Statistical model fits to simulated RHIC data
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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)
Statistical model fits to simulated RHIC data
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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 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
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 3
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
Statistical model fits to simulated RHIC data
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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
Statistical model fits to simulated RHIC data
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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
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 6
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…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 7
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)
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 8
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
Statistical model fits to simulated RHIC data
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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 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
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 10
Effect of acceptance on THERMUS parameters in UrQMD events
7.7 200
60-8
0%
0-5%
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 11
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.
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 12
BACKUP SLIDES
Statistical model fits to simulated RHIC data
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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…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 14
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)
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 15
Example time dependence of the ratios, 19.6 GeV, 0-5%
freezeout ~ 50 fm/c
Statistical model fits to simulated RHIC data
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Example time dependence of the ratios, 200 GeV, 0-5%
freezeout ~ hundreds of fm/c
Statistical model fits to simulated RHIC data
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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%
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 18
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
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 19
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
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 20
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)
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 21
Constrain μS and γS and Fit (T, μB), GCE
0-5%, 5-10%, 10-20% give ~same T distributions…
<T> decreases as b decreases…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 22
Constrain μS and γS and Fit (T, μB), GCE
double peaks disappear…
still significant overlapin 0-5%, 5-10%, 10-20%...
µB decreases as b decreases…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 23
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…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 24
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
Statistical model fits to simulated RHIC data
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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 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…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 26
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%
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 27
Centrality dependence of T
b-dependence is weak
multiple bands atlow root-s resultfrom “0,1 antibaryon”
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 28
Centrality dependence of μB
b-dependence is weak
multiple bands atlow root-s resultfrom “0,1 antibaryon”
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 29
1D T distributions by centrality bin
Statistical model fits to simulated RHIC data
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1D μB distributions by centrality bin
Statistical model fits to simulated RHIC data
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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
Statistical model fits to simulated RHIC data
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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…
Statistical model fits to simulated RHIC data
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APS April Meeting, Denver, April 14, 2013 33
Time Trajectories of “Average Events”
peripheral collisions freezeout at higher (μB,T)than do central collisions
Statistical model fits to simulated RHIC data
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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%
Statistical model fits to simulated RHIC data
Click to edit Master subtitle style
APS April Meeting, Denver, April 14, 2013 35
Constrain μS and γS and Fit (T, μB), GCE
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)….
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