Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD.

We present the first lattice calculation of the nucleon isovector unpolarized generalized parton distribution at the physical pion mass using a lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by the MILC Collaboration, with lattice spacing a≈0.09 fm and volume 64^{3}×96. We use momentum-smeared sources to improve the signal at nucleon boost momentum P_{z}≈2.2 GeV and report results at nonzero momentum transfers in [0.2,1.0] GeV^{2}. Nonperturbative renormalization in a regularization-independent momentum-subtraction scheme is used to obtain the quasidistribution before matching to the light-cone generalized parton distributions. The three-dimensional distributions H(x,Q^{2}) and E(x,Q^{2}) at ξ=0 are presented, along with the three-dimensional nucleon tomography and impact parameter-dependent distribution for selected Bjorken x at µ=3 GeV in a modified minimal subtraction scheme.

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.

Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass.

We present a state-of-the-art calculation of the isovector quark-helicity Bjorken-x distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasidistributions at proton momenta P_{z}∈{2.2,2.6,3.0} GeV on the lattice and match them systematically to the physical parton distribution using the large-momentum effective theory. We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data, in particular, Δu[over ¯](x)>Δd[over ¯](x).

Neutron Electric Dipole Moment and Tensor Charges from Lattice QCD.

We present lattice QCD results on the neutron tensor charges including, for the first time, a simultaneous extrapolation in the lattice spacing, volume, and light quark masses to the physical point in the continuum limit. We find that the "disconnected" contribution is smaller than the statistical error in the "connected" contribution. Our estimates in the modified minimal subtraction scheme at 2 GeV, including all systematics, are g_{T}^{d-u}=1.020(76), g_{T}^{d}=0.774(66), g_{T}^{u}=-0.233(28), and g_{T}^{s}=0.008(9). The flavor diagonal charges determine the size of the neutron electric dipole moment (EDM) induced by quark EDMs that are generated in many new scenarios of CP violation beyond the standard model. We use our results to derive model-independent bounds on the EDMs of light quarks and update the EDM phenomenology in split supersymmetry with gaugino mass unification, finding a stringent upper bound of d_{n}<4×10^{-28} e cm for the neutron EDM in this scenario.