# A proof algorithm associated with the dipole splitting algorithm

Source: [A proof algorithm associated with the dipole splitting algorithm](<https://www.sota2.com/research/paper/68fa32931e209131ce8894d2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:35:08.481Z

Authors: K. Hasegawa

Published: 2014-09-15T08:17:44.000Z

## 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 $n\\,jets$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1409.4174>)

[PDF](<https://arxiv.org/pdf/1409.4174.pdf>)