## SciPost Submission Page

# Two-loop splitting in double parton distributions

### by Markus Diehl, Jonathan R. Gaunt, Peter Ploessl, Andreas Schafer

#### This is not the current version.

### Submission summary

As Contributors: | Markus Diehl · Jonathan Gaunt |

Arxiv Link: | https://arxiv.org/abs/1902.08019v1 |

Date submitted: | 2019-02-28 |

Submitted by: | Diehl, Markus |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Phenomenology |

### Abstract

Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop 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 momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet 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.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 3 on 2019-5-22 Invited Report

### Strengths

1- Very well written

2- Good introduction and motivation

3- Level of detail in the explanation of calculations

4- Overall structure meaningful

5- Can follow the ideas throughout despite the paper being very long

6- Very relevant calculation for this field

7- Detailed discussion of results overall and in relation to earlier work

8- Balance of technical detail vs explanatory text well chosen

### Weaknesses

If any weakness is to be pointed out, then perhaps hints towards next steps where the results are to be applied in relation to possible measurements and accuracies at the upcoming high luminosity phase of the LHC.

### Report

An important computation is being reported on in this paper which documents a step forward in the field of double Parton scattering. The computation is very timely and is in line with the expected performance of the upcoming LHC high luminosity run. Despite being technical, this paper will nevertheless be an interesting read for students and postdocs in this and related fields as many details are explained very well.

### Requested changes

No changes requested.

### Anonymous Report 2 on 2019-4-21 Invited Report

### Strengths

A detailed analysis of DPD renormalization and sum rules

### Weaknesses

A bit technical, but that is the nature of the subject

### Report

The paper discusses the NLO renormalization of DPDs (double parton distribution functions), and the mixing of these with ordinary PDFs (i.e. single parton distribution functions). The paper makes important contributions, and should be published. The paper is rather technical, and only suitable for those studying DPDs in detail.

### Requested changes

None

### Anonymous Report 1 on 2019-4-14 Invited Report

### Strengths

The paper given an extremely careful account of these splitting function, including analytic results, details of the calculations, and a comparison with the literature.

### Weaknesses

The discussion is a little long in many places. Like for example when the authors introduce dimensional regularization, convolutions, the running strong couplings, ect. Not that introducing these basics is not useful, but the level of care makes the paper a little hard to read. More importantly, the paper is too brief on the conceptual discussion and on the physics impact.

### Report

The paper is written in a very specific style, and I cannot say I personally like it. What I am missing is some kind of discussion of the concepts behind the calculation, so readers see where things are going in each chapter. And, more importantly, I am missing a discussion of the impact of these results. If this is a paper about LHC physics, why should for instance an interested experimentalist care? This is completely unclear in this otherwise very interesting and definitely very clear paper.

### Requested changes

I would love to see a motivational discussion at the very beginning, accessible to an experimentalist or an incoming PhD student in the field; and another section 5.6 with a discussion of the results and their impact. Why do we have to know those splitting kernels and how would this calculation make for a better agreement between theory and data? The paper itself I find hard to read, but it's the way the authors want to write it, so I am fine with that.