Helicity evolution at small x: the single-logarithmic contribution

Abstract

Abstract 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 ln2(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.

Keywords

• Perturbative QCD
• Resummation