skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism

Abstract

We construct an improved implementation for combining TMD factorization transverse- momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suit- able for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. As a result, we further argue that questions regarding the shape and Q- dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.

Authors:
 [1];  [1];  [2];  [3];  [4];  [3]
  1. Pennsylvania State Univ., University Park, PA (United States)
  2. Pennsylvania State Univ., University Park, PA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  3. Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  4. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1294279
Alternate Identifier(s):
OSTI ID: 1286313
Report Number(s):
JLAB-THY-16-2245; DOE/OR/23177-3791; arXiv:1605.00671
Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1700136
Grant/Contract Number:
AC05-06OR23177; PHY-1623454; FG02-07ER41460; SC0008745
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., and Wang, B.. Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.94.034014.
Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., & Wang, B.. Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism. United States. doi:10.1103/PhysRevD.94.034014.
Collins, J., Gamberg, L., Prokudin, A., Rogers, T. C., Sato, N., and Wang, B.. Mon . "Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism". United States. doi:10.1103/PhysRevD.94.034014. https://www.osti.gov/servlets/purl/1294279.
@article{osti_1294279,
title = {Relating transverse-momentum-dependent and collinear factorization theorems in a generalized formalism},
author = {Collins, J. and Gamberg, L. and Prokudin, A. and Rogers, T. C. and Sato, N. and Wang, B.},
abstractNote = {We construct an improved implementation for combining TMD factorization transverse- momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suit- able for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. As a result, we further argue that questions regarding the shape and Q- dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.},
doi = {10.1103/PhysRevD.94.034014},
journal = {Physical Review D},
number = 3,
volume = 94,
place = {United States},
year = {Mon Aug 08 00:00:00 EDT 2016},
month = {Mon Aug 08 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9works
Citation information provided by
Web of Science

Save / Share:
  • Cited by 9
  • It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadroproduction of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge-invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of generalized transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain nonstandard, process-dependent Wilsonmore » line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counterexample that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadroproduction process, a single counterexample suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.« less
  • Some estimates for the transverse Single Spin Asymmetry, A_N, in the inclusive processes l p(transv. Pol.) --> h X, given in a previous paper, are expanded and compared with new experimental data. The predictions are based on the Sivers distributions and the Collins fragmentation functions which fit the azimuthal asymmetries measured in Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes (l p(transv. Pol.) --> l' h X). The factorisation in terms of Transverse Momentum Dependent distribution and fragmentation functions (TMD factorisation) -- i.e., the theoretical framework in which SIDIS azimuthal asymmetries are analysed -- is assumed to hold also for the inclusivemore » process l p --> h X at large P_T. The values of A_N thus obtained agree in sign and shape with the data. Some predictions are given for future experiments.« less
  • With a consistent definition of transverse-momentum dependent (TMD) light-cone wave function, we show that the amplitude for the process {gamma}*{pi}{sup 0}{yields}{gamma} can be factorized when the virtuality of the initial photon is large. In contrast to the collinear factorization in which the amplitude is factorized as a convolution of the standard light-cone wave function and a hard part, the TMD factorization yields a convolution of a TMD light-cone wave function, a soft factor and a hard part. We explicitly show that the TMD factorization holds at one-loop level. It is expected that the factorization holds beyond one-loop level because themore » cancellation of soft divergences is on a diagram-by-diagram basis. We also show that the TMD factorization helps to resum large logarithms of type ln{sup 2}x.« less