Electroweak mass difference of mesons

TL;DR

This paper calculates electroweak corrections to pseudoscalar meson masses, specifically the pion mass difference, providing precise theoretical predictions that motivate future lattice QCD studies and exploring potential BSM effects.

Contribution

It presents the first next-to-leading order electroweak correction calculation for meson mass differences, including BSM contributions, with implications for lattice QCD and experimental comparisons.

Findings

Electroweak correction to pion mass difference is approximately -0.00201 MeV.

Predicted electroweak contribution is about four times larger than current experimental precision.

Results suggest the importance of including electroweak effects in future lattice QCD calculations.

Abstract

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.