Hadronic light-by-light scattering contribution to 1S-2S transition in muonium

TL;DR

This paper calculates the hadronic light-by-light scattering effect on the 1S-2S energy transition in muonium, incorporating meson contributions to refine theoretical predictions.

Contribution

It introduces a detailed method to evaluate hadronic light-by-light effects on muonium energy levels using meson transition form factors.

Findings

Quantified the hadronic light-by-light contribution to muonium's 1S-2S transition.

Included effects of pseudoscalar, scalar, and axial vector mesons.

Provided integral and numerical results for the energy spectrum.

Abstract

We study hadronic light-by-light scattering contribution to the energy interval (1S-2S) in muonium. Various amplitudes of interaction of a muon and an electron are constructed, in which the effect of hadronic scattering of light-by-light is determined using the transition form factor of two photons into a meson. Their contributions to the particle interaction operator in the case of S-states are obtained in integral form, and to the energy spectrum in numerical form. The contributions of pseudoscalar, scalar, axial vector mesons are taken into account.