Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\& N_f$
| Title: | Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\& N_f$ |
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| Authors: | Adamiak, Daniel, Kovchegov, Yuri V., Tawabutr, Yossathorn |
| Source: | Phys.Rev.D 108 (2023) 5, 054005 |
| Publication Year: | 2023 |
| Collection: | High Energy Physics - Phenomenology Nuclear Theory |
| Subject Terms: | High Energy Physics - Phenomenology, Nuclear Theory |
| More Details: | We present a numerical solution of the revised version of the small-$x$ helicity evolution equations at large $N_c$ and $N_f$. (Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) The evolution equations are double-logarithmic in the Bjorken $x$ variable, resumming powers of $\alpha_s \, \ln^2 (1/x)$ with $\alpha_s$ the strong coupling constant. The large-$N_c \& N_f$ evolution we consider includes contributions of small-$x$ quark emissions and is thus more realistic than the large-$N_c$ one, which only involves gluon emissons. The evolution equations are written for the so-called ``polarized dipole amplitudes", which are related to the helicity distribution functions and the $g_1$ structure function. Unlike the previously reported solution of the earlier version of helicity evolution equations at large $N_c \& N_f$, our solution does not exhibit periodic oscillations in $\ln (1/x)$ for $N_f < 2 N_c$, while only showing occasional sign reversals. For $N_f = 2 N_c$, we report oscillations with $\ln (1/x)$, similar to those found earlier. We determine the intercept of our evolution for $N_f < 2 N_c$ as well as the parameters of the oscillatory behavior for $N_f = 2 N_c$. We compare our results to the existing resummation and finite-order calculations for helicity-dependent quantities in the literature. Comment: 39 pages, 16 figures |
| Document Type: | Working Paper |
| DOI: | 10.1103/PhysRevD.108.054005 |
| Access URL: | http://arxiv.org/abs/2306.01651 |
| Accession Number: | edsarx.2306.01651 |
| Database: | arXiv |
| DOI: | 10.1103/PhysRevD.108.054005 |
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