Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution

TL;DR

This paper calculates the pion-pole contribution to the hadronic light-by-light scattering correction for the muon g-2 using QCD-inspired form factors, providing a refined estimate that impacts the discrepancy between experiment and theory.

Contribution

It introduces a novel calculation method for the pion-pole contribution to muon g-2 using angular integration and Gegenbauer polynomials, differing from previous approaches.

Findings

The pion-pole contribution is estimated as +5.8(1.0) x 10^{-10}.

The total pseudoscalar contribution is +8.3(1.2) x 10^{-10}.

Results reduce the gap between experimental and theoretical muon g-2 values.

Abstract

The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the pi0 - gamma* - gamma* transition form factor based on the large-Nc and short-distance properties of QCD. The resulting two-loop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining two-dimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a_{mu}(LbyL;pi0) = +5.8 (1.0) x 10^{-10}, disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a_{mu}(LbyL;pi0)_{VMD} = +5.6 x 10^{-10}, and differs only by its overall sign from the value obtained by previous authors. Inclusion of the eta and eta-prime poles gives a total value a_{mu}(LbyL;PS) = +8.3 (1.2) x 10^{-10} for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a_{mu} and its theoretical counterpart in the standard model.