  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.
