Abstract
In the large top-mass limit, Higgs plus multi-gluon amplitudes in QCD can be computed using an effective field theory. This approach turns the computation of such amplitudes into that of form factors of operators of increasing classical dimension. In this paper we focus on the first finite top-mass correction, arising from the operator Tr(F3), up to two loops and three gluons. Setting up the calculation in the maximally supersymmetric theory requires identification of an appropriate supersymmetric completion of Tr(F3), which we recognise as a descendant of the Konishi operator. We provide detailed computations for both this operator and the component operator Tr(F3), preparing the ground for the calculation in mathcal{N} < 4, to be detailed in a companion paper. Our results for both operators are expressed in terms of a few universal functions of transcendental degree four and below, some of which have appeared in other contexts, hinting at universality of such quantities. An important feature of the result is a delicate cancellation of unphysical poles appearing in soft/collinear limits of the remainders which links terms of different transcendentality. Our calculation provides another example of the principle of maximal transcendentality for observables with non-trivial kinematic dependence.
Highlights
Form factors of local gauge-invariant operators appear ubiquitously in gauge theories and compute quantities of great phenomenological interest
In this paper we outline in detail the calculation in N = 4 supersymmetric Yang-Mills (SYM) of the two-loop form factors of two operators: Tr(F 3) and the appropriate translation given by the Konishi descendant mentioned above, with an external state of three positive-helicity gluons
In particular we will make an important observation on the terms subleading in transcendentality: the difference between the result in different theories with any amount supersymmetry and the result in N = 4 SYM is confined to a tiny class of terms, mostly simple ζn terms and coefficients of simple logarithms. This can be explained by the fact that, for the operator Tr (F 3), the matter content of the different theories only enters through oneloop sub-diagrams, allowing effectively for a supersymmetric decomposition of the computation similar to that for one-loop amplitudes [31].3. This diagrammatic explanation implies that the form factor of Tr(F 3) in QCD differs from the corresponding calculation in N = 4 SYM only by certain single-scale integrals of sub-maximal transcendentality which only bring about logarithms or constant terms
Summary
Form factors of local gauge-invariant operators appear ubiquitously in gauge theories and compute quantities of great phenomenological interest. In this paper we outline in detail the calculation in N = 4 SYM of the two-loop form factors of two operators: Tr(F 3) and the appropriate translation given by the Konishi descendant mentioned above, with an external state of three positive-helicity gluons This expands the results and observations of [26] and sets the stage for the calculations in N < 4 which will be discussed in [25]. This can be explained by the fact that, for the operator Tr (F 3), the matter content of the different theories only enters through oneloop sub-diagrams, allowing effectively for a supersymmetric decomposition of the computation similar to that for one-loop amplitudes [31].3 This diagrammatic explanation implies that the form factor of Tr(F 3) in QCD differs from the corresponding calculation in N = 4 SYM only by certain single-scale integrals of sub-maximal transcendentality which only bring about logarithms or constant terms.
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