Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays.

We present the first lattice QCD calculation of the universal axial γW-box contribution □_{γW}^{VA} to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of |V_{ud}| from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at □_{γW}^{VA}=3.65(7)_{lat}(1)_{PT}×10^{-3}. Consequently, this yields a slightly higher value of |V_{ud}|=0.973 86(11)_{exp}(9)_{RC}(27)_{NS}, reducing the previous 2.1σ tension with the CKM unitarity to 1.8σ. Additionally, we calculate the vector γW-box contribution to the axial charge g_{A}, denoted as □_{γW}^{VV}, and explore its potential implications.

Proton Mass Decomposition from the QCD Energy Momentum Tensor.

We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of N_{f}=2+1 domain wall fermion configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully nonperturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 32(4)(4)% and 36(5)(4)% respectively in the MS[over ¯] (modified minimal substraction) scheme at µ=2 GeV. A quarter of the trace anomaly gives a 23(1)(1)% contribution to the proton mass based on the sum rule, given 9(2)(1)% contribution from the u, d, and s quark scalar condensates. The u, d, s, and glue momentum fractions in the MS[over ¯] scheme are in good agreement with global analyses at µ=2 GeV.

Gluon Quasi-Parton-Distribution Functions from Lattice QCD.

We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678 MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a=0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(α_{s}) matching and the mixing from the quark PDFs.

Glue Spin and Helicity in the Proton from Lattice QCD.

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor domain-wall fermion gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin S_{G} in the Coulomb gauge in the modified minimal subtraction (MS[over ¯]) scheme is obtained with one-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of S_{G} in the range 0≤|p[over →]|<1.5 GeV is very mild, and we determine it in the large-momentum limit to be S_{G}=0.251(47)(16) at the physical pion mass in the MS[over ¯] scheme at µ^{2}=10 GeV^{2}. If the matching procedure in large-momentum effective theory is neglected, S_{G} is equal to the glue helicity measured in high-energy scattering experiments.

Strange Quark Magnetic Moment of the Nucleon at the Physical Point.

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051 GeV^{2}≲Q^{2}≲1.31 GeV^{2}. The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G_{M}^{s}(0)=-0.064(14)(09)µ_{N}. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius ⟨r_{s}^{2}⟩_{E}=-0.0043(16)(14) fm^{2}.

Connected-sea partons.

According to the path-integral formalism of the hadronic tensor, the nucleon sea contains two distinct components called the connected sea (CS) and the disconnected sea (DS). We discuss how the CS and DS are accessed in the lattice QCD calculation of the moments of the parton distributions. We show that the CS and DS components of u(x) + d(x) can be extracted by using recent data on the strangeness parton distribution, the CT10 global fit, and the lattice result of the ratio of the strange to u(d) moments in the disconnected insertion. The extracted CS and DS for u(x) + d(x) have a distinct Bjorken x dependence in qualitative agreement with expectation. The analysis also shows that the momentum fraction of u(x) + d(x) is about equally divided between the CS and DS at Q(2) = 2.5 GeV(2). Implications for the future global analysis of parton distributions are presented.