hadron matter at high energy - infn lecce webm.miller, qm04 flow of matter normal to the mach cone...
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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
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 4
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
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 6
Jet Quenching
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 7
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
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 8
2. Elliptic flow (from U. Heinz)
≠0
Space eccentricity Momentum anisotropyA collective phenomenon !!
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 9
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
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 10
A tour in RHIC&SPS data (QM05, I. Tserruya)
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 11
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
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Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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:
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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
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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
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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
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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:
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(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
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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:
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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
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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)
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
4. Comparison to Expts: Inclusive cross-sections (Au+Au@RHIC)
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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.....
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
Proton enhancement via Coalescence
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Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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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)
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ALICE. Vietri sul Mare. 30.05.06 L.MAIANI. Hadron matter @RHIC and LHC
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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 ∝
ALICE. Vietri sul Mare. 30.05.06 L.MAIANI. Hadron matter @RHIC and LHC
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Quantum numbers and mass spectrum
The inverted mass spectrum reveals the 4quark composition of the lightest scalar mesons
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
27
q-qbar, P-waves,Borchi & Gatto 1965 !!
arXiv:hep-ph/0604018, 3 Apr 2006
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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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.
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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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)
Martignano, 13/06/2005 L. Maiani. Hadron Matter at High Density LHC School
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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]
ALICE. Vietri sul Mare. 30.05.06 L.MAIANI. Hadron matter @RHIC and LHC
RCP @ LHC: f0(984) as 4-q vs q-qbar (b=14fm)
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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]
ALICE. Vietri sul Mare. 30.05.06 L.MAIANI. Hadron matter @RHIC and LHC
RAA @ LHC: f0(984) as 4-q vs q-qbar
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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]
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 33
7. Conclusions
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@ 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?
Villa Gualino 2. 14/10/2005 L. Maiani. New State of Matter 35
• 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!