Yuri V. Kovchegov🇺🇸 · M. Gabriel Santiago🇺🇸
We study the small-x asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small-x asymptotics of the quark Sivers function is given by the spin-dependent odderon, we are interested in revisiting the sub-eikonal correction considered by us earlier. We first simplify the expressions for both TMDs at small Bjorken x and then construct small-x evolution equations for the resulting operators in the large-Nc limit, with Nc the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter αsln2(1/x), where αs is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small-x asymptotics of these TMDs at large Nc: \begin{align} f_{1 \: T}^{\perp \: NS} (x \ll 1 ,k_T^2) & = C_O (x, k_T^2) \, \frac{1}{x} + C_1 (x, k_T^2) \, \left( \frac{1}{x} \right)^{3.4 \, \sqrt{\frac{\alpha_s \, N_c}{4 \pi}}} , \notag \\ h_1^{\perp \, \textrm{NS}} (x \ll 1, k_T^2) & = C (x, k_T^2) \left( \frac{1}{x} \right)^{-1}. \notag \end{align} The functions CO(x,kT2), C1(x,kT2), and C(x,kT2) can be readily obtained in our formalism: they are mildly x-dependent and do not strongly affect the power-of-x asymptotics shown above. The function CO, along with the 1/x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C1), our result shown above supersedes the one obtained in our previous work due to the new contributions identified recently.
↳ hep-phhep-exnucl-exnucl-thJHEP(2022)·42 citations