Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD

Abstract: The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an $a \approx 0.09$ fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum $P_z \approx 2.2$ GeV with nonzero momentum transfers in $[0.2,1.0]\text{ GeV}^2$. Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution before matching to the lightcone GPDs. The three-dimensional distribution $\tilde{H}(x,Q^2)$ is presented, along with the three-dimensional nucleon tomography and impact-parameter--dependent distribution for selected Bjorken $x$ at $\mu=3$ GeV in $\overline{\text{MS}}$ scheme.