NLO impact factor for inclusive photon + dijet production in e + A DIS at small x

Roy, Kaushik; Venugopalan, Raju

doi:10.1103/PhysRevD.101.034028

Title: NLO impact factor for inclusive $photon + dijet$ production in $e + A$ DIS at small $x$

Abstract

We compute the next-to-leading order (NLO) impact factor for inclusive photon +dijet production in electron-nucleus (e+A) deeply inelastic scattering (DIS) at small $$x$$. An important ingredient in our computation is the simple structure of “shock wave” fermion and gluon propagators. This allows one to employ standard momentum space Feynman diagram techniques for higher order computations in the Regge limit of fixed $Q^2$ $$\gg$$ $$Λ^2_{QCD}$$ and x → 0. Our computations in the color glass condensate (CGC) effective field theory include the resummation of all-twist power corrections $$Q^2_s / Q^2$$, where $$Q_s$$ is the saturation scale in the nucleus. We discuss the structure of ultraviolet, collinear and soft divergences in the CGC, and extract the leading logs in x; the structure of the corresponding rapidity divergences gives a nontrivial first principles derivation of the JIMWLK renormalization group evolution equation for multiparton lightlike Wilson line correlators. Explicit expressions are given for the x-independent $$O(α_s)$$ contributions that constitute the NLO impact factor. These results, combined with extant results on NLO JIMWLK evolution, provide the ingredients to compute the inclusive photon + dijet cross section at small $$x$$ to $$O(α^3_s ln(x))$$. First results for the NLO impact factor in inclusive dijet production are recovered in the soft photon limit. A byproduct of our computation is the LO photon + 3 jet (quark-antiquark-gluon) cross section.

Authors:

; Venugopalan, Raju

Publication Date:: Mon Feb 24 00:00:00 EST 2020

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

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

OSTI Identifier:: 1601716

Alternate Identifier(s):: OSTI ID: 1606186

Report Number(s):: BNL-213748-2020-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ; 034028

Grant/Contract Number:: SC0012704

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Effective field theory; Electron-ion collisions; Feynman diagrams; Quantum chromodynamics; Quark & gluon jets; Renormalization group; Strong interaction

Citation Formats


                    Roy, Kaushik, and Venugopalan, Raju. NLO impact factor for inclusive photon + dijet production in e + A DIS at small x.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.034028.

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                    Roy, Kaushik, & Venugopalan, Raju. NLO impact factor for inclusive photon + dijet production in e + A DIS at small x.  United States.  https://doi.org/10.1103/PhysRevD.101.034028

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                    Roy, Kaushik, and Venugopalan, Raju. Mon .  
"NLO impact factor for inclusive photon + dijet production in e + A DIS at small x".  United States.  https://doi.org/10.1103/PhysRevD.101.034028.

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@article{osti_1601716,

  title        = {NLO impact factor for inclusive photon + dijet production in e + A DIS at small x},

  author       = {Roy, Kaushik and Venugopalan, Raju},

  abstractNote = {We compute the next-to-leading order (NLO) impact factor for inclusive photon +dijet production in electron-nucleus (e+A) deeply inelastic scattering (DIS) at small $x$. An important ingredient in our computation is the simple structure of “shock wave” fermion and gluon propagators. This allows one to employ standard momentum space Feynman diagram techniques for higher order computations in the Regge limit of fixed $Q^2$ $\gg$ $Λ^2_{QCD}$ and x → 0. Our computations in the color glass condensate (CGC) effective field theory include the resummation of all-twist power corrections $Q^2_s / Q^2$, where $Q_s$ is the saturation scale in the nucleus. We discuss the structure of ultraviolet, collinear and soft divergences in the CGC, and extract the leading logs in x; the structure of the corresponding rapidity divergences gives a nontrivial first principles derivation of the JIMWLK renormalization group evolution equation for multiparton lightlike Wilson line correlators. Explicit expressions are given for the x-independent $O(α_s)$ contributions that constitute the NLO impact factor. These results, combined with extant results on NLO JIMWLK evolution, provide the ingredients to compute the inclusive photon + dijet cross section at small $x$ to $O(α^3_s ln(x))$. First results for the NLO impact factor in inclusive dijet production are recovered in the soft photon limit. A byproduct of our computation is the LO photon + 3 jet (quark-antiquark-gluon) cross section.},

  doi          = {10.1103/PhysRevD.101.034028},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 101,

  place        = {United States},

  year         = {Mon Feb 24 00:00:00 EST 2020},

  month        = {Mon Feb 24 00:00:00 EST 2020}

}

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Title: NLO impact factor for inclusive photon + dijet production in e + A DIS at small x

Abstract

Citation Formats

Spinor helicity methods in high-energy factorization: Efficient momentum-space calculations in the Color Glass Condensate formalism journal, July 2017

Solving the high energy evolution equation including running coupling corrections journal, June 2007

Inclusive prompt photon production in electron-nucleus scattering at small x journal, May 2018

Next-to-leading order corrections for the dipole factorization of deep inelastic scattering structure functions at low x journal, February 2012

On correlators of Reggeon fields and operators of Wilson lines in high energy QCD journal, December 2018

Introduction to the technique of dimensional regularization journal, October 1975

( γ * → q q ¯ ) -Reggeon vertex in next-to-leading order QCD journal, February 2001

Relating e + e − annihilation to high energy scattering at weak and strong coupling journal, November 2008

Non-global jet evolution at finite Nc journal, May 2004

Semihard processes in QCD journal, November 1983

The Color Glass Condensate journal, November 2010

High-energy evolution to three loops journal, February 2018

Particle production in field theories coupled to strong external sources, I: Formalism and main results journal, October 2006

S-matrix and productions amplitudes in high energy QCD journal, August 2018

Small-x physics in perturbative QCD journal, July 1997

BFKL pomeron in the next-to-leading approximation journal, June 1998

NLO corrections to the photon impact factor: Combining real and virtual corrections journal, November 2002

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

Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions journal, January 2017

Photon impact factor and k T factorization for DIS in the next-to-leading order journal, January 2013

On the Low-Burnett-Kroll theorem for soft-photon emission journal, March 1969

Energy scale(s) and next-to-leading BFKL equation journal, July 1998

Fock space distributions, structure functions, higher twists, and small x journal, March 1999

Single-inclusive jet production in polarized pp collisions at O ( α s 3 ) journal, August 2004

Improvement for color glass condensate factorization: Single hadron production in p A collisions at next-to-leading order journal, October 2019

One-loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus journal, September 2017

High Energy Scattering in Quantum Chromodynamics journal, October 2007

One-loop corrections to light cone wave functions: The dipole picture DIS cross section journal, June 2018

Color Glass Condensate in Schwinger–Keldysh QCD journal, January 2014

The process γ L * + q → ( q q ¯ g ) + q : Real corrections to the virtual photon impact factor journal, November 2001

Quantum Chromodynamics at High Energy book, September 2012

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

2D Kac-Moody symmetry of 4D Yang-Mills theory journal, October 2016

Photon impact factor in the next-to-leading order journal, February 2011

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

Study of a non-leading QCD correction to hadron calorimeter reactions journal, April 1982

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

Impact factor for high-energy two and three jets diffractive production journal, September 2014

Color glass condensate formalism, Balitsky-JIMWLK evolution, and Lipatov’s high energy effective action journal, June 2018

Asymptotic freedom in parton language journal, August 1977

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

Polarized 3 parton production in inclusive DIS at small x journal, October 2016

High energy factorization in nucleus-nucleus collisions. I journal, September 2008

A simple derivation of the JIMWLK equation journal, December 2001

On a conjecture by 't Hooft and Veltman journal, January 1974

Dimensional regularization for zero‐mass particles in quantum field theory journal, January 1974

Particle production in field theories coupled to strong external sources, II: Generating functions journal, November 2006

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

Erratum: ( γ * → q q ¯ ) -Reggeon vertex in next-to-leading order QCD [Phys. Rev. D 63 , 056014 (2001)] journal, March 2002

Jets from Quantum Chromodynamics journal, December 1977

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts journal, January 2017

Renormalization group improved small- x equation journal, November 1999

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

Photon production in high energy proton-nucleus collisions journal, July 2002

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

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

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

BFKL dynamics in jet evolution journal, November 2003

Dipole factorization for DIS at NLO: Combining the q q ¯ and q q ¯ g contributions journal, October 2017

Constraining unintegrated gluon distributions from inclusive photon production in proton–proton collisions at the LHC journal, April 2019

When does the gluon reggeize? journal, May 2015

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

Operator expansion for high-energy scattering journal, March 1996

High gluon densities in heavy ion collisions journal, February 2017

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

Sudakov suppression of the Balitsky-Kovchegov kernel journal, November 2019

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

Universality of multiparticle production in QCD at high energies journal, February 2013

Away-from-jet energy flow journal, August 2002

Jet production in hadronic collisions to0(α s 3 ) journal, June 1990

Extension of the Low Soft-Photon Theorem journal, January 1968

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NLO JIMWLK evolution unabridged journal, August 2014

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Title: NLO impact factor for inclusive $photon + dijet$ production in $e + A$ DIS at small $x$

Spinor helicity methods in high-energy factorization: Efficient momentum-space calculations in the Color Glass Condensate formalism
journal, July 2017

Solving the high energy evolution equation including running coupling corrections
journal, June 2007

Inclusive prompt photon production in electron-nucleus scattering at small x
journal, May 2018

Next-to-leading order corrections for the dipole factorization of deep inelastic scattering structure functions at low $x$
journal, February 2012

On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
journal, December 2018

Introduction to the technique of dimensional regularization
journal, October 1975

$(γ^{*} \to q \bar{q})$ -Reggeon vertex in next-to-leading order QCD
journal, February 2001

Relating e ⁺ e ⁻ annihilation to high energy scattering at weak and strong coupling
journal, November 2008

Non-global jet evolution at finite Nc
journal, May 2004

Semihard processes in QCD
journal, November 1983

The Color Glass Condensate
journal, November 2010

High-energy evolution to three loops
journal, February 2018

Particle production in field theories coupled to strong external sources, I: Formalism and main results
journal, October 2006

S-matrix and productions amplitudes in high energy QCD
journal, August 2018

Small-x physics in perturbative QCD
journal, July 1997

BFKL pomeron in the next-to-leading approximation
journal, June 1998

NLO corrections to the photon impact factor: Combining real and virtual corrections
journal, November 2002

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

Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions
journal, January 2017

Photon impact factor and $k_{T}$ factorization for DIS in the next-to-leading order
journal, January 2013

On the Low-Burnett-Kroll theorem for soft-photon emission
journal, March 1969

Energy scale(s) and next-to-leading BFKL equation
journal, July 1998

Fock space distributions, structure functions, higher twists, and small x
journal, March 1999

Single-inclusive jet production in polarized pp collisions at $O (α_{s}^{3})$
journal, August 2004

Improvement for color glass condensate factorization: Single hadron production in $p A$ collisions at next-to-leading order
journal, October 2019

One-loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus
journal, September 2017

High Energy Scattering in Quantum Chromodynamics
journal, October 2007

One-loop corrections to light cone wave functions: The dipole picture DIS cross section
journal, June 2018

Color Glass Condensate in Schwinger–Keldysh QCD
journal, January 2014

The process $γ_{L}^{*} + q \to (q \bar{q} g) + q :$ Real corrections to the virtual photon impact factor
journal, November 2001

Quantum Chromodynamics at High Energy
book, September 2012

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

2D Kac-Moody symmetry of 4D Yang-Mills theory
journal, October 2016

Photon impact factor in the next-to-leading order
journal, February 2011

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

Study of a non-leading QCD correction to hadron calorimeter reactions
journal, April 1982

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

Impact factor for high-energy two and three jets diffractive production
journal, September 2014

Color glass condensate formalism, Balitsky-JIMWLK evolution, and Lipatov’s high energy effective action
journal, June 2018

Asymptotic freedom in parton language
journal, August 1977

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

Polarized 3 parton production in inclusive DIS at small x
journal, October 2016

High energy factorization in nucleus-nucleus collisions. I
journal, September 2008

A simple derivation of the JIMWLK equation
journal, December 2001

On a conjecture by 't Hooft and Veltman
journal, January 1974

Dimensional regularization for zero‐mass particles in quantum field theory
journal, January 1974

Particle production in field theories coupled to strong external sources, II: Generating functions
journal, November 2006

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

Erratum: $(γ^{*} \to q \bar{q})$ -Reggeon vertex in next-to-leading order QCD [Phys. Rev. D 63 , 056014 (2001)]
journal, March 2002

Jets from Quantum Chromodynamics
journal, December 1977

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts
journal, January 2017

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

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

Photon production in high energy proton-nucleus collisions
journal, July 2002

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

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

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

BFKL dynamics in jet evolution
journal, November 2003

Dipole factorization for DIS at NLO: Combining the $q \bar{q}$ and $q \bar{q} g$ contributions
journal, October 2017

Constraining unintegrated gluon distributions from inclusive photon production in proton–proton collisions at the LHC
journal, April 2019

When does the gluon reggeize?
journal, May 2015

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

Operator expansion for high-energy scattering
journal, March 1996

High gluon densities in heavy ion collisions
journal, February 2017

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

Sudakov suppression of the Balitsky-Kovchegov kernel
journal, November 2019

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

Universality of multiparticle production in QCD at high energies
journal, February 2013

Away-from-jet energy flow
journal, August 2002

Jet production in hadronic collisions to0(α s 3 )
journal, June 1990

Extension of the Low Soft-Photon Theorem
journal, January 1968

Nonlinear evolution in high-density QCD
journal, May 2002

NLO JIMWLK evolution unabridged
journal, August 2014

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory
journal, December 2017

Universality of unintegrated gluon distributions at small $x$
journal, May 2011

The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
journal, May 2019

Gluon propagator in non-Abelian Weizsäcker-Williams fields
journal, September 1995

Sudakov double logarithms resummation in hard processes in the small- $x$ saturation formalism
journal, December 2013