Abstract
We compute all helicity amplitudes for four particle scattering in massless QCD with nf fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, we consider all possible configurations of external quarks and gluons. We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N3LO) calculations. The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically. We present our findings in the conventional dimensional regularisation and in the t’Hooft-Veltman schemes.
Highlights
We compute all helicity amplitudes for four particle scattering in massless QCD with nf fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory
We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N3LO) calculations
The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically
Summary
The amplitude for the scattering of four gluons can be decomposed into different colour and Lorentz tensors. Since we are considering an amplitude with four external gluons, our ansatz has tensor rank four This yields in full generality 138 independent coefficients. In this gauge, the polarisation sum that has to be carried out to obtain squared matrix elements takes the form polarisations μ i. The polarisation sum that has to be carried out to obtain squared matrix elements takes the form polarisations μ i This polarisation sum annihilates every vector pμi or pμi−1 in the amplitude. Alternative to the representation of our amplitude introduced in eq (3.10), it is useful to decompose our amplitude into different components according to the helicities of the external gluons. The projection from CDR to HV is not invertible
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