Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory

Abstract

Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF^{2}. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T_{2} in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF^{3}. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF^{3}. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T_{3}, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.

Two-Loop QCD Corrections to the Higgs Plus Three-parton Amplitudes with Top Mass Correction

“…This T 3 function also appeared as building blocks in the N = 4 form factors [45,47,52]. In our QCD results, all degree-3 parts can be express in terms of T 3 functions, plus simple ζ 3 or (ζ 2 × log) terms.…”

“…It has also been also applied to compute collinear anomalous dimensions [51]. Recently, the MTP was also verified for three gluon form factors of the the dimension-6 operators in the pure gluon sector [52][53][54][55]. In this paper, as also reported in [56], the principle was extended to the two-quark one-gluon form factors.…”

“…The generalization is in two aspects. Firstly, the maximal transcendentality principle applies to Higgs to three-parton amplitudes (or form factors) with high dimension operators, see also [52][53][54][55][56]. Secondly, as also discussed in [56], the principle applies also to Higgs amplitudes with external quark states, by a change of color factors:…”

The principle of maximal transcendentality and the four-loop collinear anomalous dimension

“…Besides anomalous dimensions, it has also been successfully applied to form factors, matrix elements of gauge-invariant operators with two or three external partons [47][48][49][50][51], and to certain configurations of semi-infinite Wilson lines [34,35]. However, it does not hold for scattering amplitudes with four or five external gluons, even at one loop [52], in the sense that there are maximally transcendental parts of the QCD one-loop amplitudes which have different rational prefactors from the corresponding N = 4 SYM amplitudes.…”

Holographic computation of Wilson loops in a background with broken conformal invariance and finite chemical potential

“…The thermal width plays an important role in the study of decay processes. The original calculation of qq binding energy in a supersymmetric N = 4 Yang-Mills theory via expectation value of a time-like Wilson loop was first done in [9] which was later extended to the finite temperature case in [10]- [12]. The holographic computation of the screening length of the moving qq inside a moving hot plasma was done in [13], [14].…”