Quark and gluon two-loop beam functions for leading-jet pT and slicing at NNLO

Abreu, Samuel; Gaunt, Jonathan R.; Monni, Pier Francesco; Rottoli, Luca; Szafron, Robert

doi:10.1007/jhep04(2023)127

Title: Quark and gluon two-loop beam functions for leading-jet p_T and slicing at NNLO

Journal Article · 25 April 2023 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep04(2023)127 · OSTI ID:1971827

^[1]; Gaunt, Jonathan R. ^[2]; Monni, Pier Francesco ^[3]; Rottoli, Luca ^[4]; Szafron, Robert ^[5]

European Organization for Nuclear Research (CERN), Geneva (Switzerland); Univ. of Edinburgh, Scotland (United Kingdom)
Univ. of Manchester (United Kingdom)
European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Univ. of Zurich (Switzerland)
Brookhaven National Lab. (BNL), Upton, NY (United States)

We compute the complete set of two-loop beam functions for the transverse momentum distribution of the leading jet produced in association with an arbitrary colour-singlet system. Our results constitute the last missing ingredient for the calculation of the jet-vetoed cross section at small veto scales at the next-to-next-to-leading order, as well as an important ingredient for its resummation to next-to-next-to-next-to-leading logarithmic order. Our calculation is performed in the soft-collinear effective theory framework with a suitable regularisation of the rapidity divergences occurring in the phase-space integrals. We discuss the occurrence of soft-collinear mixing terms that might violate the factorisation theorem, and demonstrate that they are naturally absorbed into the beam functions at two loops in the exponential rapidity regularisation scheme when performing a multipole expansion of the measurement function. As in our recent computation of the two-loop soft function, we present the results as a Laurent expansion in the jet radius R. We provide analytic expressions for all flavour channels in x space with the exception of a set of R-independent non-logarithmic terms that are given as numerical grids. We also perform a fully numerical calculation with exact R dependence, and find that it agrees with our analytic expansion at the permyriad level or better. Our calculation allows us to define a next-to-next-to-leading order slicing method using the leading-jet p_T as a slicing variable. As a check of our results, we carry out a calculation of the Higgs and Z boson total production cross sections at the next-to-next-to-leading order in QCD.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Royal Society; Swiss National Science Foundation (SNSF)

Grant/Contract Number:: SC0012704

OSTI ID:: 1971827

Report Number(s):: BNL-224260-2023-JAAM

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2023; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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