One-loop jet functions by geometric subtraction
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Received: July 9, Revised: August 21, Accepted: August 25, Published: October 19,
2020 2020 2020 2020
One-loop jet functions by geometric subtraction
a
Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands b Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, U.K. c Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observabledependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or kT algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in e+ e− collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper. Keywords: Jets, NLO Computations ArXiv ePrint: 2006.14627
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)118
JHEP10(2020)118
Avanish Basdew-Sharma,a Franz Herzog,a,b Solange Schrijnder van Velzena,c and Wouter J. Waalewijna,c
Contents 1 Introduction
1 3 3 9 10 11
3 GOJet program 3.1 Functions 3.2 Input format 3.3 Example: kT clustering algorithms
12 12 13 15
4 Applications 4.1 Cone jet 4.2 Angularities with recoil 4.3 Jet shape
16 16 17 20
5 Conclusions
20
A G2 subtraction term for rapidity divergences
22
B Counterterm mapping
22
C Azimuthal integral
24
1
Introduction
Experimental studies at the Large Hadron Collider (LHC) impose restrictions on QCD radiation in the final state, to stress test the Standard Model and search for New Physics. If these restrictions are tight, they lead to large logarithms in the corresponding cross section. For example, for Higgs plus one jet production with a veto on additional jets with transverse momentum above pveto T , the cross section takes the following form " veto # X pT mH veto n m σ pT = σ0 1 + cn,m αs ln +O , (1.1) pveto mH T n≥1 2n≥m≥0
where σ0 is the leading-order cross section, and the coefficients cn,
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