NT/RBRC hybrid seminar

Abstract: A complete understanding of parton helicity inside the proton requires the knowledge about its contribution at small Bjorken-x, which is difficult to deduce from experiments. We attempt to fill the gap by deriving a small-x helicity evolution, resumming powers of αsln2(1/x), with αs the strong coupling constant. Recently, a revised version of this evolution has been constructed, taking into account the observation that the evolution of the sub-eikonal operator, D←iDi, mixes with other helicity-dependent operators from the previous works, which are the gluon field strength, F12, and the quark axial current, ψ¯γ+γ5ψ. Based on the new evolution, a closed system of evolution equations can be constructed in the limits of large Nc or large Nc&Nf. (Here, Nc and Nf are the number of quark colors and flavors, respectively.) We numerically solve the equations in these limits and obtain the following small-x asymptotics for the g1 structure function at Nf≤5: g1(x,Q2)∼(1/x)αhαsNc/2π√, with the intercept, αh, decreasing with Nf. In particular, at the large-Nc limit, we have αh=3.66, which agrees with the earlier work by Bartels, Ermolaev and Ryskin. Once the sixth quark flavor is turned on, i.e. Nf=6, an oscillatory pattern in ln1x emerges. However, the oscillation period spans many units of rapidity, making it difficult to observe in an experiment.