Neutron-proton mass difference from gauge/gravity duality

TL;DR

This paper uses gauge/gravity duality to analytically compute the strong sector contribution to the neutron-proton mass difference in a large N QCD model, finding results consistent with lattice QCD estimates.

Contribution

It provides an analytic expression for the strong isospin breaking contribution to nucleon mass splitting within the holographic QCD framework, extending to resonances and baryons.

Findings

Strong sector contribution exceeds electromagnetic effects in nucleon mass splitting.

The contribution is approximately 0.25% of the nucleon mass, aligning with lattice QCD.

The formula is extended to Δ baryons and includes effects of isospin breaking on holographic instantons.

Abstract

Using gauge/gravity duality as a tool, we compute the strong sector, isospin breaking induced contribution to the neutron-proton mass difference in the Witten-Sakai-Sugimoto model of large $N$ QCD with two non-degenerate light flavors. The mass difference, for which we provide an analytic expression, turns out to be positive and proportional to the down-up quark mass splitting, consistently with expectations and previous estimates based on effective QCD models. Extrapolating the model parameters to fit QCD hadronic observables, we find that the strong sector contribution to the nucleon mass splitting overcomes the electromagnetic contribution and is about $0.25\%$ of the average nucleon mass in the model, a result which approaches recent lattice QCD estimates. Our formula is extended to resonances and $\Delta$ baryons. We thus use it to compute the strong sector contribution to $\Delta$ baryons mass differences. Finally, we also provide details of how isospin breaking affects the holographic instanton solution describing the baryons.