Markus Diehl, Jonathan R. Gaunt, Peter Ploessl, Andreas Schafer
SciPost Phys. 7, 017 (2019) ·
published 6 August 2019

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Double parton distributions (DPDs) receive a shortdistance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at nexttoleading order (NLO) in perturbation theory. Technically, we compute the twoloop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 > 2 splitting functions appearing in the evolution of momentumspace DPDs at NLO. We give results for the unpolarised, coloursinglet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 > 2 splitting functions are consistent with the number and momentum sum rules for DPDs.
Daniël Boer, Tom van Daal, Jonathan R. Gaunt, Tomas Kasemets, Piet J. Mulders
SciPost Phys. 3, 040 (2017) ·
published 19 December 2017

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It has been suggested that a colourentanglement effect exists in the DrellYan cross section for the 'double Todd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation formula [1]. These Todd contributions can come from the BoerMulders 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 BoerMulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leadingpower contribution to the low$Q_T$ dBM cross section at the twogluon 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 threegluon 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.
Daniël Boer, Tom van Daal, Jonathan R. Gaunt, Tomas Kasemets, Piet J. Mulders
SciPost Phys. 3, 040 (2017) ·
published 19 December 2017

· pdf
It has been suggested that a colourentanglement effect exists in the DrellYan cross section for the 'double Todd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation formula [1]. These Todd contributions can come from the BoerMulders 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 BoerMulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leadingpower contribution to the low$Q_T$ dBM cross section at the twogluon 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 threegluon 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.