Lattice Quantum Chromodynamics QCD provides a way to have a precise calculation and a new way of understanding the hadrons from first principles. From this perspective, I will first present a precise calculation of the pion form factor using overlap fermions on six ensembles of 2+1-flavor domain-wall configurations generated by the RBC/UKQCD collaboration with pion masses varying from 137 to 339 MeV. With a z-expansion fitting of our data, we find the pion mean square charge radius to be $\braket{r^2}_\pi = 0.437(7)(7) {\rm{fm^2}}$, including the systematic uncertainties from pion mass, lattice spacing and finite volume dependence. It agrees with the experimental value $\braket{r^2}_\pi = 0.434(5) {\rm{fm^2}}$ at a percent level. The second topic is lattice calculation of proton momentum and angular momentum fractions. As confirmed from experiment and lattice QCD calculation, the total helicity contribution from quark is just about $\sim 30\%$ of the proton spin. Determination of the rest contributions from quarks and gluons to the nucleon spin is a challenging and important problem. On the lattice side, one way to approach this problem is using the nucleon matrix element of the traceless, symmetric energy-momentum tensor (EMT) to determine the momentum and angular momentum distributions of up, down, strange and glue constituents. Since the EMT of each parton species are not separately conserved, we summarized their final angular momentum fractions by considering mixing and non-perturbative renormalization at $\overline{\rm{MS}}(\mu = 2 \ {\rm{GeV}})$ and use the momentum and angular momentum sum rules to normalize them.

Seminar slides: https://www.dropbox.com/sh/8k11s7xapdzwd0a/AACUkAq5Wd-GglwdVcX8USMVa?dl=0