Production of ${\eta }_c(1S,2S)$ in $e^{+}{e}^{-}$ and $pp$ collisions

Abstract

We derive the light-front wave function (LFWF) representation of the ${\gamma }^{\star }{\gamma }^{\star }\to {\eta }_c(1S),{\eta }_c(2S)$ transition form factor $F(Q_1^2,Q_2^2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of $c\bar{c}$ potentials. We compare our results to the BaBar experimental data for the ${\eta }_c(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. In addition, we present a thorough analysis of ${\eta }_c(1S,2S)$ quarkonia hadroproduction in $k_{\perp }$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^{\star }{g}^{\star }\to {\eta }_c(1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. We present the transverse momentum distributions of ${\eta }_c$ for several models of the unintegrated gluon distributions. Our calculations are performed for four distinct parametrizations for the $c\bar{c}$ interaction potential consistent with the meson spectra. We compare our results for ${\eta }_c(1S)$ to measurements by the LHCb collaboration and present predictions for ${\eta }_c(2S)$ production.

6 pages, 6 figures, a talk presented by I. Babiarz at 40th International Conference on High Energy physics - ICHEP2020, July 28 - August 6, 2020, Prague, Czech Republic (virtual meeting)