Massive three-loop form factor in the planar limit

Understand

We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors $F_1$ and $F_2$ in the large-$N_c$ limit.

• The analytic results are expressed in terms of Goncharov polylogarithms.
• This allows for a straightforward numerical evaluation.
• We also derive series expansions, including power suppressed terms, for three kinematic regions corresponding to small and large invariant masses of the photon momentum, and small velocities of the heavy quarks.