statistical model fits to simulated rhic data statistical model fits to simulated rhic data click to...

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 dataW.J. Llope

Rice University

Speculated 1st order phase boundary

QCD order parameters: Susceptibilitiesof “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 ofexperimentally measurable identified particle multiplicity distributions: Ss & Ks2

M. Stephanov, Rice Workshop, May 23-25, 2012

M. Cheng et al. PRD, 79, 074505 (2009)




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 Ss & Ks2

√sNN <mB>*

7.7 421

11.5 316

19.6 206

27 156

39 112

62.4 73

200 24

* C

leym

ans

et a

l. P

RC

73,

034

905

(200

6)

net-protonsX. Luo for STAR, QM2012

net-charge (& net-kaons)D. McDonald for STAR, QM2012

No √sNN-localized enhancementin the moments products w.r.t. Poissonand other (HRG, binomials, mixed events)

baselines was observed




UrQMD simulations

√sNN <mB>*

7.7 421

11.5 316

19.6 206

27 156

39 112

62.4 73

200 24

* C

leym

ans

et a

l. P

RC

73,

034

905

(200

6)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 beburied by events that are not near enough to the critical point toresult in the expected enhancements to the moments products.What is the variance of μB in such samples of events?

This question was studied by coupling URQMD and THERMUS.URQMD 3.3p1, default parameters, six centrality bins save identified particle multiplicities in 1fm/c time-stepsrun 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




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





Example Fits of a single event vs time, 200 GeV, 0-5%






The Variances…

Freeze-out positions on the phase diagram for 50 events

T (

GeV

)

μB (GeV)

Even in 0-5% central collisions, the variances are large…




μB 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(mB) by √sNN

200 7.7

200 7.7

Pro

babi

lity

mB (MeV)

√sNN (GeV)7.711.519.62739

62.4200

For the mB range of interest (mB>~200MeV), the mB distributions are ~200 MeV wide!Compare to expected mB-width of critical enhancement of Δ(mB)~50-100 MeV…

C. Athansiou et al., PRD 82, 074008 (2010), R. Gavai & S. Gupta, PRD 78, 114503 (2008)




Use event-by-event values of pbar/p to constrain event-by-event values of μB

Use event-by-event pbar/p ratio to gate the moments analyses!

pbar/p = exp(-2μB/T)

Temperature is a weak function ofcentrality and √sNN

S. Das for STAR, QM2012

Direct relationship between pbar/pand apparent μB values event-by-event!

Significant overlap in μB distributionsfrom different root-s values even in0-5% 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




STAR ratios of average multiplicities in centrality bins from QM2012

S. Das for STAR, QM2012

STAR used THERMUS and extracted (<mB>,<T>) from ratios of efficiency-corrected yieldsfor |y|<0.1 in specific centrality bins at √sNN = 7.7, 11.5, 39, 200 GeV

Indicates:<mB> increases w/ centrality<T> 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




Effect of acceptance on THERMUS parameters in UrQMD events

7.7 200

60-8

0%

0-5%




Summary

UrQMD events can be reasonably fit with Thermus throughout the time evolutionof single events, even at times as early as a few fm/c (!)

Variances of the mB distributions in tightly (5%-wide) centrality-selected events is apparently quite large (~200 MeV for √sNN ≤ 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 mB 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 <mB> 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<mB> and <T> decrease for increasing centrality.




BACKUP SLIDES




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…




Filtered UrQMD+Thermus simulations…

Apply “STAR” acceptance & efficiency filter to UrQMDCompare perfect, 4π, participant-only simulation results to those we measure E-by-E…

refmult, refmult2 and refmult3 vs. impact parameter with and without the filteryields in |η|<0.5, PT>0.2 GeV, and including a parameterized tracking efficiency

(parameterized tracking efficiencies from Evan Sangaline)




Example time dependence of the ratios, 19.6 GeV, 0-5%

freezeout ~ 50 fm/c




Example time dependence of the ratios, 200 GeV, 0-5%

freezeout ~ hundreds of fm/c




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%




μB from data+Thermus fits, Complete feeddown

7.7200

7.7200

general trend is as expectedμB decreases w/ inc. root-s

~central μB distributions at a given root-s are wide and significantly overlap with data from neighboring root-s values




μB from data+Thermus fits, Zero feeddown

7.7200

7.7200

general trend is as expectedμB decreases w/ inc. root-s

~central μB distributions at a given root-s are wide and significantly overlap with data from neighboring root-s values

values ~10% smaller with zerofeeddown compared to completefeeddown




data+Thermus fits, 0-5% central

complete feeddown zero feeddown

…same pbar/p=exp(-14μB) trend is seen when fitting the yields from the experimental data…

error bars here are the RMS values!(±1σ about mean)




Constrain μS and γS and Fit (T, μB), GCE

0-5%, 5-10%, 10-20% give ~same T distributions…

<T> decreases as b decreases…





double peaks disappear…

still significant overlapin 0-5%, 5-10%, 10-20%...

µB decreases as b decreases…




Constrain μS and γS and Fit (T, μB), GCE, Event-Avg Trajectories

look quite different at low root-scompared to free 4 parameter fits…

FO µB decreases as b decreases…




NDOF

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 ≥ Npar

€

Σi=1i<N i

Evan’s simulation:how probable is it to measure b if normal distributed

with means m and covariance C.(b-m)TC-1(b-m) is χ2 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 independentplot diagonal-only χ2 sum

all ratios….plot diagonal-only χ2 sum for 5! ratios…mean~10, k-1<mean<5!

keff~5 poor fit

mean~10

closer to χ2 distribution w/ k-1 DOFthen 5! DOF but not exactly the same




data+Thermus

Used same Thermus code to fit experimental π±,K±,p± yield ratios event-by-event

Yields from Daniel McDonaldDetailed bad-run and bad-event rejectionSame event and track cuts as he uses in his moments analysesCentrality from refmult2corrdE/dx+TOF plus spallation PT cut for pN=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 casewe can estimate feeddown but we don’t generally measure all the necessary parent

yieldsor 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…




μB 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 μB decreases w/ increasing root-s

essentially no difference between 0-5%, 5-10%, and 10-20%




Centrality dependence of T

b-dependence is weak

multiple bands atlow root-s resultfrom “0,1 antibaryon”




Centrality dependence of μB

b-dependence is weak

multiple bands atlow root-s resultfrom “0,1 antibaryon”




1D T distributions by centrality bin




1D μB distributions by centrality bin




Approach and codes

UrQMD 3.3p1Default parameters, only set impact parameter range and ecm only

centrality set on impact parameter in “standard” percentages assuming bmax=14fmoutput in 1 fm/c timesteps in each event

500-800 timesteps total depending on root-sin 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, μB, μS, γS) 9 or 12 ratios considered (π±, K±, p±, Λ±)Covariance from MINUIT, NDOF = Nyields - 1Mult 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 thusplot the trajectories of individual events in (μB,T) spaceplot the trajectories of averaged events in (μB,T) spaceplot the distributions of (T, μB, μS, γS) in centrality-selected events




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…




Time Trajectories of “Average Events”

peripheral collisions freezeout at higher (μB,T)than do central collisions




Fit Examples, UrQMD by root-s and centrality

7.7

200

60-80% 40-60% 20-40% 10-20% 5-10% 0-5%





In previously presented slides, (T, μS, μB, γS) were allowed to vary freely…Resulted in some events with γS pegged at 1, and others w/ low values

and two peaks in μB for non-peripheral collisions at low root-s

μS vs b and root-s from 4 par fits

γS vs b and root-s from 4 par fits

now constrain (μS, γS) values to thered curves and fit only (T, μB)….

statistical model fits to simulated rhic data statistical model fits to simulated rhic data click to...

Documents