Event by Event Fluctuations ● General remarks about fluctuations ● First order, second order ● Practical aspects Event by Event = Multi-particle correlations Thanks to J. Randrup for sharing some of his slides CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Phase diagram Can we establish this line experimentally? Have we established this line experimentally? CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Susceptibilities M E = E 0 m H Q 〈 m 〉= d F d H 〈 Q 〉= d F H d 〈 m 〉= m H Susceptibilities 〈 Q 〉= Q 2 F m = d Linear response d H 2 2 F Q = d 2 d 2 〉= m 〈 m 2 〉= Q 〈 Q Fluctuations CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
The mother of all thermal spectra and fluctuations Fluctuations at the level of 10 -5 !!! CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Heavy Ions: Event-by-Event <x 2 > <x> The physics is in the width E-by-E measures 2-particle correlations CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Fluctuations in thermal system e.g. Lattice QCD Z = Tr [ exp − H − Q Q − B B − S S ] ∂ log Z =− ∂ X = Q ,B ,S Mean : 〈 X 〉= T F ∂ X ∂ X 2 ∂ 2 ∂ 2 Variance: 〈 X 2 〉= T 2 log Z =− T 2 F ∂ X ∂ X ∂ 2 ∂ 2 Co-Variance: 〈 X Y 〉= T 2 log Z =− T F ∂ X ∂ Y ∂ X ∂ Y ∂ ∂ XY =− 1 2 F =− 1 Susceptibility: 〈 Y 〉 ∂ X ∂ Y ∂ X V V CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Lattice-QCD susceptibilities = 2c 2 12 c 4 T 30 c 6 T 2 4 χ T , μ q μ q μ q ... 2 T Rule of thumb: n 〉 c n ~〈 X X = B ,Q ,S , Alton et al, PRD 66 074507 (2002) CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
E-by-E observables ● Multiplicity fluctuations ● interesting centrality dependence at top SPS energies ● Charge fluctuations ● Resonance gas at RHIC ● no sensitivity at SPS ● Transverse momentum fluctuations ● some signal at SPS & RHIC (mostly “jets”) ● Ratio (K/π) fluctuations ● statistical at top SPS, possible signal at low SPS CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Something new: Simple Observation Or how can we test the bs-QGP Simple QGP: strangeness is carried by strange quarks Baryon Number and Strangeness are correlated Hadron Gas: strangeness is carried mostly by mesons Baryon Number and Strangeness are uncorrelated Bound state QGP: strangeness is carried by partonic bound states Baryon Number and Strangeness should be uncorrelated
<BS> and the Bound State QGP =− 3 〈 B −〈 B 〉 S −〈 S 〉 〉 =− 3 X BS C BS ≡− 3 〈 B S 〉 =− 3 〈 BS 〉 Define: 2 〉 2 〉 2 〉 X SS 〈 S −〈 S 〉 〈 S 〈 S (-3) compensates baryon-number and strangenes of quarks In a QGP phase In hadron gas phase − 3 〈 BS 〉= 3 [ ] − 3 〈 BS 〉=〈 n s 〉〈 n s 〉 6 [ ] 9 [ ] 2 〉=〈 n s 〉〈 n 〈 S s 〉 0 2 〉= K + K - K 〈 S At T=170MeV, μ=0 At all T and μ C BS = 0.66 C BS = 1
<BS> continued Independet quarks and C QS =− 3 〈 QS 〉 LATTICE QCD for T>1.1T_c 2 〉 〈 S C QS Bound state QGP C BS Gavai,Gupta, hep-lat/0510044 V.K, Majumder, Randrup PRL95:182301,2005 CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
T 1.1 T c T c μ CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
First order or second order? First order: Second order: ● Phase coexistence, bubbles ● Critical fluctuations ● Spinodal instabilities ● Diverging Susceptibilities “Latent heat” T μ CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
First or second order? Focusing ? T μ CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Second order Free Energy ● Fluctuation of order parameter at all scales ● Diverging susceptibilities ~1/(”Mass”) 2 ● Diverging correlation length ~1/(“Mass”) ● Universality ● Critical slowing down ! Order Parameter No curvature, “Mass”=0 CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Second order correlation length ~1/m σ ● Critical slowing down ● limited sensitivity on model parameters ● Max. correlation length 2-3 fm ● Translates in 3-5% effect in p t -fluctuations T/MeV 180 140 120 Bernikov, Rajagopal, hep-ph/9912274 CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
First order Free Energy ● Phase coexistence ● “Bubble” formation ● Spatial fluctuations of order parameter ● definite length scale ● Specific heat ● Dynamics: Spinodal instability Order Parameter CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
First order What are the phases? CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
“One” order parameter Baryon density Coexistence Chem. Pot. P. Braun-Munzinger and J. Stachel, Nucl.Phys.A606:320-328,1996 CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Phase diagram of strongly interacting matter Nucleon gas Nuclear liquid Hadron gas Quark-gluon plasma CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Baryon number fluctuations Strong spatial fluctuations If V domain << V, small effect on integrated Baryon Number fluctuations 2 ≈ 1 2 〉 2 〈 N 4 〈 N 〉 CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Spinodal breakup Spinodal decomposition: ● general phenomenon ● dynamical process ● typical “blob” size ● depends on details of interaction CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Spinodal decomposition in nuclear multifragmentation occurs! 32 MeV/A Xe + Sn (b=0) Bin wrt (select events with 6 IMFs) Pre-diction Experiment ( INDRA @ GANIL ) Theory ( Boltzmann-Langevin ) Borderie et al , PRL 86 (2001) 3252 Chomaz, Colonna, Randrup, … CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
N-particle correlations - is enhanced at ≈ T [J. Randrup, J. Heavy Ion Physics 22 (2005) 69] CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Kinematic clumping => Total four-momentum: Invariant-mass correlations Kinetic energy per particle (in the N -body CM frame): Distribution of : Correlation function: - is enhanced at ≈ T Same event Mixed events N =4 Higher-order correlations N =3 stand out more clearly! N =2 (but require larger samples) [J. Randrup, J. Heavy Ion Physics 22 (2005) 69]
Strangeness correlations The expanding system decomposes into plasma blobs which each contain a certain amount of strangeness: S 3 S 5 S 1 S 4 S 2 S 6 The hadronization of S n 0 each isolated blob conserves strangeness: [V. Koch, A. Majumder, J. Randrup, Phys. Rev. C (in press)]
Some numbers mean Variance: enhanced by ~10 % V QGP = 50 fm 3 V hadron = 150 fm 3 Generally: variance is more enhanced T = 170 MeV than mean CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Fluctuations (NA49, QM2004) NA49 Preliminary NA49 Preliminary K/π fluctuations increase towards lower beam energy ● – Significant enhancement over hadronic cascade model p/π fluctuations are negative ● – indicates a strong contribution from resonance decays – Where are the baryon number fluctuations???? CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
K/π Ratio Fluctuations strong where inclusive K/π peaks! CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Dynamics, event selection ... Konchakovski et al, nucl-th/0511083 All Backward Forward (like data) ● Fluctuations are sensitive to dynamics (mixing of projectile and target material?) ● Event selection/trigger affects fluctuations → large Acceptance! CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Things to do! ● Characterize the Phases – what are useful order parameters ● Test observables using static and dynamical models – Effects are small, comparable with 'trivial ones” such as quantum statistics, dynamics etc. – Only a well chosen observable / set of observables will prevent us from seeing Poisson ● e.g. can we live without neutrons? CBM-workshop, GSI, Dec 15-16, 2005 /home/vkoch/Documents/talks/GSI2005/CBM_E_by_E.
Recommend
More recommend
