Nuclear Theory Seminar

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g_1 structure function. These evolution equations resum powers of alpha_s ln^2 (1/x) in the polarization-dependent evolution along with the powers of alpha_s ln (1/x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N_c and large-N_c & N_f limits. After solving the large-N_c equations numerically we obtain the following small-x asymptotics for the flavor-singlet
g_1 structure function along with quarks helicity PDFs and TMDs (in absence of saturation effects):
g_1^S (x, Q^2) ~ \Delta q^S (x, Q^2) ~ g_{1L}^S (x, k_T^2) ~ ( 1/x )^{alpha_h} \approx t( 1/x )^{2.31 \sqrt{\alpha_s N_c/(2pi}}

This result is valid for all flavors. We also give an estimate of how much of the proton's spin may reside at small x and what impact this has on the so-called ``spin crisis.'' This work would help one better understand longitudinal polarization data to be obtained at the proposed Electron-Ion Collider (EIC).