Sin(ϕΛ−ϕS) azimuthal asymmetry in transversely polarized Λ production in SIDIS within TMD factorization at the EIC

Abstract

We investigate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ single-spin asymmetry in the transversely polarized $\mathrm{\ensuremath{\Lambda}}$ production in semi-inclusive deeply inelastic scattering process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function ${D}_{1T}^{\ensuremath{\perp}}$ of the $\mathrm{\ensuremath{\Lambda}}$ hyperon and the unpolarized TMD distribution function ${f}_{1}$ of the proton target. We adopt the spectator diquark model result and the available parametrization for ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ to numerically estimate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry at the kinematical region of the electron ion collider (EIC). To implement the TMD evolution formalism, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the distribution function of the proton and the fragmentation function of the $\mathrm{\ensuremath{\Lambda}}$. It is found that the two sets of ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ lead to different $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry, particularly in sign. We also discuss the impact of the assumptions and approximations applied in the calculations, which may bring large uncertainties to the results in the EIC. Future measurements on the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry with high precision at the EIC can provide important cross checks on the available $\mathrm{\ensuremath{\Lambda}}$ polarizing fragmentation functions, as well as constrain them more stringently.