Strangeness and the Discovery of Quark Gluon

STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004 Deconﬁnement of quarks and gluons into a plasma (QGP) at high temperature is a predicted paradigm shifting feature of strong interactions. The production of strange particles in relativistic heavy ion collisions at CERN and BNL conﬁrms that a new phase of matter with the expected properties is being formed. I will survey the key theoretical predictions and the related experimental results. Time permitting, I will discuss how the newly gained knowledge leads to the study of the hot nearly matter-antimatter symmetric post quark-gluon Universe. +50% of content is for STUDENTS.

BONUS material after 50 transparencies: THE QUARK UNIVERSE

Supported by a grant from the U.S. Department of Energy, DE-FG02-04ER41318 Johann Rafelski Department of Physics University of Arizona TUCSON, AZ, USA

1 J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 2 EXPERIMENTAL HEAVY ION PROGRAM

— LHC

CERN: LHC opens after 2007 and SPS resumes after 2009 J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 3 ...and at BROOKHAVEN NATIONAL LABORATORY

Relativistic Heavy Ion Collider: RHIC J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 4 BROOKHAVEN NATIONAL LABORATORY

12:00 o’clock PHOBOS BRAHMS 10:00 o’clock 2:00 o’clock

RHIC PHENIX 8:00 o’clock STAR 4:00 o’clock 6:00 o’clock Design Parameters: BeamEnergy = 100 GeV/u U-line 9 GeV/u No. Bunches = 57 High Int. Proton Source BAF (NASA) µg-2 9 Q= +79 No. Ions /Bunch = 1×10 LI NAC T = 10 hours BOOSTER store L = 2×1026 cm-2sec-1 Pol. Proton Source ave AGS HEP/NP

1 MeV/u Q= +32 TANDEMS

Relativistic Heavy Ion Collider: RHIC J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 5

The origin of this research program STRUCTURED VACUUM: Melt the vacuum structure and demonstrate mobility of quarks – ‘deconﬁnement’. This demonstrates that the vacuum is a key component in the understanding of what we observe in terms of the fundamental laws of nature. This leads to understanding of the origin of 99% of the rest mass present in the Universe – The Higgs mechanism covers the remaining 1% (or less). EARLY UNIVERSE: Recreate and understand the high energy density conditions pre- vailing in the Universe when nucleons formed from elementary degrees of freedom (quarks, gluons) at about 10-40µs after big bang. Hadronization of the Universe led to nearly matter-antimatter sym- 10 metric state, the sequel annihilation left the small 10− matter asymmetry, the world around us. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 6

What is deconﬁnement? A domain of (space, time) much larger than normal hadron size in which color-charged quarks and gluons are propagating, con- strained by external ‘frozen vacuum’ which abhors color.

We expect a pronounced boundary in temperature and density between confined and deconfined phases of matter: phase diagram. Deconfinement expected at both: high temperature and at high matter density. In a finite size system not a singular boundary, a ‘transformation’. THEORY FUTURE What we need as background knowledge: 1) Hot QCD in/out of equilibrium (QGP from QCD-lattice) 2) Understanding from first principles and not as descriptive method of hadronization dynamics and final hadron yields, 3) More sensitive (hadronic and other) signatures of deconfinement beware: final particles always hadrons, many decay into leptons DECONFINEMENT NOT A ‘NEW PARTICLE’, there is no answer to journalists question: How many new vacuua have you produced today? J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 7 Vacuum structure Quantum vacuum is polarizable: see atomic vac. pol. level shifts Quantum structure of gluon-quark fluctuations: glue and quark condensate evidence from LGT, ’onium sum rules Permanent fluctuations/structure in ‘space devoid of matter’: even though V Ga V = 0, with G2 Ga Gµν = 2 [B~ 2 E~ 2] , h | µν| i ≡ µν a a − a a a αs 2 2 X 4 X 4 we have V G V (2.3 0.3)10− GeV = [390(12) MeV] , h | π | i ' § and V uu¯ + dd¯ V = 2[225(9) MeV]3 . h | | i −

Vacuum and Laws of Physics Vacuum structure controls early Universe properties Vacuum determines inertial mass of ‘elementary’ particles by the way of the Higgs mechanism, m = g V h V , i ih | | i Vacuum is thought to generate color charge conﬁnement: hadron mass originates in QCD vacuum structure. Vacuum determines interactions, symmetry breaking, etc..... DO WE REALLY UNDERSTAND HOW THE VACUUM CON- TROLS INERTIA (RESISTANCE TO CHANGE IN VELOCITY)?? J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 8

Do we understand how annihilation of almost all matter-antimatter occurs?

Visible Matter Density [g cm −3 ] 15 3 −9 10 10 10 10 27 LHC 16 quarks 10 1 TeV combine RHIC atoms antimatter form disappears photons 13 neutrinos 10 decouple decouple 1 GeV SPS nuclear reactions: light nuclei formed era of 10 galaxies 10 and stars 1 MeV Particle energy Particle 7 Temperature [K] OBSERVATIONAL 10 1 keV COSMOLOGY

4 10 PARTICLE/NUCLEAR ASTROPHYSICS 1 eV

10 10 10 −12 −6 6 12 18 10 10 1 Time [s] 10 day year ky My today J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 9

CERN SPS: THE FIRST LOOK AT DECONFINED UNIVERSE IN THE LABORATORY

Micro-Bang 135

Pb QGP Pb Au Au 115 47

363

353 Big-Bang Micro-Bang

τ −∼ 10 µ s τ −∼ 4 10-23 s ∼ -10 ∼ NB / N − 10 NB / N − 0.1 Order of Magnitude ENERGY density ² 1–5GeV/fm3 = 1.8–9 1015g/cc ' Latent vacuum heat B 0.1–0.4GeV/fm3 (166–234MeV)4 ' ' 1 30 PRESSURE P = 3² = 0.52 10 barn NA35 1986: S–Ag at 200AGeV

12 TEMPERATURE T0, Tf 300–250, 175–145 MeV; 300MeV 3.5 10 K ' J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 10

THE EARLY UNIVERSE AT RHIC

STAR . . . and BRAHMS, PHOBOS: How is this maze of tracks of newly produced particles telling us what we want to know about the early Universe and its properties? Study of patterns in particle production: correlations, new flavors (strangeness, charm), resonances, etc.. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 11 TWO STEP HADRON FORMATION MECHANISM IN QGP Ω 1. GG ss¯ (thermal gluons collide) → GG cc¯ (initial parton collision) u s s s → u u g s gluon dominated reactions u d d d s s s s 2. hadronization of pre-formed d g d g s g u g u s, s,¯ c, c¯ quarks u s g s s d u u Formation of complex rarely d g s d d produced (multi)exotic flavor d s g g u (anti)particles from QGP enabled s s u d by coalescence between s, s,¯ c, c¯ d g u quarks made in different microscopic s s u reactions; this is signature of quark Ξ mobility and independent action, thus of deconfinement. Enhance- ment of flavored (strange, charm) antibaryons progressing with ‘exotic’ flavor content. AVAILABLE RESULT (SPS, RHIC): Enhancement of strange (anti)baryons progresses with strangeness content. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 12 Why Strangeness is a diagnostic tool EXPERIMENTAL REASONS • There are many strange particles allowing to study different physics questions (q = u, d): φ(ss¯), K(qs¯), K(q¯s), Λ(qqs), Λ(q¯q¯s¯), Ξ(qss), Ξ(q¯s¯s¯), Ω(sss), Ω(s¯s¯s¯) . . . resonances . . . • Strange hadrons are subject to a self analyzing decay within a few cm from the point of production; π π

Ξ Λ p

• Production rates hence statistical signiﬁcance is high; (strong interaction reaction cross sections) J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 13 THEORETICAL CONSIDERATIONS • production of strangeness in gluon fusion GG ss¯ strangeness linked to gluons from QGP; →

(a) g (b) s (c) s g s dominant processes: g GG ss¯ abundant strangeness→ g s g =evidence for gluons g s s

q (d) s 10–15% of total rate: qq¯ ss¯ → q s • coincidence of scales: ms Tc τs τ ' → ' QGP → strangeness a clock for QGP phase

• s¯ q¯ strange antibaryon enhancement at'RHIC→ (anti)hyperon dominance of (anti)baryons. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 14

(MULTI)STRANGE (ANTI)HYPERON ENHANCEMENT

WA97: central 158 A GeV Pb - Pb 10 Enhancement Enhancement

1 - 0 ± ± ± h KS Λ Ξ Λ Ξ Ω+Ω

0 1 2 1 2 3 Strangeness Enhancement GROWTH with strangeness antiquark content. Enhancement is here deﬁned with respect to the yield in p–Be collisions, scaled up with the number of collision ‘wounded’ nucleons.

0 1 2 3 4 5 6 J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 15 ENHANCEMENT AS FUNCTION OF REACTION VOLUME

> < > < pT 0, |y-ycm| 0.5 NA57 158 A GeV pT 0, |y-ycm| 0.5 NA57 158 A GeV  Ω-+Ω+

10 10 Ξ-

 Ξ+ Λ

 Λ Particle / event / wound. nucl. relative to pBe Particle / event / wound. nucl. Particle / event / wound. nucl. relative to pBe nucl. relative / event / wound. Particle 1 1

pBe pPb PbPb pBe pPb PbPb

2 3 2 3 1 10 10 10 1 10 10 10 < > < > Nwound Nwound Note the gradual onset of enhancement with reaction volume. “Canonical enhancement” (a hadronic equilibrium model) is grossly inconsistent with these results. Gradual enhancement shown predicted by kinetic strangeness production. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 16

ENHANCEMENT at low SPS Energy

> < > < pT 0, |y-ycm| 0.5 NA57 40A GeV pT 0, |y-ycm| 0.5 NA57 40A GeV

Ξ- 10 10

 Ξ+ Λ

 Λ Particle / event / wound. nucl. relative to pBe Particle / event / wound. nucl. Particle / event / wound. nucl. relative to pBe nucl. relative / event / wound. Particle 1 1

pBe PbPb pBe PbPb

1 10 102 103 1 10 102 103 < > < > Nwound Nwound At 40A GeV we still see a strong volume dependent hyperon enhancement, in agreement with expectations for deconﬁned state formation. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 17

REACTION MECHANISM OF PARTICLE PRODUCTION several CERN experiments since 1991 demonstrate symmetry of m spectra of strange baryons and antibaryons in baryon rich environment, now also⊥ observed at RHIC. Interpretation: Common matter-antimatter particle formation mechanism, little reannihilation in sequel evolution. Appears to be emission by a quark source into vacuum. Fast hadronization conﬁrmed by abundant yield of hadron resonances at RHIC and HBT particle correlation analysis: same size pion source at all energies

Practically no hadronic ‘phase’! vf No ‘mixed phase’ either! Direct emission of free-streaming hadrons from exploding ﬁlamenitating QGP QGP Develop analysis tools viable in SUDDEN QGP HADRONIZATION

Proposed reaction mechanism: ﬁlamentation/ﬁngering instability when in expansion pressure reverses. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 18 High m slope universality Discovered in S-induced ⊥ collisions, pronounced WA85 200 A GeV in Pb-Pb Interactions. TΛ = 232 MeV Why is the slope of baryons 106 and antibaryons in baryon-rich Λ Λ environment precisely the same? T

Why is the slope 105 T of diﬀerent hyperons in 3/2

1/m dN/dm [arb. units] 0 same mt range the same? Ks S W -1 Analysis+our hypothesis 1991: RΛ 104 QGP quarks coalescing in SUDDEN hadronization 1 1.5 2 2.5 3

m T [GeV] This allowed the study of ratios of particles measured only in a fraction of phase space J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 19 )

Pb 4 2

WA97 T [MeV] c 10

⊥ -2 0 T K 230 2 10 §

(GeV 1

Λ T × Λ T 289 3 -1 10  § 10 × 10 Λ T Λ 287 4 -2 Ξ § 10 Ξ + dN/dm -3 T Ξ 286 9 10T § -4 -1 -

1/m × Ω T Ξ 284 17 10 10  § -5 × 10 -2 Ω + T Ω+Ω 251 19 10 § 1 2 3 4 2 Λ within 1% of Λ m T (GeV/c ) Kaon – hyperon diﬀerence: EXPLOSIVE FLOW eﬀect J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 20

Spectra at RHIC-STAR 130+130 A GeV show the same eﬀect

h− Exponential Fit Boltzmann Fit

centrality dN/dy TE(MeV) dN/dy TB(MeV)

260.3 7.5 Ξ− 2.16 0.09 338 6 2.06 0.09 296 5 § § § § § Ξ¯+ 1.81 0.08 339 7 1.73 0.08 297 5 § § § §

163.6 5.2 Ξ− 1.22 0.11 335 16 1.18 0.11 291 13 § § § § § Ξ¯+ 1.00 0.10 349 17 0.97 0.10 302 13 § § § §

42.5 3.0 Ξ− 0.28 0.02 312 12 0.27 0.02 273 10 § § § § § Ξ¯+ 0.23 0.02 320 11 0.22 0.02 280 9 § § § § m spectra of Ξ−, Ξ−, for three centrality bins 0-10%, 10-25% and ⊥ 25-75% with h−=dNh /dη η <0.5. Statistical and p dependent sys- − || | ⊥ tematic uncertainties are presented.The p independent system- ⊥ atic uncertainties are 10%. (STAR Collaboration, PRL92 (2004) 182301) J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 21

Ξ−, Ξ− Spectra RHIC-STAR 130+130 A GeV 1 -2 )

2 - + + 10 -1 (a) Ξ (b) Ξ

10 -2 dy (GeV/c ⊥ 10 -3 N/dm 2

d -4 ⊥ 10 m π -5

1/(2 10

evt [0-10%] [10-25%] (/5) [25-75%] (/10) -6 1/N 10 0 1 2 0 1 2 2 m ⊥ - m (GeV/c ) J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 22

Discovery of early thermalization: Azimuthal asymmetry

K++K- 0 STAR

2 K 0.1 S v Λ+Λ Quark v 2 = v 2/n(p T/n) Ξ+Ξ

0.05 Quark Anisotropy Quark Anisotropy

0 0 1 2 3

Quark Transverse Mom. pT [GeV/c] Evidence for common bulk q, q¯, s, s¯-partonic matter flow. The absence of gluons at hadronization is consistent with the absence of charge fluctuations, Quark scaling: Paul Sorenson and Huan-Zhong Huang. A superb confirmation that dynamics of the fireball is in thermal partonic degrees of freedom, and quarks hadronize. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 23

SUDDEN MECHANISM: Super-cooling COLOR WIND of an exploding fireball P and ε: local in QGP particle pressure, energy density, ~v local flow velocity. The pressure component in the energy-momentum tensor: v v T ij = P δ + (P + ε) i j . ij 1 ~v 2 − The rate of momentum flow vector ~ at the surface of the fireball is obtained P from the energy-stress tensor Tkl :

~vc ~vc ~n ~ ~n = P~n + (P + ε) · . P ≡ T · 1 ~v 2 − c The pressure and energy compriseb particle and the vacuum properties: P = ~ Pp , ε = εp + . Condition = 0 reads: − B B P

~vc ~vc ~n ~n = Pp~n + (Pp + εp) · , B 1 v2 − c Multiplying with ~n, we ﬁnd, 2 2 κvc (~vc ~n) = Pp + (Pp + εp) , κ = · . B 1 v2 v2 − c c

This requires Pp < : QGP phase pressure P must be NEGATIVE. A ﬁreball surface region whichBreaches 0 and continues to ﬂow outward is torn apart in a rapid instability. This can PONL→ Y arise since matter presses again the vacuum which is not subject to collective dynamics. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 24

Phase boundary and ‘wind’ of ﬂow of matter

point hadrons Solid: point hadrons T ⇐ p finite size hadrons Dashed: finite size ⇐ Dotted: Tc(µb) P =0 for | eff −B v2 = 0, 1/10, 1/6, 1/5, 1/4, 1/3 . Thick solid: breakup with v = 0.54 (κ = 0.6) v = 0.54 c → PRL 85 (2000) 4695 ==== DEEP SUPERCOOLING ⇐ by 20 MeV P = 0 ← T ↑ H TH = 158 MeV Hagedorn temperature where P = 0, no hadron P T 0.9T 143 MeV is where supercooled QGP fireball breaks up f ' H ' equilibrium phase transformation is at 166. ' J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 25 STATISTICAL HADRONIZATION AND RESONANCES Fermi (micro canonical)-Hagedorn (grand canonical) particle ‘evap- oration’ from hot fireball:particles produced into accessible phase space, yields and spectra thus predictable. 1.0 T=140 MeV 0.9 HOW TO TEST SH: T=160 MeV T=180 MeV Study of particle yields with 0.8 π Λ same quark content, e.g. the 0.7 p relative yield of ∆(1230)/N , 0.6 K K∗/K, Σ∗(1385)/Λ, etc, which is 0.5 Ξ controlled by chemical freeze- 0.4 out temperature T : 0.3 * Resonance contribution Resonance K 3/2 m /T 0.2 N g (m T ) e ∗ φ ∗ ∗ ∗ − Ω~0 = 3/2 m/T 0.1 N g(mT ) e− 0.0 0.0 0.5 1.0 1.5 Mass Resonances decay rapidly into ‘stable’ hadrons and dominate the yield of most stable hadronic particles. Resonances test both statistical hadronization principle and per- haps more importantly, due to their short and diverse lifespan characterize the dynamics of QGP hadronization. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 26 OBSERVABLE RESONANCE YIELDS Invariant mass method: construct invariant mass from decay products: M 2 = ( m2 + p~2 + m2 + p~2 + . . .)2 (p~ + p~ + . . .)2 a a b b − a b If one of decay prop ducts rescatterq the reconstruction not assured.

Strongly interacting matter essentially non-transparent. Simplest model: If resonance decays N ∗ D + . . . within matter, resonance can disappear from view. Model→implementation:

dN ∗ dD dNrec∗ = ΓN ∗ + R, = ΓN ∗, = ΓN ∗ D σ v ρ (t) dt − dt dt − h Dj Dji j j X Γ is N ∗ in matter width, N ∗(t = 0), D(t = 0) from statistical hadronization, and ρj(t) is the time dependent particle ‘j’ density: To obtain the observable resonance yield Nrec∗ we integrate to the time t = τ spend by N ∗ in the opaque matter, and add the remainder from free INEL space decay. Regeneration term R σDi vDi ρi negligible since production reactions very much weak∝erh than scattering,i i j . Hadronic matter acts as black cloud, practically all in matter{ } ¿ {de-} cays cannot be reconstructed. Giorgio Torrieri J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 27

TWO resonance ratios combined natural widths spread ΓΣ = 150 MeV 0 ∗ 10 NA49 sudden 0.60 NA49 STAR STAR Γ =150 MeV Γ = Σ∗ Κ∗ 50 MeV Γ K*=50 MeV )

Γ = ) Σ∗ 35 MeV Λ T=200 Λ 0.40

/(all −1 /(all Thermally produced τ=1fm 10 T=175 T=200 MeV

T=150 (1385) (1385) ∗ ∗

Σ T=100 MeV T=125 Σ 0.20 τ=2 fm

T=100 MeV τ= τ=20 fm 3 fm ... −2 10 −3 −2 −1 0 0.00 10 10 10 10 0.00 0.20 0.40 0.60 * + * + K(892)/(all )K K(892)/(all )K

Dependence of the combined Σ∗/(all Λ) with K∗(892)/(all K) signals on the chemical freeze-out temperature and HG phase lifetime.

Even the ﬁrst rough measurement of K∗/K indicates that there is no long lived hadron phase. In matter widening makes this conclusion stronger.

J.R., J. Letessier and G. Torrieri, Phys. Rev. C64, 054907 (2001); C65, 069902(E) (2002) J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 28 QUARK CHEMISTRY When we compare yields of particles of diﬀerent quark content we need to consider chemical potentials, in principle one poitential for each hadron! Simpliﬁcation: follow quark content and rememe br that quarks are produced in pairs. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 29 FOUR QUARKS: s, s, q, q FOUR CHEMICAL PARAMETERS →

γi controls overall abundance Absolute chemical

of quark (i = q, s) pairs equilibrium

λi controls diﬀerence between Relative chemical

strange and non-strange quarks (i = q, s) equilibrium

HG-EXAMPLE: redistribution, production of strangeness Relative chemical equilibrium Absolute chemical equilibrium

s q q s q s q s

EXCHANGE REACTION PAIR PRODUCTION REACTION λi γi J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 30

Particle yields in chemical (non)equilibrium The counting of hadrons is conveniently done by counting the va- lence quark content (u, d, s, . . .), and it leads to characterization of HG equivalent to QGP phase. There is a natural relation of quark fugacities with hadron fugacities, for particle ‘i’ Υ Π γniλki = eσi/T i ≡ i i i but for one complication: for historical reasons hyperon number is µb 3 µb/T 2 opposite to strangeness, thus µS = 3 µs, where λq = e , λq = λuλd. Example of NUCLEONS: − two particles N, N two chemical factors, with λ3 = eµb/T , γ = γ3; → q N q σ µ + T ln γ , σ µ + T ln γ ; N ≡ b N N ≡ − b N µb/T µb/T ΥN = γN e , ΥN = γN e− . Meaning of parameters from e.g. the ﬁrst law of thermodynamics: dE + P dV T dS = σ dN + σ dN − N N = µ (dN dN) + T ln γ (dN + dN). b − N The (baryo)chemical potential µb controls the particle diﬀerence = baryon number. γ regulates the number of particle-antiparticle pairs present. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 31

STRANGENESS PRODUCTION: Theoretical perspective

STRANGENESS / NET BARYON NUMBER s/b Baryon number b is conserved, strangeness could increase slightly in hadronization. s/b ratio probes the mechanism of primordial ﬁreball baryon deposition and strangeness production. Ratio eliminates dependence on reaction geometry.

STRANGENESS / ENTROPY CONTENT s/S Strangeness s and entropy S produced predominantly in early hot parton phase. Ratio eliminates dependence on reaction geometry. Strangeness and entropy could increase slightly in hadronization. s/S relation to K+/π+ is not trivial when precision better than 25% needed.

HADRON PHASE SPACE OVERPOPULATION

γs, γq allow correct measure of yields of strangeness and baryon number, probe dynamics of hadronization, allow fast breakup without ‘mixed phase’ J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 32

QGP QGP STRANGENESS YIELD IN QGP and γs /γq

QGP 3 3 2 QGP ρ s γ 2 T (ms/T ) K2(ms/T ) s γ 0.7 s = = s π , s . QGP 2 QGP 3 2 ρb q/3 2 3 2 → b ' ln λq + (ln λq) /π γq 3 µqT + µq/π γq assumption: (α ) interaction¡ eﬀects cancel¢ out between b, s O s We consider ms = 200 MeV and hadronization T = 150 MeV,

. QGP yield at chemical equilibrium QGP QGP γs = γq = 1

At SPS λ =1.5–1.6, implies s/b 1.5. q ' Observation: s/b 0.75 γQGP/γQGP = 0.5 at SPS ' → s q Similarly for RHIC at √sNN 130 GeV we have 1 λq 1.1 and a comparison of ≥ QGP QGP ≤ ≤ the actual s/b yield allows to estimate γs /γq =0.7–0.8 at RHIC-130. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 33

HG CAN WE ESTIMATE THE EXPECTED γs ?

HG QGP COMPUTE EXPECTED RATIO OF γs /γs In sudden hadronization, V HG V QGP, T QGP T HG, the chemical occupancy factors'accommodate' the diﬀerent magnitude of particle phase space.

T = 170, γ = 1 OR T = 150, γ = 1.6 → q q

HG QGP γs /γs in sudden hadronization as function of λq. Solid lines γq = 1, and short dashed γq = 1.6. Thin lines for T = 170 and thick lines T = 150 MeV, common to both phases. γHG 2...5γQGP s ' s J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 34

Kinetic description of strangeness production

(a) g (b) s (c) s g s g

g s g g s s

q (d) s

q s The generic angle averaged cross sections for (heavy) ﬂavor s, s¯ production processes g + g s + s¯ and q + q¯ s + s¯, are: → → 2 2 4 2 2παs 4ms ms 1 7 31ms σ¯gg ss¯(s) = 1 + + tanh− W (s) + W (s) , → 3s s s2 − 8 8s ·µ ¶ µ ¶ ¸ 2 2 8παs 2ms 2 σ¯qq¯ ss¯(s) = 1 + W (s) . W (s) = 1 4ms /s → 27s s − µ ¶ p Inﬁnite QCD resummation: running αs and ms taken at the energy scale µ √s . USED: m (M ) = 90 20% MeV m (1GeV) 2.1m (M ) 200≡MeV. s Z § s ' s Z ' J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 35

WHY PERTURBATIVE STRANGENESS WORKS An essential prerequirement for the perturbative theory of strangeness production in QGP, is the relatively small experimental value α (M ) 0.118, which has s Z ' been experimentally established in recent years.

(4) αs (µ) as function of energy scale µ for a variety of initial conditions. Solid line: αs(MZ) = 0.1182 (experimental point, includes the error bar at µ = MZ).

At the scale of just above 1 GeV where typically thermal strangeness production in RHIC QGP occurs, perturbative theory makes good sense but is not completly reliable. Had αs(MZ) > 0.125 been measured 1996 than our approach from 1982 would have been invalid. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 36

Thermal averge of (strangeness p[roduction) reaction rates Kinetic (momentum) equilibration is faster than chemical, use thermal particle distributions f(p~1, T ) to obtain average rate: d3p d3p σ v f(p~ , T )f(p~ , T ) σv 1 2 12 12 1 2 . rel T d3p d3p f(p~ , T )f(p~ , T ) h i ≡ R R 1 2 1 2 Invariant reaction rate in medium:R R

gg ss¯ 1 2 gg ss¯ qq¯ ss¯ qq¯ ss¯ ss¯ gg,qq¯ ss¯ gg,qq¯ A → = ρ (t) σv → , A → = ρ (t)ρ (t) σv → , A → = ρ (t) ρ (t) σv → . 2 g h iT q q¯ h iT s ¯s h iT

1/(1 + δ1,2) introduced for two gluon processescompensates the double-counting of identical particle pairs, arising since we are summing independently both react- ing particles.

This rate enters the momentum-integrated Boltzmann equation which can be written in form of current conservation with a source term

µ ∂ρs ∂~vρs gg ss¯ qq¯ ss¯ ss¯ gg,qq¯ ∂ j + = A → + A → A → µ s ≡ ∂t ∂~x − J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 37

Strangeness density time evolution in local restframe (~v) we have :

dρs dρs¯ 1 2 gg ss¯ qq¯ ss¯ ss¯ gg,qq¯ = = ρ (t) σv → + ρ (t)ρ (t) σv → ρ (t) ρ (t) σv → dt dt 2 g h iT q q¯ h iT − s ¯s h iT

Evolution for s and s¯ identical, which allows to set ρs(t) = ρs¯(t). Use detailed balance to simplify 2 dρs ρs(t) gg ss¯ qq¯ ss¯ = A 1 , A = A → + A → dt − ρ2( ) µ s ∞ ¶ The generic solution at ﬁxed T (ρ tanh) implies that in all general cases there is an exponential approach to chemical∝ equilibrium

ρs(t) t/τs 1 e− ρs∞ → − with the characteristic time constant τs:

1 ρs( ) 12 34 1 12 34 τs gg ss¯ ∞qq¯ ss¯ A → ρ1∞ρ2∞ σsv12 T → . ≡ 2 (A → +A → +...) ≡ 1+δ1,2 h i J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 38

Characteristic time constant and γs-evolution

ss¯ σQCD→ gives τs similar to lifespan of the plasma phase! Strange quark pair production dominated by gluon fusion: G+G ss¯, also some (10%) qq¯ ss,¯ present; this is due to gluon collision rate. → ENTROPY→ CONSERVING expansion i.e. at SPS T 3V =Const. (not yet long. scaling):

dT dγs γs K1(z) 2 ms 2τ + z = 1 γ , γ (t) n (t)/n∞ , z = , K : Besself. s dt dT T K (z) − s s ≡ s s T i µ 2 ¶ 3 Once γ known, ρ (t) = ρ¯ (t) = dx ρ∞(T (t, x))γ (T (t, x), T˙ (t, x)); s h s i h s i s s evolution till t tf ,but eﬀectively production stops for T < 180 MeV. → R J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 39

What about charm? ms mc We expect that thermal charm production is of relev→ance only for T m (1 GeV) 1.5 GeV, probably not accessible. → c '

αs(MZ) = 0.118, m (M ) = 0.7 7% GeV c Z §

Lower dotted line: for fixed mc = 0.9 GeV, αs = 0.35; upper doted line: for fixed mc = 1.5 GeV, αs = 0.4 . Equillibrium density for ρ∞(m 1.5 GeV). c c ' Charm is produced relatively abundantly in first parton collisions. Benchmark: 10 cc¯ pairs in central Au–Au at RHIC-200. This yield is greater than the expected thermal equilibrium yield at hadronization of QGP. Charmonium enhancement by recombination. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 40

Probing strangeness excitation by ratio K/π The particle yield products

K K+(us¯)K (us¯ ) λ /λ λ /λ π π+(ud¯)π (ud¯ ) λ /λ λ /λ ≡ − ∝ u s s u ≡ − ∝ u d d u are muchpless dependent onp chemical conditionsqincluding baryonp density.

There is a notable enhance- central rapidity AA ment in K/π above the K+/π+ ratio recorded in pp reactions, which provides an upper limit on K/π. There is a clear 4π AA change in the speed of rise in the K/π ratio at the lower energy limit at SPS; This combined with change in nuclear NN K+/π+ > K/π compression results in a peak in the K+/π+. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 41 More SPECTACULAR: Marek Ga´zdzicki study of s/¯ d¯ 〉 + π

〈 ¯

/ Rise of s¯ Rise of d 〉

+ decrease of baryon density K 〈 0.2

0.1

A+A: NA49 AGS p+p RHIC

0 2 1 10 10

sNN (GeV) The ‘peak’ is result of two effects: approach to saturation of strangeness, followed by reduction of baryon density which allows growth of d¯. To confirm this let us eliminate from the presented measurement the last effect: J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 42

STRANGENESS vs NET BARYON CONTENT: requires ﬁt to yield data

* AGS: s/b = 0.11

Strangeness per thermal baryon deposited within rapidity slice (RHIC) or par- ticipating in the reaction (AGS, SPS) grows rapidly and continuously. YIELD MUCH GREATER THAN IN NN-REACTIONS AGS with SHARE, other results with earlier programs, soon SHARE. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 43 Excursion to Pentaquarks Statistical hadronization allows to explore the rate of production of pentaquarks which are very sensitive to chemical potentials: Θ+(1540)[uudds¯] (‘wrong strangeness’ baryon) and Ξ−−(1862)[ssqqq¯], Σ−(1776?)[sqqqq¯]. (PRC68, 061901 (2003), hep-ph/0310188)

+ Expected relative yield of Θ (1540)(left); Ξ−−(1862) and Σ−(1776?) (right), based on statistical hadronization fits at SPS and RHIC: solid lines γs and γq fitted; dashed lines γs fitted, γq = 1; dotted lines γs = γq = 1. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 44 Some issues in description of hadron yields 1. FAST phase transformation implies chemical nonequilibrium, see ‘Gadzic´ ki horn’: the phase space density is in general different in the two phases. To preserve entropy (valance quark pair number) across the phases need a jump in the phase space occupancy parameters γi. This replaces the jump in volume in a slow reequilibration with mixed phase. 2. Incorporate the complete tree of resonance decays please note: not only for yields but also most important for spectra. 3. Production weight with width of the resonances accounts for experimental reaction rates Full analysis of experimental results requires a significant numer- ical effort. Short-cut projects produce results which alter physi- cal conclusions. For this reason the Kraków-Tucson collaboration produced a public package SHARE Statistical Hadronization with Resonances which is available e.g. at http://www.physics.arizona.edu/˜torrieri/SHARE/share.html Lead author: Giorgio Torrieri. IN FUTURE: we hope that the more accurate, standardized and debugged hadronization studies will reduce misunderstandings J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 45

Charm and bottom at LHC Given high energy threshold charm (and certainly bottom)heavy ﬂavor is be- lieved to be produced predominantly in initial parton collisions and not in thermal relatively soft collisions. Will it thermalize?

Y 150 300; Y ¯ 5 15 cc¯ ' − bb ' − Precise prediction is a challenge to nLO pQCD since it requires parton distri- bution and initial time evolution within colliding nuclei. Thermal yields are at 10-30% for charm, negligible for b¯b.

No signiﬁcant reannihilation expected in dense matter evolution. The phase space occupancy rises rapidly. The way it works: assuming eﬀective thermalization of local distributions, the integral of the Boltzmann spectrum yields at each local temperature T :

m 3 g π N = k V T 3 γ (t) em/T (t), V T 3 = Const., k = . c c T (t) 2π2 2 sµ ¶ r Since at hadronization m /T 10 and m /T 30 the thermal yields need to be c ' b ' multiplied by large γc, or resp. γb to maintain the initially produced yield. We 2 expect ABOVE equilibrium yields. Since e.g. J/Ψ γc we expect multi charmed meson, baryon production enhancement. ∝ J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 46

Thermal Charm Example at LHC

thermal charm as function T , the time Total thermal charm yield as function dependent local temperature. of initial temperature. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 47

Strangeness at LHC has some surprises At LHC fast dilution of initial high density phase. Strangeness is slower to reequilibrate chemically. Initial high yield preserved, this leads to overpopulation of phase space at hadronization. Here, let us estimate the maximum possible. Limits generated by condensation boundary. For pions, an kaons mπ mK mK mπ limits are: π : γ2 e T , K : γ γ e T γ /γ e T− K/π q ≤ s q ≤ → s q ≤ →

Expect a shift toward strange meson production. Aside of K/π shown, the enhanced γs/γq will enhance other strange particles. J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 48

Near term tasks for hadronic/ﬂavor QGP signatures 1. New directions: LHC Flavor signatures = Signatures of ﬂavor

* Mixed charm-bottom states Bc(bc¯) etc. will be made extremely abundantly (comparing to pp) in the quark soup at LHC, this opens up precision laboratory of atomic QCD * Charm and bottom yield at LHC: in depth tests of small-x structure functions 2. Search for onset of deconﬁnement as function of energy and of system size Marek Ga´zdzicki with NA49 3. Resonances, statistical hadronization, bulk matter dynamics, critical (phase boundary) chemical nonequilibrium Furthermore: recall 1) J/Ψ suppression turns into enhancement as soon as ‘enough’ charm pairs per reaction available. 2) Hard parton jets: is it absorption of decay products, or energy stopping or both; relation to QGP physics? 3) Dileptons and photons are predominantly produced in ﬁnal state meson decays J. Rafelski, Arizona STRANGENESS AND THE DISCOVERY OF QUARK GLUON PLASMA Bloomington, November 30, 2004,page 49

Is QGP discovered??

At SPS and RHIC: Predicted QGP behavior conﬁrmed by strangeness and strange antibaryon enhancement which imply strange quark mobility. Enhanced source entropy content consistent with initial state thermal gluon degrees of freedom, also expected given strangeness enhancement. Chemical properties consistent with sudden hadron production in fast, ﬁlamenting breakup of QGP.

Furthermore at RHIC: quark coalescence explains features of non-azimuthally symmetric strange particle production. Early thermalization and strange quark participation in matter ﬂow. Jet quenching indicates dense and highly absorptive matter.

Strangeness excitation function ﬁngerprints QGP as the new state of matter: Probable onset of ‘valon’ quark deconﬁnement at AGS;

NEAR FUTURE The deconfinement specific hadronic ‘deep’ probe at LHC is charm and bottom flavor Search for deconfinement boundary next priority