$\psi \left(2S\right)$ enhancement in p–Pb collision as an indication of quark–gluon plasma formation at the Large Hadron Collider

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 Relativistic Heavy-Ion Collider 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 $\psi \left(2S\right)$, using pNRQCD, and show that the relative enhancement of $\psi \left(2S\right)$ vis-à-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 $\psi \left(2S\right)$ suppression effects seen at ALICE are also qualitatively explained. (paper)