Studies of the hydrodynamic evolution of matter produced in fluctuations in p¯p collisions and in ultrarelativistic nuclear collisions

In this first paper of a series of two, we present a comprehensive study of the hydrodynamic evolution of matter produced in the central region of ultrarelativistic heavy-ion collisions and in high-multiplicity fluctuations of p¯p collisions. We shall begin with a discussion of the limits of the applicability of a perfect-fluid hydrodynamic description of high-energy collisions. A simple bag-model equation of state is argued to have qualitative and semiquantitative features expected from lattice gauge theory and present theoretical understanding. We also discuss the boundary conditions for the perfect-fluid hydrodynamic equations, and what classes of simple events would correspond to simple initial conditions. The decoupling of matter at low energy density and methods for computing transverse-momentum distributions of hadrons are analyzed. We finally present the details of the computer code which we use to numerically solve the hydrodynamic equations.