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We present a precise lattice QCD calculation of the contribution to theneutron-proton mass splitting arising from strong isospin breaking,$m_n-m_p|_{QCD}=2.32\pm0.17$ MeV. We also determine $m_{\Xi^-} -m_{\Xi^0}|_{QCD} = 5.44\pm0.31$ MeV. The calculation is performed at threevalues of the pion mass, with several values of the quark mass splitting andmultiple lattice volumes, but only a single lattice spacing and an estimate ofdiscretization errors. The calculations are performed on the anisotropicclover-Wilson ensembles generated by the Hadron Spectrum Collaboration. Theomega-baryon mass is used to set the scale $a_t^{-1}=6111\pm127$ MeV, while thekaon masses are used to determine the value of the light-quark mass spitting.The nucleon mass splitting is then determined as a function of the pion mass.We observe, for the first time, conclusive evidence for non-analytic lightquark mass dependence in lattice QCD calculations of the baryon spectrum. Whenleft as a free parameter, the fits prefer a nucleon axial coupling of$g_A=1.24(56)$. To highlight the presence of this chiral logarithm in thenucleon mass splitting, we also compute the isospin splitting in thecascade-baryon system which is less sensitive to chiral dynamics. Finally, weupdate the best lattice QCD determination of the CP-odd pion-nucleon couplingthat would arise from a non-zero QCD theta-term, $\bar{g}_0 / (\sqrt{2}f_\pi) =(14.7\pm1.8\pm1.4) \cdot 10^{-3} \bar{\theta}$.  The original lattice QCD correlation functions, analysis results andextrapolated quantities are packaged in HDF5 files made publicly availableincluding a simple Python script to access the numerical results, constructeffective mass plots along with our analysis results, and perform theextrapolations of various quantities determined in this work.

Strong isospin violation and chiral logarithms in the baryon spectrum