Study of proton-nucleus collisions at high energies based on the hydrodynamical model

Abstract

We study proton-nucleus collisions at high energies using the one-dimensional hydrodynamical model of Landau with special emphasis on the effect of the size of the target nucleus and of the magnitude of velocity of sound of excited hadronic matter. We convert a collision problem of a proton and a nucleus with a spherical shape into that of a proton and a one-dimensional nuclear tunnel whose length is determined from the average impact parameter. By extending the methods developed by Milekhin and Emelyanov, we obtain the solutions of the hydrodynamical equations of proton-nucleus collisions for arbitrary target tunnel length and arbitrary velocity of sound. The connection between these solutions and observable physical quantities is established as in the work of Cooper, Frye, and Schonberg. Extensive numerical analyses are made at ${E}_{\mathrm{lab}}=200$ GeV and for the velocity of sound $u=\frac{1}{\sqrt{3}}$ of a relativistic ideal Bose gas and $u=\frac{1}{{(7.5)}^{\frac{1}{2}}}$ of an interacting Bose gas. In order to compare proton-nucleus collisions with proton-proton collisions, all the analyses are made in the equal-velocity frame. We find the following results. (1) In comparing the number of secondary particles produced in $p$-$A$ collisions ${N}_{\mathrm{pA}}$ with those in $p$-$p$ collisions ${N}_{\mathrm{pp}}$ while most of the excess of ${N}_{\mathrm{pA}}$ over ${N}_{\mathrm{pp}}$ is concentrated in the backward rapidity region, there exists also an increase of ${N}_{\mathrm{pA}}$ with $A$ in the forward rapidity region. This result is at variance with the predictions of the energy-flux-cascade model and of the coherent-production model. (2) The excess energies are contained exclusively in the backward region. We also find evidence for the following new phenomena in proton-nucleus collisions. (3) The existence of an asymmetry of average energies of secondary particles between forward and backward regions, in particular, $〈{E}_{\ensuremath{\pi}}^{b}〉\ensuremath{\gg}〈{E}_{\ensuremath{\pi}}^{f}〉$ for larger nuclear targets. Thus, energetic particles are predominantly produced in the backward region. (4) The existence of an asymmetry in the transverse masses between forward and backward regions, ${m}_{T}^{b}g{m}_{T}^{f}$ for $u=\frac{1}{{(7.5)}^{\frac{1}{2}}}$ and ${m}_{T}^{b}l{m}_{T}^{f}$ for $u=\frac{1}{\sqrt{3}}$. This asymmetry implies a similar asymmetry in the transverse momenta ${p}_{T}$. (5) The disappearance of the leading-particle effect in the forward region for $u=\frac{1}{{(7.5)}^{\frac{1}{2}}}$. Some other new findings are also discussed. The energy dependence of the above phenomena is studied in the range ${E}_{\mathrm{lab}}=200\ensuremath{-}1500$ GeV.