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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 Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); 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. https://doi.org/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. https://doi.org/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 = {Fri Apr 27 00:00:00 EDT 2018},
month = {Fri Apr 27 00:00:00 EDT 2018}
}

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Cited by: 12 works
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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


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


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


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


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

Power corrections and renormalons in Transverse Momentum Distributions
text, January 2017


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


Higgs-boson production at small transverse momentum
text, January 2013


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


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

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


Resummation of transverse momentum distributions in distribution space
text, January 2017


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


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


Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone
journal, July 2012

  • Echevarría, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)002

Electroweak gauge-boson production at small q T : Infrared safety from the collinear anomaly
journal, February 2012

  • Becher, Thomas; Neubert, Matthias; Wilhelm, Daniel
  • Journal of High Energy Physics, Vol. 2012, Issue 2
  • DOI: 10.1007/JHEP02(2012)124

Factorization and momentum-space resummation in deep-inelastic scattering
journal, January 2007


The quark form factor at higher orders
journal, August 2005

  • Moch, Sven-Olaf; Vermaseren, Jozef Antoon M.; Vogt, Andreas
  • Journal of High Energy Physics, Vol. 2005, Issue 08
  • DOI: 10.1088/1126-6708/2005/08/049

Higgs production and decay: analytic results at next-to-leading order QCD
journal, December 2005


Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
journal, January 2007

  • Anastasiou, Charalampos; Beerli, Stefan; Bucherer, Stefan
  • Journal of High Energy Physics, Vol. 2007, Issue 01
  • DOI: 10.1088/1126-6708/2007/01/082

Calculation of the transverse parton distribution functions at next-to-next-to-leading order
text, January 2014


QCD transverse-momentum resummation in gluon fusion processes
text, January 2011


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

  • Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey
  • Universität Regensburg
  • DOI: 10.5283/epub.37200

Resummation of Transverse Momentum Distributions in Distribution Space
text, January 2016


Higgs Production with a Central Jet Veto at NNLL+NNLO
text, January 2010


Higgs-Boson Production at Small Transverse Momentum
text, January 2012


Comparing and Counting Logs in Direct and Effective Methods of Resummation
text, January 2014


How bright is the proton? A precise determination of the photon parton distribution function
text, January 2016


The Photon Content of the Proton
text, January 2017


Invariant Operators in Collinear Effective Theory
text, January 2001


The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
text, January 2004


Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC
text, January 2011


Works referencing / citing this record:

Fiducial distributions in Higgs and Drell-Yan production at N3LL+NNLO
text, January 2018


Fiducial distributions in Higgs and Drell-Yan production at N3LL+NNLO
journal, December 2018

  • Bizoń, Wojciech; Chen, Xuan; Gehrmann-De Ridder, Aude
  • Journal of High Energy Physics, Vol. 2018, Issue 12
  • DOI: 10.1007/jhep12(2018)132

Fiducial distributions in Higgs and Drell-Yan production at N3LL+NNLO
text, January 2018