On the precise determination of the Tsallis parameters in proton - proton collisions at LHC energies

A detailed analysis is presented of the precise values of the Tsallis parameters obtained in $p-p$ collisions for identified particles, pions, kaons and protons at the LHC at three beam energies $\sqrt{s} = 0.9, 2.76$ and $7$ TeV. Interpolated data at $\sqrt{s} = $ 5.02 TeV have also been included. It is shown that the Tsallis formula provides reasonably good fits to the $p_T$ distributions in $p-p$ collisions at the LHC using three parameters $dN/dy$, $T$ and $q$. However, the parameters $T$ and $q$ depend on the particle species and are different for pions, kaons and protons. As a consequence there is no $m_T$ scaling and also no universality of the parameters for different particle species.