Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation

Abstract

We compute the two-loop corrections to the massless quark form factor $\gamma^* \to q\bar q$ and gluon form factor $H\to gg$ to all orders in the dimensional regularisation parameter $\epsilon=(4-d)/2$. The two-loop contributions to the form factors are reduced to linear combinations of master integrals, which are computed in a closed form, expressed as $\Gamma$-functions and generalised hypergeometric functions of unit argument. Using the newly developed HypExp-package, these can be expanded to any desired order, yielding Laurent expansions in $\epsilon$. We provide expansions of the form factors to order $\epsilon^2$, as required for ultraviolet renormalisation and infrared factorisation of the three-loop form factors.