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Title: An overview of transverse momentum dependent factorization and evolution

Abstract

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.

Authors:
 [1]
  1. Old Dominion Univ., Norfolk, VA (United States); 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:
1273415
Report Number(s):
JLAB-THY-15-2133; DOE/OR/23177-3522; arXiv:1509.04766
Journal ID: ISSN 1434-6001; PII: 521
Grant/Contract Number:
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
European Physical Journal. A
Additional Journal Information:
Journal Volume: 52; Journal Issue: 6; Journal ID: ISSN 1434-6001
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Rogers, Ted C. An overview of transverse momentum dependent factorization and evolution. United States: N. p., 2016. Web. doi:10.1140/epja/i2016-16153-7.
Rogers, Ted C. An overview of transverse momentum dependent factorization and evolution. United States. doi:10.1140/epja/i2016-16153-7.
Rogers, Ted C. Fri . "An overview of transverse momentum dependent factorization and evolution". United States. doi:10.1140/epja/i2016-16153-7. https://www.osti.gov/servlets/purl/1273415.
@article{osti_1273415,
title = {An overview of transverse momentum dependent factorization and evolution},
author = {Rogers, Ted C.},
abstractNote = {I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. Furthermore, I summarize basic results while attempting to trace their development over that past several decades.},
doi = {10.1140/epja/i2016-16153-7},
journal = {European Physical Journal. A},
number = 6,
volume = 52,
place = {United States},
year = {Fri Jun 17 00:00:00 EDT 2016},
month = {Fri Jun 17 00:00:00 EDT 2016}
}

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

Citation Metrics:
Cited by: 11works
Citation information provided by
Web of Science

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  • 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
  • Cited by 9
  • 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.