Analytic solution for the revised helicity evolution at small and large : New resummed gluon-gluon polarized anomalous dimension and intercept
Abstract
We construct an exact analytic solution of the revised small-x helicity evolution equations derived by Cougoulic et al. [J. High Energy Phys. 07 (2022) 095], based on the earlier work of Kovchegov et al. [J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 99, 054032 (2019)]. The equations we solve are obtained in the large-Nc limit (with Nc the number of quark colors) and are double logarithmic [summing powers of αsln2(1/x) with αs the strong coupling constant and x the Bjorken x variable]. Our solution provides small-x, large-Nc expressions for the flavor-singlet quark and gluon helicity parton distribution functions and for the g1 structure function, with their leading small-x asymptotics given by ΔΣ(x,Q2) ~ ΔG(x,Q2) ~ g1(x,Q2) ~ ($$^{1}_{x}$$)αh, where the exact analytic expression we obtain for the intercept αh can be approximated by αh = 3.66074√$$\frac{αsNc}{2π}$$. Our solution also yields an all-order (in αs) resummed small-x anomalous dimension ΔγGG(ω) which agrees with all the existing fixed-order calculations (to three loops). Notably, our anomalous dimension is different from that obtained in the infrared evolution equation framework developed earlier by Bartels et al. (BER) [Z. Phys. C 72, 627 (1996)] with the disagreement starting at four loops. Despite the previously reported agreement at two decimal points based on the numerical solution of the same equations, the intercept of our large-Nc helicity evolution and that of BER disagree beyond that precision, with the BER intercept at large Nc given by a different analytic expression from ours with the numerical value of α$$^{BER}_{h}$$ = 3.66394√$$\frac{αsNc}{2π}$$. We speculate on the origin of this disagreement.
- Publication Date:
- Research Org.:
- The Ohio State University, Columbus, OH (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1988311
- Alternate Identifier(s):
- OSTI ID: 1988737; OSTI ID: 2322571
- Grant/Contract Number:
- SC0004286
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 108 Journal Issue: 1; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Perturbative QCD; Gluons; Spin; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Borden, Jeremy, and Kovchegov, Yuri V. Analytic solution for the revised helicity evolution at small x and large N c : New resummed gluon-gluon polarized anomalous dimension and intercept. United States: N. p., 2023.
Web. doi:10.1103/PhysRevD.108.014001.
Borden, Jeremy, & Kovchegov, Yuri V. Analytic solution for the revised helicity evolution at small x and large N c : New resummed gluon-gluon polarized anomalous dimension and intercept. United States. https://doi.org/10.1103/PhysRevD.108.014001
Borden, Jeremy, and Kovchegov, Yuri V. Thu .
"Analytic solution for the revised helicity evolution at small x and large N c : New resummed gluon-gluon polarized anomalous dimension and intercept". United States. https://doi.org/10.1103/PhysRevD.108.014001.
@article{osti_1988311,
title = {Analytic solution for the revised helicity evolution at small x and large N c : New resummed gluon-gluon polarized anomalous dimension and intercept},
author = {Borden, Jeremy and Kovchegov, Yuri V.},
abstractNote = {We construct an exact analytic solution of the revised small-x helicity evolution equations derived by Cougoulic et al. [J. High Energy Phys. 07 (2022) 095], based on the earlier work of Kovchegov et al. [J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 99, 054032 (2019)]. The equations we solve are obtained in the large-Nc limit (with Nc the number of quark colors) and are double logarithmic [summing powers of αsln2(1/x) with αs the strong coupling constant and x the Bjorken x variable]. Our solution provides small-x, large-Nc expressions for the flavor-singlet quark and gluon helicity parton distribution functions and for the g1 structure function, with their leading small-x asymptotics given by ΔΣ(x,Q2) ~ ΔG(x,Q2) ~ g1(x,Q2) ~ ($^{1}_{x}$)αh, where the exact analytic expression we obtain for the intercept αh can be approximated by αh = 3.66074√$\frac{αsNc}{2π}$. Our solution also yields an all-order (in αs) resummed small-x anomalous dimension ΔγGG(ω) which agrees with all the existing fixed-order calculations (to three loops). Notably, our anomalous dimension is different from that obtained in the infrared evolution equation framework developed earlier by Bartels et al. (BER) [Z. Phys. C 72, 627 (1996)] with the disagreement starting at four loops. Despite the previously reported agreement at two decimal points based on the numerical solution of the same equations, the intercept of our large-Nc helicity evolution and that of BER disagree beyond that precision, with the BER intercept at large Nc given by a different analytic expression from ours with the numerical value of α$^{BER}_{h}$ = 3.66394√$\frac{αsNc}{2π}$. We speculate on the origin of this disagreement.},
doi = {10.1103/PhysRevD.108.014001},
journal = {Physical Review. D.},
number = 1,
volume = 108,
place = {United States},
year = {Thu Jul 06 00:00:00 EDT 2023},
month = {Thu Jul 06 00:00:00 EDT 2023}
}
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Works referenced in this record:
Saturation physics and deuteron–gold collisions at RHIC
journal, January 2006
- Jalilianmarian, J.; Kovchegov, Y.
- Progress in Particle and Nuclear Physics, Vol. 56, Issue 1
The three-loop splitting functions in QCD: The helicity-dependent case
journal, December 2014
- Moch, S.; Vermaseren, J. A. M.; Vogt, A.
- Nuclear Physics B, Vol. 889
Flavor singlet contribution to the structure functiong 1 at small-x
journal, December 1996
- Bartels, J.; Ermolaev, B. I.; Ryskin, M. G.
- Zeitschrift für Physik C: Particles and Fields, Vol. 72, Issue 4
Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange
journal, March 1983
- Kirschner, R.; Lipatov, L. N.
- Nuclear Physics B, Vol. 213, Issue 1
Small- Asymptotics of the Quark Helicity Distribution
journal, January 2017
- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Physical Review Letters, Vol. 118, Issue 5
Science Requirements and Detector Concepts for the Electron-Ion Collider
journal, October 2022
- Abdul Khalek, R.; Accardi, A.; Adam, J.
- Nuclear Physics A, Vol. 1026
Studying the perturbative Reggeon
journal, January 2000
- Griffiths, S.; Ross, D. A.
- The European Physical Journal C, Vol. 12, Issue 2
Running coupling effects for the singlet structure function g1 at small x
journal, January 2004
- Ermolaev, B. I.; Greco, M.; Troyan, S. I.
- Physics Letters B, Vol. 579, Issue 3-4
Small-x asymptotics of the gluon helicity distribution
journal, October 2017
- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Journal of High Energy Physics, Vol. 2017, Issue 10
The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
journal, January 2022
- Blümlein, J.; Marquard, P.; Schneider, C.
- Journal of High Energy Physics, Vol. 2022, Issue 1
The Color Glass Condensate
journal, November 2010
- Gelis, Francois; Iancu, Edmond; Jalilian-Marian, Jamal
- Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1
Gluon saturation and initial conditions for relativistic heavy ion collisions
journal, May 2014
- Albacete, J. L.; Marquet, C.
- Progress in Particle and Nuclear Physics, Vol. 76
QCD running coupling effects for the non-singlet structure function at small x
journal, April 2000
- Ermolaev, B. I.; Greco, M.; Troyan, S. I.
- Nuclear Physics B, Vol. 571, Issue 1-2
Evolution at small : The color glass condensate
journal, October 2005
- Weigert, H.
- Progress in Particle and Nuclear Physics, Vol. 55, Issue 2
High-energy operator product expansion at sub-eikonal level
journal, June 2021
- Chirilli, Giovanni Antonio
- Journal of High Energy Physics, Vol. 2021, Issue 6
Operator expansion for high-energy scattering
journal, March 1996
- Balitsky, I.
- Nuclear Physics B, Vol. 463, Issue 1
First analysis of world polarized DIS data with small- helicity evolution
journal, August 2021
- Adamiak, Daniel; Kovchegov, Yuri V.; Melnitchouk, W.
- Physical Review D, Vol. 104, Issue 3
Wilson renormalization group for low x physics: Towards the high density regime
journal, November 1998
- Jalilian-Marian, Jamal; Kovner, Alex; Leonidov, Andrei
- Physical Review D, Vol. 59, Issue 1
Quark and scalar propagators at next-to-eikonal accuracy in the CGC through a dynamical background gluon field
journal, April 2022
- Altinoluk, Tolga; Beuf, Guillaume
- Physical Review D, Vol. 105, Issue 7
On the behaviour of non-singlet structure functions at small x
journal, March 1996
- Blümlein, J.; Vogt, A.
- Physics Letters B, Vol. 370, Issue 1-2
Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
journal, November 2021
- Kovchegov, Yuri V.; Santiago, M. Gabriel
- Journal of High Energy Physics, Vol. 2021, Issue 11
The third-order QCD corrections to deep-inelastic scattering by photon exchange
journal, September 2005
- Vermaseren, J. A. M.; Vogt, A.; Moch, S.
- Nuclear Physics B, Vol. 724, Issue 1-2
Gauge-Invariant Decomposition of Nucleon Spin
journal, January 1997
- Ji, Xiangdong
- Physical Review Letters, Vol. 78, Issue 4
Rapidity loss, spin, and angular asymmetries in the scattering of a quark from the color field of a proton or nucleus
journal, July 2020
- Jalilian-Marian, Jamal
- Physical Review D, Vol. 102, Issue 1
Quark jets scattering from a gluon field: From saturation to high
journal, January 2019
- Jalilian-Marian, Jamal
- Physical Review D, Vol. 99, Issue 1
The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990
- Jaffe, R. L.; Manohar, Aneesh
- Nuclear Physics B, Vol. 337, Issue 3
Helicity evolution at small x: the single-logarithmic contribution
journal, March 2022
- Kovchegov, Yuri V.; Tarasov, Andrey; Tawabutr, Yossathorn
- Journal of High Energy Physics, Vol. 2022, Issue 3
Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
journal, August 2022
- Davies, J.; Kom, C. -H.; Moch, S.
- Journal of High Energy Physics, Vol. 2022, Issue 8
The massless three-loop Wilson coefficients for the deep-inelastic structure functions F2, FL, xF3 and g1
journal, November 2022
- Blümlein, J.; Marquard, P.; Schneider, C.
- Journal of High Energy Physics, Vol. 2022, Issue 11
Helicity evolution at small : Flavor singlet and nonsinglet observables
journal, January 2017
- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Physical Review D, Vol. 95, Issue 1
Unitarity and the BFKL pomeron
journal, March 1995
- Mueller, A. H.
- Nuclear Physics B, Vol. 437, Issue 1
Deep-inelastic structure functions at two loops
journal, May 2000
- Moch, S.; Vermaseren, J. A. M.
- Nuclear Physics B, Vol. 573, Issue 3
Sub-eikonal corrections to scattering amplitudes at high energy
journal, January 2019
- Chirilli, Giovanni Antonio
- Journal of High Energy Physics, Vol. 2019, Issue 1
Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
journal, July 2014
- Altinoluk, Tolga; Armesto, Néstor; Beuf, Guillaume
- Journal of High Energy Physics, Vol. 2014, Issue 7
The calculation of the two-loop spin splitting functions P (1) ij ( x )
journal, May 1996
- Mertig, R.; van Neerven, W. L.
- Zeitschrift f�r Physik C Particles and Fields, Vol. 70, Issue 4
Gluon TMD in particle production from low to moderate x
journal, June 2016
- Balitsky, I.; Tarasov, A.
- Journal of High Energy Physics, Vol. 2016, Issue 6
Gluon orbital angular momentum at small
journal, June 2017
- Hatta, Yoshitaka; Nakagawa, Yuya; Xiao, Bowen
- Physical Review D, Vol. 95, Issue 11
Orbital angular momentum at small x
journal, March 2019
- Kovchegov, Yuri V.
- Journal of High Energy Physics, Vol. 2019, Issue 3
Quantum Chromodynamics at High Energy
book, September 2012
- Kovchegov, Yuri V.; Levin, Eugene
- Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology
NNLO evolution of deep-inelastic structure functions: the singlet case
journal, November 2000
- van Neerven, W. L.; Vogt, A.
- Nuclear Physics B, Vol. 588, Issue 1-2
The singlet contribution to the structure function g1(x,Q2) at small x
journal, October 1996
- Blümlein, J.; Vogt, A.
- Physics Letters B, Vol. 386, Issue 1-4
Helicity-dependent generalization of the JIMWLK evolution
journal, December 2019
- Cougoulic, Florian; Kovchegov, Yuri V.
- Physical Review D, Vol. 100, Issue 11
Unitarity at small Bjorken x
journal, June 2002
- Weigert, Heribert
- Nuclear Physics A, Vol. 703, Issue 3-4
The renormalization group equation for the color glass condensate
journal, June 2001
- Iancu, Edmond; Leonidov, Andrei; McLerran, Larry
- Physics Letters B, Vol. 510, Issue 1-4
Mining for Gluon Saturation at Colliders
journal, August 2021
- Morreale, Astrid; Salazar, Farid
- Universe, Vol. 7, Issue 8
Quark and gluon helicity evolution at small x: revised and updated
journal, July 2022
- Cougoulic, Florian; Kovchegov, Yuri V.; Tarasov, Andrey
- Journal of High Energy Physics, Vol. 2022, Issue 7
Overview of the spin structure function g1 at arbitrary x and Q2
journal, April 2010
- Ermolaev, B. I.; Greco, M.; Troyan, S. I.
Proton spin structure at small-x
journal, October 2019
- Boussarie, Renaud; Hatta, Yoshitaka; Yuan, Feng
- Physics Letters B, Vol. 797
Small- x asymptotics of the quark helicity distribution: Analytic results
journal, September 2017
- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Physics Letters B, Vol. 772
Quarks at next-to-eikonal accuracy in the CGC: Forward quark-nucleus scattering
journal, July 2021
- Altinoluk, Tolga; Beuf, Guillaume; Czajka, Alina
- Physical Review D, Vol. 104, Issue 1
The spin structure of the nucleon
journal, April 2013
- Aidala, Christine A.; Bass, Steven D.; Hasch, Delia
- Reviews of Modern Physics, Vol. 85, Issue 2
What we know and what we don’t know about the proton spin after 30 years
journal, November 2020
- Ji, Xiangdong; Yuan, Feng; Zhao, Yong
- Nature Reviews Physics, Vol. 3, Issue 1
Reggeon interactions in perturbative QCD
journal, September 1995
- Kirschner, R.
- Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 3
Regge asymptotics of scattering with flavour exchange in QCD
journal, September 1995
- Kirschner, R.
- Zeitschrift für Physik C Particles and Fields, Vol. 67, Issue 3
Helicity at small x: oscillations generated by bringing back the quarks
journal, August 2020
- Kovchegov, Yuri V.; Tawabutr, Yossathorn
- Journal of High Energy Physics, Vol. 2020, Issue 8
Double logarithmic asymptotics of quantum electrodynamics
journal, September 1966
- Frolov, G. V.; Gorshkov, V. G.; Gribov, V. N.
- Physics Letters, Vol. 22, Issue 5
Unitarization of the BFKL Pomeron on a nucleus
journal, March 2000
- Kovchegov, Yuri V.
- Physical Review D, Vol. 61, Issue 7
DIS dijet production at next-to-eikonal accuracy in the CGC
journal, April 2023
- Altinoluk, Tolga; Beuf, Guillaume; Czajka, Alina
- Physical Review D, Vol. 107, Issue 7
Asymptotic freedom in parton language
journal, August 1977
- Altarelli, G.; Parisi, G.
- Nuclear Physics B, Vol. 126, Issue 2
The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014
- Leader, Elliot; Lorcé, Cédric
- Physics Reports, Vol. 541, Issue 3
Wilson renormalization group for low x physics: Gluon evolution at finite parton density
journal, November 1998
- Jalilian-Marian, Jamal; Kovner, Alex; Weigert, Heribert
- Physical Review D, Vol. 59, Issue 1
Helicity-dependent extension of the McLerran–Venugopalan model
journal, December 2020
- Cougoulic, Florian; Kovchegov, Yuri V.
- Nuclear Physics A, Vol. 1004
Soft gluons in the infinite-momentum wave function and the BFKL pomeron
journal, March 1994
- Mueller, A. H.
- Nuclear Physics B, Vol. 415, Issue 2
Intercepts of the non-singlet structure functions
journal, January 2001
- Ermolaev, B. I.; Greco, M.; Troyan, S. I.
- Nuclear Physics B, Vol. 594, Issue 1-2
Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes
journal, August 1994
- Mueller, A. H.; Patel, Bimal
- Nuclear Physics B, Vol. 425, Issue 3
Small- helicity evolution: An operator treatment
journal, March 2019
- Kovchegov, Yuri V.; Sievert, Matthew D.
- Physical Review D, Vol. 99, Issue 5
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016
- Accardi, A.; Albacete, J. L.; Anselmino, M.
- The European Physical Journal A, Vol. 52, Issue 9
Rapidity evolution of gluon TMD from low to moderate x
journal, October 2015
- Balitsky, I.; Tarasov, A.
- Journal of High Energy Physics, Vol. 2015, Issue 10
T-odd leading-twist quark TMDs at small x
journal, November 2022
- Kovchegov, Yuri V.; Santiago, M. Gabriel
- Journal of High Energy Physics, Vol. 2022, Issue 11
The N3LO scheme-invariant QCD evolution of the non-singlet structure functions F 2 NS ( x , Q 2 ) g 1 NS ( x , Q 2 )
journal, September 2021
- Blümlein, J.; Saragnese, M.
- Physics Letters B, Vol. 820
Order-αs2 corrections to the polarized structure function g1 (x, Q2)
journal, April 1994
- Zijlstra, E. B.; van Neerven, W. L.
- Nuclear Physics B, Vol. 417, Issue 1-2
Helicity evolution at small x
journal, January 2016
- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Journal of High Energy Physics, Vol. 2016, Issue 1
Factorization and high-energy effective action
journal, June 1999
- Balitsky, Ian
- Physical Review D, Vol. 60, Issue 1