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Quark and Gluon Helicity at Small x

Yuri V. Kovchegov

Department of Physics, The Ohio State University, Columbus, OH 43210, USA

https://doi.org/10.1142/9789811214950_0036Cited by:0 (Source: Crossref)

Abstract:

We determine the small-x asymptotics of the quark and gluon helicity distributions in a proton at leading order in perturbative QCD at large N_c. To achieve this, we first evaluate the quark and gluon helicity TMDs at small x, simplifying them and relating them to the so-called polarized dipole amplitudes. We then construct and solve novel small-x large-N_c evolution equations for the polarized dipole amplitudes. Our main results are the small-x asymptotics for the quark helicity distribution

Δ q \sim {(\frac{1}{x})}^{α_{h}^{q}} with α_{h}^{q} = \frac{4}{\sqrt{3}} \sqrt{\frac{α_{s} N_{c}}{2 π}} \approx 2.31 \sqrt{\frac{α_{s} N_{c}}{2 π}} (1)

$Δ q \sim {(\frac{1}{x})}^{α_{h}^{q}} with α_{h}^{q} = \frac{4}{\sqrt{3}} \sqrt{\frac{α_{s} N_{c}}{2 π}} \approx 2.31 \sqrt{\frac{α_{s} N_{c}}{2 π}} (1)$

and the small-x asymptotics of the gluon helicity distribution

Δ G \sim {(\frac{1}{x})}^{α_{h}^{G}} with α_{h}^{G} = \frac{13}{4 \sqrt{3}} \sqrt{\frac{α_{s} N_{c}}{2 π}} \approx 1.88 \sqrt{\frac{α_{s} N_{c}}{2 π}}, (2)

$Δ G \sim {(\frac{1}{x})}^{α_{h}^{G}} with α_{h}^{G} = \frac{13}{4 \sqrt{3}} \sqrt{\frac{α_{s} N_{c}}{2 π}} \approx 1.88 \sqrt{\frac{α_{s} N_{c}}{2 π}}, (2)$

both in the large-N_c limit.

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Quark and Gluon Helicity at Small x

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