Small-$x$ Asymptotics of the Gluon Helicity Distribution

Abstract

We determine the small-$x$ asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large $N_c$. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small $x$. In the process we obtain an interesting new result: in contrast to the unpolarized dipole gluon TMD case, the operator governing the small-$x$ behavior of the dipole gluon helicity TMD is different from the operator corresponding to the polarized dipole scattering amplitude (used in our previous work to determine the small-$x$ asymptotics of the quark helicity distribution). We then construct and solve novel small-$x$ large-$N_c$ evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-$x$ asymptotics for the gluon helicity distribution: $\Delta G\sim {\left(\frac{1}{x}\right)}^{{\alpha }_h^G}$ with ${\alpha }_h^G=\frac{13}{4\sqrt{3}}\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}\approx 1.88\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}$. We note that the power ${\alpha }_h^G$ is approximately 20$\%$ lower than the corresponding power ${\alpha }_h^q$ for the small-$x$ asymptotics of the quark helicity distribution defined by $\Delta q\sim {\left(\frac{1}{x}\right)}^{{\alpha }_h^q}$ with ${\alpha }_h^q=\frac{4}{\sqrt{3}}\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}\approx 2.31\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}$ found in our earlier work.

36 pages, 9 figures; v3: minus signs and factors of 2 corrected, main results remained the same

References in corpus (11)

• A first unbiased global determination of polarized PDFs and their uncertainties
• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• Evidence for polarization of gluons in the proton
• First simultaneous extraction of spin-dependent parton distributions and fragmentation functions from a global QCD analysis
• Resumming double logarithms in the QCD evolution of color dipoles
• The Construction of Gauge-Links in Arbitrary Hard Processes
• Running coupling and power corrections in nonlinear evolution at the high--energy limit
• Small-$x$ asymptotics of the quark helicity distribution
• Small-$x$ Asymptotics of the Quark Helicity Distribution: Analytic Results
• pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order

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