Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

Altinoluk, Taiga; Boussarie, Renaud

doi:10.1007/JHEP10(2019)208

Title: Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

Abstract

We show how the formulations of low x physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low x physics and moderate x formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PDFs should be taken into account even in this regime. Finally, we analyze how saturation should be understood as three distinct effects: saturation through non-linearities in the evolution equations at small x, saturation through multiple interactions with slow gluons

Authors:

Altinoluk, Taiga ^[1]; Boussarie, Renaud ^[2]

National Centre for Nuclear Research, Warsaw (Poland)
Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Dept.

Publication Date:: Mon Oct 21 00:00:00 EDT 2019

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

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

OSTI Identifier:: 1574429

Report Number(s):: BNL-212341-2019-JAAM
Journal ID: ISSN 1029-8479; TRN: US2001276

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Heavy Ion Phenomenology

Citation Formats


                    Altinoluk, Taiga, and Boussarie, Renaud. Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP10(2019)208.

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                    Altinoluk, Taiga, & Boussarie, Renaud. Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation.  United States.  https://doi.org/10.1007/JHEP10(2019)208

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                    Altinoluk, Taiga, and Boussarie, Renaud. Mon .  
"Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation".  United States.  https://doi.org/10.1007/JHEP10(2019)208.  https://www.osti.gov/servlets/purl/1574429.

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@article{osti_1574429,

  title        = {Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation},

  author       = {Altinoluk, Taiga and Boussarie, Renaud},

  abstractNote = {We show how the formulations of low x physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low x physics and moderate x formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PDFs should be taken into account even in this regime. Finally, we analyze how saturation should be understood as three distinct effects: saturation through non-linearities in the evolution equations at small x, saturation through multiple interactions with slow gluons},

  doi          = {10.1007/JHEP10(2019)208},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2019,

  place        = {United States},

  year         = {Mon Oct 21 00:00:00 EDT 2019},

  month        = {Mon Oct 21 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referenced in this record:

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Title: Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

Abstract

Citation Formats

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

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

Unitarity at small Bjorken x journal, June 2002

Unitarity and the BFKL Pomeron text, January 1994

Interplay of the CGC and TMD frameworks to all orders in kinematic twist text, January 2019

Unitarity and the BFKL pomeron journal, March 1995

The Color Glass Condensate journal, November 2010

Semihard processes in QCD journal, November 1983

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

Power corrections to TMD factorization for Z-boson production journal, May 2018

Small-x behavior and parton saturation: A QCD model journal, April 1990

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

Interplay of the CGC and TMD frameworks to all orders in kinematic twist journal, May 2019

The Color Glass Condensate text, January 2010

Power corrections to TMD factorization for Z-boson production text, January 2017

Operator expansion for high-energy scattering journal, March 1996

Factorization for High-Energy Scattering journal, September 1998

Factorization and high-energy effective action journal, June 1999

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

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

Particle production in high-energy collisions beyond the shockwave limit journal, October 2016

Higher-twist corrections to gluon TMD factorization journal, July 2017

Helicity evolution at small x journal, January 2016

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

TMD factorization for dijets + photon production from the dilute-dense CGC framework journal, July 2019

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

Azimuthal asymmetries for quark pair production in p A collisions journal, March 2013

cos ( 4 φ ) azimuthal anisotropy in small- x DIS dijet production beyond the leading power TMD limit journal, July 2016

Transverse-momentum-dependent gluon distributions from JIMWLK evolution journal, October 2016

Suppression of maximal linear gluon polarization in angular asymmetries journal, October 2017

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

TMD gluon distributions at small x in the CGC theory journal, May 2018

Gluon tomography from deeply virtual Compton scattering at small x journal, June 2017

Quark Wigner distributions and orbital angular momentum journal, July 2011

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

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

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

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

The BFKL equation from the Wilson renormalization group journal, October 1997

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

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

Vector potential versus color charge density in low- x evolution journal, December 1999

Relating different approaches to nonlinear QCD evolution at finite gluon density journal, October 2000

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

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

The color glass condensate and hadron production in the forward region journal, February 2006

Particle production at high energy and large transverse momentum: “The hybrid formalism” revisited journal, May 2011

One-Loop Factorization for Inclusive Hadron Production in p − A Collisions in the Saturation Formalism journal, March 2012

Inclusive hadron productions in p A collisions journal, September 2012

Towards the Test of Saturation Physics Beyond Leading Logarithm journal, January 2014

Matching collinear and small x factorization calculations for inclusive hadron production in p A collisions journal, July 2014

Single inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism journal, May 2015

Implementing the exact kinematical constraint in the saturation formalism journal, August 2015

Single inclusive forward hadron production at next-to-leading order journal, June 2016

CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order journal, December 2016

Use of a running coupling in the NLO calculation of forward hadron production journal, March 2018

Implementation of NLO high energy factorization in single inclusive forward hadron production journal, June 2017

Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions journal, September 2015

Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework journal, December 2016

Non-eikonal corrections to multi-particle production in the color glass condensate journal, July 2019

Improving the kinematics for low- x QCD evolution equations in coordinate space journal, April 2014

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

Collinearly-improved BK evolution meets the HERA data journal, November 2015

Collinearly improved JIMWLK evolution in Langevin form journal, August 2016

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

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

Unitarity at small Bjorken x
journal, June 2002

Unitarity and the BFKL Pomeron
text, January 1994

Interplay of the CGC and TMD frameworks to all orders in kinematic twist
text, January 2019

Unitarity and the BFKL pomeron
journal, March 1995

The Color Glass Condensate
journal, November 2010

Semihard processes in QCD
journal, November 1983

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

Power corrections to TMD factorization for Z-boson production
journal, May 2018

Small-x behavior and parton saturation: A QCD model
journal, April 1990

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

Interplay of the CGC and TMD frameworks to all orders in kinematic twist
journal, May 2019

The Color Glass Condensate
text, January 2010

Power corrections to TMD factorization for Z-boson production
text, January 2017

Operator expansion for high-energy scattering
journal, March 1996

Factorization for High-Energy Scattering
journal, September 1998

Factorization and high-energy effective action
journal, June 1999

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

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

Particle production in high-energy collisions beyond the shockwave limit
journal, October 2016

Higher-twist corrections to gluon TMD factorization
journal, July 2017

Helicity evolution at small x
journal, January 2016

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

TMD factorization for dijets + photon production from the dilute-dense CGC framework
journal, July 2019

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

Azimuthal asymmetries for quark pair production in $p A$ collisions
journal, March 2013

$\cos (4 φ)$ azimuthal anisotropy in small- $x$ DIS dijet production beyond the leading power TMD limit
journal, July 2016

Transverse-momentum-dependent gluon distributions from JIMWLK evolution
journal, October 2016

Suppression of maximal linear gluon polarization in angular asymmetries
journal, October 2017

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

TMD gluon distributions at small x in the CGC theory
journal, May 2018

Gluon tomography from deeply virtual Compton scattering at small $x$
journal, June 2017

Quark Wigner distributions and orbital angular momentum
journal, July 2011

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

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

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

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

The BFKL equation from the Wilson renormalization group
journal, October 1997

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

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

Vector potential versus color charge density in low- $x$ evolution
journal, December 1999

Relating different approaches to nonlinear QCD evolution at finite gluon density
journal, October 2000

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

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

The color glass condensate and hadron production in the forward region
journal, February 2006

Particle production at high energy and large transverse momentum: “The hybrid formalism” revisited
journal, May 2011

One-Loop Factorization for Inclusive Hadron Production in $p − A$ Collisions in the Saturation Formalism
journal, March 2012

Inclusive hadron productions in $p A$ collisions
journal, September 2012

Towards the Test of Saturation Physics Beyond Leading Logarithm
journal, January 2014

Matching collinear and small $x$ factorization calculations for inclusive hadron production in $p A$ collisions
journal, July 2014

Single inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism
journal, May 2015

Implementing the exact kinematical constraint in the saturation formalism
journal, August 2015

Single inclusive forward hadron production at next-to-leading order
journal, June 2016

CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order
journal, December 2016

Use of a running coupling in the NLO calculation of forward hadron production
journal, March 2018

Implementation of NLO high energy factorization in single inclusive forward hadron production
journal, June 2017

Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions
journal, September 2015

Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework
journal, December 2016

Non-eikonal corrections to multi-particle production in the color glass condensate
journal, July 2019

Improving the kinematics for low- $x$ QCD evolution equations in coordinate space
journal, April 2014

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

Collinearly-improved BK evolution meets the HERA data
journal, November 2015

Collinearly improved JIMWLK evolution in Langevin form
journal, August 2016