HADRON MATTER AT HIGH ENERGY - INFN Lecce webM.Miller, QM04 flow of matter normal to the Mach cone seems to be observed! See data from STAR, φ=π +/-1.23=1.91,4.37 Villa Gualino 2

Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School 1

Pb-Pb @ SPS, from NA49

Au-Au @ RHIC, from STAR

HADRON MATTER AT HIGH ENERGYLuciano Maiani, Univ. di Roma La Sapienza and INFN, Roma.

ALICE: TPC R/O chambers

Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 2

Summing up from 1st Lecture

• The fireball produced in collisions with low energy density is ~ a pion gas at some T;

• Increasing ε, e.g. by increasing c.o.m. energy and/or centrality, T increases and higher resonances are produced;

• Increasing temperature becomes difficult because more and more energy goes in exciting resonances rather then increasing kinetic energy, i.e. T: dT/dε ~(β-βc)3/2, as we approach the limiting Hagedorn temperature;

• When hadron bags are in contact, bags fuse and quarks and gluon are liberated

• A cartoon representing this:

ε/T4

TTHag~Tc~180 MeVHadron gas

Quarks & gluons~ π2/30(16+21/2nf)~16

Hagedorn gasχc and Ψ’ start fusingStrange Particles abundantly produced

signals of quark confinement: J/Psi suppression & strangeness enhancement detected at SPS

Main findings at RHIC

Particles are produced from matter which seems to be well equilibrated (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T)

Very robust collective flows were found, indicating

very strongly coupled Quark-Gluon Plasma (sQGP)

Strong quenching of large pt jets: they do not fly away freely but are mostly (up to 90%)

absorbed by the matter. The deposited energy seemTo go into hydrodynamical motion (conical flow)

E. Shuryak @ Frascati


Lecture 2: summary

1. Jet Quenching2. Elliptic flow3. Hadron production: coalescence & fragmentation4. Comparison to Expts. 5. Criptoexotic Mesons?6. Quark Counting (Work in Progress)7. Conclusions

U. Heinz, CONCEPTS OF HEAVY-ION PHYSICS, hep-ph/0407360 v1 30 Jul 2004

L. Maiani, Erice 2004http://www.roma1.infn.it/people/maiani/schools.html

Quark Matter05, Budapest, August 2005

from U. Wiedemann, Quark matter 04


Jet Quenching


Is such a sonic boom already observed?Mean Cs=.33 time average over 3 stages=>

M.Miller, QM04

flow of matter normal to the Mach cone seems to be observed! See data from STAR,

φ=π +/-1.23=1.91,4.37


2. Elliptic flow (from U. Heinz)

≠0

Space eccentricity Momentum anisotropyA collective phenomenon !!


φ

• Fourier expansion in azimuthal angle φ• no sinφ or cos φ terms allowed by symmetry• the orientation of the ellipse is found event by event• v2 is isolated by forming <cos2φ>

• integration over b or over p⊥ lead to

– v2(p⊥): differential elliptic flow

– v2(b): p⊥-integrated ell. flow

The elliptic flow coefficient v2


A tour in RHIC&SPS data (QM05, I. Tserruya)


Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter

3. FRAGMENTATION & COALESCENCE

12

Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School

• proposed by several authors, an incomplete list:in P+P: K. P. Das and R. C. Hwa, Phys. Lett. 68B, 459 (1977); 73,504(E) (1978); R. G. Roberts, R. C. Hwa, and S. Matsuda, J. Phys. G 5, 1043 (1979).

at intermediate p T:C. Gupt, R. K. Shivpuri, N. S. Verma, and A. P. Sharma, Nuovo Cimento A 75, 408 (1983).T. Ochiai, Prog. Theor. Phys. 75, 1184 (1986).T. S. Biro, P. Levai, and J. Zimanyi, Phys. Lett. B 347, 6 (1995); J. Phys. G 28, 1561 (2002).

for particle spectra:R. C. Hwa and C. B. Yang, Phys. Rev. C 66, 025205 (2002).R. J. Fries, B. Müller, C. Nonaka, and S. A. Bass, Phys. Rev.Lett. 90, 202303 (2003).V. Greco, C. M. Ko, and P. Levai, Phys. Rev. C 68, 034904 (2003).

for particle multiplicities:

F. Becattini Phys.Rev.Lett. 95 (2005) 022301

• we have used formulae and parameters from:R. J. Fries, B. Müller, and C. Nonaka, S. A. Bass, Physical Review C 68, 044902 (2003)

Coalescence in Heavy Ion Collisions

13


Where do the hadrons come from?• I. Production of harder partons (jets):

.... followed by fragmentation of the parton:

• hadrons with pT originate from parton of higher momentum: pT/z >pT , where spectrum is lower.

• Energy loss in the hadronic medium disfavours fragmentation: for a given p⊥ we need a more energetic parton.

• fragmentation in protons unfavoured w.r.t. pions.

• A simple model:

14

dNperta

d2p⊥dy

∣∣∣y=0

= KC

(1+ p⊥/B)β.

EdNhd3P

=∑a

1Z

0

dzz2Da→h(z,Q2)Ea

dNad3Pa

ΔPaPa

=ε√Pa; ε= ε0

< L>

RA

Pa, f in ! ε ·√Pa+Pa; P= z pa, f in


hadrons ? (cont’d)• II. Coalescence of quarks and gluons from the unconfined medium.

• Thermal distribution of constituents: non-relativistic limit:

• Thermal distribution of hadrons made by n-constituents:

• CM=degeneracy factor (e.g. (2s+1))

• to make a hadron with momentum P, coalescence puts together constituents with momentum P/n, i.e. where they are more abundant: coalescence wins over fragmentation at intermediate momenta

15

EadNad3pa

=V

(2π)3Ea γa e−

EaT =

V(2π)3

Ea ρa(pa)

EHdNHd3P

=CH (γaγb . . .)VEH(2π)3

[ρa(

Pn)]n

[ρa(

Pn)]n!

[e−

PHn

]n= e−PH

• Coalescence probability drops exponentially: at large p⊥ fragmentation wins

• Proton yield > pion yield is a signal of coalescence• Coalescence is a clear signal for the formation of a deconfined phase


with relativistic flow• as seen yesterday:

– volume is replaced by time-like 3-dim hypersurface – Boltzmann distribution is replaced by Touschek invariant phase space:

– v= local flow 4-velocity, u=normal to hypersurface:

• for a meson with n=2:

16

(Pv) = m⊥ cosh(η− y)coshη⊥−P⊥ cos(φ−Φ)sinhη⊥

NMd2P⊥dy

∣∣∣y=0

=CMM⊥τ(πρ2)(2π)3

γaγbZdφ

[ecosφ

P⊥ sinhη⊥2T

]2

Zdηcoshη

[e(−coshη

m⊥(P⊥/2)coshη⊥T )

]2

d3V(2π)3

Ee−ET ⇒ d3Σ

(2π)3(u ·P)e−

PµvµT


Coalescence & Elliptic flow

• Elliptic Flow provides an interesting scaling law • for non-central collisions constituents have an azimuthal distribution

• for an hadron with n constituents:

• when coalescence dominates:

17

ρa(p⊥) = f (p⊥)[1+2v2(p⊥)cos(2Φ)+ . . .]

[ρa(p⊥n

)]n " f (p⊥n

)n[1+2(n · v2(p⊥n

))cos(2Φ)+ . . .]

(v2)Hn

versusP⊥n

= universal


Quark counting @ RHIC and LHC:by Nuclear Modification Ratios

• As well as being probes for the QGP, Nuclear Modification Ratios (NMR) are useful tools for quark counting;

• in contrast to v2 (of order of few %), these ratios provide sizeable signal;

• Central to Periferal ratio (b=12 fm for Au+Au at RHIC):

• Nuclear to Proton ratio:

• NMR they are very sensitive to # of constituents• The measure of RCP and RAA at RHIC and LHC can resolve quark

composition in controversial cases.18

RHCP =Ncoll(b)Ncoll(0)

[ dNHd2P⊥(b= 0)

dNHd2P⊥(b)

]

RHAA =

dNAA

Hd2P⊥ (b= 0)

Ncoll(0)dNPPH

d2P⊥ (b)


4. Comparison to Expts: Inclusive cross-sections (Au+Au@RHIC)

19

4 6 8 10 12

0.00001

0.001

0.1

4 6 8 10 121. ! 10"8

1. ! 10"6

0.0001

0.01

1

p⊥ (GeV )p⊥ (GeV )

P+ P̄data points : PHENIXcentrality 0-5 %

π0

data points : PHENIXcentrality 0-10 %

Λ+ Λ̄data points : STARcentrality 0-5 %

2 4 6 8 10 121. ! 10"7

0.00001

0.001

0.1

2 4 6 8 10 121. ! 10"7

0.00001

0.001

0.1KSdata points : STARcentrality 0-5 %

Curves: our recalculation with the model of Fries et al.

Itzhak Tserruya QM05 Budapest 9/8/05 20

RAuAu of identified hadrons vs rapidity

• NO change of RAuAu with rapidity

Pions y=0 and y=3.1 Protons y=0 and y=3

Au+Au at 200 GeV

RAA =d2NAu+Au(b= 0)/dP2⊥Ncoll(b= 0)d2Np+p/dP2⊥

Itzhak Tserruya QM05 Budapest 9/8/05

New SPS data: RCP for h-, π, K±, K0s, p, Λ

NA49

• RCP(baryon)>RCP(meson)⇒same systematics as original Cronin data at similar √s⇒same systematics as RHIC but scaled upward

NA57

by the way... the Proton to Pion effect is seen at SPS too.....


Proton enhancement via Coalescence

22


23

Quark Counting

All this strengthens the case for sQGP with early thermalization of partonic matter made of constituent

quarks

ALICE. Vietri sul Mare. 30.05.06 L.MAIANI. Hadron matter @RHIC and LHC

5. Crypto-Exotic Mesons ?

• Old and new puzzles in meson spectroscopy point to few anomalous cases

• the case of f0(980), JPC=0++ is well-known:– almost degenerate with I=1 a0(980) which in q-qbar picture should be u-dbar– if same quarks, f0=u ubar+d dbar– shows strong affinity with K-Kbar channel: s-sbar?

• f0 is good candidate for a new class of mesons, made by diquark-antidiquark pair: earlier proposal by Joffe&Wilczeck, more recent by our group (L.M., F. Piccinini, A. Polosa, V. Riquer)

24


25

Do diquarks- antidiquarks bind? QCD

1 2

R

R

Interaction of two colored objects:

]2/3)1J(J)][R(C[gTTg eff)2(2

R22112 −+−∝>σ⋅σ<−∝

Spin-spin interaction

{qqandqq31 =><>< spin 1= +1/2 repulsion

spin 0= -3/2 attraction

Baryons in the octet:Λ=([ud] J=0 s); Σ0 =({ud}J=1s)→ Λ is lighter than Σ

{qq = octet = +1/3 repulsionsinglet = -8/3 attraction

{qq = “3bar” = -4/3 attraction“6 “ = +2/3 repulsion

g2 < !T1 ·!T2 >R=g2

2[C(2)(R)−2C(2)(1)]Energy ∝


26

Quantum numbers and mass spectrum

The inverted mass spectrum reveals the 4quark composition of the lightest scalar mesons


27

q-qbar, P-waves,Borchi & Gatto 1965 !!

arXiv:hep-ph/0604018, 3 Apr 2006


28

Compare normal (2++) with 0++

- there are 10, 0++, states: 1 4q nonet + 1 glueball??

- q-qbar explanation (Schechter et al. 1999): mixing with lowest scalars distorts spectrum.


29

Quark Counting via RCP and RAAL. Maiani, A. Polosa, C. Salgado, V. Riquer, work in progress

pT (GeV)

P+ P̄

π0

RCP

0 2 4 6 8 100.2

0.4

0.6

0.8

1

KS

Λ+ Λ̄ f0 = [qs][qbar sbar]RCP

f0 = s-sbar

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

pT (GeV)


30

Ratio: AA(Au-Au)(L. M., A. Polosa, V. Riquer, C. Salgado in preparation)

f0 = [qs][qbar sbar]

f0 = s-sbar

RAA

pT (GeV)2 4 6 8 10

1

2

3

4

π0

P+ P̄

KS

Λ+ Λ̄

f0 = (ss̄)

Ξ+ Ξ̄

f0 = [qs][q̄s̄]


RCP @ LHC: f0(984) as 4-q vs q-qbar (b=14fm)

31

RCP

Pb−Pb@LHC

pT (GeV)2 4 6 8 10

0.2

0.4

0.6

0.8

π0

P+ P̄

KS

Λ+ Λ̄

f0 = (ss̄)

Ξ+ Ξ̄

f0 = [qs][q̄s̄]


RAA @ LHC: f0(984) as 4-q vs q-qbar

32

pT (GeV)

RAA

Pb−Pb@LHC

2 4 6 8 10

0.1

0.2

0.3

0.4

0.5

π0

P+ P̄

KS

Λ+ Λ̄

f0 = (ss̄)

Ξ+ Ξ̄

f0 = [qs][q̄s̄]


7. Conclusions


@ RHIC

• Deconfined phase is showing unexpected properties• New phenomena, new probes:

• jet tomography• collective motion• b-quarkonia could be a useful probe• coalescence can help to solve old problems

• Initial quanta: Color Glass Condensate?• A very dense, fluid phase: strongly interacting Quarks and Gluons?


• initial state quanta:• hard jets• hard, heavy quarks (what about top?)• Higgs as a probe?

• bulk properties of QGP:• jet tomography• collective motion, hydrodynamical flow..• quarkonia will form from recombination: enhancement!

Useful probes @ LHC

big surprises are possible!

Documents

HADRON MATTER AT HIGH ENERGY - INFN Lecce webM.Miller, QM04 flow of matter normal to the Mach cone seems to be observed! See data from STAR, φ=π +/-1.23=1.91,4.37 Villa Gualino 2