Interplay of the CGC and TMD frameworks to all orders in kinematic twist

Altinoluk, Tolga; Boussarie, Renaud; Kotko, Piotr

doi:10.1007/JHEP05(2019)156

Title: Interplay of the CGC and TMD frameworks to all orders in kinematic twist

Abstract

A framework for an improved TMD (iTMD) factorization scheme at small x, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD k_t $$\ll$$ Q regime and the BFKL k_t~ Q regime. Here, we observe the relation between CGC and iTMD amplitudes. We first show how the dipolesize expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Lastly, we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low x framework. This allows to reinterpret the dilute expansion as a Wandzura-Wilczek approximation in the large k_t regime

Authors:

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

^[3]

National Centre for Nuclear Research, Warsaw (Poland)
Brookhaven National Laboratory (BNL), Upton, NY (United States); Polish Academy of Sciences (PAS), Krakow (Poland)
Polish Academy of Sciences (PAS), Krakow (Poland)

Publication Date:: Fri May 24 00:00:00 EDT 2019

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

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

OSTI Identifier:: 1530525

Report Number(s):: BNL-211821-2019-JAAM
Journal ID: ISSN 1029-8479

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: 5; 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, Tolga, Boussarie, Renaud, and Kotko, Piotr. Interplay of the CGC and TMD frameworks to all orders in kinematic twist.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP05(2019)156.

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                    Altinoluk, Tolga, Boussarie, Renaud, & Kotko, Piotr. Interplay of the CGC and TMD frameworks to all orders in kinematic twist.  United States.  https://doi.org/10.1007/JHEP05(2019)156

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                    Altinoluk, Tolga, Boussarie, Renaud, and Kotko, Piotr. Fri .  
"Interplay of the CGC and TMD frameworks to all orders in kinematic twist".  United States.  https://doi.org/10.1007/JHEP05(2019)156.  https://www.osti.gov/servlets/purl/1530525.

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@article{osti_1530525,

  title        = {Interplay of the CGC and TMD frameworks to all orders in kinematic twist},

  author       = {Altinoluk, Tolga and Boussarie, Renaud and Kotko, Piotr},

  abstractNote = {A framework for an improved TMD (iTMD) factorization scheme at small x, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD kt $\ll$ Q regime and the BFKL kt~ Q regime. Here, we observe the relation between CGC and iTMD amplitudes. We first show how the dipolesize expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Lastly, we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low x framework. This allows to reinterpret the dilute expansion as a Wandzura-Wilczek approximation in the large kt regime},

  doi          = {10.1007/JHEP05(2019)156},

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

  number       = 5,

  volume       = 2019,

  place        = {United States},

  year         = {Fri May 24 00:00:00 EDT 2019},

  month        = {Fri May 24 00:00:00 EDT 2019}

}

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Title: Interplay of the CGC and TMD frameworks to all orders in kinematic twist

Abstract

Citation Formats

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

TMD gluon distributions at small x in the CGC theory text, January 2018

Multi-Parton Amplitudes in Gauge Theories text, January 2005

Forward jet production at the Large Hadron Collider journal, September 2009

BCFW recursion for TMD parton scattering text, January 2015

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

Towards the Test of Saturation Physics Beyond Leading Logarithm text, January 2013

When does the gluon reggeize? journal, May 2015

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

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

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

TMD gluon distributions for multiparton processes journal, February 2019

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

Helicity amplitudes for high-energy scattering journal, January 2013

TMD gluon distributions for multiparton processes text, January 2018

Multi-parton amplitudes in gauge theories journal, February 1991

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

Suppression of maximal linear gluon polarization in angular asymmetries text, January 2017

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

BCFW recursion for off-shell gluons text, January 2014

Unitarity and the BFKL pomeron journal, March 1995

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

Evolution equations for QCD string operators journal, January 1989

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

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

Forward trijet production in proton-nucleus collisions text, January 2018

The dipole picture of high energy scattering, the BFKL equation and many gluon compound states journal, October 1995

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

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC journal, May 2017

Higher-twist corrections to gluon TMD factorization text, January 2017

Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization journal, December 2012

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

Wilson lines and gauge invariant off-shell amplitudes journal, July 2014

Helicity amplitudes for high-energy scattering text, January 2012

BCFW recursion for TMD parton scattering journal, July 2015

Unitarity at small Bjorken x journal, June 2002

Unitarity and the BFKL Pomeron text, January 1994

Relation of parton distribution functions in the Drell-Yan process to deeply inelastic scattering journal, June 1983

QCD Reggeon calculus from KLWMIJ/JIMWLK evolution: vertices, reggeization and all journal, September 2013

Forward trijet production in proton–nucleus collisions journal, May 2019

BCFW recursion for off-shell gluons journal, July 2014

Connection between complete and Möbius forms of gauge invariant operators journal, March 2012

Foundations of Perturbative QCD book, May 2011

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC text, January 2017

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks journal, December 1977

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

Asymptotic freedom in parton language journal, August 1977

The dipole form of the gluon part of the BFKL kernel journal, November 2007

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

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

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

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

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

The dipole form of the quark part of the BFKL kernel journal, April 2007

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering journal, March 2002

Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering journal, May 2002

Final state interactions and gauge invariant parton distributions journal, April 2003

Gauge link structure in quark–quark correlators in hard processes journal, August 2004

Color gauge invariance in the Drell–Yan process journal, March 2000

The construction of gauge-links in arbitrary hard processes journal, May 2006

k t Factorization for Hard Processes in Nuclei journal, January 2011

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

Saturation effects in deep inelastic scattering at low Q 2 and its implications on diffraction journal, November 1998

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

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

Feynman rules for effective Regge action journal, August 2005

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

Helicity evolution at small x journal, January 2016

Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation text, January 2019

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

TMD gluon distributions at small x in the CGC theory
text, January 2018

Multi-Parton Amplitudes in Gauge Theories
text, January 2005

Forward jet production at the Large Hadron Collider
journal, September 2009

BCFW recursion for TMD parton scattering
text, January 2015

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

Towards the Test of Saturation Physics Beyond Leading Logarithm
text, January 2013

When does the gluon reggeize?
journal, May 2015

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

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

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

TMD gluon distributions for multiparton processes
journal, February 2019

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

Helicity amplitudes for high-energy scattering
journal, January 2013

TMD gluon distributions for multiparton processes
text, January 2018

Multi-parton amplitudes in gauge theories
journal, February 1991

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

Suppression of maximal linear gluon polarization in angular asymmetries
text, January 2017

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

BCFW recursion for off-shell gluons
text, January 2014

Unitarity and the BFKL pomeron
journal, March 1995

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

Evolution equations for QCD string operators
journal, January 1989

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

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

Forward trijet production in proton-nucleus collisions
text, January 2018

The dipole picture of high energy scattering, the BFKL equation and many gluon compound states
journal, October 1995

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

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC
journal, May 2017

Higher-twist corrections to gluon TMD factorization
text, January 2017

Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization
journal, December 2012

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

Wilson lines and gauge invariant off-shell amplitudes
journal, July 2014

Helicity amplitudes for high-energy scattering
text, January 2012

BCFW recursion for TMD parton scattering
journal, July 2015

Unitarity at small Bjorken x
journal, June 2002

Unitarity and the BFKL Pomeron
text, January 1994

Relation of parton distribution functions in the Drell-Yan process to deeply inelastic scattering
journal, June 1983

QCD Reggeon calculus from KLWMIJ/JIMWLK evolution: vertices, reggeization and all
journal, September 2013

Forward trijet production in proton–nucleus collisions
journal, May 2019

BCFW recursion for off-shell gluons
journal, July 2014

Connection between complete and Möbius forms of gauge invariant operators
journal, March 2012

Foundations of Perturbative QCD
book, May 2011

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC
text, January 2017

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks
journal, December 1977

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

Asymptotic freedom in parton language
journal, August 1977

The dipole form of the gluon part of the BFKL kernel
journal, November 2007

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

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

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

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

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

The dipole form of the quark part of the BFKL kernel
journal, April 2007

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering
journal, March 2002

Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering
journal, May 2002

Final state interactions and gauge invariant parton distributions
journal, April 2003

Gauge link structure in quark–quark correlators in hard processes
journal, August 2004

Color gauge invariance in the Drell–Yan process
journal, March 2000

The construction of gauge-links in arbitrary hard processes
journal, May 2006

$k_{t}$ Factorization for Hard Processes in Nuclei
journal, January 2011

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

Saturation effects in deep inelastic scattering at low $Q^{2}$ and its implications on diffraction
journal, November 1998

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

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

Feynman rules for effective Regge action
journal, August 2005

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

Helicity evolution at small x
journal, January 2016

Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation
text, January 2019