Flavor diagonal charges of the nucleon and the sigma term

Final results from the PNDME calculations of the flavor diagonal charges of the nucleons, $g_{A,S,T}^{u,d,s}$, the pion-nucleon sigma term, $\sigma_{\pi N}=m_{u,d} g_S^{u+d}$, and the strangeness content of the nucleons $\sigma_{s}=m_{s} g_S^{s}$, obtained using eight 2+1+1-flavor HISQ ensembles generated by the MILC collaboration are presented. To remove excited-state contributions, we have carried out both the ``standard'' and ``$N \pi$'' analyses and use physics or $\chi$PT based reasoning for picking between the two for the final result. To renormalize the charges, we have carried out the calculation of the full mixing matrix for the 2+1-flavor theory using the RI-SMOM scheme on the lattice and then using perturbative results to match to $\overline{MS}$ scheme and run to a common scale of $2$~GeV. The chiral-continuum-finite-volume (CCFV) extrapolation is carried out keeping the leading corrections in each. The results for $g_{A,S,T}^{u,d,s}$ are summarized in Table~2 and for the sigma terms in Eq.~4.