Abstract
We construct a numerical solution of the recently-derived large-Nc&Nf small-x helicity evolution equations [1] with the aim to establish the small-x asymptotics of the quark helicity distribution beyond the large-Nc limit explored previously in the same framework. (Here Nc and Nf are the numbers of quark colors and flavors.) While the large-Nc helicity evolution involves gluons only, the large-Nc&Nf evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of x. Our numerical results in the large-Nc&Nf limit lead to the x-dependence of the flavor-singlet quark helicity distribution which is well-approximated by
The power \( {\alpha}_h^q \) exhibits a weak Nf-dependence, and, for all Nf values considered, remains very close to \( {\alpha}_h^q\left({N}_f=0\right)=\left(4/\sqrt{3}\right)\sqrt{\alpha_s{N}_c/\left(2\pi \right)} \) obtained earlier in the large-Nc limit [2, 3]. The novel oscillation frequency ωq and phase shift φq depend more strongly on the number of flavors Nf (with ωq = 0 in the pure-glue large-Nc limit). The typical period of oscillations for ∆Σ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with x seen in the strange quark helicity distribution extracted from the data [4,5,6,7].
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Kovchegov, Y.V., Tawabutr, Y. Helicity at small x: oscillations generated by bringing back the quarks. J. High Energ. Phys. 2020, 14 (2020). https://doi.org/10.1007/JHEP08(2020)014
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DOI: https://doi.org/10.1007/JHEP08(2020)014