Light-by-light scattering sum rules in light of new data

TL;DR

This paper analyzes light-by-light scattering sum rules using new Belle data, confirming previous results and providing new empirical insights into meson transition form factors and their impact on the muon's magnetic moment.

Contribution

It offers the first empirical extraction of the $f_2(1565)$ meson's helicity-2 transition form factor and updates the scalar and tensor meson contributions to muon g-2.

Findings

Confirmed saturation of sum rules by $ ext{η, η'}$, and $f_2(1270)$ up to 1 GeV$^2$

Empirically extracted the $f_2(1565)$ helicity-2 form factor

Updated meson contributions to muon anomalous magnetic moment

Abstract

We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson $f_2(1270)$ as well as of the scalar meson $f_0(980)$. We confirm a previous finding that the $\eta, \eta^\prime$ and helicity-2 $f_2(1270)$ contributions saturate one of these sum rules up to photon virtualities around 1 GeV$^2$. At larger virtualities, our sum rule analysis shows an important contribution of the $f_2(1565)$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the $f_2(1270)$ meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to the muon's anomalous magnetic moment.