Systematic studies of global observables by PHENIX

1. Kensuke Homma / Hiroshima Univ. 1 Systematic studies of global observables by PHENIX Longitudinal density fluctuations Meson-meson and baryon-meson correlation Kensuke Homma for the PHENIX collaboration Hiroshima University I would like to present systematic studies of global observable by PHENIX. My name is Kensuke Homma from Hiroshima Univ. The focus of my talk is search for critical behavior via global observables. I would like to present systematic studies of global observable by PHENIX. My name is Kensuke Homma from Hiroshima Univ. The focus of my talk is search for critical behavior via global observables.

2. Kensuke Homma / Hiroshima Univ. 2 Understanding of QCD phase structure Understanding of QCD phase structure is one of crucial subjects to be intensively studied. What RHIC achieved so far is the formation of dense medium and the observation that the medium carry the partonic dof. Although it is believed that RHIC can across the crossover region, the current theoretical understanding is not conclusive in finite small density. And even if crossover region, critical temperature seems to depend on the order parameter we use. Therefore we would like to introduce an order parameter as general as possible in the following analysis.Understanding of QCD phase structure is one of crucial subjects to be intensively studied. What RHIC achieved so far is the formation of dense medium and the observation that the medium carry the partonic dof. Although it is believed that RHIC can across the crossover region, the current theoretical understanding is not conclusive in finite small density. And even if crossover region, critical temperature seems to depend on the order parameter we use. Therefore we would like to introduce an order parameter as general as possible in the following analysis.

3. Kensuke Homma / Hiroshima Univ. 3 Intuitive observable: blob intensity a x blob size x The order parameter phi is defined as fluctuation size from the mean density as a function of spatial coordinate. What is shown here is the phase transition of water in a kettle in my kitchen. At RHIC, the initial temperature is much higher than Tc. In such a case, this order parameter would be very small, since the medium in higher temperature would be dense and homogenous. Therefore, as a free energy of the thermalized system, we can apply GL potential ie polynomical expansion up to the lowest 2nd order term of phi. Then we focus on the two point correlation of this order parameter. If the dimension of the system is effectively 1d, we can derive the correlation function as a simple damping form as a function of the relative distance with a typical correlation length xi. As a general signature of the phase transition, we usually look for the size of the blob as seen in this picture. However, the intensity of blob with large correlation length is also good indicator of T=Tc. Then the increase of the product between them can be sensitive quantity to determine Tc. Actually we can derive a relation that axi corresponds to chi*T based on the GL free potential form. It monotonically decreases as system density increases. However, if the T~Tc, the product jumps up. So the ……..The order parameter phi is defined as fluctuation size from the mean density as a function of spatial coordinate. What is shown here is the phase transition of water in a kettle in my kitchen. At RHIC, the initial temperature is much higher than Tc. In such a case, this order parameter would be very small, since the medium in higher temperature would be dense and homogenous. Therefore, as a free energy of the thermalized system, we can apply GL potential ie polynomical expansion up to the lowest 2nd order term of phi. Then we focus on the two point correlation of this order parameter. If the dimension of the system is effectively 1d, we can derive the correlation function as a simple damping form as a function of the relative distance with a typical correlation length xi. As a general signature of the phase transition, we usually look for the size of the blob as seen in this picture. However, the intensity of blob with large correlation length is also good indicator of T=Tc. Then the increase of the product between them can be sensitive quantity to determine Tc. Actually we can derive a relation that axi corresponds to chi*T based on the GL free potential form. It monotonically decreases as system density increases. However, if the T~Tc, the product jumps up. So the ……..

4. Kensuke Homma / Hiroshima Univ. 4 Density measurement: inclusive dNch/dh As a density measurement, we naturally use the number of charged particles.. What is shown here is the multiplicity distribution divided by the mean from pp to AuAu taken by PHENIX so far. The fit curve is NBD. Multiplicity in all collision systems and all centralities are well described by NBD curves.As a density measurement, we naturally use the number of charged particles.. What is shown here is the multiplicity distribution divided by the mean from pp to AuAu taken by PHENIX so far. The fit curve is NBD. Multiplicity in all collision systems and all centralities are well described by NBD curves.

5. Kensuke Homma / Hiroshima Univ. 5 Two point correlation via NBD Let me explain how to discuss two point correlation with the multiplicity distributions. First of all, NBD consists of mean charged particle multiplicity mu and the width parameter 1/k. If we think about a convolution between two uncorrelated emission sources, the k value of convolution can be represented by the sum of k in each source. In this case the correlation of multiplicity between two sources is round shape. On the other hand, if the emission sources are correlated, the k parameter of the convolution deviates from the sum of k in each emission sources. In such a case, the correlation of multiplicity between two sources looks like this. By measuring NBD k by fits, we can describe any kind of two point correlation. If k=1, it corresponds to BE and if k is infinite, it corresponds to Poisson distribution. Mathematically it is known that 1/k corresponds to the integral of two point correlation function.Let me explain how to discuss two point correlation with the multiplicity distributions. First of all, NBD consists of mean charged particle multiplicity mu and the width parameter 1/k. If we think about a convolution between two uncorrelated emission sources, the k value of convolution can be represented by the sum of k in each source. In this case the correlation of multiplicity between two sources is round shape. On the other hand, if the emission sources are correlated, the k parameter of the convolution deviates from the sum of k in each emission sources. In such a case, the correlation of multiplicity between two sources looks like this. By measuring NBD k by fits, we can describe any kind of two point correlation. If k=1, it corresponds to BE and if k is infinite, it corresponds to Poisson distribution. Mathematically it is known that 1/k corresponds to the integral of two point correlation function.

6. Kensuke Homma / Hiroshima Univ. 6 Differential multiplicity measurements As a measurement of the two point correlation, we perform the differential analysis on the multiplicity. We especially focus on the longitudinal space coordinate, since the system expansion speed is expected high and the intially embedded fluctuation might be able to survive even if we look at soft pions. In order to enhance the low pt statistics per collision which would be relevant for the discussion of phase transition, we used B-off data. What is shown here is the multiplicity distribution for different pseudo rapidity intervals from small to large. Again, distributions are well described by NBD.As a measurement of the two point correlation, we perform the differential analysis on the multiplicity. We especially focus on the longitudinal space coordinate, since the system expansion speed is expected high and the intially embedded fluctuation might be able to survive even if we look at soft pions. In order to enhance the low pt statistics per collision which would be relevant for the discussion of phase transition, we used B-off data. What is shown here is the multiplicity distribution for different pseudo rapidity intervals from small to large. Again, distributions are well described by NBD.

7. Kensuke Homma / Hiroshima Univ. 7 Extraction of ax product Let me explain how to extract alpha*xi from the NBD. Firstly two particle correlation function can be parameterized by the functional form based on the GL free energy. However, we found that a constant parameter is really necessary to absorb the experimental biases like centrailitiy bin width which is independent of the rapidity interval size. The inverse of NBD k is mathematically related with 2nd order factorial moment over window size. If the xi is smaller than the window size we use, we can approximate the relation like this. If beta is zero, we notice that we can extract a*xi from the slope parameter in k vs dEta. Let me explain how to extract alpha*xi from the NBD. Firstly two particle correlation function can be parameterized by the functional form based on the GL free energy. However, we found that a constant parameter is really necessary to absorb the experimental biases like centrailitiy bin width which is independent of the rapidity interval size. The inverse of NBD k is mathematically related with 2nd order factorial moment over window size. If the xi is smaller than the window size we use, we can approximate the relation like this. If beta is zero, we notice that we can extract a*xi from the slope parameter in k vs dEta.

8. Kensuke Homma / Hiroshima Univ. 8 a?, ß vs. Npart What is shown here is the beta and axi as a function of Npart in AuAU@200GeV system. As you expect, beta is systematic shift to lower value from 10% case to 5% case, while the a*x is rather stable. There seems to be non monotonic behavior in a*xi at around Npar=90 and it might be related with T~Tc. The significance depends on how we assume the base line monotonic shape. If we assume power function which is naturally expected since rho increases monotonically as a function Npart, the significance levels are 4 sigma for 5% and 3 sigma for 10% bin width cases, respectively.What is shown here is the beta and axi as a function of Npart in AuAU@200GeV system. As you expect, beta is systematic shift to lower value from 10% case to 5% case, while the a*x is rather stable. There seems to be non monotonic behavior in a*xi at around Npar=90 and it might be related with T~Tc. The significance depends on how we assume the base line monotonic shape. If we assume power function which is naturally expected since rho increases monotonically as a function Npart, the significance levels are 4 sigma for 5% and 3 sigma for 10% bin width cases, respectively.

9. Kensuke Homma / Hiroshima Univ. 9 Analysis in smaller system: Cu+Cu@200GeV We extend this analysis to another collision systems. As the different size with the same energy, we measure a*xi in Cu+Cu@200. NBD k vs dEta. Fit good with the same functional form..We extend this analysis to another collision systems. As the different size with the same energy, we measure a*xi in Cu+Cu@200. NBD k vs dEta. Fit good with the same functional form..

10. Kensuke Homma / Hiroshima Univ. 10 Analysis in lower energy: Au+Au@62.4GeV As the lower energy system keeping the same system size, we analyzed AuAu@62.4 data. Again, fit to k vs dEeta is enough accurate.As the lower energy system keeping the same system size, we analyzed AuAu@62.4 data. Again, fit to k vs dEeta is enough accurate.

11. Kensuke Homma / Hiroshima Univ. 11 Comparison of three collision systems This is a comparison of a*xi as a function of normalized mean multiplicity to that of the top 5% centrality in AuAu@200GeV. So the maximum horizontal axis value is set at 1.0. As you see, three collision systems quantitatively agree in low and higher multiplicity. However, the possible non monotonicity is prominent only in AuAu@200. We still need careful study on other systems to make a conclusive statement on the non monotonicity. If we put a biased line based on AuAu@200, the corresponding Npart is around 90. Bease upon the measurement of dET/dEta, we can deduce the corresponding Bjorken energy density and Npart~90 corresponds to 2.4GeV/fm2/c..This is a comparison of a*xi as a function of normalized mean multiplicity to that of the top 5% centrality in AuAu@200GeV. So the maximum horizontal axis value is set at 1.0. As you see, three collision systems quantitatively agree in low and higher multiplicity. However, the possible non monotonicity is prominent only in AuAu@200. We still need careful study on other systems to make a conclusive statement on the non monotonicity. If we put a biased line based on AuAu@200, the corresponding Npart is around 90. Bease upon the measurement of dET/dEta, we can deduce the corresponding Bjorken energy density and Npart~90 corresponds to 2.4GeV/fm2/c..

12. Kensuke Homma / Hiroshima Univ. 12 Are there symptoms in other observables at around the same Npart? Given this bias, let us look for other observable which show peculiar behavior as a function of Npart in AuAu@200GeV.Given this bias, let us look for other observable which show peculiar behavior as a function of Npart in AuAu@200GeV.

13. Kensuke Homma / Hiroshima Univ. 13 Meson-meson and baryon-meson fluctuations PHENIX is analyzing K/pi fluctuaitons and also p pi fluctuations. What is shown here are Nu_dyn as a function of Npart, which is defined as a combination of the 2nd order factorial moments of each species and the mixed term. As you see, the quantity in p to pi has a qualitative different behavior from that of K to pi.PHENIX is analyzing K/pi fluctuaitons and also p pi fluctuations. What is shown here are Nu_dyn as a function of Npart, which is defined as a combination of the 2nd order factorial moments of each species and the mixed term. As you see, the quantity in p to pi has a qualitative different behavior from that of K to pi.

14. Kensuke Homma / Hiroshima Univ. 14 Deviation from scaling at low KET region ? Next one is Ratio of measured v2 to fit scaling curves as a function of KET/nq in each centrality class. They indicate good NCQ scalings at around KET ~ 1 GeV. However, if we focus on the deviation from the scaling curve, the trend of proton curves is qualitatively different from that of pi and K as you seen in blue points. The relation flips at around Npart~90.Next one is Ratio of measured v2 to fit scaling curves as a function of KET/nq in each centrality class. They indicate good NCQ scalings at around KET ~ 1 GeV. However, if we focus on the deviation from the scaling curve, the trend of proton curves is qualitatively different from that of pi and K as you seen in blue points. The relation flips at around Npart~90.

15. Kensuke Homma / Hiroshima Univ. 15 Conclusion Correlation function derived from GL free energy density up to 2nd order term in the high temperature limit is consistent with what was observed in NBD k vs dh in three collision systems. This provides a way to directly determine transition points without tunable model parameters with relatively fewer event statistics. The product of susceptibility and temperature, ax as a function of Npart indicates a possible non monotonic increase at Npart~90. The corresponding Bjorken energy density is 2.4GeV/fm3 with t=1.0 fm/c and the transverse area=60fm2 The trends of ax in smaller system in the same collision energy (Cu+Cu 200GeV) and in the same system size in lower collision energy (Au+Au 62.4) as a function of mean multiplicity are similar to that of Au+Au at 200GeV except the region where the possible non monotonicity is seen. We need careful error estimates and increase of statistics for smaller size and lower energy systems to obtain the conclusive result. Combining other symptoms in the same multiplicity region, we hope to understand possibly interesting behaviors.

16. Kensuke Homma / Hiroshima Univ. 16 Backup

17. Kensuke Homma / Hiroshima Univ. 17 How about <cc> suppression? If the possible non monotinicity is really related with dynamical phase transtion, we should see the symptoms in other observable at around same energy density region. If the possible non monotinicity is really related with dynamical phase transtion, we should see the symptoms in other observable at around same energy density region.

18. Kensuke Homma / Hiroshima Univ. 18 Other symptoms?: baryon-meson correlation V2 divided by scaled curve of v2 by Nq as a function KET/nq.V2 divided by scaled curve of v2 by Nq as a function KET/nq.

19. Kensuke Homma / Hiroshima Univ. 19 KET + Number of constituent Quarks (NCQ) scaling

20. Kensuke Homma / Hiroshima Univ. 20 Future prospect It would be important to see coherent behaviors on other observables like; J/y suppression pattern, breaking point of quark number scaling of V2, fluctuation on baryon-meson production, low pt photon yield and so on to investigate what kind of phase transition is associated with ax measurement, if ax is really the indication of a phase transition. Quick finer energy and species scan with 100M events for each system would provide enough information on the structure of the possible non monotonicity. This would reveal the relation between initial temperature and speed of blob evolution and speed of medium expansion.

21. Kensuke Homma / Hiroshima Univ. 21 What is the energy density at Npart~90?

22. Kensuke Homma / Hiroshima Univ. 22 Density correlation in longitudinal space Interpretation. Interpretation.

23. Kensuke Homma / Hiroshima Univ. 23 Direct observable for Tc determination Interpretation. Interpretation.

24. Kensuke Homma / Hiroshima Univ. 24 NBD fitsin CuCu@200

25. Kensuke Homma / Hiroshima Univ. 25 Hit and dead map of East arm

26. Kensuke Homma / Hiroshima Univ. 26 Position dependent NBD corrections Require geometrical correction factor on NBD k below 2.0 h-window size dh is defined as: L=28(1-dh/DhPHENIX)

27. Kensuke Homma / Hiroshima Univ. 27 Cu+Cu@200GeV with only statistical errors

28. Kensuke Homma / Hiroshima Univ. 28 Corrected mean multiplicity <mc>