The two-loop perturbative correction to the (g-2)$_{\mu}$ HLbL at short distances

TL;DR

This paper calculates the two-loop perturbative QCD correction to the hadronic light-by-light contribution to the muon's anomalous magnetic moment at short distances, reducing uncertainties in theoretical predictions.

Contribution

It provides the first calculation of the perturbative correction to the massless quark loop in the HLbL contribution to (g-2)μ, showing the correction is small at relevant energy scales.

Findings

Perturbative correction is small for scales μ ≥ 1 GeV.

Non-perturbative effects are numerically suppressed.

Results help reduce systematic uncertainties in (g-2)μ calculations.

Abstract

The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to $(g-2)_{\mu}$ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e.~for scales $\mu\gtrsim 1\, \mathrm{GeV}$. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.