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

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 $mugtrsim 1, mathrm{GeV}$. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.