Hadron widths in mixed-phase matter.

We derive classically an expression for a hadron width in a two-phase region of hadron gas and quark-gluon plasma (QGP). The presence of QGP gives hadrons larger widths than they would have in a pure hadron gas. We find that the φ width observed in a central Au+Au collision at √ s = 200 GeV/nucleon is a few MeV greater than the width in a pure hadron gas. The part of observed hadron widths due to QGP is approximately proportional to (dN/dy). Submitted to Physical Review Letters ∗Internet: [email protected]. There is much interest in the physics of light vector mesons in ultrarelativistic nuclear collisions [1-4]. Experimental studies of the ρ may give a measure of the transition temperature to quark-gluon plasma (QGP) [2], Tc, while studies of the φ can also be used to determine Tc [3] as well as the duration of the transition and the temperature range over which the transition takes place [4]. However, no previous studies have considered the effects of QGP on hadron properties observed in ultrarelativistic nuclear collisions. These effects can be large, as much of the hadron signals come from the period during which hadronic matter and QGP coexist, and hadron properties in QGP are considerably different from those in hadronic matter. In this Letter, we derive an expression for a hadron width in a “static” mixed-phase region. This is a purely classical derivation, which doesn’t include any quantum-mechanical effects. We then use this derivation to estimate the change in the observed φ width in a central Au+Au collision at √ s = 200 GeV/nucleon, and to discuss the effect of varying projectile and/or target size and collision energy on observed hadron widths. We use standard high energy conventions, h̄ = c = kB = 1, throughout the letter. The hadron width in the mixed phase is Γm = Rm nm , (1) where Rm and nm are respectively the hadron decay rate per unit four-volume and density per unit volume in the mixed phase. Assuming that hadrons decay but are not created in the QGP, the decay rate in the QGP is equal to Area × F luxDensity × (1−SP ), where Area is the area of the hadronic matter – QGP interface, F luxDensity is the rate per unit area per unit time for hadrons to cross into the QGP, and SP is the survival probability (the probability that a given hadron survives a passage through the QGP). For simplicity, we treat the mixed-phase matter as a gas of spherical QGP droplets in hadronic matter; this is reasonable for high energy collisions, as experimental data is always taken over the whole mixed-phase period, and the four-volume of QGP is much less than the four-volume of hadronic matter. The first two quantities can just be written down: Area = ∫ ∞