Phase transitions from Hadronic to Partonic Worlds L. G. Moretto, K. A

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Presentation transcript:

Phase transitions from Hadronic to Partonic Worlds L. G. Moretto, K. A Phase transitions from Hadronic to Partonic Worlds L. G. Moretto, K. A. Bugaev, J. B. Elliott and L. Phair Lawrence Berkeley National Laboratory Nuclear Science Division Tc ≈ 18.1 MeV rc ≈ 0.53 r0 pc ≈ 0.41 MeV/fm3 Phase transitions in the Hadronic world Pairing (superconductive) Transition finite size effects: correlation length Shape transition all finite size effects, shell effects Liquid-vapor (with reservations) van der Waals-like finite size effects due to surface Phase transitions in the partonic world Q. G. P. . . . Finite size effects?

The partonic world (Q.G.P.) (a world without surface?) The M.I.T. bag model says the pressure of a Q.G.P. bag is constant: ; g: # degrees of freedom, constant p = B, constant . The enthalpy density is then which leads to an entropy of and a bag mass/energy spectrum (level density) of . This is a Hagedorn spectrum: Partonic vacuum Hadronic vacuum ? m m0 ln rH(m)

The partonic world (Q.G.P.) a constant temperature world The M.I.T. bag model : rH(m) The Hagedorn Bag Implications? The Hagedorn spectrum:

Equilibrium with Hagedorn bags: Example #1: the one dimensional harmonic oscillator BEWARE! A linear dependence of S on E spells danger to the unaware! Beware of the canonical and grand canonical ensembles! Go MICRO-canonical son! For a one dimensional harmonic oscillator with energy e in contact with a Hagedorn bag of energy E: The probability P(e) is: E e ln P(E) The most probable value of e: For E  : e  TH

Equilibrium with Hagedorn bags: Example #2: an ideal vapor of N particles of mass m and energy e The total level density: Most probable energy partition: TH is the sole temperature characterizing the system: A Hagedorn-like system is a perfect thermostat. If particles are generated by the Hagedorn bag, their concentration is: Volume independent! Saturation! Just as for ordinary water, but with only one possible temperature, TH! rH(E) ideal vapor riv particle mass = m volume = V particle number = N energy = e

The story so far . . . Anything in contact with a Hagedorn bag acquires the temperature TH of the Hagedorn bag. If particles (e.g. ps) can be created from a Hagedorn bag, they will form a saturated vapor at fixed temperature TH. If different particles (i.e. particles of different mass m) are created they will be in chemical equilibrium. rH(E)

The radiant Hagedorn bag (initial energy E0, initial radius R0) At coexistence: flux in fin = flux out fout = fparticles: Energy flux fE: rH(E) rH(E) With no containing volume the Hagedorn bag radiates itself away. Upper limit for lifetime t of Hagedorn bag: Similarities with compound nucleus: Same spectra and branching ratios Differences with compound nucleus: All quantities calculated at fixed TH

Stability of the Hagedorn bag against fragmentation If no translational or positional entropy, then the Hagedorn bag is indifferent to fragmentation. indifferent rH(m) rH(mk) rH(m3) rH(m2) rH(m4) rH(m5) rH(m1) rH(m6) If the fragments form a vapor of Hagedorn bags (except one): If the fragments form a vapor composed entirely of Hagedorn bags then: N = 1 all the mass is concentrated into a single Hagedorn bag.

Hagedorn bags are fractal The number gs of clusters with surface s on a d = 2 square lattice is: gs = q s-x exp (bss) True regardless of d or lattice. W. Broniowski et al. In the case of no surface energy: most probable sA  A  m/msc m = resonance (cluster) mass msc = single constituent mass Which gives: