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

Understand

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 $\mu\gtrsim 1\, \mathrm{GeV}$.