$\sin (\phi_\Lambda-\phi_S)$ azimuthal asymmetry in transversely polarized $\Lambda$ production in SIDIS within TMD factorization at EIC

TL;DR

This paper studies the azimuthal asymmetry in transversely polarized Lambda hyperon production in SIDIS within TMD factorization, emphasizing the role of TMD fragmentation functions and their evolution at EIC.

Contribution

It provides a numerical estimate of the $ ext{sin}(_\Lambda-_S)$ asymmetry using different models for the polarizing fragmentation function, including TMD evolution effects.

Findings

Different models predict varying signs for the asymmetry.

TMD evolution significantly affects the scale dependence of the asymmetry.

Future EIC measurements can test and refine the polarizing fragmentation functions.

Abstract

We investigate the $\sin (\phi_\Lambda-\phi_S)$ single-spin asymmetry in the transversely polarized $\Lambda$ production in semi-inclusive deeply inelastic scattering process within the framework of the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function $D_{1T}^\perp$ of the $\Lambda$ hyperon and the unpolarized TMD distribution function $f_1$ of the target nucleon. We apply two sets of $D_{1T}^{\perp,\Lambda^\uparrow/q}$, the spectator diquark model result and available parametrization, to numerically estimate the $\sin (\phi_\Lambda-\phi_S)$ asymmetry at the kinematical region of electron ion collider (EIC). We take into account the TMD evolution effect in order to include the scale dependence of the TMD distribution functions and fragmentation functions. It is found that different sets of $D_{1T}^{\perp,\Lambda^\uparrow/q}$ lead to different ${\sin (\phi_\Lambda-\phi_S)}$ asymmetry, particularly in sign. Future measurements on the $\sin (\phi_\Lambda-\phi_S)$ asymmetry with high precision at EIC can provide important cross check on the available $\Lambda$ polarizing fragmentation functions as well as constrain them more stringently.