Helicity evolution at small x: the single-logarithmic contribution

A bstract We calculate single-logarithmic corrections to the small- x flavor-singlet helicity evolution equations derived recently 1–3 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 ln 2 (1 /x ) summed up by the double-logarithmic kernel from 1–3 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 employing the light-cone perturbation theory 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.