Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions

Caucal, Paul; Salazar, Farid; Schenke, Björn; Stebel, Tomasz; Venugopalan, Raju

doi:10.1103/PhysRevLett.132.081902

Title: Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small $x$ : Complete NLO Results and Predictions

Abstract

We compute the back-to-back dijet cross section in deep inelastic scattering at small $$x$$ to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum $$P$$⊥ of the dijet pair to the dijet momentum imbalance $$q$$⊥; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $$x$$ that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Authors:

;

; Schenke, Björn;

; Venugopalan, Raju

Publication Date:: Tue Feb 20 00:00:00 EST 2024

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; Polish National Science Centre (NCN)

OSTI Identifier:: 2309786

Alternate Identifier(s):: OSTI ID: 2324881

Report Number(s):: BNL-225390-2024-JAAM
Journal ID: ISSN 0031-9007; PRLTAO; 081902

Grant/Contract Number:: SC0012704; PHY-1945471; 2019/32/C/ST2/00202; 2021/43/D/ST2/03375

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 132 Journal Issue: 8; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Caucal, Paul, Salazar, Farid, Schenke, Björn, Stebel, Tomasz, and Venugopalan, Raju. Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions.  United States: N. p., 2024. 
Web.  doi:10.1103/PhysRevLett.132.081902.

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                    Caucal, Paul, Salazar, Farid, Schenke, Björn, Stebel, Tomasz, & Venugopalan, Raju. Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions.  United States.  https://doi.org/10.1103/PhysRevLett.132.081902

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                    Caucal, Paul, Salazar, Farid, Schenke, Björn, Stebel, Tomasz, and Venugopalan, Raju. Tue .  
"Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions".  United States.  https://doi.org/10.1103/PhysRevLett.132.081902.

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@article{osti_2309786,

  title        = {Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions},

  author       = {Caucal, Paul and Salazar, Farid and Schenke, Björn and Stebel, Tomasz and Venugopalan, Raju},

  abstractNote = {We compute the back-to-back dijet cross section in deep inelastic scattering at small $x$ to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum $P$⊥ of the dijet pair to the dijet momentum imbalance $q$⊥; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $x$ that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.},

  doi          = {10.1103/PhysRevLett.132.081902},

  journal      = {Physical Review Letters},

  number       = 8,

  volume       = 132,

  place        = {United States},

  year         = {Tue Feb 20 00:00:00 EST 2024},

  month        = {Tue Feb 20 00:00:00 EST 2024}

}

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Title: Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x : Complete NLO Results and Predictions

Abstract

Citation Formats

Science Requirements and Detector Concepts for the Electron-Ion Collider journal, October 2022

Nuclear A-dependence near the saturation boundary journal, August 2003

Searching for saturation in forward dijet production at the LHC journal, October 2023

Semihard processes in QCD journal, November 1983

Forward Higgs production within high energy factorization in the heavy quark limit at next-to-leading order accuracy journal, February 2021

The electron–ion collider: assessing the energy dependence of key measurements journal, January 2019

Threshold resummation for hadron production in the small- x region journal, September 2020

Constraints on gluon evolution at small x journal, August 1996

FastJet user manual: (for version 3.0.2) journal, March 2012

Cronin effect and high- p T suppression in pA collisions journal, November 2003

Harmonics of Parton Saturation in Lepton-Jet Correlations at the Electron-Ion Collider journal, April 2023

QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider journal, May 2021

Next-to-leading order Balitsky-Kovchegov equation with resummation journal, May 2016

Renormalization group evolution of multi-gluon correlators in high energy QCD journal, December 2011

The Cronin effect, quantum evolution and the color glass condensate journal, December 2003

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

Probing gluon number density with electron-dijet correlations at EIC journal, August 2021

Single inclusive jet production in pA collisions at NLO in the small-x regime journal, July 2022

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

Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider journal, March 2020

Errata journal, March 1983

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

Azimuthal angular asymmetry of soft gluon radiation in jet production journal, September 2021

TMD factorization for dijet and heavy-meson pair in DIS journal, January 2021

Nuclear Enhancement of Universal Dynamics of High Parton Densities journal, January 2008

Back-to-back jets in QCD journal, December 1981

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO journal, August 2023

Rapidity evolution of Wilson lines at the next-to-leading order journal, December 2013

Comment of QCD exponentiation at large x journal, April 1991

Mining for Gluon Saturation at Colliders journal, August 2021

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

Combined measurement and QCD analysis of the inclusive e ± p scattering cross sections at HERA journal, January 2010

Gauge invariance of transverse momentum dependent distributions at small x journal, May 2021

Dihadron production in DIS at small x at next-to-leading order: Transverse photons journal, March 2023

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

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

Anisotropy in Dijet Production in Exclusive and Inclusive Processes journal, April 2021

High energy pA collisions in the color glass condensate approach II: quark pair production journal, October 2004

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

Suppressions of dijet azimuthal correlations in the future EIC journal, December 2021

An “all-poles” approximation to collinear resummations in the Regge limit of perturbative QCD journal, August 2005

Transverse momentum distribution in Drell-Yan pair and W and Z boson production journal, January 1985

Production of hadrons at large transverse momentum in 200-, 300-, and 400-GeV p − p and p -nucleus collisions journal, February 1979

Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO journal, November 2022

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

The next-to-leading order forward jet vertex in the small-cone approximation journal, May 2012

Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation journal, September 1998

From deep inelastic scattering to proton-nucleus collisions in the color glass condensate model journal, April 2003

Energy Dependence of the Cronin Effect from Nonlinear QCD Evolution journal, February 2004

Renormalization group improved small- x equation journal, November 1999

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

Parton distribution and decay functions journal, January 1982

Extracting many-body correlators of saturated gluons with precision from inclusive photon + dijet final states in deeply inelastic scattering journal, April 2020

Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions journal, May 2022

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

Transverse momentum dependent gluon distribution within high energy factorization at next-to-leading order journal, September 2021

High-energy factorization and small-x deep inelastic scattering beyond leading order journal, October 1994

High energy QCD at NLO: from light-cone wave function to JIMWLK evolution journal, May 2017

Incoherent diffractive dijet production in electron DIS off nuclei at high energy journal, June 2023

A resummation of large sub-leading corrections at small x journal, July 1998

Scale dependence of the small x transverse momentum dependent gluon distribution journal, March 2019

On the small-x evolution of the color quadrupole and the Weizsäcker–Williams gluon distribution journal, November 2011

The anti- k t jet clustering algorithm journal, April 2008

Dihadron production at the LHC: full next-to-leading BFKL calculation journal, June 2017

Forward $$\gamma $$+jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance journal, September 2023

The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider journal, September 2021

JIMWLK evolution in the Gaussian approximation journal, April 2012

Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture journal, August 2022

Measuring the Weizsäcker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries journal, January 2019

HERA data and collinearly-improved BK dynamics journal, April 2020

Gluon saturation and initial conditions for relativistic heavy ion collisions journal, May 2014

Probing Gluon Saturation through Dihadron Correlations at an Electron-Ion Collider conference, September 2014

Forward dihadron back-to-back correlations in p A collisions journal, January 2019

Rapidity evolution of TMDs with running coupling journal, August 2022

Triumvirate of running couplings in small-x evolution journal, March 2007

Operator expansion for high-energy scattering journal, March 1996

Title: Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small $x$ : Complete NLO Results and Predictions

Science Requirements and Detector Concepts for the Electron-Ion Collider
journal, October 2022

Nuclear A-dependence near the saturation boundary
journal, August 2003

Searching for saturation in forward dijet production at the LHC
journal, October 2023

Semihard processes in QCD
journal, November 1983

Forward Higgs production within high energy factorization in the heavy quark limit at next-to-leading order accuracy
journal, February 2021

The electron–ion collider: assessing the energy dependence of key measurements
journal, January 2019

Threshold resummation for hadron production in the small- $x$ region
journal, September 2020

Constraints on gluon evolution at small x
journal, August 1996

FastJet user manual: (for version 3.0.2)
journal, March 2012

Cronin effect and high- $p_{T}$ suppression in pA collisions
journal, November 2003

Harmonics of Parton Saturation in Lepton-Jet Correlations at the Electron-Ion Collider
journal, April 2023

QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider
journal, May 2021

Next-to-leading order Balitsky-Kovchegov equation with resummation
journal, May 2016

Renormalization group evolution of multi-gluon correlators in high energy QCD
journal, December 2011

The Cronin effect, quantum evolution and the color glass condensate
journal, December 2003

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

Probing gluon number density with electron-dijet correlations at EIC
journal, August 2021

Single inclusive jet production in pA collisions at NLO in the small-x regime
journal, July 2022

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

Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider
journal, March 2020

Errata
journal, March 1983

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

Azimuthal angular asymmetry of soft gluon radiation in jet production
journal, September 2021

TMD factorization for dijet and heavy-meson pair in DIS
journal, January 2021

Nuclear Enhancement of Universal Dynamics of High Parton Densities
journal, January 2008

Back-to-back jets in QCD
journal, December 1981

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO
journal, August 2023

Rapidity evolution of Wilson lines at the next-to-leading order
journal, December 2013

Comment of QCD exponentiation at large x
journal, April 1991

Mining for Gluon Saturation at Colliders
journal, August 2021

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

Combined measurement and QCD analysis of the inclusive e ± p scattering cross sections at HERA
journal, January 2010

Gauge invariance of transverse momentum dependent distributions at small $x$
journal, May 2021

Dihadron production in DIS at small x at next-to-leading order: Transverse photons
journal, March 2023

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

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

Anisotropy in Dijet Production in Exclusive and Inclusive Processes
journal, April 2021

High energy pA collisions in the color glass condensate approach II: quark pair production
journal, October 2004

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

Suppressions of dijet azimuthal correlations in the future EIC
journal, December 2021

An “all-poles” approximation to collinear resummations in the Regge limit of perturbative QCD
journal, August 2005

Transverse momentum distribution in Drell-Yan pair and W and Z boson production
journal, January 1985

Production of hadrons at large transverse momentum in 200-, 300-, and 400-GeV $p - p$ and $p$ -nucleus collisions
journal, February 1979

Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO
journal, November 2022

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

The next-to-leading order forward jet vertex in the small-cone approximation
journal, May 2012

Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
journal, September 1998

From deep inelastic scattering to proton-nucleus collisions in the color glass condensate model
journal, April 2003

Energy Dependence of the Cronin Effect from Nonlinear QCD Evolution
journal, February 2004

Renormalization group improved small- $x$ equation
journal, November 1999

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

Parton distribution and decay functions
journal, January 1982

Extracting many-body correlators of saturated gluons with precision from inclusive $photon + dijet$ final states in deeply inelastic scattering
journal, April 2020

Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions
journal, May 2022

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

Transverse momentum dependent gluon distribution within high energy factorization at next-to-leading order
journal, September 2021

High-energy factorization and small-x deep inelastic scattering beyond leading order
journal, October 1994

High energy QCD at NLO: from light-cone wave function to JIMWLK evolution
journal, May 2017

Incoherent diffractive dijet production in electron DIS off nuclei at high energy
journal, June 2023

A resummation of large sub-leading corrections at small x
journal, July 1998

Scale dependence of the small x transverse momentum dependent gluon distribution
journal, March 2019

On the small-x evolution of the color quadrupole and the Weizsäcker–Williams gluon distribution
journal, November 2011

The anti- k _t jet clustering algorithm
journal, April 2008

Dihadron production at the LHC: full next-to-leading BFKL calculation
journal, June 2017

Forward $$\gamma $$+jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance
journal, September 2023

The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider
journal, September 2021

JIMWLK evolution in the Gaussian approximation
journal, April 2012

Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
journal, August 2022

Measuring the Weizsäcker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries
journal, January 2019

HERA data and collinearly-improved BK dynamics
journal, April 2020

Gluon saturation and initial conditions for relativistic heavy ion collisions
journal, May 2014

Probing Gluon Saturation through Dihadron Correlations at an Electron-Ion Collider
conference, September 2014

Forward dihadron back-to-back correlations in $p A$ collisions
journal, January 2019

Rapidity evolution of TMDs with running coupling
journal, August 2022

Triumvirate of running couplings in small-x evolution
journal, March 2007

Operator expansion for high-energy scattering
journal, March 1996

Forward inclusive jet productions in pA collisions
journal, January 2023

Color glass condensate at next-to-leading order meets HERA data
journal, October 2020