# Double hard scattering without double counting

## TL;DR

This paper addresses the double counting issue in double parton scattering in proton-proton collisions by proposing a new operator-based framework, enabling higher-order calculations and better accuracy in distinguishing between single and double scattering effects.

## Contribution

The authors introduce a novel operator-based method to define double parton distributions, resolving double counting issues and facilitating higher-order perturbative calculations in double parton scattering.

## Key findings

- The framework allows estimation of higher-order contributions to single scattering.
- Identification of conditions where higher-order effects are significant.
- Guidance on when higher-order calculations are necessary for accuracy.

## Abstract

Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.