An exponential regulator for rapidity divergences

Li, Ye; Neill, Duff; Zhu, Hua Xing

doi:10.1016/j.nuclphysb.2020.115193

Title: An exponential regulator for rapidity divergences

Journal Article · Sun Nov 01 00:00:00 EDT 2020 · Nuclear Physics. B

DOI:https://doi.org/10.1016/j.nuclphysb.2020.115193· OSTI ID:1671866

Li, Ye; Neill, Duff; Zhu, Hua Xing

Finding an efficient and compelling regularization of soft and collinear degrees of freedom at the same invariant mass scale, but separated in rapidity is a persistent problem in high-energy factorization. In the course of a calculation, one encounters divergences unregulated by dimensional regularization, often called rapidity divergences. Once regulated, a general framework exists for their renormalization, the rapidity renormalization group (RRG), leading to fully resummed calculations of transverse momentum (to the jet axis) sensitive quantities. We examine how this regularization can be implemented via a multi-differential factorization of the soft-collinear phase-space, leading to an (in principle) alternative non-perturbative regularization of rapidity divergences. As an example, we examine the fully-differential factorization of a color singlet's momentum spectrum in a hadron-hadron collision at threshold. We show how this factorization acts as a mother theory to both traditional threshold and transverse momentum resummation, recovering the classical results for both resummations. Examining the refactorization of the transverse momentum beam functions in the threshold region, we show that one can directly calculate the rapidity renormalized function, while shedding light on the structure of joint resummation. Finally, we show how using modern bootstrap techniques, the transverse momentum spectrum is determined by an expansion about the threshold factorization, leading to a viable higher loop scheme for calculating the relevant anomalous dimensions for the transverse momentum spectrum.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-07CH11359; SC0011090

OSTI ID:: 1671866

Alternate ID(s):: OSTI ID: 1347931

Report Number(s):: arXiv:1604.00392; FERMILAB-PUB-16-090-PPD-T; MIT-CTP-4795; S0550321320302789; 115193; PII: S0550321320302789

Journal Information:: Nuclear Physics. B, Journal Name: Nuclear Physics. B Vol. 960 Journal Issue: C; ISSN 0550-3213

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

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