Connecting different TMD factorization formalisms in QCD

Collins, John; Rogers, Ted C.

doi:10.1103/PhysRevD.96.054011

Title: Connecting different TMD factorization formalisms in QCD

Journal Article · Mon Sep 11 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.054011· OSTI ID:1391826

Collins, John ^[1]; Rogers, Ted C. ^[2]

Penn State Univ., University Park, PA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $$\alpha_s^2$$ and $$\alpha_s^3$$. We also show that the ``non-perturbative'' functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between both versions of the CSS formalism and several formalisms based in soft-collinear effective theory (SCET). As a result, our work uses some important new results for factorization for the quark form factor, which we derive.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0013699; AC05-06OR23177

OSTI ID:: 1391826

Alternate ID(s):: OSTI ID: 1389148

Report Number(s):: JLAB-THY-17-2470; DOE/OR/23177-4138; arXiv:1705.07167; PRVDAQ

Journal Information:: Physical Review D, Vol. 96, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 38 works

Citation information provided by
Web of Science

References (71)

An overview of transverse-momentum-dependent factorization and evolution Rogers, T. C. The European Physical Journal A, Vol. 52, Issue 6 https://doi.org/10.1140/epja/i2016-16153-7	journal	June 2016
Universality of the Collins–Soper–Sterman nonperturbative function in vector boson production Konychev, Anton V.; Nadolsky, Pavel M. Physics Letters B, Vol. 633, Issue 6 https://doi.org/10.1016/j.physletb.2005.12.063	journal	February 2006
Proof of factorization for diffractive hard scattering Collins, John C. Physical Review D, Vol. 57, Issue 5 https://doi.org/10.1103/PhysRevD.57.3051	journal	March 1998
Collins asymmetries in inclusive charged $K K$ and $K π$ pairs produced in $e^{+} e^{-}$ annihilation Lees, J. P.; Poireau, V.; Tisserand, V. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.111101	journal	December 2015
Three Loop Cusp Anomalous Dimension in QCD Grozin, Andrey; Henn, Johannes M.; Korchemsky, Gregory P. Physical Review Letters, Vol. 114, Issue 6 https://doi.org/10.1103/PhysRevLett.114.062006	journal	February 2015
Jet $p_{T}$ resummation in Higgs production at ${NNLL}^{'} + NNLO$ Stewart, Iain W.; Tackmann, Frank J.; Walsh, Jonathan R. Physical Review D, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevD.89.054001	journal	March 2014
Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering Collins, John C. Physics Letters B, Vol. 536, Issue 1-2 https://doi.org/10.1016/S0370-2693(02)01819-1	journal	May 2002
Correspondence between Soft and Rapidity Anomalous Dimensions Vladimirov, Alexey A. Physical Review Letters, Vol. 118, Issue 6 https://doi.org/10.1103/PhysRevLett.118.062001	journal	February 2017
Quark and Gluon Form Factors to Three Loops Baikov, P. A.; Chetyrkin, K. G.; Smirnov, A. V. Physical Review Letters, Vol. 102, Issue 21 https://doi.org/10.1103/PhysRevLett.102.212002	journal	May 2009
Analytic results for massless three-loop form factors Lee, R. N.; Smirnov, A. V.; Smirnov, V. A. Journal of High Energy Physics, Vol. 2010, Issue 4 https://doi.org/10.1007/JHEP04(2010)020	journal	April 2010
Transverse Parton Distribution Functions at Next-to-Next-to-Leading Order: The Quark-to-Quark Case Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.242003	journal	December 2012
Analytic resummation for the quark form factor in QCD Magnea, Lorenzo Nuclear Physics B, Vol. 593, Issue 1-2 https://doi.org/10.1016/S0550-3213(00)00623-4	journal	January 2001
Rapidity Renormalization Group Chiu, Jui-yu; Jain, Ambar; Neill, Duff Physical Review Letters, Vol. 108, Issue 15 https://doi.org/10.1103/PhysRevLett.108.151601	journal	April 2012
Erratum: Proof of factorization for diffractive hard scattering [Phys. Rev. D 57, 3051 (1998)] Collins, John C. Physical Review D, Vol. 61, Issue 1 https://doi.org/10.1103/PhysRevD.61.019902	journal	November 1999
Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons Adolph, C.; Akhunzyanov, R.; Alexeev, M. G. Physics Letters B, Vol. 744 https://doi.org/10.1016/j.physletb.2015.03.056	journal	May 2015
Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production Bacchetta, Alessandro; Delcarro, Filippo; Pisano, Cristian Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/JHEP06(2017)081	journal	June 2017
Non-leading corrections to the Drell-Yan cross section at small transverse momentum Davies, C. T. H.; Stirling, W. J. Nuclear Physics B, Vol. 244, Issue 2 https://doi.org/10.1016/0550-3213(84)90316-X	journal	October 1984
Overview of Transverse Momentum Dependent Factorization Breaking Rogers, Ted C. International Journal of Modern Physics: Conference Series, Vol. 25 https://doi.org/10.1142/S2010194514600076	journal	January 2014
Equality of two definitions for transverse momentum dependent parton distribution functions Collins, John; Rogers, Ted Physical Review D, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevD.87.034018	journal	February 2013
Calculation of the transverse parton distribution functions at next-to-next-to-leading order Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)155	journal	June 2014
Back-to-back jets in QCD Collins, John C.; Soper, Davison E. Nuclear Physics B, Vol. 193, Issue 2 https://doi.org/10.1016/0550-3213(81)90339-4	journal	December 1981
Jet axes and universal transverse-momentum-dependent fragmentation Neill, Duff; Scimemi, Ignazio; Waalewijn, Wouter J. Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)020	journal	April 2017
Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)004	journal	September 2016
Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation Li, Ye; Zhu, Hua Xing Physical Review Letters, Vol. 118, Issue 2 https://doi.org/10.1103/PhysRevLett.118.022004	journal	January 2017
Fermilab Tevatron run-1 Z boson data and the Collins-Soper-Sterman resummation formalism Landry, F.; Brock, R.; Nadolsky, P. M. Physical Review D, Vol. 67, Issue 7 https://doi.org/10.1103/PhysRevD.67.073016	journal	April 2003
Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone Echevarría, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)002	journal	July 2012
The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions Grozin, Andrey G.; Henn, Johannes M.; Korchemsky, Gregory P. Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)140	journal	January 2016
Drell–Yan production at small q T , transverse parton distributions and the collinear anomaly Becher, Thomas; Neubert, Matthias The European Physical Journal C, Vol. 71, Issue 6 https://doi.org/10.1140/epjc/s10052-011-1665-7	journal	June 2011
Foundations of Perturbative QCD Collins, John Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology https://doi.org/10.1017/CBO9780511975592	book	May 2011
Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution Aybat, S. Mert; Rogers, Ted C. Physical Review D, Vol. 83, Issue 11 https://doi.org/10.1103/PhysRevD.83.114042	journal	June 2011
Resummation of threshold logarithms in effective field theory for DIS, Drell–Yan and Higgs production Idilbi, Ahmad; Ji, Xiangdong; Yuan, Feng Nuclear Physics B, Vol. 753, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2006.07.002	journal	October 2006
Back-to-back jets: Fourier transform from b to kT Collins, John C.; Soper, Davison E. Nuclear Physics B, Vol. 197, Issue 3 https://doi.org/10.1016/0550-3213(82)90453-9	journal	April 1982
Twist-2 matching of transverse momentum dependent distributions Gutiérrez-Reyes, Daniel; Scimemi, Ignazio; Vladimirov, Alexey A. Physics Letters B, Vol. 769 https://doi.org/10.1016/j.physletb.2017.03.031	journal	June 2017
Transverse momentum distribution in Drell-Yan pair and W and Z boson production Collins, J. C.; Soper, Davison E.; Sterman, George Nuclear Physics B, Vol. 250, Issue 1-4 https://doi.org/10.1016/0550-3213(85)90479-1	journal	January 1985
Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel Collins, John; Rogers, Ted Physical Review D, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevD.91.074020	journal	April 2015
A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory Chiu, Jui-Yu; Jain, Ambar; Neill, Duff Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/JHEP05(2012)084	journal	May 2012
Universality of non-leading logarithmic contributions in transverse-momentum distributions Catani, Stefano; de Florian, Daniel; Grazzini, Massimiliano Nuclear Physics B, Vol. 596, Issue 1-2 https://doi.org/10.1016/S0550-3213(00)00617-9	journal	February 2001
Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO Catani, Stefano; Cieri, Leandro; de Florian, Daniel The European Physical Journal C, Vol. 72, Issue 11 https://doi.org/10.1140/epjc/s10052-012-2195-7	journal	November 2012
Factorization and resummation for generic hierarchies between Jets Pietrulewicz, Piotr; Tackmann, Frank J.; Waalewijn, Wouter J. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)002	journal	August 2016
Analytic continuation of the Sudakov form factor in QCD Magnea, Lorenzo; Sterman, George Physical Review D, Vol. 42, Issue 12 https://doi.org/10.1103/PhysRevD.42.4222	journal	December 1990
The quark form factor at higher orders Moch, Sven-Olaf; Vermaseren, Jozef Antoon M.; Vogt, Andreas Journal of High Energy Physics, Vol. 2005, Issue 08 https://doi.org/10.1088/1126-6708/2005/08/049	journal	August 2005
Measurement of Azimuthal Asymmetries in Inclusive Charged Dipion Production in $e^{+} e^{-}$ Annihilations at $\sqrt{s} = 3.65 GeV$ Ablikim, M.; Achasov, M. N.; Ai, X. C. Physical Review Letters, Vol. 116, Issue 4 https://doi.org/10.1103/PhysRevLett.116.042001	journal	January 2016
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum Bacchetta, Alessandro; Boer, Daniël; Diehl, Markus Journal of High Energy Physics, Vol. 2008, Issue 08 https://doi.org/10.1088/1126-6708/2008/08/023	journal	August 2008
Calculation of the quark and gluon form factors to three loops in QCD Gehrmann, T.; Glover, E. W. N.; Huber, T. Journal of High Energy Physics, Vol. 2010, Issue 6 https://doi.org/10.1007/JHEP06(2010)094	journal	June 2010
Role of the nonperturbative input in QCD resummed Drell-Yan $Q_{T}$ distributions Qiu, Jianwei; Zhang, Xiaofei Physical Review D, Vol. 63, Issue 11 https://doi.org/10.1103/PhysRevD.63.114011	journal	April 2001
Parton distribution and decay functions Collins, John C.; Soper, Davison E. Nuclear Physics B, Vol. 194, Issue 3 https://doi.org/10.1016/0550-3213(82)90021-9	journal	January 1982
Factorization and momentum-space resummation in deep-inelastic scattering Becher, Thomas; Neubert, Matthias; Pecjak, Ben D. Journal of High Energy Physics, Vol. 2007, Issue 01 https://doi.org/10.1088/1126-6708/2007/01/076	journal	January 2007
Renormalization of the Wilson loops beyond the leading order Korchemsky, G. P.; Radyushkin, A. V. Nuclear Physics B, Vol. 283 https://doi.org/10.1016/0550-3213(87)90277-X	journal	January 1987
Rapidity renormalized TMD soft and beam functions at two loops Lübbert, Thomas; Oredsson, Joel; Stahlhofen, Maximilian Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)168	journal	March 2016
Investigations into the flavor dependence of partonic transverse momentum Signori, Andrea; Bacchetta, Alessandro; Radici, Marco Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)194	journal	November 2013
Calculation of the quark and gluon form factors to three loops in QCD Gehrmann, T.; Glover, E. W. N.; Huber, T. Springer https://doi.org/10.5167/uzh-41363	text	January 2010
Transverse Parton Distribution Functions at Next-to-Next-to-Leading Order: The Quark-to-Quark Case Gehrmann, Thomas; Lübbert, Thomas; Yang, Li American Physical Society https://doi.org/10.5167/uzh-69900	text	January 2012
Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO Catani, Stefano; Cieri, Leandro; Florian, Daniel Springer https://doi.org/10.5167/uzh-70103	text	January 2012
Three Loop Cusp Anomalous Dimension in QCD Grozin, Andrey; Henn, Johannes M.; Korchemsky, Gregory P. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2015-05147	text	January 2015
Correspondence between Soft and Rapidity Anomalous Dimensions Vladimirov, Alexey A. Universität Regensburg https://doi.org/10.5283/epub.38701	text	January 2017
Calculation of the transverse parton distribution functions at next-to-next-to-leading order Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin Springer https://doi.org/10.5167/uzh-107413	text	January 2014
Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey Universität Regensburg https://doi.org/10.5283/epub.37200	text	January 2016
Twist-2 matching of transverse momentum dependent distributions Gutiérrez-Reyes, Daniel; Scimemi, Ignazio; Vladimirov, Alexey A. Universität Regensburg https://doi.org/10.5283/epub.37236	text	January 2017
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum Bacchetta, Alessandro; Boer, Daniel; Diehl, Markus arXiv https://doi.org/10.48550/arxiv.0803.0227	text	January 2008
Quark and gluon form factors to three loops Baikov, P. A.; Chetyrkin, K. G.; Smirnov, A. V. arXiv https://doi.org/10.48550/arxiv.0902.3519	text	January 2009
Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone Echevarria, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio arXiv https://doi.org/10.48550/arxiv.1111.4996	text	January 2011
A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory Chiu, Jui-yu; Jain, Ambar; Neill, Duff arXiv https://doi.org/10.48550/arxiv.1202.0814	text	January 2012
Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin arXiv https://doi.org/10.48550/arxiv.1209.0682	text	January 2012
Jet p_T Resummation in Higgs Production at NNLL'+NNLO Stewart, Iain W.; Tackmann, Frank J.; Walsh, Jonathan R. arXiv https://doi.org/10.48550/arxiv.1307.1808	text	January 2013
Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised proton Adolph, C.; Akhunzyanov, R.; Alexeev, M. G. arXiv https://doi.org/10.48550/arxiv.1408.4405	text	January 2014
Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel Collins, John; Rogers, Ted arXiv https://doi.org/10.48550/arxiv.1412.3820	text	January 2014
Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey arXiv https://doi.org/10.48550/arxiv.1604.07869	text	January 2016
Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production Konychev, Anton V.; Nadolsky, Pavel M. arXiv https://doi.org/10.48550/arxiv.hep-ph/0506225	text	January 2005
The Quark Form Factor at Higher Orders Moch, S.; Vermaseren, J. A. M.; Vogt, A. arXiv https://doi.org/10.48550/arxiv.hep-ph/0507039	text	January 2005
Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering Becher, Thomas; Neubert, Matthias; Pecjak, Ben D. arXiv https://doi.org/10.48550/arxiv.hep-ph/0607228	text	January 2006
Proof of Factorization for Diffractive Hard Scattering Collins, John C. arXiv https://doi.org/10.48550/arxiv.hep-ph/9709499	text	January 1997

Cited By (2)

Nonperturbative Uncertainties on the Transverse Momentum Distribution of Electroweak Bosons and on the Determination of the $W$ Boson Mass at the LHC Bozzi, Giuseppe; Signori, Andrea Advances in High Energy Physics, Vol. 2019 https://doi.org/10.1155/2019/2526897	journal	March 2019
Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD Ebert, Markus A.; Stewart, Iain W.; Zhao, Yong arXiv https://doi.org/10.48550/arxiv.1811.00026	text	January 2018

Similar Records

Systematic Extraction of Pion Parton Distributions Using Threshold Resummation and Applications to Pion TMDs

Conference · Thu Apr 01 00:00:00 EDT 2021 · OSTI ID:1391826

Sato, Nobuo; Melnitchouk, Wolodymyr; Barry, Patrick; +3 more

Scheme dependence and transverse momentum distribution interpretation of Collins–Soper–Sterman resummation

Journal Article · Sun Nov 01 00:00:00 EDT 2015 · Physics Letters B · OSTI ID:1391826

Prokudin, Alexei; Sun, Peng; Yuan, Feng

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

Journal Article · Mon Feb 16 00:00:00 EST 2015 · Journal of High Energy Physics (Online) · OSTI ID:1391826

Boglione, M.; Gonzalez Hernandez, J. O.; Melis, S.; +1 more

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Title: Connecting different TMD factorization formalisms in QCD

Citation Formats

References (71)

Cited By (2)

Similar Records

Related Subjects