moments with (n)bd & mixed evts click to edit master subtitle style bulkcorr pwg meeting, april...

Moments with (N)BD & Mixed Evts

Click to edit Master subtitle style

Bulkcorr PWG meeting, April 17, 2013 1

Update on moments products values with (N)BD and Mixed Events baselinesW.J. Llope & D. McDonald

Rice University

Speculated 1st 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 inthe moments products.

One needs a reasonable description of the valuesin the absense of critical behavior.

CLTPoissonHRG(Negative) Binomial (G. Westfall)

Mixed Events

Here, update on the last two of these baselines, & update on the pbar/p binning results…




STAR Results (QM2012)

√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

D. McDonald for STAR, QM2012

net-charge net-K

No non-monotonicity seen

Significance of net-p dip?




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 √sNN~15 GeV




Congratulations to Dr. McDonald!

http://drupal.star.bnl.gov/STAR/theses

More details on the following can be found in Daniel McDonald’s Thesis.

Daniel produced the data points, provided the (N)BD & mixed eventsinput data, and produced the final comparison plots.I wrote the (N)BD & mixed events code.




(N)BD

T..J. Tarnosky & G. Westfall, Oct. 2012 http://arxiv.org/pdf/1210.8102v1.pdf

Functional form describes the (particle identified) multiplicity distributions ranging from NA22 & UA5 to PHENIX

Inputs:mean (μ) &variance (σ2)

Then, the values of Ck , Sσ , & Kσ2 are predicted.




Mixed Events “Sampled Singles”

Caveat: The present approach is not the same as the MSU mixed eventsGary 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, 094016 (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&evtQA as his QM2012 plots.N

p

Npb

ar 7.7 11.5 19.6 27 39 62.4 200

refmult2corr




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 NnegThen form Nnet = Npos-Nneg and Ntot = Npos+NnegFill similar 2D plots of Nnet and Ntot vs. RM2corrAnd 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

N

pbar 7.7 11.5 19.6 27 39 62.4 200

refmult2corr




Net-K

sampled singles uncertainties are notdrawn, but are similar to those onthe data points by construction…




Net-Q

Sampled singles values gobeserk for ~central events atthe highest √sNN….




“Sampled singles” does not work for net-Q central at highest root-s!

Same events!Intra-event correlations are important…




Net-p

sampled singles approachreproduces the net-p moments for all √sNN & centrality…




Net-p vs. √sNN, 0-10% central




pbar/p binning

Switching gears now…

We typically assume that tight centrality cuts (0-5%) tightly constrainthe locations of the events on the phase diagram…

…may not be a very good assumption.

bulkcorr:http://wjllope.rice.edu/fluct/protected/urqmdthermus_20120905.pdfhttp://wjllope.rice.edu/fluct/protected/urqmdthermus_20120912.pdf

lfspectra:http://wjllope.rice.edu/fluct/protected/urqmdthermus_20121019.pdf

http://wjllope.rice.edu/fluct/protected/urqmdthermus_20120905.pdf






The Variances…

Freeze-out positions on the phase diagram for 50 events from UrQMD+ThermusT

(G

eV)

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




Net-K moments with pbar/p gating




Total-p moments with pbar/p gating




Net-p moments with pbar/p gating




Residual plot…




Summary

Added (N)BD and “sampled singles” (~mixed events) curves to allSTAR preliminary moments products results plots.

The values of Sσ & Kσ2 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 & Kσ2 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…




BACKUP SLIDES




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




Fit Examples, UrQMD by root-s and centrality

7.7

200

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

moments with (n)bd & mixed evts click to edit master subtitle style bulkcorr pwg meeting, april...

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