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Splitting amplitudes at N 3 LO in QCD

Guan, Xin [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000156661295)·Herzog, Franz [Univ. of Edinburgh, Scotland (United Kingdom)] (ORCID:0000000306458197)·Ma, Yao [Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland)] (ORCID:0000000150672508)·Mistlberger, Bernhard [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000177798792)·Suresh, Adi [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000280852021)
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Abstract

In the limit where partons become collinear to each other, scattering amplitudes factorize into a product of universal, process-independent building blocks and scattering amplitudes involving fewer partons. We compute these universal building blocks — known as splitting amplitudes — for two collinear QCD partons up to third loop order in QCD. Our results describe arbitrary time-like splitting processes. Due to the violation of strict collinear factorization in space-like splitting processes, we specifically present space-like splitting amplitudes for three-parton QCD scattering amplitudes at third loop order. To achieve our results, we perform a collinear expansion of three-loop scattering amplitudes using a new expansion-by-subgraph technology, which is based on the method of regions.

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSFactorizationHigher-Order Perturbative CalculationsRenormalization Group

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Guan, Xin [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000156661295), Herzog, Franz [Univ. of Edinburgh, Scotland (United Kingdom)] (ORCID:0000000306458197), Ma, Yao [Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland)] (ORCID:0000000150672508), Mistlberger, Bernhard [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000177798792), Suresh, Adi [Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)] (ORCID:0000000280852021). 2025-01-17. Splitting amplitudes at N 3 LO in QCD. https://doi.org/10.1007/jhep01(2025)090

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