Random polarisations of the dipoles

TL;DR

This paper extends the dipole subtraction formalism for massless and massive partons to include random polarizations, enabling more efficient calculations by replacing spin sums with smooth integrations over polarization variables.

Contribution

The paper introduces a modified dipole subtraction scheme that incorporates random polarizations, simplifying calculations of matrix elements with spin degrees of freedom.

Findings

Derived new subtraction terms for random polarizations

Modified only the real subtraction terms, leaving integrated terms unchanged

Facilitates more efficient computations in perturbative QCD

Abstract

We extend the dipole formalism for massless and massive partons to random polarisations of the external partons. The dipole formalism was originally formulated for spin-summed matrix elements and later extended to individual helicity eigenstates. For efficiency reasons one wants to replace the spin sum by a smooth integration over additional variables. This requires the extension of the dipole formalism to random polarisations. In this paper we derive the modified subtraction terms. We only modify the real subtraction terms, the integrated subtraction terms do not require any modifications.