  Proton-nucleus collisions serve as an important baseline for the
understanding and interpretation of the nucleus-nucleus collisions. These
collisions have been employed to characterize the cold nuclear matter effects
at SPS and RHIC energies for the past several years, as it was thought that
Quark-Gluon Plasma (QGP) is not formed in such collisions. However, at the
Large Hadron Collider (LHC), there seems a possibility that QGP is formed
during proton-lead (p$-$Pb) collisions. In this work, we have derived an
expression for gluon induced excitation of $J/\psi$ to $\psi(2S)$, using
pNRQCD, and show that the relative enhancement of $\psi(2S)$ vis a vis
$J/\psi$, especially at high $p_T$, gives further indication that the QGP is
indeed formed in p$-$Pb collisions at the most central collisions at LHC
energy. $J/\psi$ and $\psi(2S)$ suppression effects seen at ALICE are also
qualitatively explained.
