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From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar p$ collisions

Transverse spectra of both jets and hadrons obtained in high-energy $pp$ and $p\bar p $ collisions at central rapidity exhibit power-law behavior of $1/p_T^n$ at high $p_T$. The power index $n$ is 4-5 for jet production and is 6-10 for hadron production. Furthermore, the hadron spectra spanning over 14 orders of magnitude down to the lowest $p_T$ region in $pp$ collisions at LHC can be adequately described by a single nonextensive statistical mechanical distribution that is widely used in other branches of science. This suggests indirectly the possible dominance of the hard-scattering process over essentially the whole $p_T$ region at central rapidity in high-energy $pp$ and $p \bar p$ collisions. We show here direct evidences of such a dominance of the hard-scattering process by investigating the power indices of UA1 and ATLAS jet spectra over an extended $p_T$ region and the two-particle correlation data of the STAR and PHENIX Collaborations in high-energy $pp$ and $p \bar p$ collisions at central rapidity. We then study how the showering of the hard-scattering product partons alters the power index of the hadron spectra and leads to a hadron distribution that may be cast into a single-particle nonextensive statistical mechanical distribution. Because of such a connection, the nonextensive statistical mechanical distribution may be considered as a lowest-order approximation of the hard-scattering of partons followed by the subsequent process of parton showering that turns the jets into hadrons, in high energy $pp$ and $p\bar p$ collisions.