On the polarization of the non-prompt contribution to inclusive J/$ψ$ production in pp collisions

Abstract: Of the J/$\psi$ mesons (inclusively) produced in pp collisions, a big fraction results from B decays, increasing with transverse momentum and exceeding 50\% for $p_{\rm T} > 20$ GeV. These events must be subtracted in measurements of the polarization of prompt J/$\psi$ mesons. While several studies have addressed the $\psi$(2S) and $\chi_c$ impact on the determination of the polarization of the directly-produced J/$\psi$ mesons, the theoretical and experimental knowledge of the non-prompt polarization is very poor. Furthermore, non-prompt J/$\psi$ polarization measurements can provide interesting information on quarkonium hadroproduction, complementing the studies of prompt production. We review the method of measuring the polarization of non-prompt J/$\psi$ mesons (produced in decays of unreconstructed B mesons and detected in the dilepton channel), in conditions typical of LHC experiments studying J/$\psi$ production. Realistic model-independent scenarios are validated with data from experiments studying $e^+e^- \to \Upsilon$(4S) interactions, converted to the high-momentum regime using B differential cross sections measured at the LHC. The non-prompt J/$\psi$ polarization measurements are seen to remain dependent on the event selection criteria, even after correcting for the dilepton acceptance and efficiencies. This implies that reproducible definitions of all relevant analysis choices must be reported with the polarization result, for rigorous comparisons with other measurements and/or theoretical calculations. We also discuss how the non-prompt J/$\psi$ polarization significantly depends on the relative importance of two complementary $\mathrm{B}\to {\rm J}/\psi$ decay topologies, two-body (reasonably dominated by singlet production) and multi-body (including octet contributions), providing, hence, valuable information for studies of the charmonium formation mechanisms.