Gravitational form factors of the pion from lattice QCD

TL;DR

This paper computes the gravitational form factors of the pion using lattice QCD with near-physical quark masses, providing insights into the pion's internal structure and flavor decomposition.

Contribution

It presents the first lattice QCD calculation of the pion's gravitational form factors, including flavor decomposition and nonperturbative renormalization, at near-physical pion mass.

Findings

Form factors $A^{}(t)$ and $D^{}(t)$ computed for $0 \u2264 -t < 2$ GeV$^2$

Flavor decomposition into gluon, light-quark, and strange-quark contributions

Estimates for pion momentum fraction and D-term consistent with theoretical predictions

Abstract

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 $0\leq -t< 2~\text{GeV}^2$ 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 $D^{\pi}(0)$.