“I could do this talk in 5 minutes.If we knew where the critical point is,

we could make the measurementin a day...”

The Short Version

PHENIX Capabilities forthe Low-Energy RHIC Run

Peter SteinbergChemistry Department, BNL

Workshop on the Critical Point @ RHIC, 3/9/2006

What am I doing here?

arX

iv:n

ucl-

ex/0

410003 v

3 2

5 M

ar

2005

Formation of dense partonic matter inrelativistic nucleus-nucleus collisions at RHIC:

Experimental evaluation by the PHENIXcollaboration

K. Adcox be S.S. Adler e S. Afanasiev t C. Aidala e,j

N.N. Ajitanand aw Y. Akiba w,aq,ar A. Al-Jamel a! J. Alexander aw

R. Amirikas n K. Aoki aa,aq L. Aphecetche az Y. Arai w

R. Armendariz a! S.H. Aronson e R. Averbeck ay T.C. Awes am

R. Azmoun e,ay V. Babintsev q A. Baldisseri k K.N. Barish f

P.D. Barnes ad J. Barrette ag B. Bassalleck ak S. Bathe f,ah

S. Batsouli j V. Baublis ap F. Bauer f A. Bazilevsky e,q,ar

S. Belikov e,q,s F.G. Bellaiche am S.T. Belyaev z M.J. Bennett ad

Y. Berdnikov at S. Bhagavatula s M.T. Bjorndal j

J.G. Boissevain ad H. Borel k S. Borenstein ab S. Botelho au

M.L. Brooks ad D.S. Brown a! N. Bruner ak D. Bucher ah

H. Buesching e,ah V. Bumazhnov q G. Bunce e,ar

J.M. Burward-Hoy ac,ad,ay S. Butsyk ap,ay X. Camard az

T.A. Carey ad J.-S. Chai u P. Chand d J. Chang f W.C. Chang b

L.L. Chavez ak S. Chernichenko q C.Y. Chi j J. Chiba w M. Chiu j

I.J. Choi bh J. Choi v R.K. Choudhury d T. Christ ay

T. Chujo e,bd,be M.S. Chung y,ad P. Chung aw V. Cianciolo am

C.R. Cleven o Y. Cobigo k B.A. Cole j M.P. Comets an

P. Constantin s M. Csanád m T. Csörgő x J.P. Cussonneau az

D. d’Enterria j T. Dahms ay K. Das n G. David e F. Deák m

H. Delagrange az A. Denisov q A. Deshpande ar,ay E.J. Desmond e

A. Devismes ay O. Dietzsch au B.V. Dinesh d J.L. Drachenberg a

O. Drapier ab A. Drees ay A.K. Dubey bg R. du Rietz af

A. Durum q D. Dutta d V. Dzhordzhadze ba K. Ebisu aj

Y.V. Efremenko am J. Egdemir ay K. El Chenawi be

A. Enokizono p H. En’yo aa,aq,ar B. Espagnon an S. Esumi bd

L. Ewell e T. Ferdousi f D.E. Fields ak,ar C. Finck az F. Fleuret ab

S.L. Fokin z B. Forestier ae B.D. Fox ar Z. Fraenkel bg

Preprint submitted to Elsevier Science 21 December 2005

J.E. Frantz j A. Franz e A.D. Frawley n Y. Fukao aa,aq,ar

S.-Y. Fung f S. Gadrat ae S. Garpman af,1 F. Gastineau az

M. Germain az T.K. Ghosh be A. Glenn ba A.L. Godoi au

G. Gogiberidze ba M. Gonin ab J. Gosset k Y. Goto aq,ar

R. Granier de Cassagnac ab N. Grau s S.V. Greene be

M. Grosse Perdekamp r,ar T. Gunji h S.K. Gupta d W. Guryn e

H.-Å. Gustafsson af T. Hachiya p,aq A. Hadjhenni az

J.S. Haggerty e M.N. Hagiwara a H. Hamagaki h A.G. Hansen ad

H. Hara aj H. Harada p E.P. Hartouni ac K. Haruna p M. Harvey e

E. Haslum af K. Hasuko aq R. Hayano h,bc N. Hayashi aq X. He o

M. Heffner ac T.K. Hemmick ay J.M. Heuser aq,ay M. Hibino bf

P. Hidas x H. Hiejima r J.C. Hill s D.S. Ho bh R. Hobbs ak

M. Holmes be W. Holzmann aw K. Homma p B. Hong y

A. Hoover a! T. Horaguchi aq,ar,bb H.M. Hur u T. Ichihara aq,ar

V.V. Ikonnikov z K. Imai aa,aq M. Inaba bd M. Inuzuka h

M.S. Ippolitov z D. Isenhower a L. Isenhower a M. Ishihara aq,ar

T. Isobe h M. Issah aw A. Isupov t B.V. Jacak ar,ay W.Y. Jang y

Y. Jeong v J. Jia j,ay J. Jin j O. Jinnouchi aq,ar B.M. Johnson e

S.C. Johnson ac,ay K.S. Joo ai D. Jouan an F. Kajihara h,aq

S. Kametani h,bf N. Kamihara aq,bb M. Kaneta ar J.H. Kang bh

M. Kann ap S.S. Kapoor d K. Katou bf T. Kawabata h

T. Kawagishi bd A.V. Kazantsev z S. Kelly i,j B. Khachaturov bg

A. Khanzadeev ap J. Kikuchi bf D.H. Kim ai D.J. Kim bh

D.W. Kim v E. Kim av G.-B. Kim ab H.J. Kim bh S.Y. Kim bh

Y.-S. Kim u Y.G. Kim bh E. Kinney i W.W. Kinnison ad

A. Kiss m E. Kistenev e A. Kiyomichi aq,bd K. Kiyoyama aj

C. Klein-Boesing ah S. Klinksiek ak H. Kobayashi aq,ar

L. Kochenda ap V. Kochetkov q D. Koehler ak T. Kohama p

R. Kohara p B. Komkov ap M. Konno bd M. Kopytine ay

D. Kotchetkov f A. Kozlov bg P.J. Kroon e C.H. Kuberg a,ad

G.J. Kunde ad N. Kurihara h K. Kurita aq,ar,as Y. Kuroki bd

M.J. Kweon y Y. Kwon bh G.S. Kyle a! R. Lacey aw V. Ladygin t

J.G. Lajoie s J. Lauret aw Y. Le Bornec an A. Lebedev s,z

S. Leckey ay D.M. Lee ad M.K. Lee bh S. Lee v M.J. Leitch ad

M.A.L. Leite au X.H. Li f Z. Li g,aq D.J. Lim bh H. Lim av

2

A. Litvinenko t M.X. Liu ad X. Liu g Y. Liu an Z. Liu g

C.F. Maguire be J. Mahon e Y.I. Makdisi e A. Malakhov t

M.D. Malik ak V.I. Manko z Y. Mao g,ao,aq S.K. Mark ag

S. Markacs j G. Martinez az M.D. Marx ay A. Masaike aa

H. Masui bd F. Matathias ay T. Matsumoto h,bf M.C. McCain a,r

P.L. McGaughey ad E. Melnikov q M. Merschmeyer ah

F. Messer ay M. Messer e Y. Miake bd J. Milan aw T.E. Miller be

A. Milov ay,bg S. Mioduszewski e,ba R.E. Mischke ad G.C. Mishra o

J.T. Mitchell e A.K. Mohanty d D.P. Morrison e J.M. Moss ad

T.V. Moukhanova z F. Mühlbacher ay D. Mukhopadhyay be,bg

M. Muniruzzaman f J. Murata aq,ar,as S. Nagamiya w

Y. Nagasaka aj Y. Nagata bd J.L. Nagle i,j M. Naglis bg

Y. Nakada aa T. Nakamura p B.K. Nandi f M. Nara bd

J. Newby ac,ba M. Nguyen ay L. Nikkinen ag P. Nilsson af

S. Nishimura h B. Norman ad A.S. Nyanin z J. Nystrand af

E. O’Brien e C.A. Ogilvie s H. Ohnishi e,p,aq I.D. Ojha c,be

H. Okada aa,aq K. Okada aq,ar O.O. Omiwade a M. Ono bd

V. Onuchin q A. Oskarsson af L. Österman af I. Otterlund af

K. Oyama h,bc K. Ozawa h L. Paffrath e,1 D. Pal be,bg

A.P.T. Palounek ad V. Pantuev ay V. Papavassiliou a! J. Park av

W.J. Park y A. Parmar ak S.F. Pate a! H. Pei s T. Peitzmann ah

V. Penev t J.-C. Peng r,ad H. Pereira k V. Peresedov t

D.Yu. Peressounko z A.N. Petridis s A. Pierson ak

C. Pinkenburg e,aw R.P. Pisani e P. Pitukhin q F. Plasil am

M. Pollack ay,ba K. Pope ba M.L. Purschke e A.K. Purwar ay

H. Qu o J.M. Qualls a J. Rak s I. Ravinovich bg K.F. Read am,ba

M. Reuter ay K. Reygers ah V. Riabov ap,at Y. Riabov ap

G. Roche ae A. Romana ab M. Rosati s A.A. Rose be

S.S.E. Rosendahl af P. Rosnet ae P. Rukoyatkin t V.L. Rykov aq

S.S. Ryu bh M.E. Sadler a B. Sahlmueller ah N. Saito aa,aq,ar

A. Sakaguchi p T. Sakaguchi h,bf M. Sakai aj S. Sakai bd

H. Sako bd T. Sakuma aq,bb V. Samsonov ap L. Sanfratello ak

T.C. Sangster ac R. Santo ah H.D. Sato aa,aq S. Sato e,w,bd

S. Sawada w B.R. Schlei ad Y. Schutz az V. Semenov q R. Seto f

D. Sharma bg M.R. Shaw a,ad T.K. Shea e I. Shein q

3

T.-A. Shibata aq,bb K. Shigaki p,w T. Shiina ad M. Shimomura bd

Y.H. Shin bh T. Shohjoh bd K. Shoji aa,aq I.G. Sibiriak z

A. Sickles ay C.L. Silva au D. Silvermyr ad,af,am K.S. Sim y

J. Simon-Gillo ad C.P. Singh c V. Singh c M. Sivertz e S. Skutnik s

W.C. Smith a A. Soldatov q R.A. Soltz ac W.E. Sondheim ad

S.P. Sorensen am,ba I.V. Sourikova e F. Staley k P.W. Stankus am

N. Starinsky ag P. Steinberg j E. Stenlund af M. Stepanov a!

A. Ster x S.P. Stoll e M. Sugioka aq,bb T. Sugitate p C. Suire an

J.P. Sullivan ad Y. Sumi p Z. Sun g M. Suzuki bd J. Sziklai x

T. Tabaru ar S. Takagi bd E.M. Takagui au A. Taketani aq,ar

M. Tamai bf K.H. Tanaka w Y. Tanaka aj K. Tanida aq,ar

E. Taniguchi aq,bb M.J. Tannenbaum e A. Taranenko aw

P. Tarján ! J.D. Tepe a,ad J. Thomas ay J.H. Thomas ac

T.L. Thomas ak W. Tian g,ba M. Togawa aa,aq J. Tojo aa,aq

H. Torii aa,aq,ar R.S. Towell a,ad V-N. Tram ab I. Tserruya bg

Y. Tsuchimoto p,aq H. Tsuruoka bd A.A. Tsvetkov z S.K. Tuli c

H. Tydesjö af N. Tyurin q T.J. Uam ai T. Ushiroda aj H. Valle be

H.W. van Hecke ad C. Velissaris a! J. Velkovska e,ay,be

M. Velkovsky ay R. Vertesi ! V. Veszprémi ! L. Villatte ba

A.A. Vinogradov z M.A. Volkov z A. Vorobyov ap

E. Vznuzdaev ap M. Wagner aa H. Wang f X.R. Wang o,a!

Y. Watanabe aq,ar J. Wessels ah S.N. White e N. Willis an

D. Winter j C. Witzig e F.K. Wohn s C.L. Woody e M. Wysocki i

W. Xie f,ar,bg K. Yagi bd Y. Yang g A. Yanovich q S. Yokkaichi aq,ar

G.R. Young am I. Younus ak I.E. Yushmanov z W.A. Zajc j

O. Zaudkte ah C. Zhang j Z. Zhang ay S. Zhou g S.J. Zhou bg

J. Zimányi x L. Zolin t X. Zong s (PHENIX Collaboration)

aAbilene Christian University, Abilene, TX 79699, USAbInstitute of Physics, Academia Sinica, Taipei 11529, Taiwan

cDepartment of Physics, Banaras Hindu University, Varanasi 221005, IndiadBhabha Atomic Research Centre, Bombay 400 085, India

eBrookhaven National Laboratory, Upton, NY 11973-5000, USAfUniversity of California - Riverside, Riverside, CA 92521, USA

gChina Institute of Atomic Energy (CIAE), Beijing, People’s Republic of ChinahCenter for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1

4

Thanks:G. Young, W. Zajc, J. Nagle, J. Mitchell, B. Jacak,I. Tserruya, P. Stankus, J.Jia, M. Chiu, A. Toia...

and all of PHENIX for the White Paper

Phase Diagram

This transition temperature corresponds to an energy density ε ≈ 1GeV/fm3,nearly an order of magnitude larger than that of normal nuclear matter. Asnoted above, this value is plausible based on dimensional grounds, since suchdensities correspond to the total overlap of several (light) hadrons within atypical hadron volume of 1–3 fm3. No plausible mechanism exists under whichhadrons could retain their in vacuo properties under these conditions. Latticecalculations also indicate that this significant change in the behavior of thesystem occurs over a small range in temperature (∼20 MeV), and suggest thatthe change of phase includes the restoration of approximate chiral symmetryresulting from greatly reduced or vanishing quark constituent masses.

Fig. 2. Theoretical phase diagram of nuclear matter for two massless quarks as afunction of temperature T and baryon chemical potential µ [12].

In the limit of massless noninteracting particles, each bosonic degree of free-dom contributes π

2

30 T4 to the energy density; each fermionic degree of freedom

contributes 78 this value. The corresponding “Stefan-Boltzmann” limits of theenergy density εSB for the case of 2(3) active flavor quark-gluon plasma isthen

{2f · 2s · 2q · 3c7

8+ 2s · 8c}

π2

30T 4 = 37

π2

30T 4 (1)

εSB =

{3f · 2s · 2q · 3c7

8+ 2s · 8c}

π2

30T 4 = 47.5

π2

30T 4 (2)

after summing over the appropriate flavor, spin, quark/antiquark and colorfactors for quarks and spin times color factors for gluons. The large numerical

9

Why we are here today...

0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

µq/T=1.0

µq/T=0.8

µq/T=0.6

µq/T=0.4

µq/T=0.2

µq/T=0.0

!q/T2

T/T0

(a)0.8 1 1.2 1.4 1.6 1.8 2

0

1

2

3

4

µq/T=1.0

µq/T=0.8

µq/T=0.6

µq/T=0.4

µq/T=0.2

µq/T=0.0

!I/T2

T/T0

(b)

Figure 3.3: The quark number susceptibility χq/T 2 (left) and isovector susceptibilityχI/T 2 (right) as functions of T/T0 for various µq/T ranging from µq/T = 0 (lowest curve)rising in steps of 0.2 to µq/T = 1, calculated from a Taylor series in 6th order. Also shownas dashed lines are results from a 4th order expansion in µq/T .

temperature at non-zero µq determined from the peak position of susceptibilities indeedmoves to temperatures smaller than the transition temperature T0 determined at µq = 0.The figure, however, also shows that at least for T < T0 the 6th-order contribution canbe sizeable and still suffers from statistical errors. Better statistics and the contributionfrom higher orders in the Taylor expansion thus will be needed to get good quantitativeresults for susceptibilities in the hadronic phase.

There is also a pronounced dip in χq(T ) for T/T0 ! 1.05 which, together with theincreased error bars makes the presence of a peak in χq less convincing then it is withoutthe inclusion of the µ6q-contribution. However, the error bars also reflect the problem wehave at present in determining this additional contribution with sufficient accuracy toinclude it in the calculation of higher order derivatives of the partition function. On theother side, Fig. (3.3) confirms that a significant peak is not present in the isovector channel.In fact, if a critical endpoint exists in the (T, µ)-plane of the QCD phase diagram, thisis expected to belong to the Ising universality class, implying that exactly one 3d scalardegree of freedom becomes massless at this point. Since both ψ̄ψ and ψ̄γ0ψ are isoscalarand Galilean scalars, both are candidates to interpolate this massless field, and hence wecan expect divergent fluctuations in both quark number and chiral susceptibilities at thispoint. The latter will be discussed in section 3.3.

The difference in the temperature dependence of χq and χI also reflects the strongcorrelation between fluctuations in different flavor components. This will become clear

14

Baryon Density & Dynamics

Ejiri et al (2003)

“Phase Diagram”

(GeV)µ0 0.2 0.4 0.6 0.8 1

T (G

eV)

0

0.05

0.1

0.15

0.2Thermal IThermal II

AGS

SIS

SPSRHIC

As beam energy decreases, increases baryon densityB

“Radiation”

RHIC

AGS

D. Ouerdane, BRAHMS

SPS

“Matter”

CMy-4 -2 0 2 4

dN/d

y ne

t-pro

tons

0

20

40

60

80 pAGS y

pSPS y

pRHIC y

AGS(E802,E877, E917)SPS(NA49)RHIC(BRAHMS)

Large variation in baryon density near y=0below RHIC energies

Total Entropy

(GeV)s1 10 210

)!/2

part

N"(/!chN"

0

10

20

30

40 /2sp) Data @ ppp( Data-e+e

PHOBOSPHOBOS interp.NA49E895Landau

Simple relationship between available energy andentropy, apparently valid for many systems

PHOBOS (2003)

Broken here?

Baryons suppress entropy...

)2 (GeV/cs1 10 210

)1/

4/(2

.2s

chN

0

0.5

1

1.5

-e+eA+A

-Corrected A+ABµ

Thermal Model (Param I)Thermal Model (Param II)

S =E + PV

T−

µBNBT

∆Nch

Npart/2∝

µBT

Cleymans, Stankiewicz, Steinberg, Wheaton (2005)

Thermal Model 5

0 10 20 30 40 50

\/s___

NN (GeV)

0

1

2

3

4

5

6

7

8

9

10

s/T

3

Total

Mesons

Baryons

Fig. 3. The entropy density normalised to T 3 as a function of the beam energy ascalculated in the thermal model. The contributions from baryons and mesons areshown separately.

Ratio Maximum at Maximum√sNN (GeV) Value

Λ/ 〈π〉 5.1 0.052Ξ−/π+ 10.2 0.011K+/π+ 10.8 0.22Ω−/π+ 27 0.0012

Table 1. Maxima in particle ratios as predicted by the thermal model.

• baryon chemical potential µB = 410 MeV,

• energy √sNN = 8.2 GeV.

In the statistical model this transition leads to a sharp peak in the Λ/ 〈π〉 ratio,and to moderate peaks in the K+/π+, Ξ−/π+ and Ω−/π+ ratios. Furthermore,these peaks are at different energies in the statistical model. The statistical modelpredicts that the maxima in the Λ/ 〈π〉, Ξ−/π+ and Ω−/π+ occur at increasingbeam energies.

...but not degrees of freedom

Despite strongly-varying baryon/meson ratio, total degrees of freedom (s/T3) seems to be constant

Cleymans,Oeschler,Redlich,

Wheaton(2005)

Relation to “Kink”

)1/2

F (GeV

0 5 10 15

!w

N"/!#"

0

5

10

15

20

25

NA49

Bevalac + DubnaAGS

PHOBOS

p+p, pp+

)1/2

F (GeV

0 1 2 3 4 5-1

0

1

2

FIT(A+A)-(p+p)

FIG. 4. The dependence of the total pion multiplicity per wounded nucleon on Fermi’s energy

measure F (see text for a definition) for central A+A collisions (closed symbols) and inelastic

p+p(p) interactions (open symbols). The results of NA49 are indicated by squares. The insert

shows the difference between the results for A+A collisions and the straight line parametrisation

of p+p(p) data (dashed line. The solid line shows a straight line fit to the results on high energy

(158 A·GeV and above) central Pb+Pb and Au+Au collisions. The inner error bars on the

NA49 points are statistical and the outer systematic.

24

A change inthe number of

degrees of freedom?...

Or just leavingout the non-pioncontributions to

the total?

Rapidly-changingbaryon density leadsto interesting physics!

The Low-E Scan• The critical point is a clear, compelling reason

to perform a low-E scan at RHIC• But still need to understand effect of baryon density

on dynamics

• Unprecedented opportunity to scan two orders of magnitude in CM energy with• A single machine • A single detector (x2: STAR & PHENIX) with constant

kinematic acceptance

• We should always keep our eyes open!• Need data to figure out “how things work”

Experiments atLow-Energy RHIC

(RHIC½?)

Expected RHIC RatesT. Satogata

Event Counts

CM Energy Rate Events/day

5 GeV ~3 Hz 120k⋅εvtx

8 GeV ~10 Hz 400k⋅εvtx

17 GeV ~70 Hz 2.8M⋅εvtx

Assume 4x104 beam seconds/day

Energy vs. Rapidity vs. PHENIX

CMS Energy1 10 210

Rapi

dity

0

2

4

6

Landau σ

Beam

rapid

ityRHICAGS SPS

PHENIX BBC

CENTRAL ARM

Triggering & Acceptance• ZDC - at low energy?• BBC - 3

Collision Geometry

R

R/!

b

Participant region

BinaryCollisions

Spectators

ENN/2

ENN/2

Collisions/Participant depends on NN cross section

p+p Cross Section12 40. P lots of cross sections and related quantities

10

10 2

10-1

1 10 102

103

104

105

106

107

108

elastic

total!

pp

Plab GeV/c

Cro

ss s

ecti

on (

mb

)

10

10 2

10-1

1 10 102

103

104

105

106

107

108

Plab GeV/c

elastic

total!

p_p

Cro

ss s

ecti

on

(m

b)

!s GeV

1.9 2 10 102 103 104

Figure 40.11: Total and elastic cross sections for pp and pp collisions as a function of laboratorybeam momentum and total center-of-mass energy. Corresponding computer-readable data files maybe found at http://pdg.lbl.gov/xsect/contents.html (Courtesy of the COMPAS group, IHEP,Protvino, August 2003)

6

...which turns out to be ~constant in region of interest!

“inelastic”

Bulk Observables

Multiplicity, Spectra, Strangeness

Particle Density @ η=0

NNs AND s1 10 210 310

)!/2

pa

rt N"

(/

#dN

/d

0

1

2

3

4

5AGSSPSPHOBOS

+p (inel.)pp+p/+p (NSD)pp+p/

ln(s) fit×a+b fitcs×a+b

PHOBOS Au+Au 0-6% Central

Two major deficiencies: not dN/dy, no PID.PHENIX can remedy both of these.

Transverse Dynamics

(GeV/c)Tp0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Td

pT

p

dN

!

21

10-2

10-1

1

10

102 WA980!

NA44+!

NA44-!

p NA44

NA44p

p NA49

(GeV/c)Tp0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Td

pT

p

dN

!

21

10-2

10-1

1

10

102 E866+!

E866-!

p E866

100)" E866 (p

Fig. 47. Invariant yields of p, p̄, and π as function of pT in central Pb+Pb collisionsat the SPS (

√sNN = 17 GeV) (left panel) and in central Au+Au collisions at the

AGS (√

sNN = 5 GeV) (right panel). The p̄ spectrum from the AGS is scaled upby a factor 100. All data are at mid-rapidity (y− ycm ≈ 0) and are from W98 [163],NA44 [226], NA49 [227], and E866 [228,229].

7.2 The φ Meson

We have extended our identified hadron studies to include the φ vector mesonas measured in the K+K− decay channel. The φ is a meson, and is in thatsense similar to the pion with a valence quark and antiquark, and yet its massis comparable to that of the proton.

Figure 48 shows RCP , the ratio of production in central to peripheral Au+Aucollisions scaled by binary collisions, for protons, pions and φ mesons detectedvia its KK decay channel [69] in Au+Au collisions at

√sNN = 200 GeV. A

large suppression of pions at pT > 2 GeV/c is observed (as detailed in Section6), and a lack of suppression for the protons and antiprotons as expectedfrom Fig. 46. The φ follows the suppression pattern of the pions within errors,indicating that the surprising behavior of the protons is not followed by the φ.Figure 49 shows a comparison between the pT spectral shape for protons andthe φ in central and peripheral Au+Au reactions. The two spectra agree witheach other within errors for the most central events. Thus, although the yieldsare evolving differently with collision centrality, giving rise to the deviationfrom unity of RCP , the pT distributions appear quite similar.

91

Explored by different detectors at different machines

Transverse Dynamics

s

1 102

>T

!<

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

E895

E866

NA49

NA44

WA98

STAR

PHENIX

Fig. 13. Beam-energy dependence of the extracted mean transverse expansion ve-locity as a function of beam energy from simultaneous fits to spectra of differentmass [97,98,99,100,101,48,102].

the shortest direction of the ellipsoid. This gradient produces higher momentain that direction, quickly reducing the spatial asymmetry.

The absence of any strong scattering in the early stage of the colliison wouldreduce the amount of elliptic flow that could be created. If the initially pro-duced particles are allowed to initially free stream and reach local equilibriumonly after some time delay, then the spatial anisotropy at the start of hy-drodynamic evolution will be reduced; the longer the delay, the greater thereduction. Following the prescription of Kolb et al. [78], we plot in Fig. 14 theeccentricity after a time delay ∆t compared to its value at formation time, asa function of Au+Au collision centrality. The eccentricity (ε) of the reactionzone is

ε =〈y2〉 − 〈x2〉〈y2〉 + 〈x2〉

. (7)

The eccentricity can be analytically calculated once the density profile of thenuclei is chosen (typically a Woods-Saxon shape). It can also be calculatedusing Monte Carlo techniques, where the positions of those nucleons thatparticipate in the reaction are used to calculate the averages in Eq. 7. FromFig. 14 we can see that for time delays of 2 fm/c or greater the magnitudeof the eccentricity is significantly reduced, and its shape vs. centrality is also

35

Just energy dependence of radial expansion?

Transverse Dynamics

Dramatic change in right where baryon density is changing!

How does baryon density affect transverse activity?

NA49, Hoehne QM2005

K/π Horns

!+"#/!+

K#

0.1

0.2

!-"#/!-

K#

0.05

0.1

0.15

UrQMD 2.0 HSD Hadron Gas A Hadron Gas B

(GeV)NNs1 10 102

!"#/!$#0.002

0.004

0.006

0.008

AGS NA49 RHIC

(GeV)NN

s1 10 10

2

(y

=0

)-!/-

K

0

0.1

NA49

AGS

PHENIX

(y

=0

)+!/

+K

0

0.1

0.2

FIG. 5. The energy dependence of the midrapidity K+/π+ and K−/π− ratios in central

Pb+Pb and Au+Au collisions. The results of NA49 are indicated by squares. Open triangles

indicate the A+A results for which a substantial extrapolation was done. The error bars on the

NA49 points are systematic, the statistical errors are smaller than the symbol size.

25

Shows up at mid-rapidity and in 4π results:comparison of PHENIX & STAR will be important

y=0 4π

NA49 Hadron Spectra

beamy1 2 3 4 5 6 7

RMS

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 E895 / E802 NA49

-! - K

"

+! + K

#

m (GeV)0.5 1 1.5

0.20.40.60.8

11.21.4

158 AGeV

! K "# +$ %

0.5 1 1.5

0.20.40.60.8

11.21.4

80 AGeV

! K "#

0.5 1 1.5

0.20.40.60.8

11.21.4

40 AGeV

! K "# %

0.5 1 1.5

0.20.40.60.8

11.21.4

30 AGeV

! K "#

0.5 1 1.5

RMS

0.20.40.60.8

11.21.4

20 AGeV

! K "#

dn/d

y

100

200

20 AGeV-!

30 AGeV 40 AGeV 80 AGeV 158 AGeV

10

20

30 +K

51015

-K

1

2"

0.51

1.5 #

-2 0 2

51015 #

-2 0 2 -2 0 2 -2 0 2 y-2 0 2

Rich data set, 5 energies!Widths increase log(s)Widths decrease ~m

Energy scans are crucial!

C. Blume, SQM2004

Strangeness vs. CentralityRecent results in relativistic heavy ion collisions 29

WN

0 100 200 300

!+

"#/!+

K#

0.05

0.1

0.15

0.2

p+p

C+C

Si+Si

S+S

Pb+Pb1

10

1 10 102

103

pT > 0, |y-y

cm| < 0.5

< Npart

>P

art

icle

/ e

ven

t /

pa

rtic

ipa

nt

rela

tiv

e to

pB

e

!

"-

pBe pPb PbPb

1

10

1 10 102

103

pT > 0, |y-y

cm| < 0.5

< Npart

>

Pa

rtic

le /

ev

ent

/ p

art

icip

an

t re

lati

ve

to p

Be

!#

"#+

$-+$#+

pBe pPb PbPb

Figure 16. a) (left) Total number of K+ per π+ (equivalent to Npart in S+S andAu+Au collisons at SPS [168, 77]; b)(right) dN/dy at midrapidity as a function ofNpart for strange and multi-strange baryons [169, 170] NA57

strangeness, so that the Ω’s are enhanced by a factor of roughly 20. Due to the lackof measurements in peripheral collisions, the approximate flatness of the enhancement

for Npart > 100 [169] attracted some attention as evidence of a pre-hadronic state [171]

(although the more recent data shown in Fig. 16b [170] don’t look as flat) and the same

effect is seen with K+ in Pb+Pb at CERN and Si+Au at the AGS. One pre-hadronic

state that was neglected was the quantum-mechanical excited nucleon responsible for

the Wounded Nucleon Model for pions. Multiple excitation of the incident nucleons bysuccessive collisions has little effect on the production of pions, but has a huge effect

on the production of K+ if it raises the excitation above the K+Λ threshold. Also, this

happens in the initial collisions not in the hadron gas which takes place much later in

the evolution of the system, so may not be well accounted for in ‘hadronic’ models. To

quote Ref. [171, 172] “The observed strangeness enhancement pattern thus cannot be

generated by hadronic final state interactions, but must be put in at the beginning ofthe hadronic stage.”

So, does the fact that “models based on hadronic interaction mechanisms have

consistently failed to simultaneously explain the wealth of accumulated data” [62]—

notably the strangeness enhancement both at AGS and SPS—imply that the QGP exists

at the SPS (and the AGS)? Obviously not! The fact that certain ‘hadronic models’ do or

do not explain the data is a statement about the validity of these models (which alreadyfail for strangeness in p+A production at the AGS [165]) and is certainly no justification

for drawing any conclusion about the Quark Gluon Plamsa. The strangeness data either

at that time or at present, never supported a QGP conclusion even though strangeness

enhancement was one of the original proposed signatures for the QGP (Sec. 3.2.1).

Interestingly, strangeness production and the region between the SPS and AGS

energies has drawn renewed interest lately [77, 173]. The integrated yield (over allphase space, rapidity, azimuth, pT ) is shown in Fig. 17a [56]. As noted above, there is

an enrichment of K+ in regions of large baryon density due to associated production via

How does geometry (which controls baryon stopping) affect strangeness enhancement?

PHENIX can untangle this with energy vs. centrality dependence of strangeness production

4 B. Kämpfer et al.

3.2.2. Energy Dependence

Fig. 2 suggests that increasing energy causes increased strangeness saturation. How-ever, this conclusion should be taken with caution, as Fig. 2 displays in one plotanalyses of 4π and y ≈ 0 data and data sets comprising different hadron species. As-suming that at CERN-SPS the 4π data are sensible, while at RHIC only y ≈ 0 datashould be analyzed within thermal models, then from Fig. 2 one does indeed derivethe mentioned expectation: with increasing energy, γs evolves towards saturation.

One observes in Fig. 2 that the thermal model delivers for pp and p̄p collisions[ 11] values of γs compatible with peripheral collisions.

0 100 200 300 400

Npart

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

!s

_p included

"2-fit

q2-fit

f2 from a Glauber calculation [9]

C+

C

Si+

Si Pb+Pb

0 100 200 300 400

Npart

f2 from Glauber

0% weak feed-down50% weak feed-down

0 100 200 300 400

Npart

0

0.2

0.4

0.6

0.8

1

!s

mid-rapidity

4#

RHIC

Au+ Au

CERN SPS

Pb+Pb

Fig. 1. Left panel: System-size and centrality dependencies of γs, as extractedfrom centrality-binned Pb+Pb [ 12, 13] and central C+C and Si+Si data [ 9] undervarious fit conditions, assuming 50% feeding from weak decays. Also shown is thefraction of participants which underwent multiple collisions, f2. Middle panel:Comparison of γs extracted from mid-rapidity NA49 data [ 12] with the results ofour earlier analysis of NA49 4π-yields [ 2]. Right panel: γs observed in Au+Aucollisions as extracted from PHENIX data [ 10]; f2 from our Monte Carlo basedGlauber model calculation [ 3].

4. Agreement with Data

Up to now we have reported the system-size, centrality and energy dependence of γs.The values of T coincide approximately with the chiral (deconfinement) transitiontemperature of T ∼ 165 MeV, smoothly increasing from 150 MeV at beam energy of40 AGeV. µB (the baryon potential dominating #µ) decreases from 350 to 220 MeVat CERN-SPS and drops to about 30 MeV at RHIC. The actual values dependon the data samples analyzed. The agreement of data with multiplicities from thethermal model is extremely good with the following exceptions:• φ/K+ is underpredicted for peripheral collisions at beam energy of 158 AGeV,even if the φ yields are included in the fit;

Cleymans et al

Correlations &Fluctuations

HBT, Elliptic Flow, Fluctuations

HBT SystematicsFemtoscopy in Heavy Ion Collisions 25

(fm

)lo

ng

R

0

2

4

6

(fm

)sid

eR

0

2

4

6

(fm

)o

ut

R

0

2

4

6

1/3

partN

0 2 4 6 81/3

)!/dch(dN0 2 4 6 8 10

200 GeV Au+Au PHENIX

200 GeV Au+Au STAR

17.3 GeV Pb+Pb CERES

8.7 GeV Pb+Pb CERES

4.8 GeV Au+Au E802

5.4 GeV Si+Au E802

5.4 GeV Si+Al E802

Figure 5: Pion source radius dependence on number of participants (left) and oncharged particle multiplicity (right). Data are for for Au+Au (Pb+Pb) collisionsat several values of

√sNN, and also for Si+A collisions at the lowest energy.

Average transverse momentum 〈kT 〉 ∼ 450 MeV/c for the PHENIX data and∼ 390 MeV/c for the others. Data from (121; 149; 122; 118).

ments have become a precision tool.Here, we cover the most important systematics of femtoscopic measurements

from the AGS, SPS, and RHIC. We discuss only generally the physics probedby a given systematic, appealing to intuitive schematic models such as the blastwave (72). Full interpretations and comparisons to dynamic models are given inSection 5

4.1 System size: Npart and Multiplicity

As discussed earlier, femtoscopic radii probe homogeneity regions, and not theentire source (hereafter, the term source will be used to refer to the entire sourceof particle emission). Nevertheless, the claim that two-particle correlations probespatial scales would be given little credence if the radii did not exhibit a strong,positive correlation with system size. Therefore, measuring the systematic varia-tion of the radii vs. system composition and centrality represents the most basictest of both theoretical and experimental femtoscopic techniques.

Coalescence studies (150) and two-proton measurements at the AGS (151) andSPS (152) unambiguously demonstrate that nucleon homogeneity lengths increasewith decreasing impact parameter and/or increasing projectile mass, continuingthe trend mapped at lower energies (153; 154), where directional cuts have allowedmeasurement of the shape of the homogeneity region (155; 156; 157). More de-

Excellent diagnosticof space-time dynamics

andfreezeout properties!

PHENIX will take opportunity

to measure fullrange of energiesin same detector

meson vs. baryoncorrelations?

Elliptic Flow vs. Energy

Excitation function of elliptic flow in Au+Au collisions

A. Andronic1, Y.-J. Kim1, M. Kirejczyk1, T. Kress1, P. Koczon1, Y. Leifels1, O.N. Hartmann1, N. Herrmann2,K.D. Hildenbrand1, W. Reisdorf1, A. Schüttauf1, Z. Tyminski1, Z.-G. Xiao1 (for the FOPI Collaboration)

1GSI Darmstadt, 2Universität Heidelberg

We present a complete excitation function of ellipticflow in Au+Au collisions at beam energies from 0.09 to1.49·A GeV, measured with the FOPI detector. To char-acterize the elliptic flow we study the second order Fouriercoefficient v2 = 〈cos(2φ)〉, where φ is the angle with re-spect to the reaction plane. The results are for midra-pidity (|y(0)| < 0.1), which can be covered at all beamenergies for particles identified in Z or for light particlesselected by mass (A) with the momentum cut p(0)t > 0.8(p(0)t = (pt/A)/(pcmP /AP ), y(0) = (y/yP )cm, where the sub-script P denotes the projectile).

-0.1

-0.05

0

0.05

0.1v 2

Z=1, all pt(0)

M2M3M4

-0.2

-0.1

0

0.1

10-1

1

Ebeam /A (GeV)

A≤4, xApt(0) > 0.8

Figure 1: Excitation function of elliptic flow for three cen-trality bins. Upper panel: Z=1 particles, integrated forall momentum values. Lower panel: particles with A≤4weighted with their mass, for p(0)t > 0.8.

In Fig. 1 we present the v2 excitation function for threecentrality bins, M2, M3 and M4, corresponding in a ge-ometrical approximation to impact parameter ranges 7.5-10.0, 5.5-7.5, and 2-5.5 fm, respectively. The elliptic flowshows a transition from in-plane (v2 > 0) to out-of-plane(v2 < 0, also called squeeze-out) at low energies, whichdepends on centrality. This transition was already studiedby our collaboration in great detail [1]. For data inte-grated on p(0)t , a maximum of v2 is seen around the beam

energy of 0.4 AGeV, which is more pronounced towardsmore peripheral collisions, followed by a decrease towardslarger energies. This behaviour is a complex interplay be-tween the magnitude of the fireball expansion (determinedin turn by the equation of state, but also by stopping) andspectator shadowing. Comparisons with transport mod-els will establish the importance of these data in the longquest for unraveling the nuclear EoS. The v2 pattern isvery similar to that of observables related to directed flowand stopping in the same energy range, recently completedby our collaboration [2].

The excitation function shows subtle differences in caseof high-p(0)t particles (Fig. 1, lower panel), which may orig-inate from their different participation in the expansion.

-0.1

-0.05

0

0.05

10-1

1 10 102

Ebeam /A (GeV)

v 2

in-planeout-of-plane

Au+Au M3 |y(0)|

Elliptic Flow vs. Energy

(GeV/c)Tp0 0.5 1 1.5 2 2.5

! /2

v

-0.2

0

0.2

0.4

0.6

0.8

1

", STAR, 130 GeV, 11-46%

", NA49, 17 GeV, 13-34%

", CERES, 17 GeV, 13-26%

", NA49, 8 GeV, 13-34%

Fig. 16. v2(pT )/ε vs. pT for mid-central collisions at RHIC (filled symbols) and SPS(open symbols). Dividing by eccentricity removes to first order the effect of differentcentrality selections across the experiments [50,103,70,104,105].

ages in Eq. 7 are over the participating nucleons, hence ε is calculated at thestart of the collision. The pion data in Fig. 16 show that v2(pT )/ε increasesapproximately linearly with pT for low pT . The rate of increase of v2/ε as afunction of pT is larger at RHIC [50,103] than at SPS [104,105] as can mosteasily be seen by calculating the slope of v2/ε below pT =1 GeV/c (Fig. 17).The slope (dv2/dpT )/ε increases from SPS to RHIC by approximately 50%.Hydrodynamical calculations [106] shown in Fig. 17 reproduce the data bothat RHIC and at CERN SPS within one standard deviation. More extensivecomparisons with hydro calculations will be discussed in section 3.5, while thebehavior of v2 at higher pT , which follows a scaling with respect to the numberof quarks, is discussed in Section 7.

Further insight into the expansion dynamics can be obtained from the massdependence of v2(pT ) shown in Fig. 18 for pions, kaons and protons [50] alongwith a comparison with an early hydrodynamic model calculation [107]. Thev2(pT ) for pions is larger than for kaons and protons at low pT , and this massordering has been explained as resulting from radial expansion[107] that pro-duces a larger distortion of the elliplic flow induced velocity profile for largerhadron masses. However, as will be discussed in Section 3.5, this calculationfails to reproduce the proton spectra, and attempts to remedy this failurelead to calculations that no longer reproduce the measured v2 for pions andprotons.

38

Elliptic Flow vs. Energy

(GeV)NNs10

210

d(v

2)/

d(p

t) 1

/Ge

V/c

!1

/

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8, K PHENIX 20-40%"

STAR 11-46%"

h PHENIX 20-40%

NA49 13-34%"

NA49 13-34%"

Hydro+RQMD 6fm Teaney et al."

Fig. 17. The slope of the scaled elliptic flow, (dv2/dpT )/ε, for mid-central collisionsat RHIC (filled symbols) and the SPS (open symbols). The slope is calculated fromthe data in Fig. 16 for the data pT < 1 GeV/c. The solid error bars represent thetotal systematic error including the systematic error on v2 and ε [50,103,70,104].

3.4 HBT

Bose-Einstein correlations between identical particles provide a measure ofthe space-time extent of the source at the end of the reaction. Because theextracted source parameters as measured by the HBT technique are drivenby space-time correlations, HBT results are sensitive to expansion dynamicsintegrated throughout the collision. HBT measurements were originally moti-vated by theoretical predictions of a large source size and/or a long durationof particle emission [108,109,110]—which would result from the presence of along-lived mixture of phases in the matter as it undergoes a first-order phasetransition from a quark-gluon plasma back to the hadronic phase.

In HBT analyses, multidimensional Gaussian fits are made to the normal-ized relative momentum distributions yielding fit parameters, Rlong, Rside, Rout[111], also referred to as HBT radii, where

C2 = 1 + λ exp(−R2sideq2side − R2outq2out − R2longq2long). (9)

The coordinate system is chosen so that the longitudinal direction is parallel tothe beam axis, the out direction is in the direction of the pair’s total transverse

39

Is this a “step” in theenergy dependence?Use a single detector

to reduce errors

Longitudinal Scaling of v2

beam - y!

-10 -8 -6 -4 -2 0 2

2v

0

0.01

0.02

0.03

0.04

0.0519.6 GeV

62.4 GeV

130 GeV

200 GeV

beam + y!

-2 0 2 4 6 8 10

2v

0

0.01

0.02

0.03

0.04

0.05Does particle density control elliptic flow? Baryon density?

How will this plot be modified below top SPS energy?

PHOBOS (PRL 2005)

Fluctuations

partN0 50 100 150 200 250 300 350 400

(%

)T

pF

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

PHENIX Au+Au

PHENIX min. bias p+p

Simulation, min. bias p+p, PYTHIA

)part

(Nprob

Simulation, Au+Au, constant S

)part

(Nprob

-scaled SAA

Simulation, Au+Au, R

Established technique - but dominated by moderatepT at top RHIC energies

(GeV/c)max

Tp

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 (

%)

Tp

F0

0.5

1

1.5

2

2.5

3

3.5

4

PHENIX Au+Au

PYTHIA-based Simulation

Flavor Fluctuations

Christof Roland / MITQuark Matter 2004 January 2004

Summary

• K/! fluctuations increase towards lower beam energy

• Significant enhancement over hadronic cascade model

• p/! fluctuations are negative

• indicates a strong contribution from resonance decays

NA49 Preliminary NA49 Preliminary

PHENIX is current working on an analysisof K/π fluctuations in top energy Au+Au

Stay tuned...

Flavor Fluctuations

50-500 Tracks/event

Christof Roland / MITQuark Matter 2004 January 2004

Acceptance

40 GeV: 160 GeV: 20 GeV:

Rare ProbesJet quenching, Dileptons, Open Charm

life is hard...

Onset of Jet Quenching?

(GeV/c)Tp0 1 2 3 4 5 6 7

A

A R

0.2

0.30.40.5

1

2

345

10

= 17.3 GeV)NNs+X 0--7% central [WA98] (0! "Pb+Pb

= 17.3 GeV)NNs+X 0--5% central [CERES] (±! "Pb+Au

= 19.4 GeV)NNs+X 0--8% central [WA80] (0! "S+Au

= 31 GeV)NNs+X min. bias [ISR] (0! " # + #

Fig. 31. Nuclear modification factors for π0 production at the CERN-ISR in min-imum-bias α + α reactions at

√sNN = 31 GeV [162] and for pion production at

the CERN-SPS in central Pb+Pb [163], Pb+Au [164], and S+Au [165] reactions at√sNN ≈ 20 GeV. The RAA from SPS are obtained using the p + p parametrization

proposed in ref. [166]. The shaded band around RAA = 1 represents the overall frac-tional uncertainty of the SPS data (including in quadrature the 25% uncertainty ofthe p + p reference and the 10% error of the Glauber calculation of Ncoll). Thereis an additional overall uncertainty of ±15% for the CERES data not shown in theplot [164].

hardly at all, with any final-state medium produced. The direct-photon crosssection and centrality dependence should then reflect only the properties of theinitial state, notably the product of the gluon and quark structure functionsof the Au nuclei.

The first measurement of direct photon production in Au+Au collisions atRHIC has been reported by the PHENIX collaboration (Fig. 33) [73]. Thedata exhibit pure point-like (Ncoll) scaling as a function of centrality relativeto a pQCD calculation for p + p collisions. The statistical and systematicerrors still leave some room for a small Cronin effect and/or some thermalphoton production. The observation of direct photon production establishesthe importance of gluon degrees of freedom at RHIC.

PHENIX measured the single-electron yield from nonphotonic sources in Au+Au

64

Can we finally trace the emergence of jets in A+A?Will need consistent p+p and A+A

Di-electron Physics

Low mass dielectrons may be sensitive to vector mesonmodifications. PHENIX will improve this using HBD.

765M events

e+e- Rates in PHENIXRates for Vector Meson ProductionRates for Vector Meson Production

• ’s produced in | | < 0.5• e+,e- into PHENIX central arm acceptance• pT,e > 200 MeV/c

Consider Run 8 (200 GeV Au x Au, 4x Design Luminosity) :

• Lpeak = 30 x 1026 cm-2 s-1

• L ave store = 8 x 1026 cm-2 s-1

• 20 KHz peak min. bias rate• 5.4 KHz avg min. bias rate• 10 week dedicated HBD run (central field in ± configuration)• RHIC x PHENIX = 0.5 x 0.5 = 0.25

N →e+e- = 1.2 x 105 produced in PHENIX acceptance

8.2 x 109 min. bias events produced

N →e+e- = 1.5 x 10-5 / min.bias evente+e- → PHENIX) = 1 : 0.9 : 0.7

CERES & PHENIX need 10-100’s millions of events.Will be extremely challenging in low-E RHIC

C. Woody, RHIC II Workshop

Charm Production

(GeV)s30 40 50 60 70 80 90100 200

)b

inary

b/N

µ (

cc

!

10-1

1

10

102

103

)b

inary

/dy (

nb

/Ne

!d

1

10

102

103

104

cc!

Conclusions• Unprecedented opportunity to study strongly-

interacting matter over 2 orders of magnitude in excitation energy!

• How does net baryon density affect dynamics?

• PHENIX will provide a broad and deep menu of observables• Bulk observables (entropy, flavor, dynamics)• Correlations & Fluctuations• Rare probes (iff a long, dedicated run)

• High return to modest investment

High pt azimuthal correlations - CERES 3

where NA is the number of triggers and NAB the total number of AB pairs inthe event sample. The conditional yields have been corrected for the single hadronefficiency estimated to be 85% at laboratory momenta greater than 1.0 GeV/c. Thiscorrection leads to a 1.5% systematic uncertainty on the absolute normalization.

)!"

C(

0.98

1

1.02

: 0.0 - 5.0 %geom#/#

Preliminary

: 0.0 - 5.0 %geom#/#

)!"

C(

0.98

1

1.02

: 5.0 - 10.0 %geom

#/#

Preliminary

: 5.0 - 10.0 %geom

#/#

)!"

C(

0.98

1

1.02

: 10.0 - 20.0 %geom#/#

Preliminary

: 10.0 - 20.0 %geom#/#

(radians)!"0 0.5 1 1.5 2 2.5 3

)!

"/d

(A

B d

Ntr

ig1

/N

0

0.05

0.1Preliminary

(radians)!"0 0.5 1 1.5 2 2.5 3

)!

"/d

(A

B d

Ntr

ig1

/N

0

0.05

0.1Preliminary

(radians)!"0 0.5 1 1.5 2 2.5 3

)!

"/d

(A

B d

Ntr

ig1

/N

0

0.05

0.1Preliminary

Fig. 1. Upper row: Correlation functions for the three centrality bins. The fulllines indicate flow contributions estimated with the ZYAM method. The dashedand dotted lines represent the flow contributions with (vA2 ) and (v

B2 ) varied accord-

ing to their statistical uncertainties. Lower row: Conditional yields of the jet-pairdistributions for the three centrality bins, normalized to the number of triggers.The full, horizontal bands represent the systematic uncertainty resulting from theflow constant b0 estimation by the ZYAM method. The dashed and dotted linesrepresent distributions that would result from varying (vA2 ) and (v

B2 ) values within

their statistical uncertainties.

3. Results and conclusions

The conditional yields of the (di-)jet associated particles are shown in Fig. 1. It hasbeen verified that the shapes and the yields of the near-side peaks are consistentwith PYTHIA simulations within the systematic uncertainties. On the other hand,it is observed that the away-side structures have a pronounced non-Gaussian shapeas centrality increases. This significant modification of the back-to-back structure, ispossibly caused by substantial re-interaction of the scattered partons in the medium.In the most central selection the away-side structure is rather a plateau, revealingthe existence of a local minimum at π. To extract the widths of the near-side andaway-side structures we subdivide the ∆φ distribution into two parts separated bythe global minimum. The resulting RMS values are shown as function of the number

CERES di-hadrons

7

-0.1

0

0.1

10-1

1 10 102

103

104

Ebeam (AGeV)

v2

FOPIPlastic BallLAND, protonsEOSE895E877 pions, protonsNA49 pions, protonsCERES charged part.STAR charged part.

in-plane

out-of-plane

Figure 9. Energy dependence of v2, showingdata ranging from Bevalac to RHIC energies.

max/nchn0 0.2 0.4 0.6 0.8 1

2v

0

0.02

0.04

0.06

0.08

0.1

0.12STAR

PHOBOS (Preliminary)

> 500 MeV)T

PHENIX (p

Figure 10. The STAR result comparedwith PHOBOS and PHENIX. PHENIX hasa lower pT cutoff of 500 MeV.

two-particle correlation function to extract v2,dNd∆φ

∝ 1+∑∞

n=1 2v2n cos(n∆φ) [28]. In prin-

ciple, these two methods extract the same information. However, the correlation functionmethod may be sensitive to other effects, e.g. jets or HBT, that would be missed by theother method.

The magnitude of v2 varies with the energy as well as the centrality of the collision.The centrality dependence is controlled by the eccentricity " of the nuclear overlap region.It has been shown [29,30] that when the system is dilute, v2 ∝ " × dN/dy, where therapidity density characterizes the probability of particles to rescatter. In the limit wherethe number of scatterings becomes large, only the initial geometry is important, so v2 ∝ ",and the proportionality constant can be predicted via hydrodynamic calculations[25]. Thecompiled data for the energy dependence of v2 is shown in Figure 9 (from [31]). The largeanti-flow (squeeze-out) observed in low-energy nuclear collisions is seen to change signat

√sNN = 4GeV, turning into a continuous logarithmic rise of v2 all the way to RHIC

energies. It is interesting to note that v2 at RHIC is approximately 60% higher than atthe SPS, similar to the 70% increase in dNch/dη already mentioned.

Since STAR’s original result [24], three of the four RHIC experiments have measuredthe dependence of v2 with centrality, as shown in Figure 10. Both STAR and PHOBOSmeasure the event with full azimuthal acceptance and comparable event plane resolution.PHENIX uses the correlation function method and has a lower pT cutoff of 500 MeV,both of which may explain why the PHENIX v2 result is somewhat higher than the othertwo.

The pT dependence of v2 appears to both support the hypothesis that the central regionof RHIC collisions shows hydrodynamic behavior, as well as suggest the appearance of jetquenching. STAR and preliminary PHENIX data[28] on v2(pT ) are shown in Figure 11and are in broad agreement, at least for the basic trend. Calculations given in [32] havereproduced the STAR data up to pT = 2 GeV. The same calculations also predict v2 foridentified pions and protons and finds that protons only have non-zero flow above pT ∼ 400MeV. Also shown in Figure 11 are calculations of jet quenching which incorporate the

Elliptic Flow vs. Energy

...but not degrees of freedom

)2 (GeV/cs1 10 210

3/4

)s/T

2 !(

0

5

10

15

20

25Total IMeson IBaryon I

Total IIMeson IIBaryon II

Despite changing baryon/meson ratio, total degrees of freedom (s/T3) seems to be constant

~Constant!

Cleymans, Stankiewicz, Steinberg, Wheaton (2005)

Mesons

Baryons