Small-x asymptotics of the gluon helicity distribution

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 similar to (1/x)(alpha hG) with alpha(G)(h) = 13/4 root 3 root alpha N-s(c)/2 pi approximate to 1:88 root alpha N-s(c)/2 pi. We note that the power alpha(G)(h) is approximately 20% lower than the corresponding power alpha(q)(h) for the small-x asymptotics of the quark helicity distribution defined by Delta q similar to (1/x)(alpha hq) with alpha(G)(h) = 4/root 3 root alpha N-s(c)/2 pi approximate to 2.31 root alpha N-s(c)/2 pi found in our earlier work.