Inclusive $\psi (2S)$ production at midrapidity in pp collisions at $\sqrt{s}=13$ TeV

Inclusive production of $\psi (2S)$ mesons is measured for the first time at midrapidity ($\mathrm{\mid }y\mathrm{\mid }<0.9$) in pp collisions at $\sqrt{s}=13$ TeV using the ALICE detector at the LHC. The measurement is performed in the transverse-momentum ($p_{\mathrm{T}}$) range of 4 to 16 GeV/$c$ and is based on events triggered by the Transition Radiation Detector, corresponding to an integrated luminosity of $1.7\pm 1.8\mathrm{\%}$ (syst.) pb${}^{-1}$. The $p_{\mathrm{T}}$-differential production cross section of the $\psi (2S)$ and its ratio to the J/$\psi$ production cross section are presented. The results extend the accessible $p_{\mathrm{T}}$ range down to 4 GeV/$c$, and a mild rise of the $\psi (2S)$-to-J/$\psi$ cross section ratio with increasing $p_{\mathrm{T}}$ is observed. The measurements are compared with theoretical predictions based on NRQCD and the ICEM model.