Three-loop helicity amplitudes for four-quark scattering in massless QCD

Abstract

We compute the three-loop corrections to the helicity amplitudes for q$$ \overline{q} $$ q ¯ → Q$$ \overline{Q} $$ Q ¯ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.

Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops

“…On the other hand, we use the high-energy limit as a tool to investigate the long-distance singularity structure of non-planar 2 → 2 amplitudes in general kinematics in QCD and in N = 4 super Yang-Mills (SYM), beyond the accuracy of state-of-the-art fixed-order calculations, see e.g. [42].…”

Calculational Techniques in Particle Theory

“…As it should be, the number of helicity amplitudes provides then an upper bound to the number of the independent tensors required. Recently, these ideas have been applied successfully to simplify the calculation of the three-loop corrections to 2 → 2 scattering in QCD [24,25]. A different approach was also developed, where explicit representations for the polarisation vectors and spinors are used in order to single out the different helicity configurations from the scattering amplitudes [26] Both approaches have been successfully applied to various 2 → 3 scattering processes [27][28][29].…”

$N^3LO$ calculations for $2 \to 2$ processes using Simplified Differential Equations

“…In total (in both families) there exist 91 new MI and for finding their corresponding UT basis element we used three methods. One of the methods is the Magnus Exponential [32] method applied to the DE derived by differentiating with respect to the Mandelstam variables, which we used for some lower-sector (till 7 propagators) MI 6 . For some intermediate-sector (till 9 propagators) MI we used the DlogBasis q 2 q 1 q 3 q 4…”

“…Within this framework, the current frontier for 2 → 2 scattering processes stands at N 3 LO, where the computation of three-loop Feynman Integrals (FI) is demanded. From these FI, all the families with massless internal and external particles have been calculated [1][2][3][4]7] and have been very recently used for the computation of 3-loop 4-point Amplitudes (for the first time in QCD) for the processes qq → γγ [5] and qq → qq 1 [6]. As it regards the massless families with one external off-shell leg, which are relevant for processes like e + e − → γ * → 3 j, pp → Z j and pp → H j, only one has been calculated [7,8], while no progress has been made on the computation of the families with two off-shell legs so far.…”