Helicity Evolution at Small x: the Single-Logarithmic Contribution

We calculate single-logarithmic corrections to the small-x flavor singlet helicity evolution equations derived recently in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of α_s ln(1/x), which are an important correction to the dominant powers of α_s ln²(1/x) summed up by the double-logarithmic kernel derived previously at small values of Bjorken x and with α_s the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive simultaneously include the small-x evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.