ensembles use the highly improved staggered quark (HISQ) and Symanzik gauge actions at $a = 0.088$ and 0.121 fm. We have incorporated infinite volume corrections from 3 additional DWF ensembles at ${\rm L}$ = 4.8, 6.4 and 9.6 fm and physical pion mass. For $a^{\rm W}_{{\rm con}, l}$, we find that our results on the two smaller lattice spacings are consistent with those using the unitary setup, but those at the two coarser lattice spacings are slightly different. Eventually, we predict $a^{\rm W}_{{\rm con}, l}=206.7(1.5)(1.0)$ and $a^{\rm W}_{{\rm con}, s}=26.8(0.1)(0.3)$, using linear extrapolation in $a^2$, with systematic uncertainties estimated from the difference of the central values from the RBC/UKQCD and MILC ensembles.

Light-cone gauge massive and partially-massless fields in AdS(4)

Using light-cone gauge approach, bosonic and fermionic massive and partially-massless fields in AdS(4) space are considered. For such fields, light-cone gauge action is presented. Considering the massive and partially-massless fields in helicity basis and CFT adapted basis, two simple representations of spin operators entering the light-cone gauge action are discussed. The simple representations for the spin operators are obtained by using bosonic spinor-like oscillators. The bosonic spinor-like oscillators allow also us to treat the bosonic and fermionic fields on an equal footing.

Kaon semileptonic form factors at the physical quark masses on large volumes in Nf = 2 + 1 lattice QCD

We present our results for the kaon semileptonic form factors calculated by using two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)4 at the physical light and strange quark masses in the Nf = 2+1 lattice QCD. The configurations were generated using the Iwasaki gauge action and Nf = 2 + 1 stout-smeared clover quark action. The form factors near zero momentum transfer q 2 can be calculated thanks to the large volume. Using our data, a q 2 interpolation and continuum extrapolation are carried out simultaneously. The value of |Vus | is determined using the result of the form factors at q 2 = 0 in the continuum limit. Our result of |Vus| is compared with the one determined from the CKM matrix unitarity and with those determined using recent lattice results.

Properties of the gradings on ultragraph algebras via the underlying combinatorics

There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by the integers group and the grading by the free group on the edges. In this paper, we characterize properties of these gradings in terms of the underlying combinatorial properties of the ultragraphs. More precisely, we characterize when the gradings are strong or epsilon-strong. The results regarding the free group on the edges are new also in the context of Leavitt path algebras of graphs. Finally, we also describe the relationship between the strongness of the integer grading on an ultragraph Leavitt path algebra and the saturation of the gauge action associated with the corresponding ultragraph C*-algebra.

Perturbative computation in a QED3 -inspired conformal Abelian gauge model on the lattice

We perform perturbative computations in a lattice gauge theory with a conformal measure that is quadratic in a non-compact abelian gauge field and is nonlocal, as inspired by the induced gauge action in massless QED$_3$. In a previous work, we showed that coupling fermion sources to the gauge model led to nontrivial conformal data in the correlation functions of fermion bilinears that are functions of charge $q$ of the fermion. In this paper, we compute such gauge invariant fermionic observables to order $q^2$ in lattice perturbation theory with the same conformal measure. We reproduce the expectations for scalar anomalous dimension from previous estimates in dimensional regularization. We address the issue of the lattice regulator dependence of the amplitudes of correlation functions.

RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions

We present the vector, scalar, and tensor renormalization constants (RCs) using overlap fermions with either regularization independent momentum subtraction ($\mathrm{RI}/\mathrm{MOM}$) or symmetric momentum subtraction ($\mathrm{RI}/\mathrm{SMOM}$) as the intermediate scheme on the lattice with lattice spacings $a$ from 0.04 fm to 0.12 fm. Our gauge field configurations from the MILC and RBC/UKQCD collaborations include sea quarks using either the domain wall or the HISQ action, respectively. The results show that $\mathrm{RI}/\mathrm{MOM}$ and $\mathrm{RI}/\mathrm{SMOM}$ can provide consistent renormalization constants to the $\overline{\mathrm{MS}}$ scheme, after proper ${a}^{2}{p}^{2}$ extrapolations. But at $p\ensuremath{\sim}2\text{ }\text{ }\mathrm{GeV}$, both $\mathrm{RI}/\mathrm{MOM}$ and $\mathrm{RI}/\mathrm{SMOM}$ suffer from nonperturbative effects which cannot be removed by the perturbative matching. The comparison between the results with different sea actions also suggests that the renormalization constant is discernibly sensitive to the lattice spacing but not to the bare gauge coupling in the gauge action.

Topological gauge theory for mixed Dirac stationary states in all dimensions

We derive the universal real-time $\text{U}(1)$ topological gauge field action for mixed Dirac states of fermions, described by a density matrix weighted by a gapped Dirac operator, in all dimensions. The key prerequisites are charge quantization and charge conservation; in fact, charge quantization is the root of the action's topological properties. The gauge action encodes nonquantized linear responses as expected for mixed states, but also quantized nonlinear responses, which are accessible in experiment. Our construction furthermore demonstrates how the physical pictures of anomaly inflow and bulk-boundary correspondence extend to nonequilibrium systems. Finally, we demonstrate the independence of the gauge action of the underlying equilibrium or nonequilibrium nature of dynamics stabilizing the state.