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

Understand

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.