Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes

Abstract

We study the factorization of soft and collinear singularities in dimensionallyregularized fixed-angle scattering amplitudes in massless gauge theories. Our factorization is based on replacing the hard massless partons by light-like Wilson lines, and defining gauge-invariant jet and soft functions in dimensional regularization. In this scheme the factorized amplitude admits a powerful symmetry: it is invariant under rescaling of individual Wilson-line velocities. This symmetry is broken by cusp singularities in both the soft and the eikonal jet functions. We show that the cancellation of these cusp anomalies in any multi-leg amplitude imposes all-order constraints on the kinematic dependence of the corresponding soft anomalous dimension, relating it to the cusp anomalous dimension. For amplitudes with two or three hard partons the solution is unique: the constraints fully determine the kinematic dependence of the soft function. For amplitudes with four or more hard partons we present a minimal solution where the soft anomalous dimension is a sum over colour dipoles, multiplied by the cusp anomalous dimension. In this case additional contributions to the soft anomalous dimension at three loops or beyond are not excluded, but they are constrained to be functions of conformal cross ratios of kinematic variables.

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

“…At two-loop order we have [8][9][10][11]22] 10) where the H (2) l depend on the flavour of the parton, 11) JHEP02(2015)077…”

“…They are sufficient to understand the infrared singular structure of real radiation contributions at next-to-leading order (NLO) in QCD, and have been instrumental in devising systematic subtraction schemes for NLO calculations [4][5][6]. They also form the starting point for a systematic expansion around unresolved limits to all orders in perturbation theory [7][8][9][10][11].…”

The infrared structure of gauge theory amplitudes and their high-energy limit

“…We will show that infrared divergences naturally 'Reggeize', for general t-channel color exchanges, and we will prove that the simplest form of Reggeization breaks down at NNLL accuracy. Interestingly, the general results of Regge theory also have implications on the structure of infrared poles, providing non-trivial constraints on possible corrections to the simplest ansatz for the soft anomalous dimension, the dipole formula [15,16].…”

“…Studies performed over the space of several decades (see [17] for a review), and summarized in this context in Refs. [15,18], have shown that infrared singularities factorize. Denoting by M the vector with components M J , one can write [15,16] the matrix equation…”

“…The key result of Refs. [15,16] is that Γ itself, in the case of massless particles, obeys a set of exact evolution equations which strongly constrain its kinematic dependence, tying it to the color structure of the process. The simplest all-order solution to this set of equations is the dipole ansatz for the matrix Γ, which reads…”