Search for the Critical Point of Strongly Interacting Matter at the

CERN SPS

G.Melkumov (JINR Dubna)

for NA49 collaboration

Tatranská Štrba, June 27th - July 1st, 2011

Pb+Pb at SPS energies: Energy density exceeds the

critical value ( ≈ 1 GeV / fm3 )

Signatures for deconfinement – radial & anisotropic flow– strangeness enhancement– J/Ψ,Ψ’ yield suppression– di-lepton enhancement & ρ0 modification

QCD prediction of quark-gluon deconfinement

Search for the onset of deconfinement by the energy scan at the SPS

Comprehensive study of the phase diagram of strongly interacting matter

Hadron measurements in large acceptance (yCM > y > ybeam)

Tracking by large-volume TPCs in SC magnet field

PID by dE/dx,TOF, decay topology, invariant mass

NA49 experiment at CERN SPS

Centrality determination by Forward Calorimeter

Operating 1994-2002; p+p, C+C, Si+Si and Pb+Pb interactions at center of mass energy

6.3 – 17.3 GeV for N+N interaction

PID by TOF + dE/dx

Tracking and particle identification

Tracking PID by dE/dx

What is the energy threshold for deconfinementWhat is the energy threshold for deconfinement (the lowest energy sufficient to create a partonic system)

Motivation: Statistical Model of the Early Stage (SMES) Gaździcki, Gorenstein, Acta Phys. Polon. B30, 2705 (1999)

““kink” “horn” “step”kink” “horn” “step”

entropyS 4 N

HG

HG cont.

QGP

HG

HG cont.

QGPHG

QGP

mixedphase

mixedphase

F≃ sNN

1st order phase transition to QGP between top AGS and top SPS energies sNN

7 GeV number of internal degrees of freedom (NDF) increases HG QGP (activation of partonic

degrees of freedom) total entropy and total strangeness are the same before and after hadronization (cannot

decrease QGP HG) mass of strangeness carriers decreases HG QGP (m, K, ...

> ms)

constant temperature and pressure in mixed phase

Fermi variable

F≡[ sNN−2mN 3

sNN ]1/4

Search for the onset of deconfinement

Pions measure early stage entropy. In SMES: <π>/Nw ~ NDF1/4

A+A data change from "suppression" (AGS) to "enhancement" at low SPS energiesChange of slope around 30A GeV; slope in A+A increases from ≈1 (AGS) to ≈ 1.3 (top SPS+RHIC) - consistent with increase x 3 in NDFNo change of slope in p+p data

Full phase space (4)

) ( 1.5 -

Pion energy dependence - 4π yields

M. Gazdzicki and M. Gorenstein, Acta Phys.Pol. B30 (1999) 2705

Final NA49 results on the onset of deconfinemet: C.Alt et al., PRC77,024903 (2008)

) ( 1.5 -

Pion yield per participant

NA49,C.Alt et al.,PRC77,024903(2008)

central PbPb/AuAu

1/4NNs

) ( 1.5 -

• π yield related to entropy production• steeper increase in A+A suggests 3-fold increase of initial d.o.f

• Es related to strangeness/entropy ratio• plateau consistent with prediction for deconfinement

(SMES model, M.Gazdzicki and M.Gorenstein, Acta Phys. Pol.30,2705(1999))

Onset of deconfinement

Kink

Horn

Ratio of strange particles to pions

Peaks sharply at the SPS

SMES explanation: - entropy, number of s, s quarks conserved from QGP to freeze-out - ratio of (s + s) / entropy rises rapidly with T in the hadron gas - Es drops to the predicted constant QGP level above the threshold of deconfinement :

0.21

E

g g g

g 0.74

NN

gdu

sSSS

0S

- K 4 )K K( 2 K :note

hadr

onic

mixed partonicAGSSPS

Strangeness to entropy ratio

Proposed as measure of strangeness to entropy ratio (SMES)

Es shows distinct peak at 30A GeV

Described (predicted) by model assuming phase transition (SMES)

Consistent with approximately constant temperature and pressure in mixed phase (latent heat)(softest point of EoS)

Hydrodynamical model with deconfinement phase transition starting at lower SPS energies describes data

M. Gorenstein et al., Phys. Lett. B 567 (2003) 175

S. Hama et al., Braz. J. Phys. 34 (2004) 322

Kaon inverse slope parameter

/2

T

T

m TdA e

dm dy

• The step-like feature observed at SPS energies, not seen for p+p collisions and in models without phase transition

Hydro+PTHydro+PTStep Step

Rapid changes of hadron production properties at low SPS energy most naturally explained by onset of deconfinement

NA49,C.Alt et al.,PRC77,024903(2008); M.Gazdzicki et al.,arXiv:1006.1765

NA49,C.Alt et al., PRC77,024903 (2008)

Shape of transverse mass spectra

(H.Petersen and M.Bleicher, nucl-th/0611001)

SPheRIO

Softening of transverse (step) and longitudinal (minimum of cs) features of EoS due to mixed phase (soft point of EoS)

Onset of deconfinement

Step Dale

Estimate of sound velocity

Landau hydro-dynamical model (E.Shuryak,Yad.Fiz.16, 395(1972))2

24

8ln( / 2 )

3 1y

sNN p

s

cs m

c

Minimum of sound velocity cs (softest point of EoS) around 30A GeV

→ sound velocity can be derived from measurements H.Petersen and M.Bleicher, nucl-th/0611001

wid

th o

f rap

idity

dis

trib

utio

n

sou

nd v

eloc

ity

More signals : Estimate of sound velocity

Dale

200

400

T(M

eV)

Horn Step

SPS(NA49) , RHIC(STAR) and LHC(ALICE)

Verification of SPS(NA49) results by RHIC(STAR) and LHC(ALICE) Horn- and Step- like features in hadron gas ->mixed phase->QGP transitions

• QCD considerations suggest a 1st order phase boundary ending in a critical point

• Hadro-chemical freeze-out points are obtained from statistical model fits to measured particle yields

• T and μB approach phase boundary and estimated critical point at SPS

SPS

RHIC

critical end pointFodor,Katz JHEP 04,50(2004)

Exploration of phase diagram

• Evidence of the onset of deconfinement from rapid changes of hadron production properties• Search for indications of the critical point as a maximum in fluctuations

Quark number susceptibilities

Y.Hatta and T.Ikeda, PRD67,014028 (2003) M.Asakawa et al.,PRL 101,122302(2008)

Effects (singularities) at critical point

effects of critical point are expected over a range of T,µB

hydro predicts that evolution of the system is attracted to critical point

= B/3

The presence of the critical point can deform the trajectories describing the evolution of the expanding fireball in the (T,

B) phase diagram

For a given chemical freeze-out point three isentropic trajectories (n

B/s = const.) are shown

We do not need to hit precisely the critical point because a large region can be affected

2 2( )Var n n n

n n

22

Ni

T T T Ti 1

Z - <z

z p - <p > Z (p - <p >)

TP N

pT

- measures transverse momentum fluctuations on event-by-event basis

- measures multiplicity fluctuations on event-by-event basis

If A+A is a superposition of independent N+N

pT

(A+A) = pT

(N+N) (A+A) = (N+N) + < n > part

pT is independent of N

part fluctuations < n > - mean multiplicity of hadrons from a single N+N

part - fluctuations in N

part

is strongly dependent on Npart

fluctuations For a system of independently emitted For Poissonian multiplicity distributionparticles (no inter-particle correlations)

pT

= 0 =1

Event-by-event multiplicity & transverse momentum fluctuations

Search for the critical point

A (system size)

sNN

I.Kraus et al., Phys.Rev.C76, 064903 (2007)(2006)F.

No significant energy dependence at SPS energies

CP1 location:

(CP1) = 360 MeV

T (CP1) 147 (chemical

freeze-out temperature for Pb+Pb at = 360 MeV)

base-lines for CP1

predictions (curves) are mean

pT and values for 5

energies

Data show no evidence for critical point fluctuations

Event-by-event <pT> & multiplicity fluctuations

NA49 T.Anticic et al., PRC79,044904 (2009)

NA49 C.Alt et al., PRC78,034914 (2008)

M. Stephanov, K.Rajagopal,E.Shuryak, PRD60,114028(1999) Y.Hatta and T.Ikeda, PRD67,014028(2003)

CP estimates based on:

Energy dependence for central Pb+Pb collisions

Maximum of pT

and observed for C+C and Si+Si

CP2 location:

(CP2) 250 MeV = (A+A

at 158A GeV)

T (CP2) = 178 MeV = T

chem (p+p)

CP2 predictions (curves)

normalized to reproduce pT

andvalue for central Pb+Pb collisions

Data are consistent with the CP2 predictions

System size dependence of fluctuatios

Pb+Pb - PRC78,034914 (2008) CC,SiSi - B.Lungwitz (PhD)

Pt data: PRC70,034902 (2004) pp - PRC75,064904 (2007) data:

St. Mrówczyki Phys. Lett. B465, 8 (1999)

Single particle variable - inclusive avarage

Event variable (summation runs over particles in a given event)

- averaging over events

Higher moments:

_

TTp ppzT

_

Tp

N

iTTP ppZ

T1

_

)(

_2

2

)2(

T

T

T p

p

pp zN

Z

...

nnp

n

pnp T

T

Tz

N

Z 11

2

)(_

Higher moments of <pT> fluctuation

M.A.Stepanov, Phys.Rev.Lett. 102, 032301 (2009)

Advantage: the amplitude of critical point peak is proportional to higher powers of the correlation length. Examples for second and fourth moments:

Higher moments have been advertised as a probe for the phase transition and critical point effects

Higher moments of measure (K.Grebieszkow, M.Bogusz)

Definition:

So far we were using second moment: (2)pT

1. In a superposition model (2)pT

(A+A) = (2)pT

(N+N) 2. For independently emitted particles (2)

pT = 0

According to S. Mrówczyński Phys. Lett. B465, 8 (1999) only the 3rd moment preserves the above (1. and 2.) properties of the 2nd moment (higher moments not). In particular only (2)

pT and (3)

pT are intensive as thermodynamic quantities.

ΦpT(3): 3rd moment <pT>

fluctuationsn

np

n

pnp T

T

Tz

N

Z 11

2

)(_

ΦpT

(3) has strongly intensive property like ΦpT (S.Mrowczynski,Phys.Lett.B465,8(1999))

NA49 preliminary

NA49 preliminary

Pb+Pb 7% central

Systematic errors are large

No indication of CP fluctuations

K.Grebieszkow and M.Bogusz, NA49 preliminary

Higher moments are expected to be moresensitive to fluctuations

C. R. Allton, Phys. Rev. D68 (2003), 014507quark number susceptibility:

q ≡ ∂n

q/∂μ

q,

T0 – critical temperature for μ

q = 0 (

B = 3

q)

Baryon density fluctuations appear to diverge for some critical value of the baryochemical potential

For strongly interacting matter long range baryon density fluctuations expectedA picture supported by lattice calculations

Critical phenomena and density fluctuations

Critical phenomena give rise to density fluctuations which obey the power laws.These power laws describe the density fluctuations of zero mass sigma particlesabundantly produced in AA collisions at CP as well as the density fluctuations ofnet-baryons.

The critical fluctuations (power laws) in sigma and proton sectors is motivated by the hypothesis that sigma and net-protons densities are a magnitudes of the order parameters for the second order phase transition associated with the QCD CP.

Intermittency in low mass π+π- pair density

• critical point predicted to lead to power-law density fluctuations of σ field• observation via density fluctuations of low mass π+π- pairs in pT space• power law behavior of F2(M) factorial moment expected (intermittency)

N.Antoniou et al.,Nucl.Phys.A693,799(2001);A761,149(2005)

NA49 data indicate intermittency signal for Si+Si (T.Anticic et al.,PRC81,064907(2010)). Similar critical fluctuations for Si+Si interactions observed in proton sector.

QCD Critical point close to freeze-out point of Si+Si system ?

222 ( )F M M

T.Anticic et al., PRC70, 034902 (2004)C.Alt et al., PRC75, 064904 (2007)C.Alt et al,. PRC78, 034914 (2008)T.Anticic et al., PRC79, 044904 (2009)B.Lungwitz, NA49 thesis (2008)

first hint on thehill of fluctuations?

Critical point search in fluctuations

first hint on thehill of fluctuations?

New data to be registered by NA61

Critical point of strongly interacting matter by

an observation of a hill of fluctuations in two dimensional plane (energy)-(system

size)

The critical point should lead to an increase of multiplicity and transverse momentum fluctuations

NA61 Search for the QCD critical point

10 20 30 40 80 158

energy (A GeV)

In+In

C+C

S+S

New data to be registered

by NA61

p+p

Establish the system size dependence of the anomalies observed in Pb+Pb collisions-

further test interpretation as due to the onset of

deconfinement

10 20 30 40 80 158

energy (A GeV)

It is expected that the ''horn'' like structureshould be the same for S+S and Pb+Pb collisions and then

rapidly disappear for smaller systems

?

NA61 Study of the onset of deconfinement

NA49

extrapolation

Ion physics program NA61Scan in energy and system size

A

Search for hill of fluctuations as signature of critical point

Study onset of deconfinement: disappearance of “horn” etc.

T µB

Pb+Pb

13 20 30 40 80 158

Xe+La

energy (A GeV)

Pb+Pb

Be+C

Ar+Ca

NA61 ion program

p+p

p+Pb

NA49 (1996-2002)

2009/10/11

2010/11/12

2014

2012/14

2015

P p+p

158

T T

STAR (2008-10)Au+Au

T -test of secondary ion beams

P -pilot data taken

Progress and revised plans in data taking NA61

Summary

Onset of deconfinement indicated in inclusive observables in central Pb+Pb colisions at lower SPS energies of about 30A GeV:

Results are not reproduced by hadron-string models (RQMD, UrQMD, HSD). Described (predicted) by model assuming phase transition (SMES) No indications of the critical point in the energy dependence of multiplicity and mean transverse momentum fluctuations in central Pb+Pb collisions

System size dependence of the critical point at 158A GeV shows:a maximum of mean p

T and multiplicity fluctuations in the complete

pT range consistent with the

predictions

an increase (from p+p up to Pb+Pb) of mean pT fluctuations in the

low pT region; high p

T particles show no fluctuation signal

Higher moment of Pt fluctuations measure : analysis of the 3rd moment of Pt fluctuations for the energy and system size dependence is in progress

A detailed energy and system-size scan is necessary to investigate the properties of the onset of deconfinement and to establish the existence of the critical point NA61/SHINE