Search

Isospin-breaking corrections to the hadron vacuum polarization component of the anomalous magnetic moment of the muon are needed to ensure the theoretical precision of $g_\mu -2$ is below the experimental precision. We describe the status of our work calculating, using lattice QCD, the QED correction to the light and strange connected hadronic vacuum polarization in a Dashen scheme. We report results using physical $N_f=2+1+1$ HISQ ensembles at three lattice spacings and three heavier-than-light valence quark masses., Comment: 9 pages, 4 figures, to be published in Proceedings of Science, contribution to the 39th International Symposium on Lattice Field Theory, LATTICE2022, Bonn, Germany

Over the last twenty years, work based on lattice supersymmetry has generated many new results and insights into the non-perturbative nature of string theory, quantum black holes, and gravity. This endeavor is a broad research program encompassing lattice field theory, supersymmetry, string theory, and quantum gravity. In this volume, we look at a selected subset of the topics covering recent progress in lattice supersymmetry and holography., 4 pages; Editorial for the issue "Lattice Supersymmetry and Holography" of the European Physical Journal - Special Topics

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in $\mathrm{SU}(2)$ lattice gauge theory in a gauge-invariant manner. We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase. This inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a simple $k$-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical $\beta$ and critical exponent of correlation length $\nu$ of the deconfinement phase transition., Comment: 18 pages, 19 figures, accepted version

We analyse $Z^\prime$ contributions to FCNC processes at the one-loop level. In analogy to the CKM matrix we introduce two $3\times3$ unitary matrices $\hat\Delta_d(Z^\prime)$ and $\hat\Delta_u(Z^\prime)$ which are also hermitian. They govern the flavour interactions mediated by $Z^\prime$ between down-quarks and up-quarks, respectively, with $\hat\Delta_d(Z^\prime)=\hat\Delta_u(Z^\prime)\equiv \hat\Delta_L(Z^\prime)$ for left-handed currents due to the unbroken $\text{SU(2)}_L$ gauge symmetry. This assures the suppression of these contributions to all $Z^\prime$ mediated FCNC processes at the one-loop level. As, in contrast to the GIM mechanism, one-loop $Z^\prime$ contributions to flavour observables in $K$ and $B_{s,d}$ systems are governed by down-quark masses, they are ${\cal O}(m^2_b/M^2_{Z^\prime})$ and negligible. With the ${\cal O}(m^2_t/M^2_{Z^\prime})$ suppression they are likely negligible also in the $D$ system. We present an explicit parametrization of $\hat\Delta_L(Z^\prime)$ in terms of two mixing angles and two complex phases that distinguishes it profoundly from the CKM matrix. This framework can be generalized to purely leptonic decays with matrices analogous to the PMNS matrix but profoundly different from it. Interestingly, the breakdown of flavour universality between the first two generations and the third one, both for quark and lepton couplings to $Z^\prime$, is identified as a consequence of $\hat\Delta_L(Z^\prime)$ being hermitian. The importance of the unitarity for both $\hat\Delta_L(Z^\prime)$ and the CKM matrix in the light of the Cabibbo anomaly is emphasized., Comment: 16 Pages, no figures. V2: comments on lepton flavour universality violation in quark and lepton sectors in sections 3.1 and 3.3, including two new equations, added. Conclusions unchanged. V3: Text partly rewritten so that the paper is devoted to models with a single $Z^\prime$ with only a short comment on $Z^\prime$-Tandem scenario in hep-ph/2302.013354

39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 412 (2023). doi:10.22323/1.430.0412, The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann theorem, which only requires the computation of two-point correlation functions. Both the cases of degenerate energy levels and quasi-degenerate energy levels which correspond to diagonal and transition matrix elements respectively can be considered in this formalism. As an example numerical results for the Sigma to Nucleon vector transition matrix element are presented., Published by SISSA, Trieste

The rates for decays of a nucleon into a meson and an anti-lepton depend on matrix elements that describe the hadronization of the underlying process at the quark level, induced by an effective baryon-number-violating operator. In this work, we point out new isospin and Fierz relations among proton-kaon matrix elements and demonstrate that, in general, the momentum dependence of the nucleon-to-meson form factors can be calculated from the universal final-state interactions in terms of pion-nucleon or kaon-nucleon scattering phase shifts. As an application, we consider the case in which baryon number is only violated by operators involving $\tau$ leptons. In this setup, the direct two-body processes are kinematically not allowed and nucleon decay proceeds via an off-shell $\tau$, leading, e.g., to $p\to \pi^0\ell^+\nu_\ell\bar\nu_\tau$, for which the momentum dependence of the form factors becomes necessary. We use these results to derive novel limits on such otherwise unconstrained Wilson coefficients., Comment: 8 pages, 3 figures

On configurations with 2+1-flavor dynamical domain-wall fermions, we calculate the RI/(S)MOM renormalization constants (RC) of overlap quark bilinears. Hypercubic (HYP) smearing is used to construct the overlap Dirac operator. We investigate the possible effects of the smearing on discretization errors in the RCs by varying the level of smearing from 0 to 1 and 2. The lattice is of size $32^3\times64$ and with lattice spacing $1/a=2.383(9)$ GeV. The RCs in the $\overline{\rm MS}$ scheme at 2 GeV are given at the end, with the uncertainty of $Z_T$ reaching $\le1$% for the tensor current. Results of the renormalized quark masses and hadron matrix elements show that the renormalization procedure suppresses the $\sim$ 30% difference of the bare quantities with or without HYP smearing into 3-5% level., 32 pages, 13 figures

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results., Comment: 51 pages, 8 figures, 3 appendices; v2: small corrections and clarifications to match JHEP version

One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ with lattice spacing $a$, where $\bar{g}(1/a)$ is the running coupling at renormalisation scale $\mu=1/a$ and $n_\mathrm{min}$ is a positive integer. $\hat{\Gamma}_i$ can take any positive or negative value, but is computable by next-to-leading order perturbation theory. It will impact convergence towards the continuum limit. Balog, Niedermayer and Weisz first pointed out how problematic such corrections can be in their seminal work for the O(3) model. Based on Symanzik Effective Theory for lattice QCD with Ginsparg-Wilson and Wilson quarks, various powers $\hat{\Gamma}_i$ are found due to lattice artifacts from the discretised lattice action. Those powers are sufficient when describing spectral quantities, while non-spectral quantities will require additional powers originating from corrections to each of the discretised local fields involved. This new input should be incorporated into ans\"atze used for the continuum extrapolation., Comment: 15 pages, 5 figures, topical plenary talk given at ''The 39th International Symposium on Lattice Field Theory'', 8-13 August 2022, Bonn, Germany

We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$ directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times \mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch $\theta$-dependent vacuum structure of these theories. We then calculate the one-loop potential for the $\mathbb{S}^1$-holonomy in the presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in the $\mathbb{T}^2$. The results point towards some interesting features worthy of further study., Comment: 55 pages, 7 figures. Edited to match published version in JHEP

$Z^\prime$ models belong to the ones that can most easily explain the anomalies in $b\to s \mu^+\mu^-$ transitions. However, such an explanation by a single $Z^\prime$ gauge boson, as done in the literature, is severly constrained by the $B^0_s-\bar B_s^0$ mixing. Also the recent finding, hat the mass differences $\Delta M_s$, $\Delta M_d$, the CP-violating parameter $\varepsilon_K$, and the mixing induced CP-asymmetries $S_{\psi K_S}$ and $S_{\psi \phi}$ can be simultaneously well described within the SM without new physics (NP) contributions, is a challenge for $Z^\prime$ models with a single $Z^\prime$ contributing at tree-level to quark mixing. We point out that including a second $Z^\prime$ in the model allows to eliminate simultaneously tree-level contributions to the five $\Delta F=2$ observables used in the determination of the CKM parameters while leaving the room for NP in $\Delta M_K$ and $\Delta M_D$. The latter one can be removed at the price of infecting $\Delta M_s$ or $\Delta M_d$ by NP which is presently disfavoured. This pattern is transparently seen using the new mixing matrix for $Z^\prime$ interactions with quarks. This strategy allows significant tree-level contributions to $K$, $B_s$ and $B_d$ decays thereby allowing to explain the existing anomalies in $b\to s\mu^+\mu^-$ transitions and the anticipated anomaly in the ratio $\varepsilon'/\varepsilon$ much easier than in $Z^\prime$-Single scenarios. The proposed $Z^\prime$-Tandem mechanism bears some similarities to the GIM mechanism for the suppression of the FCNCs in the SM with the role of the charm quark played here by the second $Z^\prime$. However, it differs from the latter profoundly in that only NP contributions to quark mixing are eliminated at tree-level. We discuss briefly the implied flavour patterns in $K$ and $B$ decay observables in this NP scenario., Comment: 10 pages, no figures. V2: the use of the new mixing matrix for $Z^\prime$ interactions allows a much more transparent description of this tandem and provides new insights into this framework

Using first-principle numerical simulations, we investigate the Casimir effect in zero-temperature SU(3) lattice gauge theory in 3+1 spacetime dimensions. The Casimir interaction between perfect chromometallic mirrors reveals the presence of a new gluonic state with the mass $m_{\mathrm{gt}} = 1.0(1)\sqrt{\sigma} = 0.49(5)\,\mathrm{GeV} = 0.29(3) M_{0^{++}}$ which is substantially lighter than the $0^{++}$ groundstate glueball. We call this excitation ``glueton'' interpreting it as a non-perturbative colorless state of gluons bound to their negatively colored images in the chromometallic mirror. The glueton is a gluonic counterpart of a surface electron-hole exciton in semiconductors. We also show that a heavy quark is attracted to the neutral chromometallic mirror, thus supporting the existence of a ``quarkiton'' (a ``quark exciton'') colorless state in QCD, which is formed by a single quark with its anti-quark image in the chromometallic mirror. Analogies with edge modes in topological insulators and boundary states of fractional vortices in multi-component condensates are highlighted., Comment: 8 pages, 4 figures

The Hamiltonian approach can be used successfully to study the real-time evolution of a non-Abelian lattice gauge theory on the available noisy quantum computers. In this work, results from the real-time evolution of SU(2) pure gauge theory on IBM hardware are presented. The long real-time evolution spanning dozens of Trotter steps with hundreds of CNOT gates and the observation of a traveling excitation on the lattice were made possible by using a collection of error mitigation techniques. Self-mitigation is our novel tool, which consists of using the same physics circuit as a noise-mitigation circuit., 10 pages, 14 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, LATTICE2022, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\"at Bonn, Bonn, Germany

39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 228 (2023). doi:10.22323/1.430.0228, In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions., Published by SISSA, Trieste

We test here our recently introduced new lattice method for the $\beta$-function defined over infinite Euclidean space-time in the continuum from scale changes generated by infinitesimal or finite steps of the renormalized gauge coupling on the gradient flow. Harlander and Neumann calculated in this scheme the three-loop approximation to the continuum $\beta$-function. Our goal is the nonperturbative lattice implementation of the scheme which we tested originally in the chiral limit of the sextet model and in multi-flavor QCD with ten and twelve flavors of massless fermions. Results are reported here in the SU(3) Yang-Mills gauge sector without dynamical fermions and in ten-flavor QCD with massless femions. The three-loop gradient flow based $\beta$-function of Harlander and Neumann is used to connect the $\Lambda_{\overline{\rm MS}}$ scale of the SU(3) Yang-Mills gauge theory with the nonperturbative flow time scale $t_0$, or the equivalent Sommer scale $r_0$. Similarly, the $\Lambda_{\overline{\rm MS}}$ scale is connected with a selected nonperturbative scale in the ten-flavor theory, a pilot study of our new lattice based nonperturbative $\beta$-function for high precision determination of the strong coupling $\alpha_s$ at the Z-boson pole in QCD with three massless fermion flavors. This goal is an important alternative to results from the finite volume based step $\beta$-function of the Alpha collaboration. Work is ongoing on direct application of the method to QCD with three massless fermion flavors., Comment: To appear in the Proceedings of the 39th Annual International Symposium on Lattice Field Theory - LATTICE2022 8-13 Aug, 2022; 9 pages, 8 figures. arXiv admin note: text overlap with arXiv:2203.15847

We present our calculations for the $I$ = 1/2 and 3/2 $K-\pi$ s-wave scattering length with physical quark masses, extracted from the interaction energy of Euclidean two-point functions. We use the domain wall fermion action with physical quark masses at a single lattice spacing. We are specifically interested in the systematic effects due to around-the-world terms on the overall determination of the scattering length. We present our progress and discuss the various systematic effects in our preliminary results., Comment: 39th International Symposium on Lattice Field Theory

Using the high statistics datasets of the HotQCD Collaboration, generated with the HISQ (2+1)-flavor action for light and strange quarks, and treating the charm sector in the quenched approximation, we analyze the second and fourth order cumulants of charm fluctuations and the correlations of charm with lighter conserved flavor quantum numbers. We can make use of a factor 100 larger statistics on ${N_\tau =8}$ lattices which never have been used in studies of charm fluctuations. Analyzing correlations of charm fluctuations with baryon number and electric charge fluctuations we can project onto charmed baryon and meson correlations and compare results with quark model extended hadron resonance gas model calculations. We aim at a precise determination of the dissociation temperature of charmed hadrons and will probe the sensitivity of the fluctuations observables to the presence of multiple-charmed baryons., Comment: 8 pages, 7 figures, Contribution to the 39th International Symposium on Lattice Field Theory (Lattice 2022), 08-13 August 2022, Bonn, Germany. Added one acknowledgement and corrected few typos

Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac preconditioning~\cite{Brower:2018ymy} have shown remarkable success. In this work, we discuss the performance of this staggered multi-grid algorithm in four dimensions. We also demonstrate that offloading some components of a multi-shift solve to a multi-grid solver leads to a significant performance improvement in an existing MILC spectrum workflow on the Summit and Selene supercomputers., Comment: Submission to Proceedings of Lattice 2022: the 39th International Symposium on Lattice Field Theory, Bonn, Germany

We calculate the kaon semileptonic form factors using the two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)$^4$ at the physical point. The lattice spacings are 0.063 and 0.085 fm. The configurations were generated using the Iwasaki gauge action and $N_f=2+1$ stout-smeared nonperturbatively $O(a)$-improved Wilson quark action. From the momentum transfer dependence of the form factors, we evaluate the slope and curvature for the form factors at the zero momentum transfer. Furthermore, we calculate the phase space factor, which is used to obtain $|V_{us}|$ through the kaon semileptonic decay. These results are compared with previous lattice results and experimental values., Comment: 10 pages, 8 figures, Proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany

Reducing memory traffic is critical to accelerate Lattice QCD computations on modern processors, given that such computations are memory-bandwidth bound. A commonly used strategy is mixed-precision solvers, however, these require careful treatment to ensure stable convergence. We give an overview of the strategies employed in QUDA to stabilize mixed-precision variants of Conjugate Gradient (CG), and its multi-shift brethren. Through the use of customized numerical storage formats we can significantly improve upon the precision achievable compared to IEEE numerical formats, increasing both the solver precision and stability achievable at fixed word size. We give examples using BiCGStab(l) and multi-shift CG solvers using the HISQ operator., Comment: 14 pages, 4 figures

We study phase structure and critical point of finite-temperature QCD in the heavy-quark region applying the hopping parameter expansion (HPE). We first study finite-size scaling on the critical point on $N_t=4$ lattices with large spatial volumes taking the leading order (LO) and the next-to-leading order (NLO) effects of the HPE, and find that the critical scaling of the Z(2) universality class expected around the critical point of two-flavor QCD is realized when the aspect ratio of the lattice is larger than about 9. This enables us to determine the critical point in the thermodynamic limit with high precisions. By a study of the convergence of the HPE, we confirm that the result of the critical point with the LO (NLO) approximation of the HPE is fairly accurate for $N_t=4$ (6), while we need to incorporate higher order effects for larger $N_t$. To extend the study to large $N_t$ lattices, we then develop a method to take the effects of higher-order terms of the HPE up to a sufficiently high order. We report on the status of our study on $N_t = 6$ lattice adopting the new method., 9 pages, 5 figures, Proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany

We develop a new method to determine thermal activation rates, such as for bubble nucleation, topology change, \textsl{etc.}, using 4-dimensional Euclidean methods. This allows nonperturbative study on the lattice. We then investigate the strong sphaleron rate in pure-glue QCD at temperatures between 1.3 $\Tc$ and 1000 $T_\mathrm{c}$, making contact with previous results but extending them down close to the critical temperature. The extension to full QCD will be straightforward. Limitations of the proposal (the inability to compute a certain dynamical prefactor, puzzling large-volume behavior, and the inability to treat temperatures $T < 1.3 \, T_\mathrm{c}$) are also discussed., 32 pages, 14 figures, 2 tables. Updated to JHEP version

We present a new Bjorken $x$-dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing $a=0.06,0.09, 0.12$~fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum $xP_z$ and the antiquark momentum $(1-x)P_z$ inside a meson of boost momentum $P_z$ up to 1.72 GeV along the $z$ direction, allowing us to have more accurate determination of the $x$-dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions $x\sim 0, 1$, thus obtaining the full-range $x$-dependence of the amplitude., Update to the published version in NPB

The FASTSUM Collaboration has developed a comprehensive research programme in thermal QCD using 2+1 flavour, anisotropic ensembles. In this talk, we summarise some of our recent results including thermal hadron spectrum calculations using our ``Generation 2L'' ensembles which have pion masses of 239(1) MeV. These include open charm mesons and charm baryons. We also summarise our work using the Backus Gilbert approach to determining the spectral function of the NRQCD bottomonium system. Finally, we review our determination of the interquark potential in the same system, but using our ``Generation 2'' ensembles which have heavier pion masses of 384(4) MeV., 9 pages, Contribution to the 39th International Symposium on Lattice Field theory (LATTICE2022),8th-13th August, 2022, Bonn, Germany

We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the other hand to the perturbative calculation, allowing a precise extraction of the $\Lambda_0$ parameter. This study may open the way to gradient flow calculations of correlators of chromoelectric and chromomagnetic fields, which typically arise in the nonrelativistic effective field theory factorization., Comment: 9 pages, 4 figures, Contribution to the 39th International Symposium on Lattice Field theory (LATTICE2022),8th-13th August, 2022, Bonn, Germany

To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables represented in the positional systems as a series of powers of the radix mulitplied over the summands (``digits``), which turn out to be Hermitean operators with discrete spectrum. We investigate the obtained quantum mechanical operators of digits, the commutation relations between them and the effects of choice of numeral system on the lattices and representations. Furthermore, during the construction of the digital representation renormalizations of diverging sums naturally occur., 27 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:2009.13618 v2: group commutator of coordinate and momentum shifts added

We study two- and three-particle scattering in the O(3) non-linear sigma model in 1+1 dimensions, focusing on the isospin-1 and isospin-2 channels for two particles, and the isospin-3 channel for three. We perform numerical simulations for four values of the physical volume, each at three lattice spacings, using a three-cluster generalization of the cluster update algorithm, and directly extrapolate the determined finite-volume energies to the continuum at fixed physical volume. Lattice results for two particles are then compared against exact predictions, obtained by combining analytic results for the scattering phase shifts and the (1+1)-dimensional two-particle formalism that relates these to finite-volume energies. Analogous comparisons in the three-particle sector are underway, making use of the three-particle relativistic-field-theory finite-volume formalism., 11 pages, 8 figures, contribution to the 39th International Symposium on Lattice Field Theory, 8th-13th of August 2022, Bonn, Germany

We propose a new conjecture on the relation between the species doubling of lattice fermions and the topology of manifold on which the fermion action is defined. Our conjecture claims that the maximal number of fermion species on a finite-volume and finite-spacing lattice defined by discretizing a $D$-dimensional manifold is equal to the summation of the Betti numbers of the manifold. We start with reconsidering species doubling of naive fermions on the lattices whose topologies are torus ($T^{D}$), hyperball ($B^D$) and their direct-product space ($T^{D} \times B^{d}$). We find that the maximal number of species is in exact agreement with the sum of Betti numbers $\sum^{D}_{r=0} \beta_{r}$ for these manifolds. Indeed, the $4D$ lattice fermion on torus has up to $16$ species while the sum of Betti numbers of $T^4$ is $16$. This coincidence holds also for the $D$-dimensional hyperball and their direct-product space $T^{D} \times B^{d}$. We study several examples of lattice fermions defined on discretized hypersphere ($S^{D}$), and find that it has up to $2$ species, which is the same number as the sum of Betti numbers of $S^{D}$. From these facts, we conjecture the equivalence of the maximal number of fermion species and the summation of Betti numbers. We discuss a program for proof of the conjecture in terms of Hodge theory and spectral graph theory., Comment: 31 pages, 16 figures

A study of two-pion scattering for the isospin channels, I=0 and I=2, using lattice QCD is presented. Möbius 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 nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the I=0 and I=2 channels are consistent with 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→ππ decay, on physical-mass ensembles using the GEVP.

We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic $B_{(s)}$-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration's gauge ensembles with lattice spacings down to $a\approx0.03$ fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows for absolutely normalized vector currents, bypassing the need for perturbative matching, which has been a source of uncertainty in previous calculations of $B$-meson decay form factors by our collaboration. All preliminary form-factor results are blinded., Contribution to the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany. arXiv admin note: substantial text overlap with arXiv:2111.05184

We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional sub-leading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find $a_\mu^{\rm W} = 235.56(65)(50) \times 10^{-10}$, which is in $3.8\sigma$ tension with the recently published dispersive result of Colangelo et al., $a_\mu^{\rm W} = 229.4(1.4) \times 10^{-10}$, and in agreement with other recent lattice determinations. We also provide a result for the standard short-distance window. The results reported here are unchanged compared to our presentation at the Edinburgh workshop of the g-2 Theory Initiative in 2022., Comment: 24 pages, 15 figures

The sector of decay constants of the octet of light pseudoscalar mesons in the framework of 'resummed' $SU(3)$ chiral perturbation theory is investigated. A theoretical prediction for the decay constant of $\eta$-meson is compared to a range of available determinations. Compatibility of these determinations with the latest fits of the $SU(3)$ low energy coupling constants is discussed. Using a Bayesian statistical approach, constraints on the low energy coupling constants $L_4^r$ and $L_5^r$, as well as higher order remainders to the decay constants $F_K$ and $F_\eta$, are extracted from the most recent experimental and lattice QCD inputs for the values of the decay constants., Comment: 18 pages, 11 figures. arXiv admin note: text overlap with arXiv:1912.09164

We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from the compact $U(1)$ lattice gauge field by generalizing L\"uscher's constriction so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb{Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle $\theta\to q\theta$ suggested from the Witten effect, our construction provides a lattice implementation of the mixed 't~Hooft anomaly between the $\mathbb{Z}_q$ one-form symmetry and the time reversal symmetry in the $U(1)$ gauge theory with matter fields of charge~$q\in2\mathbb{Z}$ when $\theta=\pi$, which was studied by Honda and Tanizaki [J. High Energy Phys. \textbf{12}, 154 (2020)] in the continuum framework., Comment: 18 pages. The final version to appear in PTEP

The conventional Casimir effect has been studied in the continuous spacetime, but to elucidate its counterpart in the lattice space is an important subject. Here, we discuss various types of Casimir effects for quantum fields on the lattice. By using a definition of the Casimir energy on the lattice, we show that the Casimir effect for the Wilson fermion is similar to that for the continuous Dirac fermion. We apply our definition to an effective Hamiltonian describing Dirac semimetals, such as Cd$_{3}$As$_{2}$ and Na$_{3}$Bi, and find an oscillatory behavior of the Casimir energy as a function of film thickness of semimetals. We also study contributions from Landau levels under magnetic fields and the Casimir effect for nonrelativistic particle fields on the lattice., 9 pages, 6 figures; Proceedings of The 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany

Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in $1+1$D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in $2+1$D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in $2+1$D LGTs, albeit it is generally less pronounced than in $1+1$D, and highly depends on the matter configuration of the initial state. Through suitable matter configurations, we are able to relate and compare the $1+1$D and $2+1$D cases, showing that the main ingredient for the strength of DFL in our setup is the \textit{propagation directionality} of matter. Our results suggest that, generically, DFL is weakened with increasing spatial dimension, although it can be made independent of the latter by minimizing the propagation directionality of matter in the initial state., $7$ pages, $4$ figures

We report on an old computation of propagators of massless scalar fields on an ensemble of configurations in the 4D path integral of Euclidean dynamical triangulations in the collapsed (crumpled) phase. The resulting quantum average is used to calculate the scale factor of a rotational invariant metric in a 4-dimensional space. This new scale factor is non-zero at the origin, which we assume to be caused by the presence of the well-known singular structure in the collapsed phase. It depends on an overall integration constant. A transformation to a metric in (1+3)-dimensions reveals Euclidean black hole features at an instant in time, with a horizon separating interior and exterior parts. Effective Einstein equations in the presence of a `geometric condensate' are assumed, and computed with the software OGRe. We find similarities with the energy density and pressure of gravastars, as well as remnants, and investigate their dependence on the integration constant., 13 pages; rearranged Introduction, added comments, added 3 references to CDT

By considering the example of $SU(2)$ gluodynamics, we check numerically the idea that the strong correlation of the Polyakov loop with the longitudinal gluon propagator and related quantities can be used to substantially reduce the finite-volume effects as well as to extrapolate in temperature over the critical domain., 6 pages, 4 figures

Previous Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions (TMDs) focused on the case of transversely polarized nucleons, and thus did not encompass two leading-twist TMDs associated with longitudinal polarization, namely, the helicity TMD and the worm-gear TMD corresponding to transversely polarized quarks in a longitudinally polarized nucleon. Based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections, TMD observables characterizing the aforementioned two TMDs are evaluated, utilizing an RBC/UKQCD domain wall fermion ensemble at the physical pion mass., 9 pages, 4 figures, to appear in the proceedings of the 39th International Symposium on Lattice Field Theory, LATTICE2022, PoS LATTICE2022, 103

In this study, we extend the HAL QCD method to a case where a total momentum of a two-particle system is non-zero and apply it to the $I=2$ S-wave $\pi\pi$ scattering in order to confirm its validity. We derive a fundamental relation of an energy-independent non-local potential defined in the center of mass frame with NBS wave functions in a laboratory frame. Based on the relation, we propose the time-dependent method to extract potentials, often used in practice for the HALQCD method in the center of mass frame. For numerical simulations in the $I=2$ $\pi\pi$ system, we employ (2+1)-flavor gauge configurations on a $32^3 \times 64$ lattice at the lattice spacing $a \approx 0.0907$ fm and $m_{\pi} \approx 700$ MeV. Both effective leading order (LO) potentials and corresponding phase shifts obtained in laboratory frames agree with those obtained in the center-of-mass frame by the conventional HAL QCD method within somewhat larger statistical errors. In addition, we observe a consistency in scattering phase shifts between ours and results by the finite-volume method as well. The HAL QCD method with non-zero total momenta, established in this study, brings more flexibility to the HAL QCD method, which enables us to handle systems having the same quantum numbers with a vacuum or to access energy regions prohibited in the center of mass frame., Comment: 25 pages, 16 figures

This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity, based on a lattice regularization of the quantum-gravitational path integral. It is shown that inside the, so-called, de Sitter phase one recovers a four-dimensional semiclassical universe, where behaviour of the scale factor is consistent with classical solutions of Einstein's field equations and fluctuations of the scale factor are very accurately described by a simple minisuperspace effective action. It is argued that some of the phase transitions bordering the semiclassical phase are higher-order transitions, which opens a possibility of defining a continuum limit of CDT. Finally, it is discussed how to define the renormalization group flow in CDT and then how to search for a UV fixed point in which, in the spirit of asymptotic safety, quantum theory of gravity could become non-perturbatively renormalizable and thus valid up to arbitrarily short distance scales., Contribution to the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore), expected to appear in 2023

To cure the problem of finding the global maximum of the gauge functional in maximal center gauge we present the Ensemble averaged Maximal Center Gauge (EaMCG). It allows for a vortex specific extraction of the quark-antiquark potential from an ensemble of gauge copies. Evaluating center projected Wilson loops we compare EaMCG with other center vortex based measurements of the string tension in SU(2)., 13 pages

Gauge covariant smearing based on the 3D lattice Laplacian can be used to create extended operators that have better overlap with hadronic ground states. For staggered quarks, we make use of two-link parallel transport to preserve taste properties. We have implemented the procedure in QUDA. We present the performance of this code on the NVIDIA A100 GPUs in Indiana University's Big Red 200 supercomputer and on the AMD MI250X GPUs in Oak Ridge Leadership Computer Facility's (OLCF's) Crusher and discuss its scalability. We also study the performance improvement from using NVSHMEM on OLCF's Summit. Reusing precomputed two-link products for all sources and sinks, it reduces the total smearing time for a baryon correlator measurement by a factor of 100-120 as compared with the original MILC code and reduces the overall time by 60-70%., 10 pages, 6 figures, proceedings of the 39th International Symposium on Lattice Field Theory (Lattice 2022), 8-13 August, 2022, Bonn, Germany

We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number density $\rho_q$ by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that at high temperature, the Lee-Yang zeros lie on the negative real semi-axis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark density discontinuity at the transition line., Comment: 11 pages, 5 figures; Fig.1, Fig.4 improved, typos corrected, discussion of statistical errors added

I discretize axion string configuration coupled to a Dirac fermion, which in the continuum binds a massless chiral fermion in its core when the winding is one. I show that such a configuration can host one or more chiral fermions when regulated on the lattice. Realization of these chiral fermions relies on the presence of Wilson-like terms similar to the Wilson term used in lattice domain wall fermions. The number of chiral fermions on the string jumps as the Wilson-like parameter is varied with respect to the other mass scales in the problem. These jumps coincide with phase transitions along a two dimensional surface passing through the string's core. A one-loop Feynman diagram is used to demonstrate how anomaly inflow works in this lattice regularized theory., Comment: Typo corrected, new references added and style files changed

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}\bar K$ interaction, we have investigated the near-threshold $P$-wave $B_s$ states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the $D_s$ sector by fitting the lattice data. The masses of the bottom-strange partners of the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ are predicted to be $M_{B^{*}_{s0}}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B^{*}_{s1}}= 5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two $P$-wave $B_s$ states are the mixtures of the bare $\bar b s$ core and $B^{(*)}\bar K$ component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the $0^+$ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the $T$-matrix of the $B\bar K$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation., 20 pages, 4 figures. Version accepted by JHEP

Polarizabilities reveal valuable information on the internal structure of hadrons in terms of charge and current distributions. For neutral hadrons, the standard approach is the background field method. But for a charged hadron, its acceleration under the applied field complicates the isolation of the polarization energy. In this work, we explore an alternative method based on four-point functions in lattice QCD. The approach offers a transparent picture on how polarizabilities arise from photon, quark, and gluon interactions. We carry out a proof-of-concept simulation on the electric polarizability of a charged pion, using quenched Wilson action on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV. We show in detail the evaluation and analysis of the four-point correlation functions and report results on charge radius and electric polarizability. Our results from connected diagrams suggest that charged pion $\alpha_E$ is due to a cancellation between elastic and inelastic contributions. It would be interesting to see how the cancellation plays out at smaller pion masses in future simulations., Comment: 24 pages, 13 figures, 2 tables. Version accepted for publication in PRD

The 39th International Symposium on Lattice Field Theory , Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 052 (2022). doi:10.22323/1.430.0052, Substantial progress has been made recently in the generation of master-field ensembles. This has to be paired with efficient techniques to compute observables on gauge field configurations with a large volume. Here we present the results of the computation of hadronic observables, including hadron masses and meson decay constants, on large-volume and master-field ensembles with physical volumes of up to $(18\,\mathrm{fm})^4$ and $m_\pi L$ up to $25$, simulated using $N_{\mathrm{f}}=2+1$ stabilized Wilson fermions. We obtain sub-percent determinations from single gauge configurations with the combined use of position-space techniques, volume averages and master-field error estimation., Published by SISSA, Trieste

Next generation high-precision neutrino scattering experiments have the goal of measuring the as-of-yet unknown parameters governing neutrino oscillation. This effort is hampered by the use of large nuclear targets: secondary interactions within a nucleus can confuse the interpretation of experimental data, leading to ambiguities about the initial neutrino interaction in scattering events. The distribution of energies for neutrino events must instead be inferred from the responses of a sum of dissimilar event topologies. For this reason, precise neutrino cross sections on nucleon targets are of vital importance to the neutrino oscillation experimental program. On the other hand, the necessary experimental data for neutrino scattering with elementary targets are scarce because of the weak interaction cross section, which leads to poorly-constrained nucleon and nuclear cross sections. Lattice QCD is uniquely positioned to provide the requisite nucleon amplitudes needed to enable high-precision oscillation experiments. In particular, LQCD has the ability to probe axial matrix elements that are challenging to isolate or completely inaccessible to experiments. In these proceedings, I will discuss some of my work to quantify neutrino cross sections with realistic uncertainty estimates, primarily focusing on neutrino quasielastic scattering and the nucleon axial form factor. I will also outline how the needs of next-generation neutrino oscillation experimental programs can be met with modern dedicated LQCD computations., 18 pages, 5 figures. Plenary talk given at the Lattice 2022 conference

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions., Comment: 94 pages, 23 figures, GGI workshop "Phase Transitions in Particle Physics" review - v2: minor revisions and typo corrected, matches accepted version on PPNP

The many-body entanglement between two finite (size-$d$) disjoint vacuum regions of non-interacting lattice scalar field theory in one spatial dimension -- a $(d_A \times d_B)_{\rm mixed}$ Gaussian continuous variable system -- is locally transformed into a tensor-product "core" of $(1_A \times 1_B)_{\rm mixed}$ entangled pairs. Accessible entanglement within these core pairs exhibits an exponential hierarchy, and as such identifies the structure of dominant region modes from which vacuum entanglement could be extracted into a spatially separated pair of quantum detectors. Beyond the core, remaining modes of the "halo" are determined to be AB-separable in isolation, as well as separable from the core. However, state preparation protocols that distribute entanglement in the form of $(1_A \times 1_B)_{\rm mixed}$ core pairs are found to require additional entanglement in the halo that is obscured by classical correlations. This inaccessible (bound) halo entanglement is found to mirror the accessible entanglement, but with a step behavior as the continuum is approached. It remains possible that alternate initialization protocols that do not utilize the exponential hierarchy of core-pair entanglement may require less inaccessible entanglement. Entanglement consolidation is expected to persist in higher dimensions and may aid classical and quantum simulations of asymptotically free gauge field theories, such as quantum chromodynamics., Comment: 11 pages, 3 figures, 10 pages supplemental material. The manuscript has been re-organized and elaborated to improve clarity