Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Update on moments products values with (N)BD and Mixed Events baselines W.J. Llope & D. McDonald Rice University Speculated 1 st order phase boundary M. Stephanov, Rice Workshop, May 23-25, 2012 Moments products directly related to lattice susceptibility ratios (QCD order parameters). Also proportional to powers of the correlation length in the NLSM. We are looking for non-monotonic behavior in the moments products. One needs a reasonable description of the values in the absense of critical behavior. CLT Poisson HRG (Negative) Binomial (G. Westfall) Mixed Events Here, update on the last two of these baselines, & update on the pbar/p binning results…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, STAR Results (QM2012) √s NN * * Cleymans et al. PRC 73, (2006) net-protons X. Luo for STAR, QM2012 D. McDonald for STAR, QM2012 net-chargenet-K No non-monotonicity seen Significance of net-p dip?

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Significance of net-p dip near 19.6 GeV? J. Nagle, last talk at QM2012 what the NLSM would actually expect for a CP at √s NN ~15 GeV

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Congratulations to Dr. McDonald! More details on the following can be found in Daniel McDonald’s Thesis. Daniel produced the data points, provided the (N)BD & mixed events input data, and produced the final comparison plots. I wrote the (N)BD & mixed events code.

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, (N)BD T..J. Tarnosky & G. Westfall, Oct Functional form describes the (particle identified) multiplicity distributions ranging from NA22 & UA5 to PHENIX Inputs: mean (μ) & variance (σ 2 ) Then, the values of C k, Sσ, & Kσ 2 are predicted.

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Mixed Events  “Sampled Singles” Caveat: The present approach is not the same as the MSU mixed events Gary is always warning that there were many lessons learned from NA49 on how to do this incorrectly! The present approach is different … cf. G. Torrieri et al., J. Phys. G, 37, (2010) So, starting now, I will call the present approach something else: “sampled singles” The only input is the 2D distributions of Npos vs. RM2corr and Nneg vs. RM2corr. where pos = p, K +, q + and neg = pbar, K -, q - same plots for K ±, q ± … Filled at exactly the same spot in DM’s code where the deviates plots are filled… …i.e. includes all the same track cuts, PID, and run&evt QA as his QM2012 plots. Np Npbar refmult2corr

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Sampled Singles method In every slice of RM2corr, sample one value of Npos and one value of Nneg, Nevt times. In each sample at a given RM2corr, one then has a value for Npos and Nneg Then form Nnet = Npos-Nneg and Ntot = Npos+Nneg Fill similar 2D plots of Nnet and Ntot vs. RM2corr And then extract the moments (products) and do the CBW corrections as usual… Destroys all intra-event correlations between Npos and Nneg, reproduces singles distributions, & has the same statistical certainty as the data by construction… Np Npbar refmult2corr

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-K sampled singles uncertainties are not drawn, but are similar to those on the data points by construction…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-Q Sampled singles values go beserk for ~central events at the highest √s NN ….

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, “Sampled singles” does not work for net-Q central at highest root-s! Same events! Intra-event correlations are important…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-p sampled singles approach reproduces the net-p moments for all √s NN & centrality…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-p vs. √s NN, 0-10% central

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, pbar/p binning Switching gears now… We typically assume that tight centrality cuts (0-5%) tightly constrain the locations of the events on the phase diagram… …may not be a very good assumption. bulkcorr: lfspectra:

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, The Variances… Freeze-out positions on the phase diagram for 50 events from UrQMD+Thermus T (GeV) μ B (GeV) Even in 0-5% central collisions, the variances are large…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, μ B distributions at freeze-out, 0-5% and 5-10% central Run UrQMD to fm/c in each of thousands of events, plot Probability(  B ) by √s NN Probability  B (MeV) √s NN (GeV) For the  B range of interest (  B >~200MeV), the  B distributions are ~200 MeV wide! Compare to expected  B -width of critical enhancement of Δ(  B )~ MeV… C. Athansiou et al., PRD 82, (2010), R. Gavai & S. Gupta, PRD 78, (2008)

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Use event-by-event values of pbar/p to constrain event-by-event values of μ B Use event-by-event pbar/p ratio to gate the moments analyses! pbar/p = exp(-2μ B /T) Temperature is a weak function of centrality and √s NN S. Das for STAR, QM2012  Direct relationship between pbar/p and apparent μ B values event-by-event! Significant overlap in μ B distributions from different root-s values even in 0-5% central collisions trend also holds for less central events w/ non-zero pbar and p multiplicities error bars here are the RMS values! (±1σ about mean) 0-5% centrality 14 = 2/T  T~140MeV

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-K moments with pbar/p gating

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Total-p moments with pbar/p gating

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Net-p moments with pbar/p gating

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Residual plot…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Summary Added (N)BD and “sampled singles” (~mixed events) curves to all STAR preliminary moments products results plots. The values of Sσ & Kσ 2 for Net-K, Net-p, and Total-p are generally reproduced by the sampled singles approach. i.e. intra-event correlations have no effect on these moments products values, moments products are completely described by the singles distributions… The values of Sσ & Kσ 2 for Net-q at higher root-s & central collisions are not at all reproduced by the sampled singles approach. Intra-event correlations are important for net-q. This is interesting and should be discussed further… pbar/p gating… Sampled singles baseline important, as the phase space is being sculpted… Excellent agreement for most bins…

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, BACKUP SLIDES

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Approach and codes UrQMD 3.3p1 Default parameters, only set impact parameter range and ecm only centrality set on impact parameter in “standard” percentages assuming b max =14fm output in 1 fm/c timesteps in each event timesteps total depending on root-s in each timestep, ignore spectators and count multiplicity of 20 different particles (light hadrons and hyperons) Thermus Standalone application that reads the UrQMD files and fits the multiplicity ratios in every timestep in every event Grand Canonical Ensemble, fit parameters: (T, μ B, μ S, γ S ) 9 or 12 ratios considered (π±, K±, p±, Λ±) Covariance from MINUIT, N DOF = N yields - 1 Mult errors in each time step & evt taken as Poisson (~√N) – but not that important Also fit “averaged events” (in a given centrality bin) in each time step Can thus plot the trajectories of individual events in (μ B,T) space plot the trajectories of averaged events in (μ B,T) space plot the distributions of (T, μ B, μ S, γ S ) in centrality-selected events

Moments with (N)BD & Mixed Evts Click to edit Master subtitle style Bulkcorr PWG meeting, April 17, Fit Examples, UrQMD by root-s and centrality % 40-60% 20-40% 10-20% 5-10% 0-5%