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Electroweak mass difference of mesons. (arXiv:2308.00030v1 [hep-ph])

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We consider electroweak (EW) gauge boson corrections to the masses of
pseudoscalar mesons to next to leading order (NLO) in $\alpha_s$ and $1/N_C$.
The pion mass shift induced by the $Z$-boson is shown to be
$m_{\pi^\pm}-m_{\pi^0} = -0.00201(12)$ MeV. While being small compared to the
electromagnetic mass shift, the prediction lies about a factor of $\sim 4$
above the precision of the current experimental measurement, and a factor
$O(10)$ below the precision of current lattice calculations. This motivates
future implementations of these EW gauge boson effects on the lattice. Finally,
we consider BSM contributions to the pion mass difference.

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