Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle

Abstract

We obtain, for the first time, the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet production at LHC. The computation is based on the on-shell unitarity method combined with integration by parts reduction. We work in conventional dimensional regularization and obtain analytic expressions renormalized in the modified minimal subtraction scheme. The two-loop anomalous dimensions present operator mixing behavior. The infrared divergences agree with that predicted by Catani and the finite remainders take remarkably simple forms, where the maximally transcendental parts are identical to the corresponding results in N=4 super-Yang-Mills theory. The parts of lower transcendentality turn out to be also largely determined by the N=4 results.

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

“…The maximally transcendental part of the form factors of the operators O S and O C is the same as that of the half-BPS operator Tr(X 3 ) in the N = 4 SYM theory, regardless of the amount of supersymmetry (including N = 0) [1]. The latter statement was confirmed by a recent explicit computation in [19].…”

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

“…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:…”

“…We will apply the planar D-dimensional unitarity method in the computation of H → 3g amplitude. In the pure gluon sector the non-planar contribution vanishes at 2 loops [53] and the amplitude is proportional to the simple color factor N 2 c , so the planar unitarity cut gives the full result. In the presence of internal quark legs, the amplitude contain N 0 c and N −2 c contributions.…”

On interpolating anomalous dimension of twist-two operators with general spins

“…(Here, "transcendentality" refers to transcendentality degree which characterizes the "complexity" of mathematical numbers or functions, for example, the Riemann zeta value ζ n and the polylogarithm Li n have degree n.) This is a conjecture expected to be true perturbatively to all orders. Further evidences of these correspondences were also found for other observables such as amplitudes and Wilson lines [12,13,14,15,16]. These little understood mystical correspondence between N = 4 SYM and QCD indicates there is a deep connection between the two theories.…”