1

Differential elliptic flow of identified hadrons & number of constituent quark

(NCQ) scaling at FAIR

Partha Pratim Bhaduri

Subhasis Chattopadhyay

VECC, Kolkata

Over past two decades, relativistic heavy-ion collision experiments are performed around the world; ultimate aim is to map the QCD phase diagram & to discover the new state of QCD matter the Quark Gluon Plasma (QGP).

The Compressed Baryonic Matter (CBM) experiment at FAIR : exploration of the QCD phase diagram at high net baryon densities and moderate temperatures. EL = 10 – 40 GeV/n.

Main challenge is to predict unambiguous & experimentally viable probes to indicate the formation of dense partonic medium.

Collective flow of the produced particles in the transverse plane of the collision signature of the creation of thermalized matter nuclear collisions.

Of particular interest is the elliptic flow parameter (v2) ; signals a strong evidence for the creation of a hot & dense system at a very early stage in the non-central collisions.

Introduction

M. Oldenburg 3

xz

y

px

py

y

x

● non-central collisions: azimuthal anisotropy in coordinate-space● interactions asymmetry in momentum-space● sensitive to early time in the system’s evolution

● Measurement: Fourier expansion of the azimuth particle distribution

Elliptic flow v2

...)2cos2cos21(2

121

vv

d

dN 12 cos 2 , tan ( )y

x

pv

p

v2 (pT) : Differential elliptic flow

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Elliptic Flow at RHIC

• A large elliptic flow is found for identified hadrons• Data is well described by hydrodynamics in low pT region.• Hydrodynamic mass ordering at low pT (pT<= 1.5 GeV/c)• Baryon-Meson crossing at intermediate pT (1.5 < pT < 5 GeV/c)• NCQ scaling

Recombination Extended to Elliptic Flow

Number of constituent quark (NCQ) scaling

For hadron formation by

coalescenc e or recombination of partons

v2

meson pT

2 v2

quark pT

2

v2

baryon pT

3 v2

quark pT

3

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NCQ scaling in KENCQ scaling in KETT /n /n

KET = mT – m0

mT2 = pT

2 + m02

Excellent KET/n scaling for the full measured range Contrast to pT scaling

Models used for the study :

1. UrQMD (hadronic transport model)2. AMPT - string melting (partonic transport model)

3. AMPT- default (hadronic transport model)

System : Au + AuEnergy : EL = 25 GeV/n & 40 GeV/nImpact parameter : b = 5 - 9 fm.

What we have done:1. To study the differential elliptic flow of identified hadrons in the FAIR energy regime.

2. To test the NCQ scaling of v2 of identified hadrons .

Hydrodynamic mass ordering at low pT

Baryon-Meson crossing at high pT

Differential elliptic flow at top (40A GeV) & intermediate (25A GeV) FAIR energies

Elliptic Flow : comparison of different models

Partonic scatterings enhance the flow

Accepted for publication in PRC

Constituent Quark Number Scaling

No reasonable NCQ scaling in pT over the investigated pT range Ruling out of recombination picture ?

Accepted for publication in PRC

Transverse Kinetic Energy (KET = mT – m0) scaling

Remarkable scaling behaviour by UrQMD (hadronic) & AMPT with string melting (partonic)

Accepted for publication in PRC

Summary

• Observations at FAIR are quite in-line with the elliptic flow measurements at RHIC. Hadron mass ordering at low pT ; switch over at high pT.

• Partonic scattering enhances the flow.

• No, reasonable NCQ scaling is found in pT , over the investigated pT range

• Remarkable scaling is found with respect to KET by both UrQMD & string melting version of AMPT.

• Insensitive to distinguish between hadronic & partonic phase.

• Relative values of v2 might serve as a better observable at FAIR to indicate the formation of a partonic medium .

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Thank you

Back Ups

Observations

• However a remarkable scaling behavior is indeed found with respect to KET by both UrQMD & string melting version of AMPT.

• This can be attributed to hydrodynamic mass scaling

• The degree of scaling seems to be better for UrQMD than AMPT.

• Observation of NCQ scaling w.r.t KET by both hadronic & partonic model makes this observable rather insensitive to indicate the formation of partonic matter at FAIR.

• If at all, a universal scaling behavior of elliptic flow is observed at RHIC, whether it should be interpreted as a signature of color de-confinement is still a debated issue.

• Relative values of v2 might serve as a better observable.

Comparison with existing data (NA49)

AMPT with string-melting slightly over estimates the flow UrQMD & default AMPT under estimates the flow at high pT

Large error bar in the data !! No conclusive picture

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Why Elliptic Flow ?

• The probe for early time– The dense nuclear overlap is

ellipsoid at the beginning of heavy ion collisions

– Pressure gradient is largest in the shortest direction of the ellipsoid

– The initial spatial anisotropy evolves (via interactions and

density gradients ) Momentum-space anisotropy

– Signal is self-quenching with time

React

ion

plan

e

X

Z

Y

Px

Py Pz

dN

dÏ •

1

2 π1 2 v

1cos Ï• 2 v

2cos 2 Ï• . . . 1

2 cos 2 , tan ( )y

x

pv

p

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Coordinate-SpaceAnisotropy

Momentum-SpaceAnisotropy

Elliptic flow v2

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Why Elliptic Flow ?

• The probe for early time– The dense nuclear overlap is

ellipsoid at the beginning of heavy ion collisions

– Pressure gradient is largest in the shortest direction of the ellipsoid

– The initial spatial anisotropy evolves (via interactions and

density gradients ) Momentum-space anisotropy

– Signal is self-quenching with time

React

ion

plan

e

X

Z

Y

Px

Py Pz

dN

dÏ •

1

2 π1 2 v

1cos Ï• 2 v

2cos 2 Ï• . . . 1

2 cos 2 , tan ( )y

x

pv

p

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Why Elliptic Flow ?

xxx

pyy

x x

py

x

pyy

x

Interactions among the produced particles lead to pressure gradients which generate an azimuthal anisotropy in particle emission or elliptic flow, measured by v2, from which can be obtained valuable information about the early dynamics after the collision

x

yz

x

yz

x

yz

x

yz

x

yz

x

yz

Spatial anisotropy Momentum anisotropy

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Resent PHENIX Elliptic Flow Data

Detailed differential measurements now available for π, K, p, φ, d, D

22Substantial elliptic flowSubstantial elliptic flow signals are observed for a variety signals are observed for a variety

of particle species at RHIC. Indication of of particle species at RHIC. Indication of rapid rapid thermalizationthermalization? ?

RHIC Elliptic Flow Data

23Substantial elliptic flowSubstantial elliptic flow signals are observed for a variety signals are observed for a variety

of particle species at RHIC. Indication of of particle species at RHIC. Indication of rapid rapid thermalizationthermalization? ?

RHIC Elliptic Flow Data

Quark Matter 2006, Shanghai China

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Identified particle v2 at 200 GeV

• v2 appears to saturate at ~0.13 for K0.13 for KSS and ~0.20 for 0.20 for with the saturation setting in at different pT.

PRL 92(04) 052302

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Elliptic flow at RHIC and perfect fluid hydrodynamics Elliptic flow at RHIC and perfect fluid hydrodynamics

The v2 measurements at RHIC are in a good agreement with the predictions of ideal relativistic hydrodynamics

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Scaling breaks

Elliptic flow scales with KET up to KET ~1 GeV Indicates hydrodynamic behavior Possible hint of quark degrees of freedom become apparent at higher KET

Baryons scale togetherMesons scale together

PHENIX preliminary

= mT

– m

Transverse kinetic energy scalingTransverse kinetic energy scaling

( WHY ? )( WHY ? ) 21

2Therm colKE KE KE m u

P PHENIX article submitted to PRL: nucl-ex/0608033

Quark Matter 2006, Shanghai China

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In this scenario we can infer the value of the parton v2 in the relevant pT region (~7%).

For hadron formation by

coalescence of co-moving partons

v2

meson pT

2 v2

quark pT

2

v2

baryon pT

3 v2

quark pT

3

NCQ-scaling: Partonic flow

Hiroshi Masui / University of Tsukuba

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Partonic Collectivity (ii)

• Hydro + NCQ scaling describes v2 for a variety of particles measured at RHIC– Scaling breaks for higher pT

PHENIX PRELIMINARY WWND 2006, M. Issah

K0S, (STAR) : PR 92, 052302 (2004)

(STAR) : PRL 95, 122301 (2005)

(STAR) : preliminary

Data :QM2005, PHENIX

K0S

STAR preliminary0-80% Au+Au 200GeVYan Lu SQM05P. Sorensen SQM05M. Oldenburg QM05

SQM2006, S. Esumi

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NCQ (pNCQ (pTT/n) scaling compared to KE/n) scaling compared to KETT /n /n

KET/n scaling works for the full measured range with deviation less than 10% from the universal scaling curve NCQ- scaling works only at 20% level for pt>2 GeV/c and breakes below with clear systematic dependence on the mass

PHENIX Preliminary

NCQ- Scaling

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Elliptic flow of multistrange hadrons (φ, Ξ and ) with their large masses and small hadronic behave like

other particles → consistent with the creation of elliptic flow on partonic level before hadron formation

Multi-strange baryon elliptic flow at RHIC (STAR)

STAR preliminary

200 GeV Au+Au

From M. Oldenburg SQM2006 talk (STAR)

J. Phys G 32, S563 (2006)

Scaling test

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Elliptic flow at FAIR

AMPT calculations: C.M. Ko at CPOD 2007

Measure flow for all particles over CBM energy range

DJ/

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QCD Phase Diagram

What does theory expect? → mainly predictions from lattice QCD:

• crossover transition from partonic to hadronic matter at small B and high T

• critical endpoint in intermediate range of the phase diagram • first order deconfinement phase transition at high B but moderate T

The Compressed Baryonic Matter (CBM) experiment : Exploration of the phase diagram at very high baryon densities and moderate temperatures to look for :

De-confinement phase transition at high temperature & baryon densityIn-medium modification of hadrons – signal of the onset of chiral symmetry restoration.Location of the critical end point

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Thank you

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C. Blume et al. (NA49 at CERN-SPS), nucl-ex/0409008

Discontinuity in strangeness production: signature for phase transition ?

Decrease of baryon-chemicalpotential: transition frombaryon-dominatedto meson-dominated

matter

?

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Extra Slides

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Net-baryon densities in central Au+Au collisions at FAIR:consistent picture from transport models

Compilation by J. Randrup, CBM Physics Book, in preparationsee also I.C. Arsene et al., Phys. Rev. C 75 (2007) 034902

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High density matter at CBM

• high baryon and energy densities created in central Au+Au collisions

• remarkable agreement between different models

• maximum net baryon densities from 5 - 40 AGeV ~ 1 - 2 fm-3 ~ (6 – 12) 0

(net baryon density = 1 fm-3 ~60)

• max. excitation energy densities from 5 - 40 AGeV ~ (0.8 – 6) GeV/fm3

(* = – mN, total energy density)

net baryon density

CBM physics book (to be published)

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Introduction• States of matter, their defining features and transition between them always been one of the fundamental issues

of physics. Strongly interacting matter opens up a new chapter for such studies.

• Statistical QCD predicts at high temperature and/or densities, strongly interacting matter will undergo a transition from color neutral hadronic phase to a state of de-confined color charged quarks & gluons – quark gluon plasma (QGP)

Neutron starsEarly universe

Compression heating quark-gluon matter (pion production)

baryons hadrons partons

In laboratory Relativistic heavy-ion collisions (RHIC) are the only tool to produce such exotic states of QCD matter

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CBM Physics : keywords

• physics program complementary to RHIC, LHC

• rare probes

What does theory expect? → mainly predictions from lattice QCD:

• crossover transition from partonic to hadronic matter at small B and high T

• critical endpoint in intermediate range of the phase diagram

• first order deconfinement phase transition at high B but moderate T

However ...

• deconfinement = chiral phase transition ?

• hadrons and quarks at high ?

• signatures (measurable!) for these structures/ phases?

• how to characterize the medium?

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RHIC result: new state of matter = perfect liquid? Tf = 160 – 165 MeV

L-QCD Predictions: TC = 151 ± 7 ± 4 MeV ( μB=0 ) (Z. Fodor, arXiv:0712.2930 hep-lat) TC = 192 ± 7 ± 4 MeV ( μB=0 ) (F. Karsch, arXiv:0711.0661 hep-lat) crossover transition at μB=0 (Z. Fodor, arXiv:0712.2930 hep-lat) 1. order phase transition with critical endpoint at μB > 0

High-energy heavy-ion collision experiments:

RHIC, LHC: cross over transition, QGP at high T and low ρLow-energy RHIC: search for QCD-CP with bulk observables NA61@SPS: search for QCD-CP with bulk observables CBM@FAIR: scan of the phase diagram with bulk and rare observables

Exploring the QCD Phase diagram

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SIS 100 Tm

SIS 300 Tm

Structure of Nuclei far from Stability

cooled antiproton beam:Hadron Spectroscopy

Compressed Baryonic Matter

The future Facility for Antiproton an Ion Research (FAIR)

Ion and Laser Induced Plasmas:

High Energy Density in Matter

low-energy antiproton beam:antihydrogen

Primary beams:1012 /s 238U28+ 1-2 AGeV4·1013/s Protons 90 GeV1010/s U 35 AGeV (Ni 45 AGeV)

Secondary beams:rare isotopes 1-2 AGeVantiprotons up to 30 GeV

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In medium effects: Dileptons

[Rapp, Wambach, Adv. Nucl. Phys. 25 (2000) 1, hep-ph/9909229]

• dileptons are penetrating probes!

• modifications in hot and dense matter expected –

see CERES, NA50, NA60, HADES

best way to measure? e+e- ↔ +-

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Quarkonium dissociation temperatures: (Digal, Karsch, Satz)

Measure excitation functions of J/ψ and ψ' in p+p, p+A and A+A collisions !

rescaled to 158 GeV

Probing the quark-pluon plasma with charmonium

J/ψ ψ'

sequential dissociation?

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High density matter at CBM

• high baryon and energy densities created in central Au+Au collisions

• remarkable agreement between different models

• maximum net baryon densities from 5 - 40 AGeV ~ 1 - 2 fm-3 ~ (6 – 12) 0

(net baryon density = 1 fm-3 ~60)

• max. excitation energy densities from 5 - 40 AGeV ~ (0.8 – 6) GeV/fm3

(* = – mN, total energy density)

net baryon density

CBM physics book (to be published)

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Collapse of proton flow : order of transition??

• collapse elliptic flow of protons at lower energies signal for first order phase transition?! [e.g. Stoecker, NPA 750 (2005) 121, E. Shuryak, hep-ph/0504048]

• full energy dependence needed!central

midcentral

peripheral

[NA49, PRC68, 034903 (2003)]

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Summary: CBM physics topics and observables

Onset of chiral symmetry restoration at high B

in-medium modifications of hadrons (,, e+e-(μ+μ-), D)

Deconfinement phase transition at high B

excitation function and flow of strangeness (K, , , , ) excitation function and flow of charm (J/ψ, ψ', D0, D, c) (e.g. melting of J/ψ and ψ') exitation function of low-mass lepton pairs

The equation-of-state at high B

collective flow of hadrons particle production at threshold energies (open charm?)

QCD critical endpoint excitation function of event-by-event fluctuations (K/π,...)

CBM Physics Book in preparation

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Detector requirements

Systematic investigations:A+A collisions from 8 to 45 (35) AGeV, Z/A=0.5 (0.4) (up to 8 AGeV: HADES)p+A and p+p collisions from 8 to 90 GeV

observables detector requirements & challenges

strangeness production: K,

charm production: J/, D

flow excitation function

event-by-event fluctuations

e+e-

open charm

tracking in high track density environment (~ 1000)

hadron ID

lepton ID

myons, photons

secondary vertex reconstruction

(resolution 50 m)

large statistics: large integrated luminosity:

high beam intensity (109 ions/sec.) and duty cycle

beam available for several months per year

high interaction rates (10 MHz)

fast, radiation hard detector

efficient trigger

rare signals!

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SIS100/300

Multiplicity in central Au+Au collisionsW. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745

Rare particles with high statisticsHigh beam intensityInteraction rate: 10 MHzFast detectors/DAQ

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STS tracking – heart of CBM

Challenge: high track density 600 charged particles in 25o

Task

• track reconstruction:

0.1 GeV/c < p 10-12 GeV/c

p/p ~ 1% (p=1 GeV/c)

• primary and secondary vertex reconstruction (resolution 50 m)

• V0 track pattern recognition

D+ → ++K- (c = 312 m)

D0 → K-+ (c = 123 m)

silicon pixel

and strip detectors

add detectors for particle identification behind the STS

→ challenge for di-leptons!

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In medium : D-mesons

[E. Bratkovskaya, W. Cassing, private communication]

• Dropping D-meson masses with increasing light quark density

might give a large enhancement of the open charm yield at 25 A GeV !

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• In laboratory we create such conditions through high energy heavy ion collisions : hot and dense nuclear matter in the collision zone.

• Exploration of QCD phase diagram – address the fundamental aspects of QCD : – De-confinement phase transition at high temperature & baryon density

– In-medium modification of hadrons – signal of the onset of chiral symmetry restoration.

• SPS (CERN) & RHIC (BNL) : study the QCD phase diagram is studied in the region of high temperatures and low baryon densities.

• The up-coming LHC experiments will continue towards higher temperatures and lower net baryon densities.

• The Compressed Baryonic Matter (CBM) experiment will explore the phase diagram at very high baryon densities and moderate temperatures.

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• Low-mass: Medium modified

spectral density• Intermediate

mass: Radiation from

QGP• High mass: J/ etc.,

suppression

In medium effects: Dileptons

•Dileptons are penetrating probes

•Carries undistorted information of the collision zone

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CBM Physics – keywords

• physics program complementary to RHIC, LHC

• rare probes

What does theory expect? → mainly predictions from lattice QCD:

• crossover transition from partonic to hadronic matter at small B and high T

• critical endpoint in intermediate range of the phase diagram

• first order deconfinement phase transition at high B but moderate T

However ...

• deconfinement = chiral phase transition ?

• hadrons and quarks at high ?

• signatures (measurable!) for these structures/ phases?

• how to characterize the medium?

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