# Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon

## TL;DR

This paper develops a model-independent dispersive approach to calculate the hadronic-light-by-light contribution to the muon g-2, specifically focusing on the pion-pion intermediate states and rescattering effects, improving precision over previous models.

## Contribution

It introduces a dispersive framework combining partial-wave expansion and fits to experimental data to accurately evaluate the pion box contribution to muon g-2, including rescattering effects.

## Key findings

- Calculated the pion box contribution as -15.9(2)×10^{-11}.
- Estimated rescattering effects add approximately -8(1)×10^{-11}.
- Provided a combined estimate for the pion box and rescattering effects as -24(1)×10^{-11}.

## Abstract

We present a first model-independent calculation of $\pi\pi$ intermediate states in the hadronic-light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon $(g-2)_\mu$ that goes beyond the scalar QED pion loop. To this end we combine a recently developed dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_\mu^{\pi\text{-box}}=-15.9(2)\times 10^{-11}$. We then construct suitable input for the $\gamma^*\gamma^*\to\pi\pi$ helicity partial waves based on a pion-pole left-hand cut and show that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate $S$-wave rescattering effects to the full pion box and leads to our final estimate for the sum of these two contributions: $a_\mu^{\pi\text{-box}} + a_{\mu,J=0}^{\pi\pi,\pi\text{-pole LHC}}=-24(1)\times 10^{-11}$.