Strong-Isospin Violation in the Neutron-Proton Mass Difference from Fully-Dynamical Lattice QCD and PQQCD

TL;DR

This work targets the strong-isospin-violating part of the neutron-proton mass difference by combining fully-dynamical lattice QCD with partially-quenched QCD in a mixed-action framework (domain-wall valence quarks on MILC sea configurations). One-loop PQHBχPT, constrained by the MILC light-quark mass ratio $\eta = m_u/m_d$, is used to relate lattice nucleon masses to the isospin-violating parameter and extrapolate to the physical point. The main result is $M_n - M_p|^{d-u} = 2.26 \pm 0.57 \pm 0.42 \pm 0.10$ MeV, consistent with the experimental strong piece, supporting a reliable separation of strong and electromagnetic contributions. This approach advances a quantitative, first-principles handle on charge-symmetry breaking in the nucleon sector and sets the stage for refined determinations of CSB effects in nuclear processes.

Abstract

We determine the strong-isospin violating component of the neutron-proton mass difference from fully-dynamical lattice QCD and partially-quenched QCD calculations of the nucleon mass, constrained by partially-quenched chiral perturbation theory at one-loop level. The lattice calculations were performed with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b=0.125 fm, lattice spatial size of L=2.5 fm and pion masses ranging from m_pi ~ 290 MeV to ~ 350 MeV. At the physical value of the pion mass, we predict M_n - M_p |(d-u) = 2.26 +- 0.57 +- 0.42 +- 0.10 MeV where the first error is statistical, the second error is due to the uncertainty in the ratio of light-quark masses, eta=m_u/m_d, determined by MILC, and the third error is an estimate of the systematic due to chiral extrapolation.

Figures (5)

• Figure 1: Effective mass plots for the ratios of proton correlation functions that give rise to the mass splittings $\Delta M_p(V_a,V_b,V_c;V_1)$ with $a,b,c$=$1,2$.
• Figure 2: Effective mass plots for the ratios of proton correlation functions that give rise to the mass splittings $\Delta M_p(V_a,V_b,V_c;V_1)$with $a,b,c$=$1,3$.
• Figure 3: Effective mass plots for the ratios of proton correlation functions that give rise to the mass splittings $\Delta M_p(V_a,V_b,V_c;V_2)$ with $a,b,c$=$1,2$.
• Figure 4: The partially-quenched proton mass differences (in MeV) calculated from the $b m_l=0.007$ and $0.010$ MILC lattices plotted vs the pion mass composed of sea quarks. Various data have been displaced horizontally by small amounts for display purposes. A lattice spacing of $b=0.125~{\rm fm}$ has been used.
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