Soft-Collinear Mode for Jet Rates in Soft-Collinear Effective Theory

Chien, Yang-Ting; Lee, Christopher; Hornig, Andrew

doi:10.1103/PhysRevD.93.014033

Title: Soft-Collinear Mode for Jet Rates in Soft-Collinear Effective Theory

Journal Article · Fri Jan 29 00:00:00 EST 2016 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.93.014033· OSTI ID:1334119

Chien, Yang-Ting ^[1]; Lee, Christopher ^[1]; Hornig, Andrew ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division

We propose the addition of a new "soft-collinear" mode to soft collinear effective theory (SCET) below the usual soft scale to factorize and resum logarithms of jet radii R in jet cross sections. We consider exclusive 2-jet cross sections in e⁺e^- collisions with an energy veto Λ on additional jets. The key observation is that there are actually two pairs of energy scales whose ratio is R: the transverse momentum QR of the energetic particles inside jets and their total energy Q, and the transverse momentum ΛR of soft particles that are cut out of the jet cones and their energy Λ. The soft-collinear mode is necessary to factorize and resum logarithms of the latter hierarchy. We show how this factorization occurs in the jet thrust cross section for cone and k_T-type algorithms at O(α_s) and using the thrust cone algorithm at O(α$$2\atop{s}$$). We identify the presence of hard-collinear, in-jet soft, global (veto) soft, and soft-collinear modes in the jet thrust cross section. We also observe here that the in-jet soft modes measured with thrust are actually the "csoft" modes of the theory SCET₊. We dub the new theory with both csoft and soft-collinear modes "SCET₊₊". We go on to explain the relation between the "unmeasured" jet function appearing in total exclusive jet cross sections and the hard-collinear and csoft functions in measured jet thrust cross sections. We do not resum logs that are non-global in origin, arising from the ratio of the scales of soft radiation whose thrust is measured at Q$${{\tau}}$$/R and of the soft-collinear radiation at 2ΛR. Their resummation would require the introduction of additional operators beyond those we consider here. The steps we outline here are a necessary part of summing logs of R that are global in nature and have not been factorized and resummed beyond leading-log level previously.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1334119

Alternate ID(s):: OSTI ID: 1236513

Report Number(s):: LA-UR-15-26983

Journal Information:: Physical Review D, Vol. 93, Issue 1; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 45 works

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