A Bayesian analysis of light-front models and the nucleon's charmed sigma term

Abstract

We present the results of a recent analysis to study the nucleon's charm sigma term, $\sigma_{c\overline{c}}$. We construct a minimal model in terms of light-front variables and constrain the range of possibilities using extant knowledge from deeply inelastic scattering (DIS) and Bayesian parameter estimation, ultimately computing $\sigma_{c\overline{c}}$ in an explicitly covariant manner. We find a close correlation between a possible nonperturbative component of the charm structure function, $F^{c\overline{c}}_{2,\, \mathrm{IC}}$, and $\sigma_{c\overline{c}}$. Independent of prescription for the covariant relativistic quark-nucleon vertex, we determine $\sigma_{c\overline{c}}$ under several different scenarios for the magnitude of intrinsic charm (IC) in DIS, namely $\langle x \rangle_{c+\overline{c}} = 0.1\%$, $0.35\%$, and $1\%$, obtaining for these $\sigma_{c\overline{c}} = 4 \pm 4$, $12 \pm 13$, and $32 \pm 34$ MeV, respectively. These results imply the existence of a reciprocity between the IC parton distribution function (PDF) and $\sigma_{c\overline{c}}$ such that new information from either DIS or improved determinations of $\sigma_{c \overline{c}}$ could significantly impact constraints to the charm sector of the proton wave function.