Three-loop helicity amplitudes for quark-gluon scattering in QCD

Abstract

We compute the three-loop helicity amplitudes for q q → gg and its crossed partonic channels, in massless QCD. Our analytical results provide a non-trivial check of the color quadrupole contribution to the infrared poles for external states in different color representations. At high energies, the qg → qg amplitude shows the predicted factorized form from Regge theory and confirms previous results for the gluon Regge trajectory extracted from qq → qq and gg → gg scattering.

Three-Loop Four-Point Scattering Amplitudes in Massless Gauge Theories

“…The computations presented here and in [3][4][5] allowed us to verify up to three loops the structure of IR singularities in QCD predicted by the equations above. This provides a highly non-trivial check of our results and of the techniques described here.…”

“…In fact, one can perform the Feynman-diagrammatic computation only for the partial amplitudes which are independent under crossings of the external momenta and obtain the rest only at the end. For the processes above, this means one can restrict the computation to just A [1] 4𝑔 , A [4] 4𝑔 , A [1] 𝑞𝑔 , A [3] 𝑞𝑔 , A [1] 4𝑞 , A [2] 4𝑞 . In order to compute the set of independent partial amplitudes, we further decompose them in Lorentz (or spin) space.…”

“…Having identified the H [𝑖 ] 𝝀 as "physical" quantities, we can now compute them perturbatively. Details on the computation of the 𝑔𝑔 → 𝑔𝑔, 𝑞 q → 𝑔𝑔 and 𝑞 q → Q𝑄 channels up to three loops can be found on [3][4][5]. To sum up, there are two major bottlenecks in these computations: (1) performing the Dirac and color algebra arising from Feynman diagrams; (2) reducing the large number of Feynman integrals (𝑂 (10 7 ) for 𝑔𝑔 → 𝑔𝑔) to a basis of master integrals and subsequently including of the integration-by-parts (IBPs) identities in the amplitude.…”

“…The three-loop calculations presented here and in [3][4][5] allowed us to compute the last missing ingredient for the characterization of the signature even/odd amplitudes at NLL/NNLL, 𝑖.𝑒. the three loop Regge trajectory, and check Regge factorisation to this accuracy across all partonic channels for 2 → 2 scattering in QCD.…”

“…The first analytic results for a QCD three-loop four-point amplitude were obtained for the process 𝑞 q → 𝛾𝛾 and presented in [2]. Building on this, we review the calculations presented in [3][4][5], where the computation of all four-parton channels up to three-loops in full QCD was tackled for the first time. The presence of four colored particles in the external states allows for more complex interactions, involving long range exchanges of color charge between initial and final state.…”