Does Quarkonia Suppression serve as a probe for the deconfinement in small systems?

In high multiplicity proton-proton $(p-p)$ collisions, the formation of a deconfined state of quarks and gluons akin to Heavy Ion Collisions (HIC) has been a subject of significant interest. In proton-proton ($p-p$) collisions, the transverse size of the system is comparable to the longitudinal (Lorentz contracted) dimension, unlike the case in Nucleus-Nucleus ($A-A$) collision, leading to a hitherto unexplored effect of rapid decrease of temperature of the medium on quark-antiquark bound states. This allows us to probe a unique possibility of hadronization occurring before quarkonia dissociation within the medium. In small systems, a rapid change in temperature also introduces sudden changes in the Hamiltonian. This scenario prompts consideration of non-adiabatic evolution, challenging the traditional adiabatic framework. We demonstrate that non-adiabatic evolution may extend the longevity of quark-anti-quark bound states in $p-p$ collisions, even at higher multiplicities, offering new insights into the dynamics of strongly interacting matter produced in smaller collision systems.