Helicity-dependent generalization of the JIMWLK evolution

doi:10.1103/PhysRevD.100.114020

Title: Helicity-dependent generalization of the JIMWLK evolution

Abstract

We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller in [Phys. Lett. B 523, 243 (2001)] for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived in J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 95, 014033 (2017); J. High Energy Phys. 10 (2017) 198; Phys. Rev. D 99, 054032 (2019)]. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").

Authors:

;

Publication Date:: 2019-12-11

Research Org.:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1579283

Alternate Identifier(s):: OSTI ID: 1604157

Grant/Contract Number:: SC0004286

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; perturbative QCD; proton spin; helicity; Electron-Ion Collider

Citation Formats


                    Cougoulic, Florian, and Kovchegov, Yuri V. Helicity-dependent generalization of the JIMWLK evolution.  United States: N. p., 2019. 
        Web.  doi:10.1103/PhysRevD.100.114020.

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                    Cougoulic, Florian, & Kovchegov, Yuri V. Helicity-dependent generalization of the JIMWLK evolution.  United States.  doi:10.1103/PhysRevD.100.114020.

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                    Cougoulic, Florian, and Kovchegov, Yuri V. Wed .  
        "Helicity-dependent generalization of the JIMWLK evolution".  United States.  doi:10.1103/PhysRevD.100.114020.

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@article{osti_1579283,

  title        = {Helicity-dependent generalization of the JIMWLK evolution},

  author       = {Cougoulic, Florian and Kovchegov, Yuri V.},

  abstractNote = {We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller in [Phys. Lett. B 523, 243 (2001)] for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived in J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 95, 014033 (2017); J. High Energy Phys. 10 (2017) 198; Phys. Rev. D 99, 054032 (2019)]. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").},

  doi          = {10.1103/PhysRevD.100.114020},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {12}

}

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DOI: 10.1103/PhysRevD.100.114020

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Works referenced in this record:

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Title: Helicity-dependent generalization of the JIMWLK evolution

Abstract

Citation Formats

Collinear singularities and running coupling corrections to gluon production in CGC journal, July 2008

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

Studying the perturbative Reggeon journal, January 2000

Next-to-next-to-eikonal corrections in the CGC journal, January 2016

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

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

Non-Abelian Weizsäcker-Williams field and a two-dimensional effective color charge density for a very large nucleus journal, November 1996

More remarks on high energy evolution journal, March 2006

Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy journal, December 2015

Sivers function in the quasiclassical approximation journal, March 2014

Remarks on high energy evolution journal, March 2005

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

Unitarity and the BFKL pomeron journal, March 1995

Universal features of JIMWLK and BK evolution at small x journal, July 2004

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

The shape of the proton at high energies journal, December 2014

Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions journal, July 2014

Single Spin Asymmetries from a Single Wilson Loop journal, March 2016

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

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Gluon orbital angular momentum at small x journal, June 2017

Orbital angular momentum at small x journal, March 2019

Small- x F 2 structure function of a nucleus including multiple Pomeron exchanges journal, June 1999

Nonlinear gluon evolution in the color glass condensate: II journal, May 2002

Unitarity at small Bjorken x journal, June 2002

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

Proton spin structure at small-x journal, October 2019

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

Nonlinear gluon evolution in the color glass condensate: I journal, September 2001

Reggeon interactions in perturbative QCD journal, September 1995

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

Resumming double logarithms in the QCD evolution of color dipoles journal, May 2015

The saturation scale and its x-dependence from Λ polarization studies journal, January 2009

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

Computing quark and gluon distribution functions for very large nuclei journal, March 1994

Polarized hyperons from pA scattering in the gluon saturation regime journal, March 2003

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

Next-to-leading order evolution of color dipoles journal, January 2008

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

Soft gluons in the infinite-momentum wave function and the BFKL pomeron journal, March 1994

A simple derivation of the JIMWLK equation journal, December 2001

Single transverse-spin asymmetries in forward pion production at high energy: Incorporating small- x effects in the target journal, October 2006

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

Non-linear evolution in QCD at high-energy beyond leading order journal, April 2019

Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes journal, August 1994

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

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

Helicity evolution at small x journal, January 2016

Collinearly improved JIMWLK evolution in Langevin form journal, August 2016

Factorization and high-energy effective action journal, June 1999

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

Collinear singularities and running coupling corrections to gluon production in CGC
journal, July 2008

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

Studying the perturbative Reggeon
journal, January 2000

Next-to-next-to-eikonal corrections in the CGC
journal, January 2016

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

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

Non-Abelian Weizsäcker-Williams field and a two-dimensional effective color charge density for a very large nucleus
journal, November 1996

More remarks on high energy evolution
journal, March 2006

Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy
journal, December 2015

Sivers function in the quasiclassical approximation
journal, March 2014

Remarks on high energy evolution
journal, March 2005

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

Unitarity and the BFKL pomeron
journal, March 1995

Universal features of JIMWLK and BK evolution at small x
journal, July 2004

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

The shape of the proton at high energies
journal, December 2014

Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
journal, July 2014

Single Spin Asymmetries from a Single Wilson Loop
journal, March 2016

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

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

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

Orbital angular momentum at small x
journal, March 2019

Small- x $F_{2}$ structure function of a nucleus including multiple Pomeron exchanges
journal, June 1999

Nonlinear gluon evolution in the color glass condensate: II
journal, May 2002

Unitarity at small Bjorken x
journal, June 2002

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

Proton spin structure at small-x
journal, October 2019

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

Nonlinear gluon evolution in the color glass condensate: I
journal, September 2001

Reggeon interactions in perturbative QCD
journal, September 1995

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

Resumming double logarithms in the QCD evolution of color dipoles
journal, May 2015

The saturation scale and its x-dependence from Λ polarization studies
journal, January 2009

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

Computing quark and gluon distribution functions for very large nuclei
journal, March 1994

Polarized hyperons from pA scattering in the gluon saturation regime
journal, March 2003

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

Next-to-leading order evolution of color dipoles
journal, January 2008

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

Soft gluons in the infinite-momentum wave function and the BFKL pomeron
journal, March 1994

A simple derivation of the JIMWLK equation
journal, December 2001

Single transverse-spin asymmetries in forward pion production at high energy: Incorporating small- $x$ effects in the target
journal, October 2006

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

Non-linear evolution in QCD at high-energy beyond leading order
journal, April 2019

Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes
journal, August 1994

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

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

Helicity evolution at small x
journal, January 2016

Collinearly improved JIMWLK evolution in Langevin form
journal, August 2016

Factorization and high-energy effective action
journal, June 1999

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