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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 1 Statistical model fits to simulated RHIC data W.J. Llope Rice University Speculated 1 st order phase boundary QCD order parameters: Susceptibilities of “charges” B, S, Q, calculable on the lattice. Critical opalescence (divergent correlation length) calculable from the non-linear sigma model Direct correspondence to products of moments of experimentally measurable identified particle multiplicity distributions: S & K 2 M. Stephanov, Rice Workshop, May 23-25, 2012 M. Cheng et al. PRD, 79, 074505 (2009)

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 2 STAR Results (QM2012) Basic approach in STAR is: take data at different beam energies, select central collisions, & then look for “non-monotonic behavior” of moments products S & K 2 √s NN * 7.7421 11.5316 19.6206 27156 39112 62.473 20024 * Cleymans et al. PRC 73, 034905 (2006) net-protons X. Luo for STAR, QM2012 net-charge (& net-kaons) D. McDonald for STAR, QM2012 No √s NN -localized enhancement in the moments products w.r.t. Poisson and other (HRG, binomials, mixed events) baselines was observed

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 3 UrQMD simulations √s NN * 7.7421 11.5316 19.6206 27156 39112 62.473 20024 * Cleymans et al. PRC 73, 034905 (2006) This approach assumes that a tight (5%) centrality cut at a given beam energy tightly constrains the events on the phase diagram… If this is not true, then the signal of critical behavior could be buried by events that are not near enough to the critical point to result in the expected enhancements to the moments products. What is the variance of μ B in such samples of events? This question was studied by coupling U R QMD and T HERMUS. U R QMD 3.3p1, default parameters, six centrality bins save identified particle multiplicities in 1fm/c time-steps run Thermus for each time-step in each event, GCE M. Lisa, Workshop On Fluctuations, Correlations and RHIC LE Runs, BNL, Oct 2011 T. Tarnowsky for STAR, QM2011

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 4 Example Fits of a single event vs. time, 19.6 GeV, 0-5% t=5fm/c t=20fm/c t=40fm/c t=60fm/c t=80fm/c t=100fm/c t=200fm/c t=500fm/c

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 5 Example Fits of a single event vs time, 200 GeV, 0-5% t=5fm/c t=20fm/c t=40fm/c t=60fm/c t=80fm/c t=100fm/c t=200fm/c t=800fm/c

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 6 The Variances… Freeze-out positions on the phase diagram for 50 events T (GeV) μ B (GeV) Even in 0-5% central collisions, the variances are large…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 7 μ B distributions at freeze-out, 0-5% and 5-10% central Run UrQMD to 500-800 fm/c in each of thousands of events, plot Probability( B ) by √s NN 2007.7 2007.7 Probability B (MeV) √s NN (GeV) 7.7 11.5 19.6 27 39 62.4 200 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 )~50-100 MeV… C. Athansiou et al., PRD 82, 074008 (2010), R. Gavai & S. Gupta, PRD 78, 114503 (2008)

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 8 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 200 7.7 error bars here are the RMS values! (±1σ about mean) 0-5% centrality 14 = 2/T T~140MeV

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 9 STAR ratios of average multiplicities in centrality bins from QM2012 S. Das for STAR, QM2012 STAR used T HERMUS and extracted (, ) from ratios of efficiency-corrected yields for |y|<0.1 in specific centrality bins at √s NN = 7.7, 11.5, 39, 200 GeV Indicates: increases w/ centrality slightly increases w/ centrality Can this be reproduced with the present simulations? …apply an STAR filter to the UrQMD events B. Abelev et al. (STAR Collaboration), PRC 79 (2009) 34909

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 10 Effect of acceptance on T HERMUS parameters in UrQMD events 7.7 200 60-80% 0-5%

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 11 Summary UrQMD events can be reasonably fit with Thermus throughout the time evolution of single events, even at times as early as a few fm/c (!) Variances of the B distributions in tightly (5%-wide) centrality-selected events is apparently quite large (~200 MeV for √s NN ≤ 30 GeV) Implication is that finer steps in beam energy (except for ~15GeV, this run!) are not what we need now. What is needed is more events, and if possible, improved detectors (iTPC upgrade). Events can be sorted by apparent B based on event-by-event values of the pbar/p ratio… Study net-charge and net-Kaon moments gated on pbar/p directly… net-proton and total-proton moments can also be studied, but require a new baseline due to correlation of pbar/p and the multiplicity observable… Increasing values with icnreasing centrality measured by STAR in the GCE seem to be a reflection of the very narrow acceptance (|y|<0.1) used in this analysis. A “perfect detector” measuring everything from the participant zone would see and decrease for increasing centrality.

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 12 BACKUP SLIDES

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 13 net-p distributions vs y from NA49 a very narrow rapidity slice at y=0 does not refect the whole participant zone top 7% central collisions…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 14 Filtered UrQMD+Thermus simulations… Apply “STAR” acceptance & efficiency filter to UrQMD Compare perfect, 4π, participant-only simulation results to those we measure E-by-E… refmult, refmult2 and refmult3 vs. impact parameter with and without the filter yields in |η| 0.2 GeV, and including a parameterized tracking efficiency (parameterized tracking efficiencies from Evan Sangaline)

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 15 Example time dependence of the ratios, 19.6 GeV, 0-5% freezeout ~ 50 fm/c

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 16 Example time dependence of the ratios, 200 GeV, 0-5% freezeout ~ hundreds of fm/c

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 17 Fit Examples, UrQMD by root-s and centrality, Acceptance Filtered 7.7 200 60-80% 40-60% 20-40% 10-20% 5-10% 0-5%

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 18 μ B from data+Thermus fits, Complete feeddown 7.7 200 7.7 200 general trend is as expected μ B decreases w/ inc. root-s ~central μ B distributions at a given root-s are wide and significantly overlap with data from neighboring root-s values

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 19 μ B from data+Thermus fits, Zero feeddown 7.7 200 7.7 200 general trend is as expected μ B decreases w/ inc. root-s ~central μ B distributions at a given root-s are wide and significantly overlap with data from neighboring root-s values values ~10% smaller with zero feeddown compared to complete feeddown

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 20 data+Thermus fits, 0-5% central complete feeddownzero feeddown …same pbar/p=exp(-14μ B ) trend is seen when fitting the yields from the experimental data… error bars here are the RMS values! (±1σ about mean)

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 21 Constrain μ S and γ S and Fit (T, μ B ), GCE 0-5%, 5-10%, 10-20% give ~same T distributions… decreases as b decreases…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 22 Constrain μ S and γ S and Fit (T, μ B ), GCE double peaks disappear… still significant overlap in 0-5%, 5-10%, 10-20%... µ B decreases as b decreases…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 23 Constrain μ S and γ S and Fit (T, μ B ), GCE, Event-Avg Trajectories look quite different at low root-s compared to free 4 parameter fits… FO µ B decreases as b decreases…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 24 N DOF For N non-zero yields, one can form ratios… i.e. for π ±,K ±,p ± –> up to N=6 non-zero yields –> 15 non-zero ratios possible Of these 15 non-zero ratios from N non-zero yields, N-1 are independent… I am only fitting events if N-1 ≥ N par Evan’s simulation: how probable is it to measure b if normal distributed with means m and covariance C. (b-m) T C -1 (b-m) is χ 2 distributed with k DOF m = meas (vector with k values) b = model (vector with k values) C = meas covariance (k×k matrix) v = meas variances (diagonal of C) only yields…. k=5 measurements are independent plot diagonal-only χ 2 sum all ratios…. plot diagonal-only χ 2 sum for 5! ratios …mean~10, k-1

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 25 data+Thermus Used same Thermus code to fit experimental π ±,K ±,p ± yield ratios event-by-event Yields from Daniel McDonald Detailed bad-run and bad-event rejection Same event and track cuts as he uses in his moments analyses Centrality from refmult2corr dE/dx+TOF plus spallation P T cut for p N=6 π ±,K ±,p ± yields calculated for all directly identified tracks with |η|<0.5 But, BTW, there is a problem re: feeddown contributions to the observed yields…. Thermus can be run in two modes. - No Decays: i.e. Input yields do not include any feeddown contributions (this is how I appropriately run the UrQMD+Thermus simulations) - Allow Decays: i.e. Input yields include 100% of the possible feeddown from all particles known to Thermus (fit or not) with known branching fractions AFAIK, our data is not consistent with either case we can estimate feeddown but we don’t generally measure all the necessary parent yields or we can completely ignore feeddown, but there is typically a 1-3fm dca cut applied …I’ll just run Thermus in both modes and will provide both sets of results…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 26 μ B from data+Thermus fits: 0-5%, 5-10%, and 10-20% centrality only Here, using 4 parameter fits – which look fine in general – non-zero ratios are reproduced… DK off (zero feeddown) DK on (complete feeddown) general trend is as expected μ B decreases w/ increasing root-s essentially no difference between 0-5%, 5-10%, and 10-20%

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 27 Centrality dependence of T b-dependence is weak multiple bands at low root-s result from “0,1 antibaryon”

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 28 Centrality dependence of μ B b-dependence is weak multiple bands at low root-s result from “0,1 antibaryon”

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 29 1D T distributions by centrality bin

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 30 1D μ B distributions by centrality bin

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 31 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 500-800 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

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 32 Impact Parameters Codes run on the DAVINCI farm at Rice, generally 50-100 nodes available each day… Run as many events through thermus as fits in 24hrs of wall clock time… Few 100s to few 1000s evts in each root-s and centrality bin…

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 33 Time Trajectories of “Average Events” peripheral collisions freezeout at higher (μ B,T) than do central collisions

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 34 Fit Examples, UrQMD by root-s and centrality 7.7 200 60-80% 40-60% 20-40% 10-20% 5-10% 0-5%

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Statistical model fits to simulated RHIC data Statistical model fits to simulated RHIC data Click to edit Master subtitle style APS April Meeting, Denver, April 14, 2013 35 Constrain μ S and γ S and Fit (T, μ B ), GCE In previously presented slides, (T, μ S, μ B, γ S ) were allowed to vary freely… Resulted in some events with γ S pegged at 1, and others w/ low values and two peaks in μ B for non-peripheral collisions at low root-s μ S vs b and root-s from 4 par fits γ S vs b and root-s from 4 par fits now constrain (μ S, γ S ) values to the red curves and fit only (T, μ B )….

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