Pion pole light-by-light contribution to g-2 of the muon in a nonlocal chiral quark model

TL;DR

This paper calculates the pion pole contribution to the muon g-2 using a nonlocal chiral quark model, accounting for full kinematic dependence and QCD constraints, resulting in a value consistent with other models.

Contribution

It introduces a nonlocal chiral quark model that incorporates full kinematic dependence and QCD constraints to evaluate the pion pole contribution to muon g-2.

Findings

The pion pole contribution to muon g-2 is estimated as (6.3-6.7) x 10^-10.

Including pion virtuality dependence reduces the result by about 15%.

The model satisfies QCD constraints proposed by Melnikov and Vainshtein.

Abstract

We calculate the pion pole term of the light-by-light contribution to the $g-2$ of the muon in the framework of an effective chiral quark model with instanton-like nonlocal quark--quark interaction. The full kinematic dependence of the pion-photon transition form factors is taken into account. The dependence of form factors on the pion virtuality decreases the result by about 15% in comparison to the calculation where this dependence is neglected. Further, it is demonstrated that the QCD constraints suggested by Melnikov and Vainshtein are satisfied within the model. The corresponding contributions originate from the box diagram as well from the pion-pole term. Our chiral nonlocal model result for the pion-pole light-by-light contribution to $(g-2)/2$ of the muon is $(6.3-6.7) \cdot10^{-10}$, which is in the ball park of other effective-model calculations.