Diphoton Amplitudes in Three-Loop Quantum Chromodynamics.

Fabrizio Caola,Lorenzo Tancredi,Andreas Von Manteuffel

doi:10.1103/physrevlett.126.112004

Fabrizio Caola, Lorenzo Tancredi + Show 1 more

Open Access

https://doi.org/10.1103/physrevlett.126.112004

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Abstract

We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in QCD. We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.

Highlights

Multiloop scattering amplitudes in quantum chromodynamics (QCD) are a crucial ingredient for the precision physics program carried out at particle colliders such as the Large Hadron Collider at CERN
In the recent past, such calculations played a fundamental role for the Higgs characterization [1], for the extraction of fundamental parameters of the standard model (SM) [2,3], and for the study of electroweak bosons [4,5,6] and the top quark [7], to mention a few examples
These investigations allow for a deep scrutiny of the SM, which is essential for establishing its validity and for revealing possible tensions pointing toward new physics

Summary

Published by the American Physical Society

Multitude of phenomenological studies up to NNLO in QCD [51,52,53]. we would like to stress that despite the aforementioned simplifications, this process still contains all of the analytic complexity of a generic massless 2 → 2 scattering process. It may seem puzzling that we find five independent tensor structures when we have only four helicity amplitudes (not considering charge conjugation). This mismatch is easy to explain, : the decomposition Eq (5) is valid for arbitrary dimension d. Since eventually we are only interested in the d → 4 limit, it is convenient to reorganize the tensors Ti and choose for T5 a linear combination that is identically zero when four-dimensional external states are considered.

We then write the scattering amplitude as

The relation between renormalized and bare coupling is given by

FðkÞ i of

The finite remainders

With these definitions we find