Colour unwound - disentangling colours for azimuthal asymmetries in Drell-Yan scattering

TL;DR

This paper investigates the colour structure of double T-odd contributions in low transverse momentum Drell-Yan scattering, finding that the results align with standard factorisation predictions and highlighting the role of Glauber gluons.

Contribution

It provides the first explicit calculation of the leading-power double Boer-Mulders cross section at two-gluon exchange, confirming the factorisation formula and clarifying the role of Glauber gluons.

Findings

Results agree with the standard factorisation formula.

Glauber gluons are crucial in the colour disentanglement process.

Diagrams with three-gluon vertices are essential for cancellation.

Abstract

It has been suggested that a colour-entanglement effect exists in the Drell-Yan cross section for the 'double T-odd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation formula [1]. These T-odd contributions can come from the Boer-Mulders or Sivers transverse momentum dependent distribution functions. The different colour structure should be visible already at the lowest possible order that gives a contribution to the double Boer-Mulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leading-power contribution to the low-$Q_T$ dBM cross section at the two-gluon exchange order in the context of a spectator model. The computation is performed using a method of regions analysis with Collins subtraction terms implemented. The results conform with the predictions of the factorisation formula. In the cancellation of the colour entanglement, diagrams containing the three-gluon vertex are essential. Furthermore, the Glauber region turns out to play an important role - in fact, it is possible to assign the full contribution to the dBM cross section at the given order to the region in which the two gluons have Glauber scaling. A similar disentanglement of colour is found for the dS effect.