Dispersion relation for hadronic light-by-light scattering

Massimiliano Procura,Martin Hoferichter,Peter Stoffer,Gilberto Colangelo

doi:10.1051/epjconf/201611801030

Abstract

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g − 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam’s double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

Highlights

The anomalous magnetic moment of the muon (g − 2)μ has been measured [1] and computed to very high precision of about 0.5 ppm
We present a dispersive description of the hadronic light-by-light (HLbL) tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance
Using Mandelstam’s double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors

Summary

Introduction

The anomalous magnetic moment of the muon (g − 2)μ has been measured [1] and computed to very high precision of about 0.5 ppm (see e.g. [2]). The anomalous magnetic moment of the muon (g − 2)μ has been measured [1] and computed to very high precision of about 0.5 ppm We have constructed a generating set of Lorentz structures for the HLbL tensor that is free of kinematic singularities and zeros. This simplifies significantly the calculation of the HLbL contribution to (g − 2)μ. Within our dispersive formalism, the definitions of both the pion-pole and pion-box topologies are unambiguous. By constructing a Mandelstam representation for the scalar functions, we prove that the box topologies are equal to the scalar QED (sQED) contribution multiplied by pion vector form factors. First numerical results for the pion-box topologies are shown and future steps are discussed

Lorentz structure of the HLbL tensor

Mandelstam representation

The dispersive formulation

Conclusion and outlook