Interferometry of direct photons in Pb+Pb collisions at 158 AGeV

We present final results from the WA98 experiment which provide first measurements of Bose-Einstein correlations of direct photons in ultrarelativistic heavy ion collisions. Invariant interferometric radii were extracted in the range $100<K_T<300$ MeV/c and compared to interferometric radii of charged pions. The yield of direct photons for $100<p_T<300$ MeV/c was extracted from the correlation strength parameter and compared to the yield of direct photons measured in WA98 at higher $p_T$ with the statistical subtraction method, and to predictions of a fireball model.Comment: 4 pages, 3 figures, proceedings for Quark Matter 200

Sustaining supercooled mixed phase via resonant oscillations of the order parameter

We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as in models of pre-heating after inflation. In the context of condensed matter systems, it could be temperature $T$, or pressure, external electric/magnetic field etc. We show that with suitable driving frequency and amplitude, the system remains in a type of mixed phase, without ever completing transition to the stable phase, even when the oscillating parameter of the free energy remains below the corresponding critical value (for example, with oscillating temperature, $T$ always remains below the critical temperature $T_c$). This phenomenon may have important implications. In cosmology, it will imply prolonged mixed phase in a first order transition due to coupling with background oscillating fields. In condensed matter systems, it will imply that using oscillating temperature (or, more appropriately, pressure waves) one may be able to sustain liquids in a mixed phase indefinitely at low temperatures, without making transition to the frozen phase.Comment: 17 pages, 7 figures, Expanded version with more detail

Thermal Particle and Photon Production in Pb+Pb Collisions with Transverse Flow

Particle and photon production is analyzed in the presence of transverse flow using two approximations to describe the properties of the hadronic medium, one containing only $\pi, \rho, \omega$, and $\eta$ mesons (simplified equation of state) and the other containing hadrons and resonances from the particle data table. Both are considered with and without initial quark gluon plasma formation. In each case the initial temperature is fixed by requiring $dN_{ch}/dy \sim$ 550 in the final state. It is shown that most observables are very sensitive to the equation of state. This is particularly evident when comparing the results of the simplified equation of state in the scenarios with and without phase transition. The hadronic gas scenario leads to a substantially higher rate for the $p_T$-distribution of all particles. In the complete equation of state with several hundreds of hadronic resonances, the difference between the scenarios with and without phase transition is rather modest. Both photon and particle spectra, in a wide $p_T$ range, show very similar behavior. It is therefore concluded that from the $p_T$ spectra it will be hard to disentangle quark gluon plasma formation in the initial state. It is to be stressed however, that there are conceptual difficulties in applying a pure hadronic gas equation of state at SPS-energies. The phase transition scenario with a quark gluon plasma present in the initial state seems to be the more natural one.Comment: 9 pages RevTeX figures in postscript forma

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

Velocity of sound in relativistic heavy-ion collisions

We have studied the rapidity distribution of secondary hadrons produced in nucleus-nucleus collisions at ultra-relativistic energies within the ambit of the Landau's hydrodynamical model. A reasonable description of the data can also be obtained by using the Bjorken's hydrodynamical model if the boost invariance is restricted to a finite rapidity range. The sensitivity of the hadronic spectra on the equation of state vis- a -vis the velocity of sound has been discussed. The correlation between the velocity of sound and the freeze-out temperature has been indicated. The effects of the non-zero widths of various mesonic and baryonic degrees of freedom up to the mass value ~ 2.5 GeV is seen to be small.Comment: 9 pages and 11 figures. Major changes. To appear in Physical Review

Scaling of hadronic transverse momenta in a hydrodynamic treatment of relativistic heavy ion collisions

The transverse momenta of hadrons in central nucleus-nucleus collisions are evaluated in a boost invariant hydrodynamics with transverse expansion. Quark gluon plasma is assumed to be formed in the initial state which expands and cools via a first order phase transition to a rich hadronic matter and ultimately undergoes a freeze-out. The average transverse momentum of pions, kaons, and protons is estimated for a wide range of multiplicity densities and transverse sizes of the system. For a given system it is found to scale with the square-root of the particle rapidity density per unit transverse area, and consistent with the corresponding values seen in $p\overline{p}$ experiments at 1800 GeV, suggesting a universal behaviour. The average transverse momentum shows only an approximate scaling with multiplicity density per nucleon which is at variance with the $p\overline{p}$ data.Comment: 6 pages including 9 figure