High Energy Physics Lattice

Using 10-16 units of Nvidia DGX-1, we have generated the first gauge ensemble forNf=2+1+1lattice QCD with physical(u/d,s,c)domain-wall quarks, on the644lattice with lattice spacinga∼0.064fm (L>4fm, andMπL>3). The salient feature of this gauge ensemble is that the chiral symmetry is preserved to a high precision and all topological sectors are sampled ergodically. In this paper, we present the first results of the topological susceptibility and the ground-state hadron mass spectra.

We present the first realistic lattice QCD calculation of theγW-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of theγWloop is calculated using a lattice QCD simulation, complemented by the perturbative QCD result at high momenta. Using the pion semileptonic decay as an example, we demonstrate the feasibility of the method. By using domain wall fermions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axialγW-box correction to the semileptonic pion decay,□VAγW∣∣π=2.830(11)stat(26)sys×10−3, with the total uncertainty controlled at the level of∼1\%. This study sheds light on the first-principles computation of theγW-box correction to the neutron decay, which plays a decisive role in the determination of|Vud|.

We present, for the first time, an \textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in theMS¯¯¯¯¯¯¯scheme at a scale of 2 GeV. We give results on theΔu+(x)andΔd+(x), including disconnected quark loop contributions, as well as on theΔs+(x). For the latter we achieve unprecedented precision compared to the phenomenological estimates.

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor non-singlet (u−d) unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-xdependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distributionqvand the combination with antiquarksqv+2q¯, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever \emph{ab initio} determinations of PDFs fully consistent with global fits in the wholex-range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g.\ singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

We consider the three dimensional SU(2) Yang-Mills theory with adjoint static color sources, studying by lattice simulations how the shape of the flux tube changes when increasing the distance between them. The disappearance of the flux tube at string breaking is quite abrupt, but precursors of this phenomenon are present already when the separation between the sources is smaller than its critical value, a fact that influences also some details of the static potential.

To study the CP-violation using theK0−K¯0oscillation, we need the kaon bag parameter which represents QCD corrections in the leading Feynman diagrams. The lattice QCD provides us with the only way to evaluate the kaon bag parameter directly from the first principles of QCD. However, a calculation of relevant four quark operators with theoretically sound Wilson-type lattice quarks had to carry a numerically big burden of extra renormalizations and resolution of extra mixings due to the explicit chiral violation. Recently, the Small Flow-time eXpansion (SFtX) method was proposed as a general method based on the gradient flow to correctly calculate any renormalized observables on the lattice, irrespective of the explicit violations of related symmetries on the lattice. To apply the SFtX method, we need matching coefficients, which relate finite operators at small flow-times in the gradient flow scheme to renormalized observables in conventional renormalization schemes. In this paper, we calculate the matching coefficients for four quark operators and quark bi-linear operators, relevant to the kaon bag parameter.

In these proceedings we address the computation of quark-line disconnected diagrams in lattice QCD. The evaluation of these diagrams is required for many phenomenologically interesting observables, but suffers from large statistical errors due to the vacuum and random-noise contributions to their variances. Motivated by a theoretical analysis of the variances, we introduce a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. The use of these estimators reduces the cost of the computation by one to two orders of magnitude over standard estimators depending on the fermion bilinear. As a concrete application, we show the impact of these findings on the computation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji's sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and transverse momentum, they permit a direct evaluation of the cross product of the latter. They are defined through proton matrix elements of a quark bilocal operator containing a Wilson line; the choice in Wilson line path allows one to continuously interpolate from Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen to be significantly enhanced in magnitude compared to Ji quark orbital angular momentum, confirming previous results.

We present a preliminary computation of potentials between two static quarks innf=2QCD with O(a) improved Wilson fermions. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 \cite{Bicudo:2019ymo}) to study quarkonium resonances and bound states.

Recent studies on lattice QCD have shown the emergence of large symmetries at high temperature. This includes not only the restorationSU(nF)L?SU(nF)R, but also the effective emergence of an unexpected symmetry group, namelySU(2)CS, which containsU(1)Aas subgroup. At the same time, at highT, a gap in Dirac spectrum appears. As it is argued in several works of \textit{L. Glozman et al.}, there should be a connection between a gap in the Dirac spectrum and the presence ofSU(2)CS.In this paper, we analyze whether the quark propagator can be invariant underSU(nF)L?SU(nF)RandSU(2)CStransformations, in case of a gap in the Dirac spectrum, and consequently the invariance of hadron correlators, giving the condition for a quark propagator to be invariant underSU(2)CS.