High Energy Physics Lattice

We compute the composition of the bottomoniumΥ(nS)states (includingΥ(10860)) and the newΥ(10753)resonance reported by Belle in terms of quarkonium and meson-meson components. We use a recently developed novel approach utilizing lattice QCD string breaking potentials for the study of resonances. This approach is based on the Born Oppenheimer approximation and the unitary emergent wave method and allows to compute the poles of theSmatrix. We focus onI=0bottomoniumSwave bound states and resonances, where the Schrödinger equation is a set of coupled differential equations. One of the channels corresponds to a confined heavy quark-antiquark pairb¯b, the others to pairs of heavy-light mesons. In a previous study only one meson-meson channelB¯(∗)B(∗)was considered. Now we also include the closed strangeness channelB¯(∗)sB(∗)sextending our formalism significantly to have a more realistic description of bottomonium. We confirm the new Belle resonanceΥ(10753)as a dynamical meson-meson resonance with around85%meson-meson content. Moreover, we identifyΥ(4S)andΥ(10860)as states with both sizable quarkonium and meson-meson contents. With these results we contribute to the clarification of ongoing controversies in the vector bottomonium spectrum.

This work continues our program of lattice-QCD baryon physics using staggered fermions for both the sea and valence quarks. We present a proof-of-concept study that demonstrates, for the first time, how to calculate baryon matrix elements using staggered quarks for the valence sector. We show how to relate the representations of the continuum staggered flavor-taste groupSU(8)FTto those of the discrete lattice symmetry group. The resulting calculations yield the normalization factors relating staggered baryon matrix elements to their physical counterparts. We verify this methodology by calculating the isovector vector and axial-vector chargesgVandgA. We use a single ensemble from the MILC Collaboration with 2+1+1 flavors of sea quark, lattice spacinga≈0.12fm, and a pion massMπ≈305MeV. On this ensemble, we find results consistent with expectations from current conservation and neutron beta decay. Thus, this work demonstrates how highly-improved staggered quarks can be used for precision calculations of baryon properties, and, in particular, the isovector nucleon charges.

Electric dipole moments (EDMs) of nucleons and nuclei are actively considered as direct evidence of the CP violation. Calculations of nucleon EDMs on lattice are required to connect the quark- and hadron- level effective CP violating interactions within QCD or other CP violating sources in new physics beyond the standard model. Among them, the theta-induced nucleon EDM, that is the only such renormalizable interaction, has widely been investigated on a lattice. In the report, we review recent developments of the lattice calculations of nucleon EDM induced QCD theta term.

Confinement defined as the absence of certain (colored in QCD) particle like excitations in S-matrix is investigated in the nonperturbative framework of Schwinger-Dyson equations solved in Minkowski space. We revise the method based on utilization of generalized spectral representation and improve existing techniques, such that the method turns to be particularly suited for strong coupling quantum field theories with confinement. The method is applied to strong quenched QED and toSU(3)Yang-Mills theory in 3+1 dimensions. Result for the gluonic spectral function has been obtained, for which purpose the equation for the gluon propagator has been solved in the gauge invariant manner. The gluon propagator, instead of having a real pole, has an unusual infrared structure that consists from two oppositely signed Cauchy resonances.

We study the Polyakov loop and theZ2symmetry in the latticeZ2+Higgs theory in 4D Euclidean space using Monte Carlo simulations. The results show that this symmetry is realised in the Higgs symmetric phase for large number of temporal lattice sites. To understand the dependence on the number of temporal sites, we consider a one dimensional model by keeping terms of the original action corresponding to a single spatial site. In this approximation the partition function can be calculated exactly as a function of the Polyakov loop. The resulting free energy is found to have theZ2symmetry in the limit of large temporal sites. We argue that this is due toZ2invariance as well as dominance of the distribution or density of states corresponding to the action.

We study the signs of criticality in conserved charge fluctuations and related observables of finite temperature QCD at vanishing chemical potential, as we approach the chiral limit of two light quarks. Our calculations have been performed on gauge ensembles generated using Highly Improved Staggered Quark (HISQ) fermion action, with pion masses ranging from 140 MeV to 55 MeV.

In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum tensor, all while realizing automaticO(a)improvement. Taking the modern summation-by-parts formulation for finite differences as starting point and combining it with insight from the finite volume strategies of computational electrodynamics I show how the concept of a conserving discretization can be realized for non-Abelian lattice gauge theory. Major steps in the derivation are illustrated using Abelian gauge theory as example.

Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.

Using the general formalism presented in Refs. [1,2], we study the finite-volume effects for the2+J→2matrix element of an external current coupled to a two-particle state of identical scalars with perturbative interactions. Working in a finite cubic volume with periodicityL, we derive a1/Lexpansion of the matrix element throughO(1/L5)and find that it is governed by two universal current-dependent parameters, the scalar charge and the threshold two-particle form factor. We confirm the result through a numerical study of the general formalism and additionally through an independent perturbative calculation. We further demonstrate a consistency with the Feynman-Hellmann theorem, which can be used to relate the1/Lexpansions of the ground-state energy and matrix element. The latter gives a simple insight into why the leading volume corrections to the matrix element have the same scaling as those in the energy,1/L3, in contradiction to earlier work, which found a1/L2contribution to the matrix element. We show here that such a term arises at intermediate stages in the perturbative calculation, but cancels in the final result.

There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, and charm sea quark gauge ensembles generated in the staggered formalism by the MILC collaboration. We study the continuum limit using inverse lattice spacings froma−1≈1.6GeV to3.5GeV, identical to recent studies by FNAL/HPQCD/MILC and Aubin et al. and similar to the recent study of BMW. Our calculation exhibits a tension for the particularly interesting window result ofaud,conn.,isospin,Wμfrom0.4fm to1.0fm with previous results obtained with a different discretization of the vector current on the same gauge configurations. Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention. In this work we also provide results foraud,conn.,isospinμ,as,conn.,isospinμ,aSIB,conn.μfor the total contribution and a large set of windows. For the total contribution, we findaHVP LOμ=714(27)(13)10−10,aud,conn.,isospinμ=657(26)(12)10−10,as,conn.,isospinμ=52.83(22)(65)10−10, andaSIB,conn.μ=9.0(0.8)(1.2)10−10, where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.