Strong contribution to octet baryon mass splittings

Abstract

We calculate the $m_d-m_u$ contribution to the mass splittings in baryonic isospin multiplets using SU(3) chiral perturbation theory and lattice QCD. Fitting isospin-averaged perturbation theory functions to PACS-CS and QCDSF-UKQCD Collaboration lattice simulations of octet baryon masses, and using the physical light quark mass ratio $m_u/m_d$ as input, allows $M_n-M_p$, $M_{\Sigma^-}-M_{\Sigma^+}$ and $M_{\Xi^-}-M_{\Xi^0}$ to be evaluated from the full SU(3) theory. The resulting values for each mass splitting are consistent with the experimental values after allowing for electromagnetic corrections. In the case of the nucleon, we find $M_n-M_p= 2.9 \pm 0.4 \textrm{MeV}$, with the dominant uncertainty arising from the error in $m_u/m_d$.