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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.
Many low-energy, particle-physics experiments seek to reveal new fundamental physics by searching for very rare scattering events on atomic nuclei. The interpretation of their results requires quantifying the non-linear effects of the strong interact
The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of t
We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and three volu
We present a lattice calculation of the neutron and proton electric dipole moments (EDMs) with $N_f=2+1$ flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in
We present a calculation of the mass of the 1S0 pseudoscalar anti-b c (Bc) state using a non-perturbative measurement from quenched lattice QCD. We find M_Bc = 6.386(9)(98)(15) GeV where the first error is statistical, the second systematic due to th