On the different forms of the kinematical constraint in BFKL

Deak, Michal; Kutak, Krzysztof; Li, Wanchen; Staśto, Anna M.

doi:10.1140/epjc/s10052-019-7171-z

Title: On the different forms of the kinematical constraint in BFKL

Abstract

We perform a detailed analysis of the different forms of the kinematical constraint imposed on the low x evolution that appear in the literature. We find that all of them generate the same leading anti-collinear poles in Mellin space which agree with BFKL up to NLL order and up to NNLL in N=4 sYM. The coefficients of subleading poles vanish up to NNLL order for all constraints and we prove that this property should be satisfied to all orders. We then demonstrate that the kinematical constraints differ at further subleading orders of poles. We quantify the differences between the different forms of the constraints by performing numerical analysis both in Mellin space and in momentum space. It can be shown that in all three cases BFKL equation can be recast into the differential form, with the argument of the longitudinal variable shifted by the combination of the transverse coordinates.

Authors:: Deak, Michal; Kutak, Krzysztof; Li, Wanchen; Staśto, Anna M.

Publication Date:: 2019-08-07

Research Org.:: Pennsylvania State Univ., University Park, PA (United States)

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

OSTI Identifier:: 1619363

Alternate Identifier(s):: OSTI ID: 1610239

Grant/Contract Number:: FG02-93ER40771; SC0002145

Resource Type:: Published Article

Journal Name:: European Physical Journal. C, Particles and Fields

Additional Journal Information:: Journal Name: European Physical Journal. C, Particles and Fields Journal Volume: 79 Journal Issue: 8; Journal ID: ISSN 1434-6044

Publisher:: Springer

Country of Publication:: Germany

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics

Citation Formats


                    Deak, Michal, Kutak, Krzysztof, Li, Wanchen, and Staśto, Anna M. On the different forms of the kinematical constraint in BFKL.  Germany: N. p., 2019. 
Web.  doi:10.1140/epjc/s10052-019-7171-z.

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                    Deak, Michal, Kutak, Krzysztof, Li, Wanchen, & Staśto, Anna M. On the different forms of the kinematical constraint in BFKL.  Germany.  https://doi.org/10.1140/epjc/s10052-019-7171-z

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                    Deak, Michal, Kutak, Krzysztof, Li, Wanchen, and Staśto, Anna M. Wed .  
"On the different forms of the kinematical constraint in BFKL".  Germany.  https://doi.org/10.1140/epjc/s10052-019-7171-z.

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@article{osti_1619363,

  title        = {On the different forms of the kinematical constraint in BFKL},

  author       = {Deak, Michal and Kutak, Krzysztof and Li, Wanchen and Staśto, Anna M.},

  abstractNote = {We perform a detailed analysis of the different forms of the kinematical constraint imposed on the low x evolution that appear in the literature. We find that all of them generate the same leading anti-collinear poles in Mellin space which agree with BFKL up to NLL order and up to NNLL in N=4 sYM. The coefficients of subleading poles vanish up to NNLL order for all constraints and we prove that this property should be satisfied to all orders. We then demonstrate that the kinematical constraints differ at further subleading orders of poles. We quantify the differences between the different forms of the constraints by performing numerical analysis both in Mellin space and in momentum space. It can be shown that in all three cases BFKL equation can be recast into the differential form, with the argument of the longitudinal variable shifted by the combination of the transverse coordinates.},

  doi          = {10.1140/epjc/s10052-019-7171-z},

  journal      = {European Physical Journal. C, Particles and Fields},

  number       = 8,

  volume       = 79,

  place        = {Germany},

  year         = {2019},

  month        = {8}

}

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Title: On the different forms of the kinematical constraint in BFKL

Abstract

Citation Formats

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

Small x resummation with quarks: Deep-inelastic scattering journal, August 2008

Transverse momentum dependent splitting functions at work: Quark-to-gluon splitting journal, December 2016

Screening effects in the ultra-high energy neutrino interactions journal, August 2003

Energy consumption and jet multiplicity from the leading log BFKL evolution journal, February 2003

Coherence effects in initial jets at small Q2/s journal, January 1988

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Broadening and saturation effects in dijet azimuthal correlations in p-p and p-Pb collisions at s N N = 5.02 TeV journal, August 2019

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Small-x behaviour of initial state radiation in perturbative QCD journal, May 1990

Small-x physics in perturbative QCD journal, July 1997

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

Pomeron Eigenvalue at Three Loops in N = 4 Supersymmetric Yang-Mills Theory journal, December 2015

The gluon splitting function at moderately small x journal, May 2004

Running coupling Balitskiĭ-Fadin-Kuraev-Lipatov anomalous dimensions and splitting functions journal, September 2001

QCD coherence in the structure function and associated distributions at small x ★ journal, July 1995

TMD splitting functions in $$k_T$$ k T factorization: the real contribution to the gluon-to-gluon splitting journal, March 2018

Exact kinematics in the small- x evolution of the color dipole and gluon cascade journal, April 2009

Energy conservation and saturation in small- x evolution journal, July 2005

Unified BFKL and Gribov-Lipatov-Altarelli-Parisi description of F 2 data journal, October 1997

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

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

Small- resummation and HERA structure function data journal, April 2001

Measurement of the proton structure function F2 in ep scattering at HERA journal, October 1993

Diffusion into infrared and unitarization of the Balitskiĭ-Fadin-Kuraev-Lipatov Pomeron journal, April 2002

BFKL next-to-next-to-leading order journal, October 2007

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The CCFM uPDF evolution uPDFevolv Version 1.0.00 journal, October 2014

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

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Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data journal, April 2018

Measurement of the proton structure function F2 (x, Q2) in the low-x region at HERA journal, October 1993

Resummation effects in the forward production of Z 0 + jet at the LHC journal, September 2015

Factorization Of Hard Processes In QCD book, July 1989

The CCFM Monte Carlo generator CASCADE Version 2.2.03 journal, November 2010

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

Renormalization group improved small- x Green’s function journal, December 2003

QCD coherence in initial state radiation journal, January 1990

DGLAP and BFKL equations in the N=4 supersymmetric gauge theory journal, June 2003

QCD coherence in high-energy reactions journal, April 1988

Asymptotic freedom in parton language journal, August 1977

Possible parametrization of parton distributions incorporating singular smallx behaviour implied by QCD and its phenomenological implications for HERA journal, June 1990

The linked dipole chain model for DIS journal, May 1996

Dijet production at hadron-hadron colliders in the Balitskii-Fadin-Kuraev-Lipatov approach journal, November 1997

Resummation of singlet parton evolution at small journal, May 2000

Global fit to scattering data with next-to-leading logarithmic BFKL resummations journal, February 2007

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

Extending QCD perturbation theory to higher energies journal, December 2003

A matrix formulation for small- x singlet evolution journal, August 2007

Collinearly improved JIMWLK evolution in Langevin form journal, August 2016

Renormalization group improved small- x equation journal, November 1999

Factorization and resummation of small x scaling violations with running coupling journal, January 2002

A collinear model for small- x physics journal, October 1999

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

Small x resummation with quarks: Deep-inelastic scattering
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Transverse momentum dependent splitting functions at work: Quark-to-gluon splitting
journal, December 2016

Screening effects in the ultra-high energy neutrino interactions
journal, August 2003

Energy consumption and jet multiplicity from the leading log BFKL evolution
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Coherence effects in initial jets at small Q2/s
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The gluon splitting function at moderately small x
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Running coupling Balitskiĭ-Fadin-Kuraev-Lipatov anomalous dimensions and splitting functions
journal, September 2001

QCD coherence in the structure function and associated distributions at small x ★
journal, July 1995

TMD splitting functions in $$k_T$$ k T factorization: the real contribution to the gluon-to-gluon splitting
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Exact kinematics in the small- $x$ evolution of the color dipole and gluon cascade
journal, April 2009

Energy conservation and saturation in small- x evolution
journal, July 2005

Unified BFKL and Gribov-Lipatov-Altarelli-Parisi description of $F_{2}$ data
journal, October 1997

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

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

Small- resummation and HERA structure function data
journal, April 2001

Measurement of the proton structure function F2 in ep scattering at HERA
journal, October 1993

Diffusion into infrared and unitarization of the Balitskiĭ-Fadin-Kuraev-Lipatov Pomeron
journal, April 2002

BFKL next-to-next-to-leading order
journal, October 2007

Small- x dynamics in forward–central dijet correlations at the LHC
journal, October 2014

An anomalous dimension for small x evolution
journal, December 2003

Small-x resummation from HELL
journal, November 2016

The CCFM uPDF evolution uPDFevolv Version 1.0.00
journal, October 2014

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

Transverse-momentum-dependent quark splitting functions in k T -factorization: real contributions
journal, January 2016

Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data
journal, April 2018

Measurement of the proton structure function F2 (x, Q2) in the low-x region at HERA
journal, October 1993

Resummation effects in the forward production of $Z_{0} + jet$ at the LHC
journal, September 2015

Factorization Of Hard Processes In QCD
book, July 1989

The CCFM Monte Carlo generator CASCADE Version 2.2.03
journal, November 2010

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

Renormalization group improved small- $x$ Green’s function
journal, December 2003

QCD coherence in initial state radiation
journal, January 1990

DGLAP and BFKL equations in the N=4 supersymmetric gauge theory
journal, June 2003

QCD coherence in high-energy reactions
journal, April 1988

Asymptotic freedom in parton language
journal, August 1977

Possible parametrization of parton distributions incorporating singular smallx behaviour implied by QCD and its phenomenological implications for HERA
journal, June 1990

The linked dipole chain model for DIS
journal, May 1996

Dijet production at hadron-hadron colliders in the Balitskii-Fadin-Kuraev-Lipatov approach
journal, November 1997

Resummation of singlet parton evolution at small
journal, May 2000

Global fit to scattering data with next-to-leading logarithmic BFKL resummations
journal, February 2007

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

Extending QCD perturbation theory to higher energies
journal, December 2003

A matrix formulation for small- x singlet evolution
journal, August 2007

Collinearly improved JIMWLK evolution in Langevin form
journal, August 2016

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

Factorization and resummation of small x scaling violations with running coupling
journal, January 2002

A collinear model for small- x physics
journal, October 1999