of the Quark Universe CINPP, Kolkata, 6 February 2005

[ I] Probing the Universe with Heavy Ions [ II] Recreating the early Universe in the laboratory Energy to matter: the (al)chemy of particle production: Use as a diagnostic tool of QGP formation [III] Hadronization of the Quark Universe ( i) Scale of Universe hadronization time ( ii) Formation of (visible) matter (iii) Chemical potentials in the early Universe (iv) Baryon to photon ratio, mixed phase (v) Particle populations in the early Universe [IV] Inhomogeneous Matter-Antimatter Universe? ( i) Distillation process (ii) Mass (a)symmetry? Mike Fromerth & [ V] Final Remarks and CERN

1 J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 2

Stages in the evolution of the Universe

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 and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 3

The study of hadronic particle production in relativistic heavy ion collision experiments at SPS, RHIC, LHC provides the knowledge required to develop the understanding of the physics of the Uni- verse at the time period THE VISIBLE MATTER AS WE KNOW IT HAS BEEN FORMED In the process • we discover a new state of matter, the QUARK-GLUON PLASMA. • We learn about mechanisms how energy turns into particles WHEN MATTER, ANTIMATTER AND MESON are formed • we learn about the period of STRANGENESS AND ANTIMAT- TER DISAPPEARANCE. Little is known today about this rel- atively long lasting phase of the Universe evolution in which the Universe cools down by two orders of magnitude. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 4

II RECREATING THE EARLY UNIVERSE IN LABORATORY

Micro-Bang 135

81

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 heat B ' 0.1–0.4GeV/fm3 ' (166–234MeV)4

1 30 PRESSURE P = 3² = 0.52 10 barn S–Ag Reaction at 200AGeV (by NA35)

12 TEMPERATURE T0, Tf 300–250, 175–145 MeV; 300MeV'3.5 10 K J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 5

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 and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 6

(Al)chemy of particle production

Ω

u s s s u u g u s d d d s s s s d g d g s g u g u u s g u s s d u d s d d g d s g g u s u d s d g u s s u Ξ

Hadron formation from a drop of deconfined matter which filled the early Universe Expect creation of complex rarely seen (multi, strange, anti-) particles enabled by available populations of particles (strange quarks etc) made in independent microscopic reactions. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 7 Strangeness: a popular laboratory QGP 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 de- cay within a few cm from the point of production; π π

Ξ Λ p

• Production rates hence statistical significance is high; J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 8 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 ' τQGP → strangeness a clock for QGP phase

• s¯ ' q¯→ strange antibaryon enhancement at RHIC (anti)hyperon dominance of (anti)baryons. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 9

III Hadronization of the Quark Universe What we know: Upon QGP hadronization in the early Universe there is as much matter as antimatter (to within 10−9). This symmetry diminishes progressively during the annihilation period. Questions and Issues • Chemical conditions in the early Universe (chemical potentials, equilibria) • Mechanisms and conditions at hadronization (conflict of Gibbs conditions with superselection rules such as charge conserva- tion/neutrality) • When do antinucleons, strangeness, pions disappear (chemical nonequilibrium in hadron phase)? • How much antimatter remains in the homogeneous/non-homogeneous Universe? • What happens to the Universe during matter-antimatter anni- hilation? Very Large Scale Structure formation? • Influence on nucleosynthesis epoch? J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 10 Time scale in Universe hadronization The expanding Universe cools, the hot quark-gluon plasma freezes into individual hadrons. In laboratory we do this suddenly, in the early Universe slowly as seen on time scale of strong interactions.

STRONG INTERACTIONS TIME CONSTANT: Nucleon size / light velocity' 10−23s

UNIVERSE HADRONIZATION TIME CONSTANT: 2 3c B0 GeV τU = = 36 µs , B0 = 0.19 r32πGB r B fm3 Naively, 4B is energy density inside particles like protons, and is the amount of energy required per unit of volume to deconfine quarks. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 11

10–50 µs Hadronization Timescale in the Universe Universe has two components: luminous matter ²l and at this early time scale probably still a small ‘cold’ dark matter ²d energy density component. The pressure is all due the luminous component: P = Pl. R − 1 R Einstein Equations: µν 2gµν = 8πGTµν comprise two dynamical equations for the size scale R(t) of the Robertson-Walker metric: dr ds2 = gµνdx dx = dt2 − R2 + r2dθ2 + r2 sin2 θdφ2 : µ ν ·1 − kr2 ¸

µν 1. Consider T ;ν = 0, describing entropy conserving expansion: dV 3 dR 3dR d² dE + P dV = T dS = 0, dE = d(²V ), = , = − . V R R ² + P ' 0 3 NOTE: for ² = ²l + ²d and ²d ²d/R (cold dark matter) this reduces to exactly

3dR d²l = − keep in mind Pd ¿ Pl. R ²l + P

2. We use the 0-0 component of Einstein equations R˙ 2 k 8π + = G² R2 R2 3 In a flat (k = 0) Robertson-Walker Universe we find exactly: 2 2 ²˙l = 24πG (²l + ²d) (²l + P ) , P = (²l − 4B)/3 + Pd J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 12

10–50 µs Hadronization Timescale in the Universe When dark component is insignificant: 2 ²l = B coth (t/τU), and by matching at a given pressure we find the magnitude of the time the Uni- verse inflates through the mixed hadron phase.

Pressure (upper) and temperature (lower part) in the Universe, as func- tion of time, in the vicinity of the phase transition from the deconfined phase to the confined phase. Solid lines, B1/4 = 195 MeV; dotted lines, B1/4 = 170 MeV (lower part) and B1/4 = 220 MeV (upper part) all for αs = 0.6 (reduces the active quark-gluon degrees of freedom). J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 13 Production of Matter of our Era Our objective is to understand the chemical conditions at the emergence of matter as we know it today in the early Universe period at hadronization of quark-gluon plasma. This establishes the initial particle densities which can be followed to the end of the hadron gas era. Quantitative Tasks 1) Identify the chemical conservation laws constraining potentials µ(T ) and the pertinent conservation laws;

2) Trace out chemical potentials as function of temperature, which itself we can study separately as function of time (see above) – this separation is convenient given the lack of knowledge about dark matter;

3) Evaluate the chemical (particle) flavor composition of the Uni- verse during evolution toward the condition of neutrino decoupling at T ' 1 MeV t ' 10 s 4) Explore the quark-hadron phase transformation dynamics, and establish potential for conserved quantum (baryon, electrical charge) number distillation; J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 14 CHEMICAL POTENTIALS IN THE UNIVERSE The slow hadronization of the Universe implies chemical equilib- rium is reached for all hadronic reactions (phase space occupancy saturated), and there is full participation of electromagnetically interacting photon and lepton degrees of freedom. • Photons in chemical equilibrium, assume the Planck distribu- tion, implying a zero photon chemical potential; i.e.: µγ = 0

• Whenever chemical and thermal equilibrium is attained, reac- tions such as f + f¯ ­ 2γ are allowed, (here f and f¯ are a fermion – antifermion pair), hence: µf = −µf¯ • Minimization of the Gibbs free energy implies that for any re- action νiAi = 0, where νi are the reaction equation coefficients of the chemical species Ai, chemical equilibrium arises for the condition: νiµi = 0

• Example: weak interaction reactions lead to: µs = µd = µu + ∆µl − − − ≡ µe µνe = µµ µνµ = µτ µντ ∆µl J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 15

• For the “large mixing angle” solution the neutrino oscillations ≡ νe ­ νµ ­ ντ imply that: µνe = µνµ = µντ µν note that the mixing is accelerated in ‘dense’ matter.

PROCEDURE: There are three chemical potentials which are ‘free’ and we choose to follow: µd, µe, and µν. (we need physical observables to fix these values)

Quark chemical potentials are convenient to characterize the particle abundances in the hadron phase, e.g. Σ0 (uds) has chem- ical potential µΣ0 = µu + µd + µs

The baryochemical potential is: µ + µ µ + µ 3 3 µ ≡ P N = 3 d u = 3µ − ∆µ = 3µ − (µ − µ ). b 2 2 d 2 l d 2 e ν J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 16

Chemical Conditions The three chemical potentials not constrained by chemical reactions are obtained from the physical constraints: i. Local electrical charge neutrality (Q = 0):

nQ ≡ Qi ni(µi, T ) = 0, Xi

where Qi and ni are the charge and number density of species i. ii. Net lepton number equals net baryon number (L = B):

nL − nB ≡ (Li − Bi) ni(µi, T ) = 0, Xi (standard condition in baryo-genesis models, generalization to finite B − L easily possible) iii. Universe evolves adiabatically i.e. at constant in time entropy-per-baryon S/B σ σ (µ , T ) ≡ i i i = 1.3 § 0.1 × 1010 ⇐= how do we know this? nB Pi Bi ni(µi, T ) P J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 17

Baryon to photon ratio in the Universe

G. A. Steigman, astro−ph/0202187 (2002) 1 −10 η ≡ nB/nγ = 5.5 § 1.5 × 10 Deuterium Abundance and Nucleosynthesis Modeling 0.8

Baryon density perturbations and anisotropy 0.6 in the Cosmic Microwave Background at photon freeze−out Likelihood

0.4

0.2 SNIa magnitude−redshift combined with the Sunyaev−Zeldovich effect

0 0 5 10 15 η 10 γ 10 = 10 B/ +0.3 × −10 Revised by W-MAP: η = 6.1−0.2 10 ; This yields entropy per baryon: S = S nγ = 8.0 = 1.3 § 0.1 1010 nB nγ nB η + − (Sγ + Sν + Si)/nγ is evaluated using stat.mech. and remembering e e reheating of photons. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 18

Mixed Phase at Phase Transformation Mixed phase partition function for the SLOW phase transformation period:

VHG VQGP ln Ztot = ln ZHG + ln ZQGP Vtot = VHG + VQGP Vtot Vtot At QGP hadronization there is in general unequal conserved quan- tum number density in QGP and in hadron gas (HG) phases. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 19

TRACING µd IN THE UNIVERSE T (MeV) 700 170 100 10 2 10 10 -6 313.6 MeV 0 10 10 -7 µ -2 -8 d 10 10 10 20 30 40 50 µ e µ ν

(MeV) -4

µ 10 mixed phase HG / QGP 1 eV 10 -6 Minimum µb = 1.1 § 0.1 § 0.16 eV 10 -8 10 0 10 1 10 2 10 3 10 4 t ( µ s) J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 20

TRACING µd IN A UNIVERSE

11 150 S/B = 4.5 x 10 10 S/B = 4.5 x 10 9 S/B = 4.5 x 10 125 8 S/B = 4.5 x 10 7 S/B = 4.5 x 10 6 100 S/B = 4.5 x 10 5 S/B = 4.5 x 10

75 T (MeV)

50

25

Fromerth & Rafelski, January 2003 0 -6 -4 -2 0 2 10 10 10 10 10 µ (MeV) d J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 21

Hadronic Particle Densities 10 40 nuclear dens. protons neutrons 35 π 0 10 − ) π 3 π + lambdas 30 antiprotons 10 antineutrons antilambdas 10 25 atomic dens. density (particles / cm (particles density 10 20

15 10 1 10 100 T (MeV) Note the baryon freeze-out at T ' 37 MeV and that pion density remains at baryon density down to T ' 4.5 MeV J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 22

Lepton Densities 10 40 nuclear dens. electrons muons 35 taus 10 positrons )

3 antimuons antitaus neutrinos (total) 10 30 antineutrinos (total)

10 25 atomic dens. density (particles / cm (particles density 10 20

15 10 1 10 100 T (MeV) J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 23

Energy in luminous hadronic Universe

Dark Matter dilutes by factor 6 the role of luminous matter: The Universe is matter dominated at hadron phase transition, and since decoupling of radiation from matter. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 24 Thoughts about inhomogeneous Universe The hadron Universe emerging from quark-gluon plasma hadroniza- tion is initially nearly matter-antimatter symmetric. The baryon asymmetry is at most ' 10−9 and perhaps zero if the Universe were today inhomogeneous, divided into huge domains filled with mat- ter and antimatter, respectively. Such separation of phases requires distillation processes which must operate on a time scale compa- rable to the age of the EARLY Universe. These would compete with the annihilation of matter with antimatter, which otherwise proceeds while the temperature drops from the phase transition value of ' 160–170 MeV toward a few MeV.

A mechanism which could drive separation of phases in mixed phase: at a given chemical condition both the baryon and charge density are different in the quark-gluon plasma and hadron gas phases. This was noticed by Witten in his 1984 paper, and ex- ploited by A. Olinto for generation of current and thus magnetic field in the Universe. As matter of principle any baryon-antibaryon separation requires a CP-violating force, distillation will only en- hance a preexisting asymmetry. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 25

Distillation Process–Separation of Phases Mixed phase partition function for the SLOW phase transformation period:

VHG VQGP ln Ztot = ln ZHG + ln ZQGP Vtot = VHG + VQGP Vtot Vtot At QGP hadronization there is in general unequal conserved quan- tum number (e.g. charge) density in QGP and in hadron gas (HG) phases.

The constraints are accordingly, e.g. for charge: QGP HG − QGP HG Q = 0 = nQ VQGP + nQ VHG = Vtot (1 fHG) nQ + fHG nQ h i fHG ≡ VHG/Vtot is the fraction of space belonging to HG phase. Anal- ogous expressions considered for L − B and S/B.

Note: Mixed phase lasts ' 10 µs (25% of prior lifespan), assume that fHG changes linearly in time. Actual values will require dy- namic nucleation and transport theory description of the phase transformation. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 26

Charge (and baryon number) asymmetry distillation

Initially at fHG = 0 all matter in QGP phase, as hadronization progresses with fHG → 1 the baryon component in hadronic gas reaches 100%.

The constraint to a charge neutral universe conserves the SUM of charges in both fractions. Charge in each fraction can be and is non-zero. 0.1

0.05 B

/ n 0 Q n Even a small charge separation be- tween phases introduces a finite -0.05 non-zero local Coulomb potential HG QGP and this amplifies any existent -0.1 baryon asymmetry (protons vs 0 0.5 1 antiprotons). f HG Strangeness distillation mechanism proposed for RHIC has the same physical origin, but there is no time to build mixed phase. In the early Universe where there is time for weak interaction decay, electrical current can arise, and can lead to spontaneous generation of magnetic fields. J. Rafelski, Arizona and CERN Hadronization of the Quark Universe CINPP, Kolkata, 6 February, 2005, page 27

FINAL REMARKS

Theoretical study of the early Universe beginning at t = 10 µs is possible

We have control of: chemical potentials, particle abundances, but not of phase transition dynamics

Strangeness in early Universe under study

Distillation of baryon number in domains of the Universe a possibility

We begin to transfer the ‘know-how’ from the study of nuclear collisions to the study of the early Universe

I thank the dynamic CINPP meeting chairman, Prof. Dipak Ghosh for introducing me to the celebrated Jadavpur University, for fantastic or- ganization of the conference, and very generous hospitality in Calcutta.