Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment

Search for a Possible QCD Critical Point using the STAR Experiment

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Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 1

Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment

W.J. Llope, for the STAR CollaborationRice University

Trajectories at low baryochemical potential, mB

2nd order in the Chiral Limit (mq = 0)Cross-over transition with mq ≠ 0

Trajectories at high baryochemical potential, mB

Theory suggests a 1st order transition…

If so, does a Critical Point (CP) existsomewhere between these extremes?

Finding the CP in the theory(lattice, s-model) is hard…

finite latticefermion sign problemquark masses, s-quark quenching

So, find the CP experimentally!arXiv:1007.2613




A cartoon of the Phase Diagram (experimentalist’s view)

Top beam energy at RHIC: crossover transition from QGP to HG.

Decreasing the beam energy increases the baryochemical potential

Systematic study of the data as a function of the beam energy allows a “scan” in streaks across the phase diagram...

STAR BES data sets fromRHIC Runs 10 and 11(2010-2011)




An experimental avenue to finding a possible Critical Point

So how could we find such a Critical Point if it exists?Assume that it’s going to have the same basic features of other CPs

divergence of the susceptibilities, c… e.g. magnetism transitions 0801.4256v2 divergence of the correlation lengths, x… e.g. critical opalescence

CO2 near the liquid-gas transition

liquid SF6 at 37atm heated to ~43.9 Cand then cooled

Brown University Undergraduate Physics Demonstration

arXiv:0711.0336

Volume

Pure SU(3) Gauge Theory, Polyakov Loop

Susceptibilities

Full QCD, Lattice

T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869M. Smoluchowski, Annalen der Physik, 25 ( 1908) 205 - 226A. Einstein, Annalen der Physik, 33 (1910) 1275-1298




Zooming in on the QCD Phase Diagram

Unlike macroscopic systems, in HI collisions:

finite system sizefinite system lifetimecritical “slowing down”

hep-ph/0912274v2

So, x cannot diverge to ∞xmax ~ 2-3 fmx“natural” ~ 0.5 fm

…How close is FO curve to CP?

compression done…most of Entropy produced…

hep-ph/0402115arXiv:0809.3450v1 arXiv:0803.2449

So, concentrate on observables that are extremely sensitive to the value of x…...Statistical moments of identified particle multiplicities




Sensitivity of cumulants to the Critical Point from the theory

Multiplicity cumulants related to conserved qty’s Q,B,S can be calculated on the lattice…

m1 ~ c(3)T / [c(2)T2] ~ x7/2 Skewness * Standard Deviation m2 ~ c(4) / [c(2)T2] ~ x5 Kurtosis * Variance m3 ~ c(4)T / [c(2)/T] ~ x5/2 Kurtosis * Standard Deviation / Skewness

StephanovarXiv:0809.3450v1

arXiv:0509051 arXiv:610116 PhysRevD.79.074505

In the Nonlinear Sigma Model, the cumulants of the occupation numbers (integral=multiplicity) are also related to x… the higher the order of the moment, the higher the dependence on x….

m0 = C2/C1 = Mm1 = C3/C2 = Ssm2 = C4/C2 = Ks2

m3 = C4/C3 = Ks/S

Gavai&GuptaarXiv:1001.3796




Sensitivity of the cumulants in a Non-linear Sigma Model

An ansatz reproducing the expected behavior or the correlation length vs mB:Athanasiou et al.arXiv:1006.4636v2

results in huge increases in the4th order cumulant for protons...

this ansatz in experimental unitsconvert mB into √sNN and T for x>1fm using (√sNN,mB,T) parameterizations hep-ph/0511094

perhaps mB (√sNN) doesn’t have to be right on top of the CP to see the effects on the moments

lattice suggests this value… Gavai&Gupta, PRD 78,114503 (2008)

×400!




Moments as an experimentalist can see them...

Experimentally: The average values of powers of the deviates give cumulants, moments, and moments products....

STAR, Phys. Rev. Lett. 105 (2010) 022302

No. of particles in a single event...

Average No. of particles in all“similar” events...

Direct comparison of theoretical and experimental quantities!




The Solenoidal Tracker at RHIC (STAR)

Time Projection Chamber (TPC) Time Of Flight (TOF) Solenoidal Magnet




STAR Particle Identification and Acceptance

TPC “dE/dx”

TOF M2

High efficiency PID from TPC and TOFin a wide (|h|<1) and azimuthally complete acceptance




Selected Spectra and Ratios

TPC & TOF π, K, p spectra √sNN =39 GeV

Ratios of integrated yields

model described on next slide...




Where are we on the Phase Diagram?

Statistical-Thermal Model (THERMUS) Computer Physics Communications 180 (2009) 84–106

Free Parameters: T, mb = 1/T-1 (fermions), +1 (bosons)Z = partition functionV = volumem = massK2 = Bessel functiong = degeneracy

- Grand Canonical ensemble

...(mB,T) values depend on √sNN

and centrality

(using only the π±, K±, p± ratios)




Getting to sensible experimental moments results...

So, what we have to do is “simple.”Turn the “big knob” (√sNN ~ mB) and “fine knob” (centrality)…

& then measure the multiplicity distributions of identified particlesin ensembles of similar events...

& then measure the various moments of these distributions…& then plot the moments values vs √sNN or mB…

Golden signal is a “non-monotonic behavior” of the 3rd and 4th moments vs √sNN or mB...

...i.e. a significant & √sNN-localized deviation of the moments from “baselines”that are defined by Poisson statistics, the Hadron Resonance Gas model, etc...

But life is not quite this simple, of course….

All “non-thermal” contributions to the moments values must be carefully controlled...physical: Volume fluctuations (try to control via centrality cuts)

Jets, weak decays, etc.experimental: Time dependence in run (bad RDOs, missing sectors, etc.)

Time dependence in fills (backgrounds) and, esp. at low √sNN, dependence on tuning

Effects of event & track quality cuts, PID contamination…Autocorrelations between centrality cuts and moments values...

Dependence of moments values on width of centrality bins…Getting these experimental aspects under control has taken a considerable amount of work...

(see next slide)




Volume Normalization and Baselines

Several approaches to define what the moments would be in the absence of any contributions from critical behavior...

Poisson Statisticshigher moments are simple functions of the mean values

Ss = (M+ - M-)/(M+ + M-)Ks2 = 1

Central Limit Theoremmean values vs centrality “predict” higher moments if particle production is from large number of independent sources

Hadron Resonance Gas Model

Karsch&Redlich, PLB 695, 136 (2011)

Raw moments are not volume normalized. “CLT normalization”: look at moments products, Ss, Ks2

“intensive normalized cumulants”: divide by mean multiplicity, w3 = k3/M, w4 = k4/M




Results: net-protons

No statistically-significant non-monotonicbehavior of 3rd and 4th moments values

Values consistent with the baselines +10% -20%

CLT & multiplicity normalization give similar results

net-protons are a proxyof the Baryon number(conserved)




Results: Total protons

Sigma field is “isospin blind” Athanasiou et al. arXiv:1006.4636v2

Net- and Total-Proton results are very similar....




Results: Net-Kaons

net-Kaons are a possible proxy of the Strangeness number (conserved)




Results: Net-Charge

Npos-Nneg is a proxy of the Charge number (conserved)

HRG




Summary

“moments” - cumulants, normalized cumulants, moments and moments products – have been suggested to be extremely sensitive to the proximity of a CP, if it exists...

high(er) moments go like the correlation length, ξ, to high(er) powers

The STAR Experiment has collected significant data sets over a wide range of energiesfrom √sNN = 7.7 to 200 GeV

We see no significant non-monotonic behavior of the moments values at the presentlyavailable beam energies.

...Insufficient statistics at lowest values? (these are event hungry observables!)

...mB width of the critical enhancement region, D, is much narrower than expected?

...It’s hiding between available beam energies?

wide gaps!




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Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment