Transverse single-spin asymmetry in the low-virtuality leptoproduction of open charm as a probe of the gluon Sivers function

We study the low-virtuality inclusive leptoproduction of open charm, p^↑l →D⁰+X as a probe of the gluon Sivers function. We perform the analysis in a generalized parton model framework. At leading order, this process is sensitive only to the gluon content of the proton. Hence any detection of a transverse single-spin asymmetry in this process would be clear indication of a non-zero gluon Sivers function (GSF). Considering COMPASS and a future Electron-Ion Collider (EIC), we present predictions for asymmetry using fits for the GSF available in literature. Predictions for peak asymmetry values lie in the range of 0.8% to 13%. We also present estimates of the upper bound on the asymmetry as obtained with a maximal gluon Sivers function. Further, for the case of the Electron-Ion Collider, we evaluate the asymmetry in the muons decaying from the D -meson and find that the asymmetry is well preserved in the kinematics of the muons. Peak values of the muon asymmetry are close to those obtained for the D -meson and lie in the range 0.75% to 11%.