Massive three-loop form factor in the planar limit

Abstract

Abstract:We compute the three-loop QCD corrections to the massive quark-anti-quarkphoton 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.

Three-loop massive form factors: complete light-fermion corrections for the vector current

“…Three-loop corrections in the large-N c limit for the vector current form factor have been computed in ref. [2]. In this paper we extend these considerations and compute the complete contributions (i.e.…”

“…In fact, the 1/ǫ 1 pole of the α n s term of Z is proportional to the n-loop correction to Γ cusp (see, e.g., ref. [2]. 1 )…”

“…We adapt the notation from ref. [2] and write 4) where the factor Z, which is defined in the MS scheme and thus only contains poles in ǫ, absorbs the infrared divergences and F f is finite. The coefficients of the poles of Z are determined by the QCD beta function and Γ cusp .…”

“…As far as massless form factors are concerned the stateof-the-art is four loops where different groups have contributed to partial results [3][4][5][6][7][8]. Massive quark form factors are known to two loops [9] including O(ǫ) [2,10] and O(ǫ 2 ) terms [11,12]. Three-loop corrections in the large-N c limit for the vector current form factor have been computed in ref.…”

“…We provide analytic results for all master integrals which are not present in the large-N c calculation considered in refs. [1,2]. …”