Phase transitions of second and zero kind in high-energy physics: A phenomenological field-theoretical approach.σmodel and superfluidity of hadronic matter

We introduce the temperature concept of Fermi, Landau, and Hagedorn associated with the energy of an elementary-particle reaction into the thermodynamics of field theory constructed by Weinberg for external temperature. For weak and electromagnetic interactions this implies that the phase transitions predicted within a unified gauge theory of electromagnetic and weak interactions should be looked for in elementary-particle interactions at very high energies (cosmic rays). The experimental observation of these effects which might include, e.g., conservation of strangeness in weak interactions will constitute one of the most clear-cut confirmations of the unified gauge theory. We formulate a phenomenological field theory at finite temperature and derive all the relevant thermodynamical quantities (thermodynamical potential, pressure, entropy, energy, specific heat, and velocity of sound). We consider two possible types of phase transitions, namely of second order and of zero order (Hagedorn type). We discuss the implications of phase transitions in strong interactions for the momentum distribution of secondaries. In the particular case of the $\sigma$ model we find a phase transition of the second kind induced by the energy of the reaction and a phonon-like excitation spectrum for the pion cloud inside the nucleon in the spontaneously-broken-symmetry phase, giving support to the idea that hadronic matter has superfluid properties. This leads to scaling effects at low excitation energies in scattering reactions on nucleons. The broken symmetry is restored at a critical temperature $T_c$ in agreement with previous phenomenological predictions based on a superfluid approach to strong interactions. Above $T_c$ the parton masses vanish, which leads again to scaling, but this time in the high-energy-transfer domain. Conservation of axial-vector currents is found to hold in both phases. In the $T>\mathrm{}{T}_c$ phase we expect chiral multiplets.