Ab initio calculation of the neutron-proton mass difference

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Science  27 Mar 2015:
Vol. 347, Issue 6229, pp. 1452-1455
DOI: 10.1126/science.1257050

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Weighing the neutron against the proton

Elementary science textbooks often state that protons have the same mass as neutrons. This is not far from the truth—the neutron is about 0.14% heavier (and less stable) than the proton. The precise value is important, because if the mass difference were bigger or smaller, the world as we know it would likely not exist. Borsanyi et al. calculated the mass difference to high precision using a sophisticated approach that took into account the various forces that exist within a nucleon. The calculations reveal how finely tuned our universe needs to be.

Science, this issue p. 1452


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 Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.

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