Ab initio calculation of the neutron-proton mass difference

Sz. Borsanyi, S. Durr, Z. Fodor, C. Hoelbling, S.D. Katz, S. Krieg, L. Lellouch, T. Lippert, A. Portelli, K.K. Szabo, B.C. Toth

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.