Gravitational form factors of the pion from lattice QCD
Daniel C. Hackett, Patrick R. Oare, Dimitra A. Pefkou, Phiala E. Shanahan
Abstract
The two gravitational form factors of the pion, ${A}^{\ensuremath{\pi}}(t)$ and ${D}^{\ensuremath{\pi}}(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\ensuremath{\le}\ensuremath{-}t<2\text{ }\text{ }{\mathrm{GeV}}^{2}$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass ${m}_{\ensuremath{\pi}}\ensuremath{\approx}170\text{ }\text{ }\mathrm{MeV}$ and ${N}_{f}=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange-quark contributions is presented in the $\overline{\mathrm{MS}}$ scheme at energy scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$, with renormalization factors computed nonperturbatively via the RI-MOM scheme. Using monopole and $z$-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and $D$ term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for ${D}^{\ensuremath{\pi}}(0)$.