Precision calculations of nucleon charges $g_A$, $g_S$, $g_T$

TL;DR

This paper provides a detailed analysis of nucleon scalar, axial, and tensor charges using lattice QCD, achieving precise tensor charge estimates and highlighting the need for higher statistics for other charges.

Contribution

It presents a comprehensive error analysis and stable tensor charge calculations on multiple lattice ensembles, advancing nucleon charge determinations in lattice QCD.

Findings

Tensor charge estimated with 5% precision.

Higher statistics needed for accurate $g_A$ and $g_S$.

Analysis of operator mixing relevant to nEDM.

Abstract

We present a detailed analysis of statistical and systematic errors in the calculation of matrix elements of iso-vector scalar, axial and tensor charges between a neutron and a proton state. These analyses are being done on dynamical $N_f=2+1+1$ HISQ configurations generated by the MILC Collaboration using valence clover fermions. Using ensembles at three values of the lattice spacing ($a=0.12,\ 0.09,$ and $0.06$ fm) and three values of the quark mass ($M_\pi \approx 310,\ 220$ and $130$ MeV) we find that the estimates of the tensor charge are stable and it can be extracted with $5\%$ precision with O(10,000) measurements. We also find that higher statistics are needed to resolve the various uncertainties in the calculation of $g_A$ and improve the signal in $g_S$, which with present data has large errors. A brief status report on the mixing and renormalization of novel operators contributing to nEDM is also given.