Valence quark transversity at small x

Kovchegov, Yuri V.; Sievert, Matthew D.

doi:10.1103/PhysRevD.99.054033

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-N_c 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:: Kovchegov, Yuri V.; Sievert, Matthew D.

Publication Date:: Fri Mar 29 00:00:00 EDT 2019

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.

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                    Kovchegov, Yuri V., & Sievert, Matthew D. Valence quark transversity at small x.  United States.  https://doi.org/10.1103/PhysRevD.99.054033

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                    Kovchegov, Yuri V., and Sievert, Matthew D. Fri .  
"Valence quark transversity at small x".  United States.  https://doi.org/10.1103/PhysRevD.99.054033.

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@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         = {Fri Mar 29 00:00:00 EDT 2019},

  month        = {Fri Mar 29 00:00:00 EDT 2019}

}

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Title: Valence quark transversity at small x

Abstract

Citation Formats

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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

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Exclusive processes in perturbative quantum chromodynamics journal, November 1980

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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

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Quantum Chromodynamics at High Energy book, September 2012

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

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Title: Valence quark transversity at small $x$

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
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Exclusive processes in perturbative quantum chromodynamics
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Small- $x$ Asymptotics of the Quark Helicity Distribution
journal, January 2017

Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange
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First Extraction of Transversity from a Global Analysis of Electron-Proton and Proton-Proton Data
journal, May 2018

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