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Title: A fast and accurate method for perturbative resummation of transverse momentum-dependent observables

Abstract

Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transformmore » that needs to be performed just once for all observables and kinematics, to any desired accuracy.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [2]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Fudan Univ., Shanghai (China). Key Lab. of Nuclear Physics and Ion-beam Application (MOE) and Inst. of Modern Physics
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Laboratory Directed Research and Development (LDRD) Program
Contributing Org.:
TMD Topical Collaboration
OSTI Identifier:
1440437
Report Number(s):
LA-UR-17-27820
Journal ID: ISSN 1029-8479; TRN: US1900732
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Atomic and Nuclear Physics

Citation Formats

Kang, Daekyoung, Lee, Christopher, and Vaidya, Varun. A fast and accurate method for perturbative resummation of transverse momentum-dependent observables. United States: N. p., 2018. Web. doi:10.1007/JHEP04(2018)149.
Kang, Daekyoung, Lee, Christopher, & Vaidya, Varun. A fast and accurate method for perturbative resummation of transverse momentum-dependent observables. United States. doi:10.1007/JHEP04(2018)149.
Kang, Daekyoung, Lee, Christopher, and Vaidya, Varun. Fri . "A fast and accurate method for perturbative resummation of transverse momentum-dependent observables". United States. doi:10.1007/JHEP04(2018)149. https://www.osti.gov/servlets/purl/1440437.
@article{osti_1440437,
title = {A fast and accurate method for perturbative resummation of transverse momentum-dependent observables},
author = {Kang, Daekyoung and Lee, Christopher and Vaidya, Varun},
abstractNote = {Here, we propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons (γ*, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.},
doi = {10.1007/JHEP04(2018)149},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}

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Works referenced in this record:

Next-to-Next-to-Leading-Order Logarithmic Corrections at Small Transverse Momentum in Hadronic Collisions
journal, November 2000


Small transverse momentum distributions in hard processes
journal, August 1979


QCD analysis of jets recoiling against large transverse momentum muon pairs
journal, November 1978


Combined threshold and transverse momentum resummation for inclusive observables
journal, March 2017

  • Muselli, Claudio; Forte, Stefano; Ridolfi, Giovanni
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)106

An effective field theory for collinear and soft gluons: Heavy to light decays
journal, May 2001


Fragmentation in jets at NNLO
journal, September 2014


Correspondence between Soft and Rapidity Anomalous Dimensions
journal, February 2017


Lepton pair production at large transverse momentum in second order QCD
journal, January 1983


Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion
journal, December 2002


Top mass effects in Higgs production at next-to-next-to-leading order QCD: Virtual corrections
journal, September 2009


Origin of the large perturbative corrections to Higgs production at hadron colliders
journal, February 2009


Vector boson production in joint resummation
journal, February 2017

  • Marzani, Simone; Theeuwes, Vincent
  • Journal of High Energy Physics, Vol. 2017, Issue 2
  • DOI: 10.1007/JHEP02(2017)127

Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass
journal, September 2009


Electroweak corrections to high energy processes using effective field theory
journal, March 2008


Rapidity Renormalization Group
journal, April 2012


Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production
journal, November 2014

  • D’Alesio, Umberto; Echevarria, Miguel G.; Melis, Stefano
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)098

Second-order corrections to the Drell-Yan process at large transverse momentum
journal, August 1981


Higgs Transverse-Momentum Resummation in Direct Space
journal, June 2016


QCD transverse-momentum resummation in gluon fusion processes
journal, April 2011


Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC
journal, November 2011

  • de Florian, Daniel; Ferrera, Giancarlo; Grazzini, Massimiliano
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)064

Higgs production with a central jet veto at NNLL+NNLO
journal, April 2011

  • Berger, Carola F.; Marcantonini, Claudio; Stewart, Iain W.
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)092

The complete computation of high-pT W and Z production in second-order QCD
journal, June 1989


Vector Boson Production at Hadron Colliders: A Fully Exclusive QCD Calculation at Next-to-Next-to-Leading Order
journal, August 2009


Resummation of transverse momentum distributions in distribution space
journal, February 2017

  • Ebert, Markus A.; Tackmann, Frank J.
  • Journal of High Energy Physics, Vol. 2017, Issue 2
  • DOI: 10.1007/JHEP02(2017)110

The photon content of the proton
journal, December 2017

  • Manohar, Aneesh V.; Nason, Paolo; Salam, Gavin P.
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)046

Calculation of the transverse parton distribution functions at next-to-next-to-leading order
journal, June 2014

  • Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)155

Invariant operators in collinear effective theory
journal, September 2001


Universal transverse momentum dependent soft function at NNLO
journal, March 2016


Higgs Production with Large Transverse Momentum in Hadronic Collisions at Next-to-Leading Order
journal, June 1999


Summing Sudakov logarithms in B X s γ in effective field theory
journal, December 2000


Analysis of vector boson production within TMD factorization
journal, January 2018


Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order
journal, September 2016

  • Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)004

Energy evolution for the Sivers asymmetries in hard processes
journal, August 2013


QCD radiative corrections to electroweak-boson production at large transverse momentum in hadron collisions
journal, October 1989

  • Gonsalves, Richard J.; Pawłowski, Jerzy; Wai, Chung-Fai
  • Physical Review D, Vol. 40, Issue 7
  • DOI: 10.1103/PhysRevD.40.2245

The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
journal, November 2001


Power corrections and renormalons in Transverse Momentum Distributions
journal, March 2017

  • Scimemi, Ignazio; Vladimirov, Alexey
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)002

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation
journal, January 2017


Comparing and counting logs in direct and effective methods of QCD resummation
journal, April 2014

  • Almeida, Leandro G.; Ellis, Stephen D.; Lee, Christopher
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)174

Drell–Yan production at small q T , transverse parton distributions and the collinear anomaly
journal, June 2011


Thrust at N 3 LL with power corrections and a precision global fit for α s ( m Z )
journal, April 2011


The three-loop QCD β-function and anomalous dimensions
journal, April 1993


Production of Drell–Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy
journal, January 2011


Transverse momentum resummation in soft collinear effective theory
journal, December 2005


Resummation of threshold logarithms in effective field theory for DIS, Drell–Yan and Higgs production
journal, October 2006


Renormalization-group improved prediction for Higgs production at hadron colliders
journal, April 2009


The fully-differential quark beam function at NNLO
journal, December 2014

  • Gaunt, Jonathan R.; Stahlhofen, Maximilian
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)146

Hard scattering factorization from effective field theory
journal, July 2002


Next-to-leading order QCD corrections to differential distributions of Higgs boson production in hadron–hadron collisions
journal, July 2002


Transverse momentum in Drell-Yan processes
journal, June 1978


How Bright is the Proton? A Precise Determination of the Photon Parton Distribution Function
journal, December 2016


Transverse momentum distribution in Drell-Yan pair and W and Z boson production
journal, January 1985


A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory
journal, May 2012

  • Chiu, Jui-Yu; Jain, Ambar; Neill, Duff
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)084

Joint transverse momentum and threshold resummation beyond NLL
journal, November 2016


Transverse momentum distributions from effective field theory with numerical results
journal, March 2011


The gell-mann-low function of QCD in the three-loop approximation
journal, June 1980


Transverse momentum distribution through soft-gluon resummation in effective field theory
journal, October 2005


Role of the nonperturbative input in QCD resummed Drell-Yan Q T distributions
journal, April 2001


The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004


Momentum-space resummation for transverse observables and the Higgs p⊥ at N3LL+NNLO
journal, February 2018

  • Bizoń, Wojciech; Monni, Pier Francesco; Re, Emanuele
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)108

Rapidity renormalized TMD soft and beam functions at two loops
journal, March 2016

  • Lübbert, Thomas; Oredsson, Joel; Stahlhofen, Maximilian
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)168

Higgs-boson production at small transverse momentum
journal, May 2013

  • Becher, Thomas; Neubert, Matthias; Wilhelm, Daniel
  • Journal of High Energy Physics, Vol. 2013, Issue 5
  • DOI: 10.1007/JHEP05(2013)110

Renormalization of the Wilson loops beyond the leading order
journal, January 1987


Soft-collinear factorization in effective field theory
journal, February 2002


Treating the b quark distribution function with reliable uncertainties
journal, December 2008