Small- x helicity evolution: An operator treatment

Kovchegov, Yuri V.; Sievert, Matthew D.

doi:10.1103/PhysRevD.99.054032

Title: Small- $x$ helicity evolution: An operator treatment

Abstract

We rederive the small-x evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we rederive the double-logarithmic small-x evolution equations for quark helicity in terms of the “polarized Wilson lines,” the operators consisting of light-cone Wilson lines with one or two noneikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark subeikonal operators. We show that the double-logarithmic small-x evolution of the “polarized dipole amplitude” operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-x asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity.

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:: 1503931

Alternate Identifier(s):: OSTI ID: 1604162

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. Small- x helicity evolution: An operator treatment.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.99.054032.

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                    Kovchegov, Yuri V., & Sievert, Matthew D. Small- x helicity evolution: An operator treatment.  United States.  https://doi.org/10.1103/PhysRevD.99.054032

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                    Kovchegov, Yuri V., and Sievert, Matthew D. Fri .  
"Small- x helicity evolution: An operator treatment".  United States.  https://doi.org/10.1103/PhysRevD.99.054032.

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@article{osti_1503931,

  title        = {Small- x helicity evolution: An operator treatment},

  author       = {Kovchegov, Yuri V. and Sievert, Matthew D.},

  abstractNote = {We rederive the small-x evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we rederive the double-logarithmic small-x evolution equations for quark helicity in terms of the “polarized Wilson lines,” the operators consisting of light-cone Wilson lines with one or two noneikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark subeikonal operators. We show that the double-logarithmic small-x evolution of the “polarized dipole amplitude” operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-x asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity.},

  doi          = {10.1103/PhysRevD.99.054032},

  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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Works referenced in this record:

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Title: Small- x helicity evolution: An operator treatment

Abstract

Citation Formats

Renormalizable Lagrangians for massive Yang-Mills fields journal, December 1971

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

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, February 1996

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

Flavor singlet contribution to the structure functiong 1 at small-x journal, December 1996

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

An Introduction to Quantum Field Theory book, January 1993

Studying the perturbative Reggeon journal, January 2000

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

Classical gluon production amplitude for nucleus-nucleus collisions: First saturation correction in the projectile journal, March 2015

Linearly polarized small- x gluons in forward heavy-quark pair production journal, January 2018

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

Operator expansion for high-energy scattering journal, March 1996

Wilson renormalization group for low x physics: Towards the high density regime journal, November 1998

Green’s function in the color field of a large nucleus journal, August 1994

Gauge-Invariant Decomposition of Nucleon Spin journal, January 1997

Elastic scattering of a quark from a color field: Longitudinal momentum exchange journal, October 2017

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

The g1 problem: Deep inelastic electron scattering and the spin of the proton journal, June 1990

Distribution of linearly polarized gluons inside a large nucleus journal, September 2011

-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

Anisotropy of the semiclassical gluon field of a large nucleus at high energy journal, April 2015

Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus journal, May 1997

Sub-eikonal corrections to scattering amplitudes at high energy journal, January 2019

Gluon TMD in particle production from low to moderate x journal, June 2016

Gluon and Wilson loop TMDs for hadrons of spin ≤ 1 journal, October 2016

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

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

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Perturbative odderon in the dipole model journal, April 2004

Gluon orbital angular momentum at small x journal, June 2017

Quantum Chromodynamics at High Energy book, September 2012

The renormalization group equation for the color glass condensate journal, June 2001

Proton Spin Structure from Measurable Parton Distributions journal, October 2012

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

Reggeon interactions in perturbative QCD journal, September 1995

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

Gluon recombination and shadowing at small values of x journal, May 1986

Inclusive gluon production in deep inelastic scattering at high parton density journal, March 2002

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

Unitarization of the BFKL Pomeron on a nucleus journal, March 2000

Medium induced transverse momentum broadening in hard processes journal, February 2017

The angular momentum controversy: What’s it all about and does it matter? journal, August 2014

Wilson renormalization group for low x physics: Gluon evolution at finite parton density journal, November 1998

Valence quark transversity at small x journal, March 2019

A simple derivation of the JIMWLK equation journal, December 2001

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

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all journal, September 2016

Rapidity evolution of gluon TMD from low to moderate x journal, October 2015

Odderon in the color glass condensate journal, October 2005

Helicity evolution at small x journal, January 2016

Factorization and high-energy effective action journal, June 1999

Gluon distribution functions for very large nuclei at small transverse momentum journal, April 1994

Title: Small- $x$ helicity evolution: An operator treatment

Renormalizable Lagrangians for massive Yang-Mills fields
journal, December 1971

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

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

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

Flavor singlet contribution to the structure functiong 1 at small-x
journal, December 1996

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

An Introduction to Quantum Field Theory
book, January 1993

Studying the perturbative Reggeon
journal, January 2000

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

Classical gluon production amplitude for nucleus-nucleus collisions: First saturation correction in the projectile
journal, March 2015

Linearly polarized small- $x$ gluons in forward heavy-quark pair production
journal, January 2018

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

Operator expansion for high-energy scattering
journal, March 1996

Wilson renormalization group for low x physics: Towards the high density regime
journal, November 1998

Green’s function in the color field of a large nucleus
journal, August 1994

Gauge-Invariant Decomposition of Nucleon Spin
journal, January 1997

Elastic scattering of a quark from a color field: Longitudinal momentum exchange
journal, October 2017

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

The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990

Distribution of linearly polarized gluons inside a large nucleus
journal, September 2011

-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

Anisotropy of the semiclassical gluon field of a large nucleus at high energy
journal, April 2015

Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus
journal, May 1997

Sub-eikonal corrections to scattering amplitudes at high energy
journal, January 2019

Gluon TMD in particle production from low to moderate x
journal, June 2016

Gluon and Wilson loop TMDs for hadrons of spin ≤ 1
journal, October 2016

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

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

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Perturbative odderon in the dipole model
journal, April 2004

Gluon orbital angular momentum at small $x$
journal, June 2017

Quantum Chromodynamics at High Energy
book, September 2012

The renormalization group equation for the color glass condensate
journal, June 2001

Proton Spin Structure from Measurable Parton Distributions
journal, October 2012

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

Reggeon interactions in perturbative QCD
journal, September 1995

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

Gluon recombination and shadowing at small values of x
journal, May 1986

Inclusive gluon production in deep inelastic scattering at high parton density
journal, March 2002

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

Unitarization of the BFKL Pomeron on a nucleus
journal, March 2000

Medium induced transverse momentum broadening in hard processes
journal, February 2017

The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014

Wilson renormalization group for low x physics: Gluon evolution at finite parton density
journal, November 1998

Valence quark transversity at small $x$
journal, March 2019

A simple derivation of the JIMWLK equation
journal, December 2001

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

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016

Rapidity evolution of gluon TMD from low to moderate x
journal, October 2015

Odderon in the color glass condensate
journal, October 2005

Helicity evolution at small x
journal, January 2016

Factorization and high-energy effective action
journal, June 1999

Gluon distribution functions for very large nuclei at small transverse momentum
journal, April 1994