Analytic solution for the revised helicity evolution at small $x$ and large $N_c$ : New resummed gluon-gluon polarized anomalous dimension and intercept

Journal Article · Thu Jul 06 00:00:00 EDT 2023 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.108.014001· OSTI ID:1988311

Borden, Jeremy ; Kovchegov, Yuri V.

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-N_c limit (with N_c the number of quark colors) and are double logarithmic [summing powers of α_sln²(1/x) with α_s the strong coupling constant and x the Bjorken x variable]. Our solution provides small-x, large-N_c 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 α_h can be approximated by α_h = 3.66074√$$\frac{αsNc}{2π}$$. Our solution also yields an all-order (in α_s) 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-N_c helicity evolution and that of BER disagree beyond that precision, with the BER intercept at large N_c 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.

• Research Organization: The Ohio State University, Columbus, OH (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: SC0004286
• OSTI ID: 1988311
• Alternate ID(s): OSTI ID: 1988737; OSTI ID: 2322571
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Vol. 108 Journal Issue: 1; ISSN 2470-0010
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English

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