Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation

Abstract

We compute the two-loop corrections to the massless quark form factor ${\gamma }^{\ast }\to q\bar{q}$ 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.

9 pages, latex, typo corrected in eq.16

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