Lattice computation of the nucleon scalar quark contents at the physical point

TL;DR

This paper reports a lattice QCD calculation of the scalar quark contents of nucleons, providing precise estimates of sigma terms and quark contents at the physical point, with implications for understanding nucleon structure.

Contribution

The study presents the first high-precision lattice QCD determination of nucleon scalar quark contents using extensive ensembles at physical pion mass.

Findings

Calculated $f^N_{ud}$ and $f^N_s$ with statistical and systematic errors.

Derived sigma terms: $\sigma_{\pi N}$ and $\sigma_{sN}$ with uncertainties.

Estimated the ratio $y_N$ indicating the strange quark contribution to nucleon mass.

Abstract

We present a QCD calculation of the $u$, $d$ and $s$ scalar quark contents of nucleons based on $47$ lattice ensembles with $N_f = 2+1$ dynamical sea quarks, $5$ lattice spacings down to $0.054\,\text{fm}$, lattice sizes up to $6\,\text{fm}$ and pion masses down to $120\,\text{MeV}$. Using the Feynman-Hellmann theorem, we obtain $f^N_{ud} = 0.0405(40)(35)$ and $f^N_s = 0.113(45)(40)$, which translates into $\sigma_{\pi N}=38(3)(3)\,\text{MeV}$, $\sigma_{sN}=105(41)(37)\,\text{MeV}$ and $y_N=0.20(8)(8)$ for the sigma terms and the related ratio, where the first errors are statistical and the second are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).