Heavy quark form factors at three loops in the planar limit

J Ablinger,J Blümlein,P Marquard,N Rana,C Schneider

doi:10.1016/j.physletb.2018.05.077

J Ablinger, J Blümlein + Show 3 more

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https://doi.org/10.1016/j.physletb.2018.05.077

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Abstract

We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for all first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.

Highlights

Form factors are the matrix elements of local composite operators between physical states
We consider the decay of a virtual massive boson of momentum q into a pair of heavy quarks of mass m, momenta q1 and q2 and color c and d, through a vertex Xcd, where Xcd = ΓμA,cd, ΓS,cd and ΓP,cd indicates the coupling to an axialvector, a scalar and a pseudoscalar boson, respectively
The Feynman diagrams for the different form factors are generated using QGRAF [18], the color algebra is performed using Color [19], the output of which is processed using Q2e/Exp [20,21] and FORM [22, 23] in order to express the diagrams in terms of a linear combination of a large set of scalar integrals

Summary

Introduction

Form factors are the matrix elements of local composite operators between physical states. We calculate both the color–planar and complete light quark non-singlet threeloop contributions to the massive form factors for axialvector, scalar and pseudoscalar currents. The contributions up to O(ε2) for all the massive two-loop form factors were obtained in Ref.

Results

Conclusion