Abstract
We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-Nc limit, where only planar Feynman diagrams contribute.
Highlights
We consider the three-point functions of the currents in eq (1.1) and a quark-anti-quark pair
Three-loop corrections are only known for well-defined subsets of the vector form factor: the large-Nc limit has been computed in ref. [7] using the master integrals of [15]
An interesting feature of the form factors is the presence of infrared poles that can be described by a universal function, the cusp anomalous dimension Γcusp [38,39,40], which is independent of the external current
Summary
The techniques and the setup of the programs, which are used to obtain the results of this paper, are straightforward extensions of the works [7, 10] and we refrain from repeating in detail the technical descriptions. After inserting the ǫ-expanded results for the master integrals into the expressions for the form factors we obtain the one- and two-loop expressions expanded up to order ǫ4 and ǫ2, respectively. In all cases the counterterm contributions are obtained by rescaling the bare parameters with the corresponding renormalization constants, Zαs, ZmOS and Z2OS The latter is needed to three loops whereas two-loop corrections for Zαs and ZmOS are required. For the scalar and pseudo-scalar form factors the overall factor m has to be renormalized (to three-loop order), which we choose to do in the MS scheme Note that this is the natural choice if F s or F p are used for Higgs boson production or decay since m takes over the role of the Yukawa coupling. Note that in our case the overall renormalization constants of all currents in eq (1.1) are equal to unity
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