It has been observed that lattice QCD calculations of the nucleon mass show a strikingly linear dependence upon the pion mass such that $m_N[\textrm{MeV}] = 800 + m_\pi$ is a remarkably good lattice- phenomenological estimate of the nucleon mass at a given pion mass for pion masses in the range $170 \leq m_\pi \leq 800$ MeV. If the goodness of this extrapolation persists to the physical pion mass, this has important implications for the pion-nucleon sigma term, which would be $\sigma_{\pi N} \sim 68$ MeV with this extrapolation function. We will use recent lattice QCD results of the nucleon mass determined with Möbius Domain Wall Fermions solved on gradient flowed $2+1+1$ dynamical HISQ ensembles at three lattice spacings and pion masses in the range $130 \leq m_\pi \leq 400$ MeV to study the fully continuum and infinite volume extrapolated nucleon mass as a function of the pion mass. We will explore if there are statistically significant deviations from the observed phenomenological behavior observed and provide a preliminary estimate of the pion-nucleon sigma term determined in this extrapolation.

Hadron Spectroscopy and Interactions