Proton-proton collisions in the hydrodynamic theory

Inspired by some earlier successes of Landau's hydrodynamic theory in explaining the data on high-energy multiparticle production in proton-proton collisions, we investigate exact formulas for the pion inclusive distribution in (1) the hydrodynamic theory, and (2) a statistical variant of this theory in which the thermal motion of the emitted particles is taken into account. All theoretical predictions of the exact spectra are without any free parameters. The results are (1) the exact spectra at Fermi National Accelerator Laboratory (FNAL) and CERN Intersecting Storage Rings energies are substantially broader than those obtained from the formula derived by Landau, (2) at $\sqrt{s}=52.8\mathrm{}$ GeV the exact hydrodynamic theory gives a good description of the experimental data up to a center-of-mass rapidity of approximately 3, and (3) only Landau's original formula for the spectrum gives a satisfactory description of the FNAL data at $s\simeq 565$ Ge${\mathrm{V}}^2$. We also obtain a formula for the average multiplicity without any adjustable parameter, and find that it gives an excellent description of the data above $s\simeq 100$ Ge${\mathrm{V}}^2$.