Connecting different TMD factorization formalisms in QCD
In the original CollinsSoperSterman (CSS) presentation of the results of transversemomentumdependent (TMD) factorization for the DrellYan 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 ``nonperturbative'' functions as obtained from fits to data are equal in the two schemes. We compile the higherorder 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 softcollinear effective theory (SCET). As a result, our work uses some important new results for factorization for the quark form factor, which we derive.
 Authors:

^{[1]};
^{[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)
 Publication Date:
 Report Number(s):
 JLABTHY172470; DOE/OR/231774138; arXiv:1705.07167
Journal ID: ISSN 24700010; PRVDAQ
 Grant/Contract Number:
 SC0013699; AC0506OR23177
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1391826
 Alternate Identifier(s):
 OSTI ID: 1389148
Collins, John, and Rogers, Ted C. Connecting different TMD factorization formalisms in QCD. United States: N. p.,
Web. doi:10.1103/PhysRevD.96.054011.
Collins, John, & Rogers, Ted C. Connecting different TMD factorization formalisms in QCD. United States. doi:10.1103/PhysRevD.96.054011.
Collins, John, and Rogers, Ted C. 2017.
"Connecting different TMD factorization formalisms in QCD". United States.
doi:10.1103/PhysRevD.96.054011. https://www.osti.gov/servlets/purl/1391826.
@article{osti_1391826,
title = {Connecting different TMD factorization formalisms in QCD},
author = {Collins, John and Rogers, Ted C.},
abstractNote = {In the original CollinsSoperSterman (CSS) presentation of the results of transversemomentumdependent (TMD) factorization for the DrellYan 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 ``nonperturbative'' functions as obtained from fits to data are equal in the two schemes. We compile the higherorder 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 softcollinear effective theory (SCET). As a result, our work uses some important new results for factorization for the quark form factor, which we derive.},
doi = {10.1103/PhysRevD.96.054011},
journal = {Physical Review D},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {9}
}