Short-distance HLbL contributions to the muon g-2

TL;DR

This paper derives short-distance constraints for the hadronic light-by-light contribution to the muon g-2, showing the dominance of the massless quark loop and improving theoretical precision crucial for understanding the muon anomaly.

Contribution

It introduces a systematic operator product expansion for the hadronic light-by-light contribution, emphasizing the dominance of the massless quark loop at short distances.

Findings

Massless quark loop is numerically dominant.

Derived constraints for three large photon virtualities.

Operator product expansion in static background field.

Abstract

The current $3.7\sigma$ discrepancy between the Standard Model prediction and the experimental value of the muon anomalous magnetic moment could be a hint for the existence of new physics. The hadronic light-by-light contribution is one of the pieces requiring improved precision on the theory side, and an important step is to derive short-distance constraints for this quantity containing four electromagnetic currents. Here, we derive such short-distance constraints for three large photon loop virtualities and the external fourth photon in the static limit. The static photon is considered as a background field and we construct a systematic operator product expansion in the presence of this field. We show that the massless quark loop, i.e. the leading term, is numerically dominant over non-perturbative contributions up to next-to-next-to leading order, both those suppressed by quark masses and those that are not.