Sean Gavin Wayne State University 1 st Order

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Sean Gavin Wayne State University 1 st Order Phase Transition in Ion Collisions? 4

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 /

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

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?

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