Fluctuations and Search for the QCD Critical Point

Transcription

1 Fluctuations and Search for the QCD Critical Point Kensuke Homma Hiroshima University. Integrated multiplicity fluctuations. Differential multiplicity fluctuations 3. K to π and p to π fluctuations 4. est of v scaling at low transverse kinetic energy he QCD Critical Point Workshop Aug, 008 in IN, Univ. of Washington, U.S.A. Kensuke Homma / Hiroshima Univ.

2 Kensuke Homma / Hiroshima Univ. Analysis on integrated multiplicity fluctuations

3 Kensuke Homma / Hiroshima Univ. 3 Quark Number Susceptibility Consider quark number susceptibility, χ q at the critical point. χ q <q q> n,μ/ μ his is related to the isothermal compressibility: k χ q,μ/n,μ In a continuous phase transition, k diverges at the critical point k c C γ B.-J. Schaefer and J. Wambach, Phys. Rev. D

4 Integrated Multiplicity Fluctuations Multiplicity fluctuations may be sensitive to divergences in the compressibility of the system near the critical point. Grand Canonical Ensemble ω N Scaled Variance N + σ ω μ μ k NBD Multiplicity fluctuations have been measured in the following systems: 00 GeV Au+Au 6.4 GeV Au+Au 00 GeV Cu+Cu 6.4 GeV Cu+Cu.5 GeV Cu+Cu k B 00 GeV p+p baseline μ k V Survey completed as a function of centrality, charge and p. Kensuke Homma / Hiroshima Univ. 4

5 Kensuke Homma / Hiroshima Univ. 5 Multiplicity Fluctuations and Negative Binomial Distributions Multiplicity distributions in hadronic and nuclear collisions can be well described by the Negative Binomial Distribution. UA5 E80 UA5: sqrts546 GeV p-pbar, Phys. Rep E80: 4.6A GeV/c O+Cu, Phys. Rev. C NBD P k n σ μ Γ n + k μ / k Γ n Γ k + μ / k + μ k μ < n > n + μ / k k Bose-Einstein k Poisson k

6 Kensuke Homma / Hiroshima Univ. 6 Au+Au, Cu+Cu, p+p with NBD Distributions 00 GeV Au+Au 00 GeV Cu+Cu 6.4 GeV Cu+Cu 6.4 GeV Au+Au Red lines represent the NBD fits. he distributions have been normalized to the mean and scaled for visualization. Distributions measured for 0.<p <.0 GeV/c..5 GeV Cu+Cu 00 GeV p+p

7 Kensuke Homma / Hiroshima Univ. 7 Simple base line: Participant Superposition Model In a Participant Superposition Model, multiplicity fluctuations are given by: ω N ω n + <N>ω Np where ω σ /μ. ω N total fluctuation, ω n fluctuation in each source e.g. hadron-hadron collision, ω Np fluctuation in number of sources participants, <N>mean multiplicity per wounded nucleon. After correcting for fluctuations due to impact parameter, ω N ω n is independent of centrality. Multiplicity fluctuations are also dependent on acceptance: ω n + fω n - where f N accepted /N total. ω n fluctuations from each source in 4π

8 Multiplicity Fluctuation Results Bottom line: Near the critical point, the multiplicity fluctuations should exceed the superposition model expectation No significant evidence for critical behavior is observed. Centrality dependence is dominated by elliptic flow Superposition model at 00 GeV taken from PHENIX measurements of 00 GeV p+p. he results agree with UA5 measurements in PHENIX s pseudorapidity window. Superposition model at GeV taken from NA measurements in PHENIX s pseudorapidity window. Superposition model at 6 GeV taken from interpolation of UA5 results in PHENIX s pseudorapidity window. Kensuke Homma / Hiroshima Univ. 8

9 String Percolation Model Kensuke Homma / Hiroshima Univ. 9 String percolation: strings form clusters of geometrically overlapping strings and each cluster emits particles depending on the number strings. As the centrality increases, the number of clusters decreases along with the variance of the number of strings per cluster, which results in a decrease of scaled variance. Shown in green are the direct predictions of the string percolation model PRC7, for 00 GeV Au+Au, scaled down to the PHENIX acceptance. Percolation still does not explain the plateau in the most peripheral Au+Au collisions.

10 Kensuke Homma / Hiroshima Univ. 0 CLAN Model A. Giovannini et al., Z. Phys. C he CLAN model was developed to attempt to explain the reason that p+p multiplicities are described by NBD rather than Poisson distributions. Hadron production is modeled as independent emission of a number of hadron clusters, N c, each with a mean number of hadrons, n c. hese parameters can be related to the NBD parameters: N c k NBD log + µ ch /k NBD and <n c > µ ch /k NBD /log + µ ch /k NBD. A+A collsions exhibit weak clustering characteristics, independent of collision energy.

11 Kensuke Homma / Hiroshima Univ. Charge and p -Dependence As with acceptance, with no chargedependent correlation, the scaled variance will scale: If p-dependence is random, the scaled variance should scale with <N> in the same manner as acceptance: ω p + fω p,max - ω +- + fω inclusive - where f0.5. Within errors, no charge dependence of the fluctuations is seen for 00 GeV Au+Au.

12 Kensuke Homma / Hiroshima Univ. Analysis on differential multiplicity fluctuations

13 Kensuke Homma / Hiroshima Univ. 3 Density Density-density correlation in longitudinal space density correlation in longitudinal space dy y dz y t y z cosh cosh sinh τ τ τ + + cosh cosh,, 0 φ φ φ τ φ δ U y y y x d dy g h g S y In narrow midrapidity region like PHENIX, coshy~ and y~. Longitudinal space coordinate z can be transformed into rapidity coordinate in each proper frame of sub element characterized by a formation time τ at which dominant density fluctuations are embedded. Due to relatively rapid & symmetric expansion in y, analysis in y would have an advantage to extract initial fluctuations compared to analysis in transverse plane in high energy collision. Longitudinal multiplicity density fluctuation from the mean density can be an order parameter: ρ ρ φ

14 Kensuke Homma / Hiroshima Univ. 4 Direct observable for c determination Direct observable for c determination G a k a g g h c k c k k k ξ χ ξ φ φ χ + φ φ φ φ φ φ h c b a A g h g ,, GL free energy density g with φ ~ 0 from high temperature side is insensitive to transition order, but it can still be sensitive to c spatial correlation φ disappears at c 0 c a a 0 / c y k y ik k a A e A Y N y G k A a Y N dy e y G Y + ξ ξ φ φ ξ Correlation length -D two point correlation function Susceptibility in long wavelength limit Product between correlation length and amplitude can also be a good indicator for ~c Susceptibility Fourier analysis on G y<φ0φy>

15 Intuitive observable: blob intensity α x blob size ξ At RHIC Order parameter φρ<ρ> φ<< in >>c, Ginzburg-LandauGL free energy up to wo point correlation <φ φ > in -D longitudinal space C α exp / ξ αξ χ 0 < ρ > < ρ > nd order term / c k Non monotonic increase of αξ indicates ~c w.r.t. monotonically decreasing baseline as mean density <ρ> increases. c <c Many length scales appear a typical φ k disappears GL with higher order terms Kensuke Homma / Hiroshima Univ. 5

16 Kensuke Homma / Hiroshima Univ. 6 source wo point correlation via NBD Uncorrelated sources Correlated sources kk kk kk +k kk k!k +k kk NBD source + P k n σ μ Γ n + k μ / k Γ n Γ k + μ / k source + μ k μ < n > n k Bose-Einstein k k Poisson + μ / k /k corresponds to integral of two point correlation

17 Kensuke Homma / Hiroshima Univ. 7 Differential multiplicity measurements δ Probability A.U. Δ<0.7 integrated over Δφ<π/ PHENIX: s NN 00GeV Phys. Rev. C 76, small δ Zero magnetic field to enhance low pt statistics per collision event. large δ NBD can well describe n/μ differential distribution too.

18 Kensuke Homma / Hiroshima Univ. 8 Extraction of Extraction of αξ αξ product product β α ρ ρ ρ ρ ξ δ + / /,,, e C C β δ ξ δ αξ ρ δ δ ξ δ δ δ + + / 0 0 /, e d d C n n n k / δ ξ β δ αξ δ << + k Exact relation with NBD k Fit with approximated functional form Parametrization of two particle correlation β α ρ ρ ρ ρ ξ δ + /,,, e C C β absorbs rapidity independent bias: Npart fluctuation and reaction plane rotation and v Look at slopes 0% 5% Approximated functional form δ kδ Phys. Rev. C 76,

19 Kensuke Homma / Hiroshima Univ. 9 β αξ, β vs. Npart Dominantly Npart fluctuations and possibly correlation in azimuth 5% 0% β is systematically shift to lower values as the centrality bin width becomes smaller from 0% to 5%. his is understood as fluctuations of Npart for given bin widths αξ Au+Au@00GeV Phys. Rev. C 76, % 0% Npart αξ product, which is monotonically related with χ k0 indicates the non-monotonic behavior around Npart ~ 90. αξ χk 0 / ρ ρ Significance with Power + Gaussian: 3.98 σ 5%, 3. σ 0% Significance with Line + Gaussian:.4 σ 5%,.69 σ 0% C

20 Analysis in smaller system: Kensuke Homma / Hiroshima Univ. 0 Cu+Cu@00GeV 5% bin width Cu+Cu@00GeV 5% bin width

21 Analysis in lower energy: Kensuke Homma / Hiroshima Univ. Au+Au@6.4GeV Au+Au@6.4GeV

22 Kensuke Homma / Hiroshima Univ. Corrected mean multiplicity <μ< c > Cu+Cu@00GeV 0% bin width Cu+Cu@00GeV 5% bin width Au+Au@6.4GeV 0% bin width

23 Comparison of three collision systems Kensuke Homma / Hiroshima Univ. 3 Npart~90 in AuAu@00GeV Au+Au@00GeV ε BJ τ~.4gev/fm /c Phys. Rev. C 76, αξ Cu+Cu@00GeV Au+Au@00GeV Phys. Rev. C 76, <μ c >/<μ c Normalized mean multiplicity to that of top 5% in Au+Au@00GeV Au+Au@6.4GeV

24 Slides from HP08 P. Sorensen Kensuke Homma / Hiroshima Univ. 4

25 Similarity to SAR ridge results at low p Kensuke Homma / Hiroshima Univ. 5 Au+Au@00GeV Peak Amplitude Au+Au 00 GeV 6 GeV Peak Width αξμ Cu+Cu@00GeV SAR Preliminary SAR Preliminary Au+Au@00GeV ε BJ M. Daugherity: QM008 ε BJ Au+Au@6.4GeV Equivalent quantity; χ αξμ amplitude x width shows similar trends to what SAR sees. <μ c >/<μ c

26 Kensuke Homma / Hiroshima Univ. 6 Do we see other peculiar centrality dependence? - K to π and p to π fluctuations - est of quark number scaling of v at low KE

27 Kensuke Homma / Hiroshima Univ. 7 Meson-meson and baryon-meson fluctuations π π K K K, π + π K dyn π K π K Au+Au@00GeV π π p p p, π + π p dyn π p π p Au+Au@00GeV Npart ~90

28 Kensuke Homma / Hiroshima Univ. 8 Number of constituent Quarks NCQ scaling of v Scaling holds well for different centralitie

29 Deviation from scaling at low KE region? Npart ~90 In lower KE, there seems to be different behaviors between baryon and mesons. he transition is at Npart~90. Low mass sigma field may repulse pions and attract protons according to E.Shuryak hep-ph/ Can this phenomenon be understood as such effects? Kensuke Homma / Hiroshima Univ. 9

30 Kensuke Homma / Hiroshima Univ. 30 Summary. Scaled variance shows no significant divergent behavior in all collisions systems achieved at RHIC so far.. he product between normalized amplitude and correlation length in two particle correlation function, αξ as a function of Npart in Au+Au at 00GeV indicates a possible non monotonic increase at Npart~90. he trends of αξ in smaller system in the same collision energy and in the same system size in lower collision energy as a function of mean multiplicity are similar to that of Au+Au at 00GeV except the region where the possible non monotonicity is seen. Since the exponential form is still valid to explain all k vs. δ, this implies that the system is not just on c yet. ransitions of the two point functional form from exp to power would be a measurable clear signature of the phase transition. 3. p to π fluctuation shows qualitatively different Npart dependence from K to π fluctuations. 4. At low KE below 0.3 GeV, the deviation of p from quark number scaled curve is opposite in sign to that of π and K. Interestingly the sign flips at around Npart~90.