Ab initio calculation of the neutron-proton mass difference

TLDR

The existence and stability of atoms rely on neutrons being more massive than protons, a 0.14 % mass difference that would have produced a dramatically different universe if it were slightly different. We show that this mass difference results from the competition between electromagnetic and mass isospin‑breaking effects. We performed lattice QCD+QED calculations with four nondegenerate Wilson fermion flavors to compute the neutron–proton mass splitting. The computed splitting is 300 keV, exceeding zero by 5 σ, and isospin splittings for Σ, Ξ, D, and Ξcc multiplets were determined with precision surpassing some experimental measurements.

Abstract

The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14\% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of $300$ kilo-electron volts, which is greater than $0$ by $5$ standard deviations. We also determine the splittings in the $\Sigma$, $\Xi$, $D$ and $\Xi_{cc}$ isospin multiplets, exceeding in some cases the precision of experimental measurements.