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

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

Section: Extension To Two Loops and Discussionsupporting

confidence: 73%

Subleading Regge limit from a soft anomalous dimension

Brüser¹,

Caron-Huot

Henn

2018

“…It is conjectured that for certain QFTs like the N = 4 Super Yang-Mills (SYM) theory quantum corrections often evaluate to pure combinations of MPLs of uniform weight. This conjecture is supported by many explicit results in N = 4 SYM not only for scattering amplitudes [5,41,, but also for certain anomalous dimensions [38,[71][72][73][74][75][76][77], form factors [78][79][80][81], correlation functions [82][83][84][85][86] and correlators of semi-infinite Wilson lines [87,88]. This overwhelming list of results hints towards the fact that the property of uniform weight is not coincidental, but an intrinsic mathematical feature of the theory.…”

Section: Introductionmentioning

confidence: 76%

Elliptic Feynman integrals and pure functions

Broedel

Duhr

Dulat

et al. 2019

113

153

We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-loop Feynman integrals with up to three external legs and express them in terms of our functions. We observe that in all cases they evaluate to pure combinations of elliptic multiple polylogarithms of uniform weight. This is the first time that a notion of uniform weight is observed in the context of Feynman integrals that evaluate to elliptic polylogarithms.

“…The principle was also verified for other quantities like Wilson lines [49,50]. 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].…”

mentioning

confidence: 86%

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

Jin

Yang

2020

We obtain the two-loop QCD corrections to Higgs plus three-parton amplitudes with dimension-seven operators in Higgs effective field theory. This provides the two-loop S-matrix elements for Higgs plus one-jet production at LHC with top-mass correction. We apply efficient unitarity plus IBP methods which are described in detail. We also study the color decomposition of the fermion cuts and find a connection between fundamental and adjoint representations which can reduce non-planar to planar unitarity cuts. We obtain final results in simple analytic form which exhibits intriguing hidden structure. The principle of maximal transcendentality is found to be satisfied for all results. The lower transcendentality parts also contain universal building blocks and can be written in compact analytic forms, suggesting further hidden structures.