# The role of meson exchanges in light-by-light scattering

## TL;DR

This paper investigates how meson exchange mechanisms, including s-, t-, and u-channel contributions with off-shell corrections, influence light-by-light scattering cross sections, highlighting potential interference effects relevant for collider experiments.

## Contribution

It introduces the first comprehensive analysis of t- and u-channel meson exchanges with off-shell effects in light-by-light scattering, expanding beyond previous s-channel focused studies.

## Key findings

- Meson exchanges can significantly alter cross sections depending on vertex form factors.
- Interference effects among meson groups and with fermion-box amplitudes are notable.
- Potential relevance for interpreting recent ultraperipheral heavy-ion collision measurements.

## Abstract

We discuss the role of meson exchange mechanisms in $\gamma \gamma \to \gamma \gamma$ scattering. Several pseudoscalar ($\pi^0$, $\eta$, $\eta'(958)$, $\eta_c(1S)$, $\eta_c(2S)$), scalar ($f_{0}(500)$, $f_0(980)$, $a_0(980)$, $f_0(1370)$, $\chi_{c0}(1P)$) and tensor ($f_2(1270)$, $a_2(1320)$, $f_2'(1525)$, $f_2(1565)$, $a_2(1700)$) mesons are taken into account. We consider not only $s$-channel but also for the first time $t$- and $u$-channel meson exchange amplitudes corrected for off-shell effects including vertex form factors. We find that, depending on not well known vertex form factors, the meson exchange amplitudes interfere among themselves and could interfere with fermion-box amplitudes and modify the resulting cross sections. The meson contributions are shown as a function of collision energy as well as angular distributions are presented. Interesting interference effects separately for light pseudoscalar, scalar and tensor meson groups are discussed. The meson exchange contributions may be potentially important in the context of a measurement performed recently in ultraperipheral collisions of heavy ions by the ATLAS collaboration. The light-by-light interactions could be studied in future in electron-positron collisions by the Belle II at SuperKEKB accelerator.