Double counting (proof technique)

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.

Abstract: Poor emissions accounting could undermine carbon markets The 24th international climate conference in Katowice, Poland, in December 2018 was a major achievement in the multilateral response to climate change. More than 190 countries managed to agree on nearly all elements of a comprehensive rulebook that puts flesh on the bones of the 2015 Paris Agreement. The rules require, for the first time, that all countries provide detailed information on their climate change mitigation targets and regularly report on their progress in implementing and achieving them. However, one important chapter is still missing: rules for international carbon markets discussed under Article 6 of the Paris Agreement. Competing views on how to avoid “double counting”—counting the same emission reduction more than once to achieve climate mitigation targets—were a major roadblock to reaching consensus. Completing the missing chapter on Article 6 will be one of the key tasks when countries reconvene at the 25th international climate conference in Santiago, Chile, in December of this year. We highlight why resolving double counting is critical for achieving the goals of the Paris Agreement and identify essential ingredients for a robust outcome that ensures environmental effectiveness and facilitates cost-effective mitigation.

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.