Kinetic freeze-out and diffusion dynamics in small-system asymmetric collisions at sqrt(sNN)=200 GeV in light of a generalized Fokker-Planck distribution

Abstract

A generalized Fokker-Planck solution is used to examine the transverse momentum ($p_{T}$) spectra of neutral pions generated in small-system asymmetric collisions, $p$-Al, $p$-Au, $d$-Au, and $^3$He-Au, at $\sqrt{s_{NN}}=200$ GeV. This framework provides a cohesive explanation of particle production over a broad range of transverse momenta. We extract the energy scale governing the transition between a thermal and a hard regime, the effective temperature ($T$), and the exponents determining the high-momentum falloff from fits to PHENIX data. $T$ increases systematically with the collision centrality and colliding system size, ranging from about 0.33 GeV in peripheral $p$-Al collisions to 0.45 GeV in central $^3$He-Au collisions. This increase is correlated with the average number of participant nucleons, $<N_{part}>$, and the charged-particle pseudorapidity density, $<dN_{ch}/dη>$, indicating that larger and more central collisions create a denser, more strongly interacting medium that freezes out at a higher temperature. The acquired transition scale and power-law exponents follow consistent patterns across systems and centralities, revealing details about the sharpness of the transition from thermal to hard processes, and the relative strength of momentum-space diffusion versus drag. Interestingly, when the gold target dominates the collision geometry in the largest system ($^3$He-Au), the transition scale becomes nearly independent of centrality, signifying saturation of the diffusion process. Our findings demonstrate that the generalized Fokker-Planck solution is a sensitive probe of transport properties and non-extensive dynamics in the quark-gluon plasma produced even in small-system relativistic collisions, and it consistently describes pion spectra in this set of collisions.