A proof algorithm associated with the dipole splitting algorithm

TL;DR

This paper introduces a proof algorithm that verifies the cancellation of subtraction terms in the dipole splitting algorithm, enhancing the reliability of QCD NLO corrections in collider processes.

Contribution

The paper presents a new proof algorithm (PRA) that analytically confirms the vanishing of all subtraction terms in the dipole splitting algorithm, improving consistency checks in QCD calculations.

Findings

PRA effectively verifies the cancellation of subtraction terms.

Application demonstrated in hadron collider processes $pp \to \mu^{+}\mu^{-}$, 2 jets, and n jets.

Enhances reliability of NLO QCD corrections.

Abstract

We present a proof algorithm associated with the dipole splitting algorithm (DSA). The proof algorithm (PRA) is a straightforward algorithm to prove that the summation of all the subtraction terms created by the DSA vanishes. The execution of the PRA provides a strong consistency check including all the subtraction terms --the dipole, I, P, and K terms-- in an analytical way. Thus we can obtain more reliable QCD NLO corrections. We clearly define the PRA with all the necessary formulae and demonstrate it in the hadron collider processes $pp \to \mu^{+}\mu^{-},\,2\,jets$, and $n\,jets$.