The transverse-momenta distributions in high-energy $pp$ collisions -- A statistical-mechanical approach

We analyze LHC available data measuring the distribution probability of transverse momenta~$p_T$ in proton-proton collisions at $\sqrt{s}=0.9\text{TeV}$ (CMS, ALICE, ATLAS) and $\sqrt{s}=7\text{TeV}$ (CMS, ATLAS). A remarkably good fitting can be obtained, along fourteen decades in magnitude, by phenomenologically using $q$-statistics for a {\it single} particle of a two-dimensional relativistic ideal gas. The parameters that have been obtained by assuming $$\text{d}$N/p_T$\text{d}$p_T$\text{d}$y \propto e_q^{-E_T/T}$atmid-rapidityare,inallcases,$q \simeq 1.1$and$T\simeq 0.13,$\text{GeV}$$ (which satisfactorily compares with the pion mass). This fact suggests the approximate validity of a “no-hair” statistical-mechanical description of the hard-scattering hadron-production process in which the detailed mechanisms of parton scattering, parton cascades, parton fragmentation, running coupling and other information can be subsumed under the stochastic dynamics in the lowest-order description. In addition to that basic structure, a finer analysis of the data suggests a small oscillatory structure on top of the leading $q$-exponential. The physical origin of such intriguing oscillatory behavior remains elusive, though it could be related to some sort of fractality or scale-invariance within the system.