Tr(F3) supersymmetric form factors and maximal transcendentality. Part II. 0 < mathcal{N} < 4 super Yang-Mills

Andreas Brandhuber,Brenda Penante,Gabriele Travaglini,Martyna Kostacińska

doi:10.1007/jhep12(2018)077

Andreas Brandhuber, Brenda Penante + Show 2 more

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https://doi.org/10.1007/jhep12(2018)077

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Abstract

The study of form factors has many phenomenologically interesting applications, one of which is Higgs plus gluon amplitudes in QCD. Through effective field theory techniques these are related to form factors of various operators of increasing classical dimension. In this paper we extend our analysis of the first finite top-mass correction, arising from the operator Tr(F3), from mathcal{N} = 4 super Yang-Mills to theories with mathcal{N} < 4, for the case of three gluons and up to two loops. We confirm our earlier result that the maximally transcendental part of the associated Catani remainder is universal and equal to that of the form factor of a protected trilinear operator in the maximally supersymmetric theory. The terms with lower transcendentality deviate from the mathcal{N} = 4 answer by a surprisingly small set of terms involving for example ζ2, ζ3 and simple powers of logarithms, for which we provide explicit expressions.

Highlights

One-loop minimal form factorsFor the reader’s convenience we quote here the one-loop correction to the minimal form factor of the operators OS and OC, calculated in [2, 18]:2
Top quarks is replaced by a set of local interactions in an expansion in 1/mt where mt is the top mass
In [6] it was found that the form factor remainder for the half-BPS bilinear scalar operator Tr(X2) in N = 4 super Yang-Mills (SYM) captures the maximally transcendental part of the remainder computed in pure Yang-Mills of the operator Tr(F 2) with a state of three gluons [7]

Summary

One-loop minimal form factors

For the reader’s convenience we quote here the one-loop correction to the minimal form factor of the operators OS and OC, calculated in [2, 18]:2. The result for the one-loop form factor of the two operators OC and OS is operatorindependent, and theory-independent, i.e. the same whether computed in pure or supersymmetric Yang-Mills. This is due to the fact that both the tree-level form factor (2.1) and the four-gluon tree-level amplitude entering the one-loop cut are identical in any YangMills theory. We compute the minimal form factors FOS (1+, 2+, 3+; q) and FOC (1+, 2+, 3+; q) at two loops and in theories with less-than-maximal supersymmetry

An effective supersymmetric decomposition

Modifications to the two-particle cut

Catani form factor remainder and renormalisation

Discussion

A One-loop integral functions

B Numerators