# Polarized Parton Distributions at Small x

Because parton distribution functions (PDFs) are measured at finite center-of-mass energies, they must always be extrapolated to high-energy asymptotics where x goes to zero. This extrapolation is especially important for the determination of sum rules, such as the contribution to the proton spin, which require integrating the PDF over the full range of x from zero to one. In determining the high-energy / small-x asymptotics of the PDFs, it is useful and necessary to have input from theory to aid and interpret the phenomenological extraction of the PDFs. In this talk, I will discuss and derive the small-x evolution equations in QCD which govern the small-x asymptotics of the quark and gluon PDFs. Starting from the most familiar Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution equations for the unpolarized quark and gluon PDFs, I will introduce the tools and techniques before proceeding to the polarized quark and gluon helicity PDFs. Unlike the unpolarized BFKL equation, the evolution equations for polarized radiation are double-logarithmic; this stronger small-x evolution raises the possibility that the polarized PDFs may be significantly enhanced in the small-x regime. In solving the evolution equations, I will show that there is indeed a significant enhancement in the quark and gluon helicity PDFs, which may constitute an important missing contribution to the proton spin puzzle.