Gravitational form factors of the pion from lattice QCD

The two gravitational form factors of the pion, $A^{\pi }(t)$ and $D^{\pi }(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\le -t<2{\text{GeV}}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_{\pi }\approx 170\text{ MeV}$ 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 $\overline{\text{MS}}$ scheme at energy scale $\mu =2\text{ GeV}$, 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 $D^{\pi }(0)$.