  Transverse momentum spectra of negative and positive pions produced at
mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton
collisions over a center-of-mass energy, $\sqrt{s}$, range from a few GeV to
above 10 TeV are analyzed by the blast-wave fit with Boltzmann (Tsallis)
distribution. The blast-wave fit results are well fitting to the experimental
data measured by several collaborations. In a particular superposition with
Hagedorn function, both the excitation functions of kinetic freeze-out
temperature ($T_0$) of emission source and transverse flow velocity ($\beta_T$)
of produced particles obtained from a given selection in the blast-wave fit
with Boltzmann distribution have a hill at $\sqrt{s}\approx10$ GeV, a drop at
dozens of GeV, and then an increase from dozens of GeV to above 10 TeV.
However, both the excitation functions of $T_0$ and $\beta_T$ obtained in the
blast-wave fit with Tsallis distribution do not show such a complex structure,
but a very low hill. In another selection for the parameters or in the
superposition with the usual step function, $T_0$ and $\beta_T$ increase
generally quickly from a few GeV to about 10 GeV and then slightly at above 10
GeV, there is no such the complex structure, when also studying nucleus-nucleus
collisions.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Experiment;Nuclear Theory