Built on

J. C. Collins and D. E. Soper, “Back-to-back jets in QCD,” Nucl. Phys. B193
1983
Earlier work this paper cites.
C. Davies and W. J. Stirling, “Nonleading corrections to the Drell-Yan cross-section at small transverse momentum,” Nucl. Phys. B244
1984
Earlier work this paper cites.
J. C. Collins, D. E. Soper, and G. Sterman, “Transverse momentum distribution in Drell-Yan pair and W W and Z Z boson production,” Nucl. Phys. B250
1985
Earlier work this paper cites.
G. Korchemsky and A. Radyushkin, “Renormalization of the Wilson loops beyond the leading order,” Nucl. Phys. B283
1987
Earlier work this paper cites.
L. Magnea and G. F. Sterman, “Analytic continuation of the Sudakov form-factor in QCD,” Phys. Rev. D42
1990
Earlier work this paper cites.
J. C. Collins, “Proof of factorization for diffractive hard scattering,” Phys. Rev. D57
2000
Earlier work this paper cites.
S. Catani, D. de Florian, and M. Grazzini, “Universality of nonleading logarithmic contributions in transverse momentum distributions,” Nucl. Phys. B596
2001
Earlier work this paper cites.
J.-w. Qiu and X.-F. Zhang, “Role of the nonperturbative input in QCD resummed Drell-Yan Q T Q_{T} distributions,” Phys. Rev. D63
2001
Earlier work this paper cites.
L. Magnea, “Analytic resummation for the quark form-factor in QCD,” Nucl. Phys. B593
2001
Earlier work this paper cites.
J. C. Collins, “Leading-twist single-transverse-spin asymmetries: Drell-Yan and deep-inelastic scattering,” Phys. Lett. B536
2002
Earlier work this paper cites.
J.-w. Qiu and X.-f. Zhang, “Role of nonperturbative input in QCD resummed heavy boson Q T Q_{T} distribution,” in Proceedings, 37th Rencontres de Moriond, 2002 QCD and high energy hadronic interactions: Les Arcs, Savoie, France, Mar 16-23, 2002 (2002) pp. 169–172, arXiv:hep-ph/0205115 [hep-ph]
2002
Earlier work this paper cites.
F. Landry, R. Brock, P. M. Nadolsky, and C.-P. Yuan, “Tevatron Run-1 Z Z boson data and Collins-Soper-Sterman resummation formalism,” Phys. Rev. D67
2003
Earlier work this paper cites.
S. Moch, J. Vermaseren, and A. Vogt, “The quark form-factor at higher orders,” JHEP 0508
2005
Earlier work this paper cites.
A. V. Konychev and P. M. Nadolsky, “Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production,” Phys. Lett. B633
2006
Earlier work this paper cites.
A. Idilbi, X.-d. Ji, and F. Yuan, “Resummation of threshold logarithms in effective field theory for DIS, Drell-Yan and Higgs production,” Nucl. Phys. B753
2006
Earlier work this paper cites.

Similar

T. Becher, M. Neubert, and B. D. Pecjak, “Factorization and momentum-space resummation in deep-inelastic scattering,” JHEP 01
2007
Cited alongside, same era.
A. Bacchetta, D. Boer, M. Diehl, and P. J. Mulders, “Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum,” JHEP 08
Original
2008
Cited alongside, same era.
P. A. Baikov, K. G. Chetyrkin, A. V. Smirnov, V. A. Smirnov, and M. Steinhauser, “Quark and gluon form factors to three loops,” Phys. Rev. Lett. 102
Original
2009
Cited alongside, same era.
T. Gehrmann, E. W. N. Glover, T. Huber, N. Ikizlerli, and C. Studerus, “Calculation of the quark and gluon form factors to three loops in QCD,” JHEP 06
Original
2010
Cited alongside, same era.
R. N. Lee, A. V. Smirnov, and V. A. Smirnov, “Analytic results for massless three-loop form factors,” JHEP 04

Then

C. Adolph et al. (COMPASS), “Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons,” Phys. Lett. B744
Original
2015
Later among the works it cites.
J. Collins and T. Rogers, “Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel,” Phys. Rev. D91
Original
2015
Later among the works it cites.
A. Grozin, J. M. Henn, G. P. Korchemsky, and P. Marquard, “Three-loop cusp anomalous dimension in QCD,” Phys. Rev. Lett. 114
Original
2015
Later among the works it cites.
M. G. Echevarria, I. Scimemi, and A. Vladimirov, “Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order,” JHEP 09
Original
2016
Later among the works it cites.

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2017

Connecting Different TMD Factorization Formalisms in QCD

Collins, John, Rogers, Ted C.

Understand

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.