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.
- Authors:
- 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}
}
https://doi.org/10.1103/PhysRevD.108.014001
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