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Title: Valence quark transversity at small x

Abstract

In our previous work we established a formalism which allows one to determine the small-x asymptotics of any transverse momentum-dependent parton distribution function (TMD PDF) of the proton at small values of strong coupling. In this paper we apply this formalism to the valence quark transversity TMD. We relate the valence quark transversity to the transversely polarized dipole scattering amplitude, written in terms of the fundamental transversely polarized “Wilson line” operator, an expression for which we derive explicitly as well. We then write down the evolution equation for the transversely polarized dipole amplitude. Solving that equation we arrive at the following small-x asymptotics of the valence quark transversity in the large-Nc limit: $${h}_{1T}^{v}(x,{k}_{T}^{2}){\sim}{h}_{1T}^{{\perp}v}(x,{k}_{T}^{2}){\sim}{(\frac{1}{x})}^{{-}1+2\sqrt{\frac{{{\alpha}}_{s}{N}_{c}}{2{\pi}}}}$$. This result is in agreement with one of the two possible small-$x$ asymptotics for the transverse structure function found previously by Kirschner, Mankiewicz, Schäfer, and Szymanowski [Z. Phys. C 74, 501 (1997)].

Authors:
;
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1504280
Alternate Identifier(s):
OSTI ID: 1604160
Grant/Contract Number:  
SC0004286; AC52-06NA25396
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 5; 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; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Kovchegov, Yuri V., and Sievert, Matthew D. Valence quark transversity at small x. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.99.054033.
Kovchegov, Yuri V., & Sievert, Matthew D. Valence quark transversity at small x. United States. doi:10.1103/PhysRevD.99.054033.
Kovchegov, Yuri V., and Sievert, Matthew D. Fri . "Valence quark transversity at small x". United States. doi:10.1103/PhysRevD.99.054033.
@article{osti_1504280,
title = {Valence quark transversity at small x},
author = {Kovchegov, Yuri V. and Sievert, Matthew D.},
abstractNote = {In our previous work we established a formalism which allows one to determine the small-x asymptotics of any transverse momentum-dependent parton distribution function (TMD PDF) of the proton at small values of strong coupling. In this paper we apply this formalism to the valence quark transversity TMD. We relate the valence quark transversity to the transversely polarized dipole scattering amplitude, written in terms of the fundamental transversely polarized “Wilson line” operator, an expression for which we derive explicitly as well. We then write down the evolution equation for the transversely polarized dipole amplitude. Solving that equation we arrive at the following small-x asymptotics of the valence quark transversity in the large-Nc limit: ${h}_{1T}^{v}(x,{k}_{T}^{2}){\sim}{h}_{1T}^{{\perp}v}(x,{k}_{T}^{2}){\sim}{(\frac{1}{x})}^{{-}1+2\sqrt{\frac{{{\alpha}}_{s}{N}_{c}}{2{\pi}}}}$. This result is in agreement with one of the two possible small-$x$ asymptotics for the transverse structure function found previously by Kirschner, Mankiewicz, Schäfer, and Szymanowski [Z. Phys. C 74, 501 (1997)].},
doi = {10.1103/PhysRevD.99.054033},
journal = {Physical Review D},
number = 5,
volume = 99,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.99.054033

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Cited by: 4 works
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Works referenced in this record:

Saturation physics and deuteron–gold collisions at RHIC
journal, January 2006


Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution
journal, February 2016


First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints
journal, April 2018


Baryon stopping and valence quark distribution at small x
journal, January 2004


Exclusive processes in perturbative quantum chromodynamics
journal, November 1980


Chiral-odd parton distributions and Drell-Yan processes
journal, May 1992


Small- x Asymptotics of the Quark Helicity Distribution
journal, January 2017


Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange
journal, March 1983


First Extraction of Transversity from a Global Analysis of Electron-Proton and Proton-Proton Data
journal, May 2018


Solution of the NLO BFKL equation and a strategy for solving the all-order BFKL equation
journal, June 2013

  • Chirilli, Giovanni A.; Kovchegov, Yuri V.
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)055

Quantum chromodynamics and other field theories on the light cone
journal, August 1998


Studying the perturbative Reggeon
journal, January 2000

  • Griffiths, S.; Ross, D. A.
  • The European Physical Journal C, Vol. 12, Issue 2
  • DOI: 10.1007/s100529900240

Small-x asymptotics of the gluon helicity distribution
journal, October 2017

  • Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)198

Semihard processes in QCD
journal, November 1983


The Color Glass Condensate
journal, November 2010


Gluon saturation and initial conditions for relativistic heavy ion collisions
journal, May 2014


Evolution at small : The color glass condensate
journal, October 2005


Small- x asymptotics of the quark helicity distribution: Analytic results
journal, September 2017


Reggeon interactions in perturbative QCD
journal, September 1995

  • Kirschner, R.
  • Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 3
  • DOI: 10.1007/BF01556138

Transversity and Collins functions from SIDIS and e + e data
journal, March 2007


Regge asymptotics of scattering with flavour exchange in QCD
journal, September 1995

  • Kirschner, R.
  • Zeitschrift für Physik C Particles and Fields, Vol. 67, Issue 3
  • DOI: 10.1007/BF01624588

Positivity Constraints for Spin-Dependent Parton Distributions
journal, February 1995


Regge asymptotics of scattering amplitudes in the logarithmic approximation of QCD
journal, March 1986

  • Kirschner, R.
  • Zeitschrift für Physik C Particles and Fields, Vol. 31, Issue 1
  • DOI: 10.1007/BF01559604

Relations between generalized and transverse momentum dependent parton distributions
journal, August 2007


New mechanism for generating a single transverse spin asymmetry
journal, August 2012


Transverse polarisation of quarks in hadrons
journal, March 2002


Quark-antiquark exchange in γ* γ* scattering
journal, September 2003


Small- x helicity evolution: An operator treatment
journal, March 2019


-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order
journal, November 2012


Helicity evolution at small x : Flavor singlet and nonsinglet observables
journal, January 2017


First extraction of valence transversities in a collinear framework
journal, March 2013

  • Bacchetta, Alessandro; Courtoy, A.; Radici, Marco
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)119

Measuring the transverse polarization of quarks in the proton
journal, September 1992

  • Cortes, J. L.; Pire, B.; Ralston, J. P.
  • Zeitschrift für Physik C Particles and Fields, Vol. 55, Issue 3
  • DOI: 10.1007/BF01565099

Helicity evolution at small x
journal, January 2016

  • Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)072

Production of dimuons from high-energy polarized proton-proton collisions
journal, May 1979


Small x behaviour of the chirally-odd parton distribution h 1 ( x , Q 2 )
journal, May 1997

  • Kirschner, R.; Mankiewicz, L.; Schäfer, A.
  • Zeitschrift f�r Physik C Particles and Fields, Vol. 74, Issue 3
  • DOI: 10.1007/s002880050412