The Soft Anomalous Dimension at four loops in the Regge Limit

Abstract

The soft anomalous dimension governs the infrared divergences of scattering amplitudes in general kinematics to all orders in perturbation theory. By comparing the recent Regge-limit results for 2 → 2 scattering (through Next-to-Next-to-Leading Logarithms) in full colour to a general form for the soft anomalous dimension at four loops we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.

The infrared structure of perturbative gauge theories

“…[430] in a formulation allowing for a much more direct comparison with infrared factorisation: this made possible the first direct calculation of a contribution to the soft anomalous dimension matrix going beyond the dipole formula, at the four-loop level. A systematic development of the framework proposed in [430] has led to the determination of the soft anomalous dimension matrix for 2 → 2 scattering amplitudes at NLL accuracy to all orders in perturbation theory [431][432][433], and at NNLL accuracy up to four loops [350,351,434,435]. This result, in turn, establishes for the first time the presence of quartic Casimir contributions to the soft anomalous dimension matrix, beyond those induced by the cusp anomalous dimension.…”

“…More recently, further constraints on the infrared matrix, arising from the high-energy limit, were uncovered in Refs. [351,[431][432][433][434][435]: the high-energy limit of the infrared matrix is now known to all-orders at next-to-leading logarithmic (NLL) accuracy, while NNLL contributions constrain the quartic Casimir component at four loops.…”

Two-parton scattering in the high-energy limit: climbing two- and three-Reggeon ladders

“…In practice, the information obtained in particular kinematic limits, such as the Regge limit, can be used to reconstruct the structure of infrared divergences in full kinematic. Preliminary steps in this direction, using the new information obtained in [13,14,23], have been carried out in [24], and have been discussed in another talk in this conference, [44], to which we refer for further details.…”

“…An additional motivation to investigate multi-loop corrections in the high-energy limit is that it provides information on the infrared singularity structure of amplitudes. Further discussion of this aspect can be found in the original papers [11][12][13]20,23,24] and in a talk given at this conference [44], to which we refer for further details.…”

“…Here we limit ourselves to one application, namely, the extraction of the soft anomalous dimension, (see refs. [24,44]) which can be obtained by combining the knowledge of the amplitude in the high-energy limit with the infrared factorization theorem, as discussed for the even amplitude at NLL accuracy. In this case, the calculation of the tower M (−, , −2) gives access to ∆ (+, , −2) .…”