Helicity evolution at small x : Revised asymptotic results at large Nc and Nf

Abstract

We present a numerical solution of the revised version [J. High Energy Phys. 07 (2022) 095] of the small-x helicity evolution equations from [J. High Energy Phys. 01 (2016) 072, Phys. Rev. D 99, 054032 (2019)] at large Nc and Nf. (Here Nc and Nf are the numbers of quark colors and flavors, respectively.) The evolution equations are double-logarithmic in the Bjorken x variable, resumming powers of αsln2(1/x) with αs the strong coupling constant. The large-Nc&Nf evolution we consider includes contributions of small-x quark emissions and is thus more realistic than the large-Nc one, which only involves gluon emissons. The evolution equations [J. High Energy Phys. 07 (2022) 095, J. High Energy Phys. 01 (2016) 072, Phys. Rev. D 99, 054032 (2019)] are written for the so-called “polarized dipole amplitudes,” which are related to the helicity distribution functions and the g1 structure function. Unlike the previously reported solution [J. High Energy Phys. 08 (2020) 014] of the earlier version of helicity evolution equations at large Nc&Nf [J. High Energy Phys. 01 (2016) 072, Phys. Rev. D 99, 054032 (2019)], our solution does not exhibit periodic oscillations in ln(1/x) for Nf<2Nc, while only showing occasional sign reversals. For Nf=2Nc, we report oscillations with ln(1/x), similar to those found earlier in [J. High Energy Phys. 08 (2020) 014]. We determine the intercept of our evolution for Nf<2Nc as well as the parameters of the oscillatory behavior for Nf=2Nc. We compare our results to the existing resummation [Z. Phys. C 72, 627 (1996)] and finite-order calculations for helicity-dependent quantities in the literature.