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 [1-3] in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of alpha(s) ln( )(1/x), which are an important correction to the dominant powers of alpha(s) ln(2) (1/x) summed up by the double-logarithmic kernel from [1-3] at small values of Bjorken x and with alpha(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.

Automated summary

We calculate single-logarithmic corrections to the small-x flavor-singlet helicity evolution equations derived recently in the double-logarithmic approximation. These corrections are important in correcting the dominant powers of alpha(s) ln(2) (1/x) summed up by the double-logarithmic kernel from [1-3] at small Bjorken x values and with strong coupling constant alpha(s).