Production of axial-vector mesons at $e^+ e^-$ collisions with double-tagging as a way to constrain the axial meson LbL contribution to muon g-2 and/or hyperfine splitting of muonic hydrogen

TL;DR

This paper calculates the production cross sections of axial-vector mesons in $e^+ e^-$ collisions to help constrain their contribution to the muon g-2 anomaly and muonic hydrogen hyperfine splitting, emphasizing the importance of future measurements.

Contribution

It provides theoretical predictions for $f_1(1285)$ meson production at Belle II using various $ ext{γ}^* ext{γ}^* o f_1(1285)$ vertices, highlighting differences among models.

Findings

Different vertices yield significantly different cross section predictions.

Future $e^+ e^-$ collider measurements can test and constrain the vertices and form factors.

Predictions are made for potential measurements at Belle II.

Abstract

We calculate cross sections for production of axial-vector $f_1(1285)$ mesons for double-tagged measurements of the $e^+ e^- \to e^+ e^- f_1(1285)$ reaction. Different $\gamma^* \gamma^* \to f_1(1285)$ vertices from the literature are used. Both integrated cross section as well as differential distributions are calculated. Predictions for a potential measurement at Belle II are presented. Quite different results are obtained for the different vertices proposed in the literature. Future measurements at $e^+ e^-$ colliders could test and/or constrain the $\gamma^* \gamma^* \to f_1 (a_1, f_1')$ vertices and associated form factors, known to be important ingredients for calculating contributions to anomalous magnetic moment of muon and hyperfine splitting of levels of muonic atoms.