Sean Gavin Wayne State University 1 st Order
- Slides: 26
Sean Gavin Wayne State University 1 st Order Phase Transition in Ion Collisions? 4 familiar flow signals probe small bubbles 4 fluctuation signals probe large bubbles I. Extraordinary fluctuations from 1 st order transition 4 simple example: baryon fluctuations at high density II. Diffusion dynamics for conserved order parameter 4 slow rapidity diffusion fluctuations can survive with D. Bower & C. Pruneau
Baryon Density: the Other Order Parameter QCD with two massless quarks = 0: 2 nd order chiral transition = c: tricritical point > c: 1 st order = baryon chemical potential C Berges, Rajagopal; Stephanov et al; Shuryak et al. Real World QCD = 0: “smooth” crossover = c: critical point > c: 1 st order transition ~ liquid-gas C
1 st Order Transition Fluctuations net baryon density > 0 Berges & Rajagopal, et al. 1 st order phase separation 4 bimodal distribution before -- “mixed phase” of densities 4 hadronic bubbles, density h plasma, q 4 = 0 transition may be “nearly” 1 st order signatures of bubbles 4 interferometry Pratt, Siemens 4 variance of net baryon number after
Baryon Number Fluctuations bimodal distribution of densities within each event “mixed phase” 4 plasma fraction f 4 N net baryons in y variance: ask: do these fluctuations survive?
Bubble Formation Baryon Fluctuations phase transition baryonic bubbles number of bubbles varies event by event few bubbles many bubbles before z after find: baryon number fluctuates in a rapidity slice
Rapidity Fluctuations Can Survive expansion fast: diffusion slower: z ~ (D )1/2 diffusion const. D ~ 2 -10 fm Prakash et al. ; Heiselberg et al. before y find: expansion inhibits spread in rapidity – observable! S. Gavin, nucl-th/9908070 after
Phase Separation A. J. Bray, Ad. Phys. 43 (1994) 357; M. Grant et al. free energy vs. baryon density for mixed phase: 4 two phases h, q 4 Ising-like near TC 4 surface tension diffusion dynamics for conserved 4 diffusion coefficient D = 2 m 2 M
Phase Separation Dynamics quench system deep into coexistence region T f 0 dynamics: bubbles from runaway density waves 4 fastest growing mode – time scale R R D 1 fm 4 wavelength R corr. length 1 fm 4 nonlinear evolution for t >> R
Benchmark Simulations random initial distribution (2+1 d) early domain formation phase separation 4 no expansion 4 eternal 50 -50% mixed phase 4 droplets merge, reduce surfaces
Phase Separation in Ion Collisions S. Gavin, nucl-th/9908070; D. Bower and S. Gavin, in progress longitudinal flow + diffusion: 4 v j. D ; diffusion current j. D 4 Bjorken flow: vz~ z/ , proper time evolution following a quench 4 quench at 1 < 0 < 10 fm 4 assume R ~ correlation length ~ 1 fm 4 outcome depends on 0 / R
Evolution with Expansion expansion stable for > 0 initial 0 fm 0 R fm q y h x find: droplets, but few connected regions
Variance of Baryon Number 4 simulate 1000 “events” – initial 0= 5 fm 4 baryon number N for strips: y z or z 4 compute V = N N , V excess over Poisson y no expansion Find: 4 variance rises initially 4 falls after stabilized ( = 0) 4 y falls less quickly y z 0
Variance in Collisions? need 0/ R >> 1 for large V 4 expansion time scale ~ 0 4 phase separation time ~ R droplets must form before system exits unstable region 0 = 5 fm 0 = 2 fm 0
Summary: Baryon Fluctuations “Ordinary” fluctuations 4 QGP vs. HG Jeon & Koch; Asakawa et al. Stephanov and Shuryak Extraordinary? – 1 st order transition 4 meson fluctuations 4 baryon fluctuations Heiselberg, Baym, Jackson S. G. Baryon fluctuations at high density – theory easier 4 conserved – fluctuations in rapidity bins preserved 4 time to develop? Maybe Bower, S. G.
Latest Evolution expansion stabilizes system: 4 stable for > c 4 diffusion smears droplets expansion: droplets distributed over a larger volume q c sp h y x
Later Evolution expansion stabilizes system: 4 stable for > c q expansion spreads droplets over a larger volume y h x 3 c 15 sp
Observable Fluctuations high density phase: 4 fraction f ~ 0. 25 {1 - [b/(3 fm)]2 }, diluted by diffusion 4 density contrast N = Nq - Nh 4 event generator compute: 4 normally energy independent 4 1 if nothing happens
Phase Separation Dynamics expansion – quench system deep into coexistence region f 0 T dynamics: runaway density waves – fastest growing mode 4 time scale sp D 1 fm 4 sp corr. length 1 fm 4 nonlinear evolution for t >> sp t= 100 sp
Event Classes Novel Fluctuations Two event classes with different means 4 e. g. antiprotons 4 fraction f of novel events Turn plasma off? centrality! Vary Find range where plasma and hadronic classes coexist? Gavin & Pruneau To NA 49: how does K/ vary with centrality?
Fluctuations Survive Diffusion expansion stretches diffusion homogenizes expansion of mesons fast: z ~ diffusion slower: z ~ (D )1/2 expansion inhibits rapidity spread -- random walk limited hadronization H ~ 10 fm diffusion const. D ~ 2 -10 fm Prakash et al. ; Heiselberg et al. y
Diffusion diffusion alters baryon current: 4 diffusion current j. D I D i (local rest frame) baryon density , diffusion constant D 4 longitudinal flow vz~ z/ proper time baryon diffusion in spatial rapidity
Phase Separation in Ion Collisions S. Gavin, nucl-th/9908070; D. Bower and S. Gavin, in progress longtudinal flow + diffusion: 4 v j. D ; diffusion current j. D 4 Bjorken flow: vz~ z/ , proper time evolution following a quench 4 quench at 1 < c < 10 fm 4 assume sp ~ corr. length ~ 1 fm drives system out of unstable region T
Origin of fluctuations expansion -- quench system deep into coexistence region mechanical instability / < 0 fragmentation runaway modes fastest mode (~ DCC) sp (|D|ksp) -1 < 1 fm ksp-1 m -1 bubble size
Baryon Number Fluctuations bimodal distribution of densities within each event “mixed phase” 4 plasma fraction f 4 N net baryons in y ask: do these fluctuations survive?
1 st Order Transition Fluctuations 1 st order at net baryon density > 0? Berges & Rajagopal, et al. 4 hadronic bubbles, density h plasma, q 4 bimodal distribution before of densities -- “mixed phase” fluctuations enhance variance of baryon number 4 plasma fraction f 4 N net baryons in Dy after
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