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 $0\leq -t< 2~\text{GeV}^2$ 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 non-perturbatively via the RI-MOM scheme. Using monopole and (modified) $z$-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 $D^{\pi}(0)$.Comment: 28 pages, 17 figures, 7 table

Lattice QCD constraints on the parton distribution functions of ³He

The fraction of the longitudinal momentum of 3He that is carried by the isovector combination of u and d quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to mπ ∼ 800 MeV. With a naive extrapolation to the physical quark masses, this constraint is consistent with, and more precise than, determinations from global nuclear parton distribution function fits through the nNNPDF framework. It is thus concretely demonstrated that lattice QCD calculations of light nuclei have imminent potential to enable more precise determinations of the u and d parton distributions in light nuclei and to reveal the QCD origins of the EMC effect