T-odd Leading-Twist Quark TMDs at Small $x$: Sub-Eikonal Evolution of the Sivers Function

28 Mar 2023, 17:30
20m
Centennial Room ABC (MSU Kellogg Center)

Centennial Room ABC

MSU Kellogg Center

Parallel talk WG2: Small-x, Diffraction and Vector Mesons WG2

Speaker

M Gabriel Santiago (Center for Nuclear Femtography)

Description

We study the small-$x$ asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs). 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 expression for the TMD at small Bjorken $x$ and then construct small-$x$ evolution equations for the resulting operators in the large-$N_c$ limit, with $N_c$ the number of quark colors. The evolution equations resum all powers of the double-logarithmic parameter $\alpha_s \, \ln^2 (1/x)$, where $\alpha_s$ is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically, we arrive at the following leading small-$x$ asymptotics at large $N_c$:
\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
\end{align}
The functions $C_O (x, k_T^2)$ and $C_1 (x, k_T^2)$ 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 $C_O$, along with the $1/x$ factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with $C_1$), our result shown above supersedes the one obtained in our previous work due to the new contributions identified recently.

Submitted on behalf of a Collaboration? No
Participate in poster competition? No

Primary authors

M Gabriel Santiago (Center for Nuclear Femtography) Prof. Yuri Kovchegov

Presentation materials