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Physics letters / B 829, 137069 (2022). doi:10.1016/j.physletb.2022.137069, We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with O($a$)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height M$_5$=1+O(g$_0^2$) have the same, approximate, form of the asymptotic cutoff effects: Ka$^2$[$\bar{g}^2$(a$^{−1}$)]$^{0.760}$. A domain wall height M$_5$=1.8, as often used, introduces large mass-dependent K′(m)a$^2$[$\bar{g}^2$(a$^{−1}$)]$^{0.518}$ effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents $\hat{\Gamma}$ of $\bar{g}^2$(a$^{−1}$) but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level O(a$^2$) improvement, which is easy to do [2], should be used in the future – both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases., Published by North-Holland Publ., Amsterdam

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., Comment: matched to the version accepted by PRD

We reconstruct ghost and gluon spectral functions in 2 þ 1 flavor QCD with Gaussian process regression. This framework allows us to largely suppress spurious oscillations and other common reconstruction artifacts by specifying generic magnitude and length scale parameters in the kernel function. The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point. For the infrared and ultraviolet extensions of the lattice propagators as well as the low-frequency asymptotics of the ghost spectral function, we utilize results from functional computations in Yang-Mills theory and QCD. This further reduces the systematic error significantly. Our numerical results are compared against a direct real-time functional computation of the ghost and an earlier reconstruction of the gluon in Yang-Mills theory. The systematic approach presented in this work offers a promising route toward unveiling real-time properties of QCD, We thank A. Cyrol, F. Gao, L. Kades, J. Y. Lin, J. Papavassiliou, and A. Rothkopf for discussions. We thank P. Boucaud and F. De Soto for an earlier collaboration and for their help in the preparation of the lattice data. We are indebted to the RBC/ UKQCD Collaboration, especially to P. Boyle, N. Christ, Z. Dong, N. Garron, C. Jung, B. Mawhinney, and O. Witzel, for access to the lattices used in this work. We also thank the members of the fQCD Collaboration for discussions and collaborations on related subjects. J. R. Q. acknowledges the support of MICINN Grant No. PID2019-107844GB-C22. Numerical computations have used resources of CINES, GENCI IDRIS (Project No. 52271) and of the IN2P3 computing facility in France. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy Grant No. EXC 2181/ 1-390900948 (the Heidelberg STRUCTURES Excellence Cluster), under the Collaborative Research Centre SFB 1225 (ISOQUANT), EMMI, and BMBF Grant No. 05P18VHFCA

1-27 (2021). doi:10.1103/PhysRevResearch.3.023201, The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the 1+1-, 2+1-, and 3+1-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (M��bius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height $M_5=1+{\rm O}(g_0^2)$ have the same, approximate, form of the asymptotic cutoff effects: $ K\,a^2\left[\bar g^2(a^{-1})\right]^{0.760}$. A domain wall height $M_5=1.8$, as often used, introduces large mass-dependent $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents $\hat\Gamma_i$ of $\bar g^2(a^{-1})$ but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level ${\rm O}(a^2)$ improvement, which is easy to do [2], should be used in the future -- both for the fermion and the gauge action. It improves the asymptotic behavior in all cases.

Physics letters / B 809, 135713 (2020). doi:10.1016/j.physletb.2020.135713, We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in 1+1 dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of N≥3 , the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size., Published by North-Holland Publ., Amsterdam

We present a detailed analysis of the kinetic and mass terms associated with the Landau gauge gluon propagator in the presence of dynamical quarks, and a comprehensive dynamical study of certain special kinematic limits of the three-gluon vertex. Our approach capitalizes on results from recent lattice simulations with (2+1) domain wall fermions, a novel nonlinear treatment of the gluon mass equation, and the nonperturbative reconstruction of the longitudinal three-gluon vertex from its fundamental Slavnov-Taylor identities. Particular emphasis is placed on the persistence of the suppression displayed by certain combinations of the vertex form factors at intermediate and low momenta, already known from numerous pure Yang-Mills studies. One of our central findings is that the inclusion of dynamical quarks moderates the intensity of this phenomenon only mildly, leaving the asymptotic low-momentum behavior unaltered, but displaces the characteristic "zero crossing" deeper into the infrared region. In addition, the effect of the three-gluon vertex is explored at the level of the renormalization-group invariant combination corresponding to the effective gauge coupling, whose size is considerably reduced with respect to its counterpart obtained from the ghost-gluon vertex. The main upshot of the above considerations is the further confirmation of the tightly interwoven dynamics between the two- and three-point sectors of QCD., Comment: 32 pages, 10 figures

Progress of theoretical and experimental physics 2020(4), 043B04 (2020). doi:10.1093/ptep/ptaa031, We propose a nonperturbative formulation of the Atiyah–Patodi–Singer (APS) index in lattice gauge theory in four dimensions, in which the index is given by the |$\eta$| invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set of the free domain-wall fermion we perturbatively show in the continuum limit that the curvature term in the APS theorem appears as the contribution from the massive bulk extended modes, while the boundary |$\eta$| invariant comes entirely from the massless edge-localized modes., Published by Oxford Univ. Press, Oxford

Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD's renormalisation-group-invariant process-independent effective charge, $\hat\alpha(k^2)$. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, this coupling saturates at infrared momenta: $\hat\alpha(0)/\pi=0.97(4)$. Amongst other things: $\hat\alpha(k^2)$ is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by $\hat\alpha(k^2)$ suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions., Comment: 10 pages, 4 figures

We report on the first computation of the strong running coupling at the physical point (physical pion mass) from the ghost-gluon vertex, computed from lattice simulations with three flavors of Domain Wall fermions. We find $\alpha_{\overline{\rm MS}}(m_Z^2)=0.1172(11)$, in remarkably good agreement with the world-wide average. Our computational bridge to this value is the Taylor-scheme strong coupling, which has been revealed of great interest by itself because it can be directly related to the quark-gluon interaction kernel in continuum approaches to the QCD bound-state problem., Comment: 6 pages, 3 figures, v2: references added

Physical review letters 96(5), 052001 (2006). doi:10.1103/PhysRevLett.96.052001, The nucleon axial charge is calculated as a function of the pion mass in full QCD. Using domain wall valence quarks and improved staggered sea quarks, we present the first calculation with pion masses as light as 354 MeV and volumes as large as (3.5 fm)^3. We show that finite volume effects are small for our volumes and that a constrained fit based on finite volume chiral perturbation theory agrees with experiment within 7% statistical errors., Published by APS, College Park, Md.

Universität Hamburg, Diss., 2002; 121 pp., (2002). doi:10.3204/DESY-THESIS-2002-044, Published by Deutsches Elektronen-Synchrotron, DESY, Hamburg