Is it possible to calculate neutron half-life theoretically? For example, from lattice QCD or something?
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Yes, it has been done in lattice QCD .
The most studied nucleon matrix element is that of the axial charge g_A. Because it can be measured precisely in neutron-decay experiments g_A provides a benchmark for of the accuracy of lattice-QCD nucleon matrix element calculations. The present quoted errors in lattice calculations of g_A are 6-10% but the lattice determinations are all systematically lower than the experimental measurement by about 10%, indicating the presence of an underestimated uncertainty.
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