Phase transitions in the early universe Phase transitions in the early universe

Cosmological phase transition… …when the universe cools below 175 MeV seconds after the big bang seconds after the big bang Quarks and gluons form baryons and mesons Quarks and gluons form baryons and mesons before: simply not enough volume per particle available before: simply not enough volume per particle available

Heavy ion collision Phase Phase transition ? Seen in experiment ?

Cosmological relics ? Cosmological relics ? Only if transition is first order Only if transition is first order Out of equilibrium physics is crucial Out of equilibrium physics is crucial Otherwise : the universe forgets detailed initial conditions after phase transition Otherwise : the universe forgets detailed initial conditions after phase transition In thermal equilibrium only a few quantities like temperature T or chemical potential μ determine the state In thermal equilibrium only a few quantities like temperature T or chemical potential μ determine the state

Cosmological phase transitions QCD phase transition T=175 MeV QCD phase transition T=175 MeV Electroweak phase transition T=150 GeV Electroweak phase transition T=150 GeV baryogenesis ? baryogenesis ? GUT phase transition(s) ? T=10 16 GeV GUT phase transition(s) ? T=10 16 GeV monopoles,cosmic strings ? monopoles,cosmic strings ? “inflation” T=10 15 GeV “inflation” T=10 15 GeV primordial density fluctuations ! primordial density fluctuations ! primordial magnetic fields ? primordial magnetic fields ?

Order of the phase transition is crucial ingredient for cosmological phase transition and experiments ( heavy ion collisions ) Order of the phase transition is crucial ingredient for cosmological phase transition and experiments ( heavy ion collisions )

Order of the phase transition temperature dependence of order parameter

Second order phase transition

First order phase transition First order phase transition

Electroweak phase transition ? s after big bang s after big bang fermions and W-,Z-bosons get mass fermions and W-,Z-bosons get mass standard model : crossover standard model : crossover baryogenesis if first order baryogenesis if first order ( only for some SUSY – models ) ( only for some SUSY – models ) bubble formation of “ our vacuum “ bubble formation of “ our vacuum “ Reuter,Wetterich ‘93 Kuzmin,Rubakov,Shaposhnikov ‘85, Shaposhnikov ‘87

Electroweak phase diagram M.Reuter,C.WetterichNucl.Phys.B408,91(1993)

Masses of excitations (d=3) O.Philipsen,M.Teper,H.Wittig ‘97 small M H large M H

Continuity

Higgs phase and confinement can be equivalent – then simply two different descriptions (pictures) of the same physical situation then simply two different descriptions (pictures) of the same physical situation Is this realized for QCD ? Necessary condition : spectrum of excitations with the same quantum numbers in both pictures - known for QCD : mesons + baryons - - known for QCD : mesons + baryons -

QCD at high temperature Quark – gluon plasma Quark – gluon plasma Chiral symmetry restored Chiral symmetry restored “Deconfinement” ( no linear heavy quark potential at large distances ) “Deconfinement” ( no linear heavy quark potential at large distances ) Lattice simulations : both effects happen at the same temperature Lattice simulations : both effects happen at the same temperature

Chiral symmetry restoration at high temperature High T SYM =0 =0 Low T SSB =φ 0 ≠ 0 =φ 0 ≠ 0 at high T : less order more symmetry examples: magnets, crystals

QCD – phase transition Quark –gluon plasma Quark –gluon plasma Gluons : 8 x 2 = 16 Gluons : 8 x 2 = 16 Quarks : 9 x 7/2 =12.5 Quarks : 9 x 7/2 =12.5 Dof : 28.5 Dof : 28.5 Chiral symmetry Chiral symmetry Hadron gas Hadron gas Light mesons : 8 Light mesons : 8 (pions : 3 ) (pions : 3 ) Dof : 8 Dof : 8 Chiral sym. broken Chiral sym. broken Large difference in number of degrees of freedom ! Strong increase of density and energy density at T c !

Understanding the phase diagram

quark-gluon plasma “deconfinement” quark matter : superfluid B spontaneously broken nuclear matter : B,isospin (I3) spontaneously broken, S conserved Phase diagram for ms > mu,d vacuum

Order parameters Nuclear matter and quark matter are separated from other phases by true critical lines Nuclear matter and quark matter are separated from other phases by true critical lines Different realizations of global symmetries Different realizations of global symmetries Quark matter: SSB of baryon number B Quark matter: SSB of baryon number B Nuclear matter: SSB of combination of B and isospin I 3 Nuclear matter: SSB of combination of B and isospin I 3 neutron-neutron condensate neutron-neutron condensate

quark-gluon plasma “deconfinement” quark matter : superfluid B spontaneously broken nuclear matter : B,isospin (I3) spontaneously broken, S conserved vacuum Phase diagram for ms > mu,d

“minimal” phase diagram for equal nonzero quark masses “minimal” phase diagram for equal nonzero quark masses

Endpoint of critical line ? Endpoint of critical line ?

How to find out ? How to find out ?

Methods Methods Lattice : You have to wait until chiral limit Lattice : You have to wait until chiral limit is properly implemented ! is properly implemented ! Models : Quark meson models cannot work Models : Quark meson models cannot work Higgs picture of QCD ? Higgs picture of QCD ? Experiment : Has T c been measured ? Experiment : Has T c been measured ? Indications for Indications for first order transition ! first order transition !

Lattice

Lattice results e.g. Karsch,Laermann,Peikert Critical temperature in chiral limit : N f = 3 : T c = ( 154 ± 8 ) MeV N f = 2 : T c = ( 173 ± 8 ) MeV Chiral symmetry restoration and deconfinement at same T c

pressure pressure

realistic QCD precise lattice results not yet available precise lattice results not yet available for first order transition vs. crossover for first order transition vs. crossover also uncertainties in determination of critical temperature ( chiral limit …) also uncertainties in determination of critical temperature ( chiral limit …) extension to nonvanishing baryon number only for QCD with relatively heavy quarks extension to nonvanishing baryon number only for QCD with relatively heavy quarks

Models

Analytical description of phase transition Needs model that can account simultaneously for the correct degrees of freedom below and above the transition temperature. Needs model that can account simultaneously for the correct degrees of freedom below and above the transition temperature. Partial aspects can be described by more limited models, e.g. chiral properties at small momenta. Partial aspects can be described by more limited models, e.g. chiral properties at small momenta.

Universe cools below 175 MeV… Both gluons and quarks disappear from Both gluons and quarks disappear from thermal equilibrium : mass generation thermal equilibrium : mass generation Chiral symmetry breaking Chiral symmetry breaking mass for fermions mass for fermions Gluons ? Gluons ? Analogous situation in electroweak phase transition understood by Higgs mechanism Analogous situation in electroweak phase transition understood by Higgs mechanism Higgs description of QCD vacuum ? Higgs description of QCD vacuum ?

Higgs phase and confinement can be equivalent – then simply two different descriptions (pictures) of the same physical situation then simply two different descriptions (pictures) of the same physical situation Is this realized for QCD ? Necessary condition : spectrum of excitations with the same quantum numbers in both pictures Higgs picture with mesons,baryons as excitations?

Higgs picture of QCD “spontaneous breaking of color “ “spontaneous breaking of color “ in the QCD – vacuum in the QCD – vacuum octet condensate octet condensate for N f = 3 ( u,d,s ) for N f = 3 ( u,d,s ) C.Wetterich, Phys.Rev.D64,036003(2001),hep-ph/

Quark –antiquark condensate

Octet condensate ≠ 0 : ≠ 0 : “Spontaneous breaking of color” “Spontaneous breaking of color” Higgs mechanism Higgs mechanism Massive Gluons – all masses equal Massive Gluons – all masses equal Eight octets have vev Eight octets have vev Infrared regulator for QCD Infrared regulator for QCD

Flavor symmetry for equal quark masses : for equal quark masses : octet preserves global SU(3)-symmetry octet preserves global SU(3)-symmetry “diagonal in color and flavor” “diagonal in color and flavor” “color-flavor-locking” “color-flavor-locking” (cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek) (cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek) All particles fall into representations of All particles fall into representations of the “eightfold way” the “eightfold way” quarks : 8 + 1, gluons : 8 quarks : 8 + 1, gluons : 8

Quarks and gluons carry the observed quantum numbers of isospin and strangeness of the baryon and vector meson octets ! They are integer charged!

Low energy effective action γ=φ+χγ=φ+χ

…accounts for masses and couplings of light pseudoscalars, vector-mesons and baryons !

Phenomenological parameters 5 undetermined parameters 5 undetermined parameters predictions predictions

Chiral perturbation theory + all predictions of chiral perturbation theory + determination of parameters

Chiral phase transition at high temperature High temperature phase transition in QCD : Melting of octet condensate Melting of octet condensate Lattice simulations : Deconfinement temperature = critical temperature for restoration of chiral symmetry Why ? Why ?

Simple explanation : Simple explanation :

Higgs picture of the QCD-phase transition A simple mean field calculation gives roughly reasonable description that should be improved. A simple mean field calculation gives roughly reasonable description that should be improved. T c =170 MeV T c =170 MeV First order transition First order transition

Experiment

Has the critical temperature of the QCD phase transition been measured ?

Heavy ion collision Heavy ion collision

Chemical freeze-out temperature T ch =176 MeV Chemical freeze-out temperature T ch =176 MeV hadron abundancies

Exclusion argument Exclusion argument hadronic phase with sufficient production of Ω : excluded !! excluded !!

Exclusion argument Assume T is a meaningful concept - Assume T is a meaningful concept - complex issue, to be discussed later complex issue, to be discussed later T ch < T c : hadrochemical equilibrium T ch < T c : hadrochemical equilibrium Exclude T ch much smaller than T c : Exclude T ch much smaller than T c : say T ch > 0.95 T c say T ch > 0.95 T c 0.95 < T ch /T c < < T ch /T c < 1

Has T c been measured ? Observation : statistical distribution of hadron species with “chemical freeze out temperature “ T ch =176 MeV Observation : statistical distribution of hadron species with “chemical freeze out temperature “ T ch =176 MeV T ch cannot be much smaller than T c : hadronic rates for T ch cannot be much smaller than T c : hadronic rates for T< T c are too small to produce multistrange hadrons (Ω,..) T< T c are too small to produce multistrange hadrons (Ω,..) Only near T c multiparticle scattering becomes important Only near T c multiparticle scattering becomes important ( collective excitations …) – proportional to high power of density ( collective excitations …) – proportional to high power of density P.Braun-Munzinger,J.Stachel,C.Wetterich, Phys.Lett.B (2004) T ch ≈T c

T ch ≈ T c T ch ≈ T c

Phase diagram Phase diagram = σ ≠ 0 = σ ≠ 0 ≈0 ≈0

Temperature dependence of chiral order parameter Temperature dependence of chiral order parameter Does experiment indicate a first order phase transition for μ = 0 ? Does experiment indicate a first order phase transition for μ = 0 ?

Second order phase transition for T only somewhat below T c : the order parameter σ is expected to the order parameter σ is expected to be close to zero and be close to zero and deviate substantially from its vacuum value deviate substantially from its vacuum value This seems to be disfavored by observation of chemical freeze out !

Temperature dependent masses Chiral order parameter σ depends on T Chiral order parameter σ depends on T Particle masses depend on σ Particle masses depend on σ Chemical freeze out measures m/T for many species Chemical freeze out measures m/T for many species Mass ratios at T just below T c are Mass ratios at T just below T c are close to vacuum ratios close to vacuum ratios

Ratios of particle masses and chemical freeze out Ratios of particle masses and chemical freeze out at chemical freeze out : ratios of hadron masses seem to be close to vacuum values ratios of hadron masses seem to be close to vacuum values nucleon and meson masses have different characteristic dependence on σ nucleon and meson masses have different characteristic dependence on σ m nucleon ~ σ, m π ~ σ -1/2 m nucleon ~ σ, m π ~ σ -1/2 Δσ/σ < 0.1 ( conservative ) Δσ/σ < 0.1 ( conservative )

first order phase transition seems to be favored by chemical freeze out first order phase transition seems to be favored by chemical freeze out …or extremely rapid crossover

conclusion Experimental determination of critical temperature may be more precise than lattice results Experimental determination of critical temperature may be more precise than lattice results Rather simple phase structure is suggested Rather simple phase structure is suggested Analytical understanding is only at beginning Analytical understanding is only at beginning

end

How far has first order line been measured? How far has first order line been measured? hadrons hadrons quarks and gluons

hadronic phase with sufficient production of Ω : excluded !! excluded !! Exclusion argument for large density

First order phase transition line First order phase transition line hadrons hadrons quarks and gluons μ=923MeV transition to nuclear nuclear matter matter

quark-gluon plasma “deconfinement” quark matter : superfluid B spontaneously broken nuclear matter : B,isospin (I3) spontaneously broken, S conserved vacuum Phase diagram for ms > mu,d

Is temperature defined ? Does comparison with equilibrium critical temperature make sense ?

Prethermalization J.Berges,Sz.Borsanyi,CW Scalar – fermion – model with Yukawa coupling bulk quantity mode quantity

Vastly different time scales for “thermalization” of different quantities here : scalar with mass m coupled to fermions ( linear quark-meson-model ) ( linear quark-meson-model ) method : two particle irreducible non- equilibrium effective action ( J.Berges et al )

Prethermalization equation of state p/ε Prethermalization equation of state p/ε similar for kinetic temperature

different “temperatures” different “temperatures”

Mode temperature n p :occupation number for momentum p late time: Bose-Einstein or Fermi-Dirac distribution

Kinetic equilibration before chemical equilibration Kinetic equilibration before chemical equilibration

Once a temperature becomes stationary it takes the value of the equilibrium temperature. Once chemical equilibration has been reached the chemical temperature equals the kinetic temperature and can be associated with the overall equilibrium temperature. Comparison of chemical freeze out temperature with critical temperature of phase transition makes sense

Key argument Two particle scattering rates not sufficient to produce Ω Two particle scattering rates not sufficient to produce Ω “multiparticle scattering for Ω-production “ : dominant only in immediate vicinity of T c “multiparticle scattering for Ω-production “ : dominant only in immediate vicinity of T c

Mechanisms for production of multistrange hadrons Many proposals Hadronization Hadronization Quark-hadron equilibrium Quark-hadron equilibrium Decay of collective excitation (σ – field ) Decay of collective excitation (σ – field ) Multi-hadron-scattering Multi-hadron-scattering Different pictures ! Different pictures !

Hadronic picture of Ω - production Should exist, at least semi-quantitatively, if T ch < T c ( for T ch = T c : T ch >0.95 T c is fulfilled anyhow ) ( for T ch = T c : T ch >0.95 T c is fulfilled anyhow ) e.g. collective excitations ≈ multi-hadron-scattering (not necessarily the best and simplest picture ) (not necessarily the best and simplest picture ) multihadron -> Ω + X should have sufficient rate Check of consistency for many models Necessary if T ch ≠ T c and temperature is defined Way to give quantitative bound on T ch / T c

Energy density Lattice simulations Lattice simulations Karsch et al Karsch et al even more dramatic for first order for first order transition transition

Production time for Ω multi-meson scattering π+π+π+K+K -> Ω+p Ω+p strong dependence on “pion” density strong dependence on “pion” density P.Braun-Munzinger,J.Stachel,CW

extremely rapid change lowering T by 5 MeV below critical temperature : lowering T by 5 MeV below critical temperature : rate of Ω – production decreases by rate of Ω – production decreases by factor 10 factor 10 This restricts chemical freeze out to close vicinity of critical temperature This restricts chemical freeze out to close vicinity of critical temperature 0.95 < T ch /T c < < T ch /T c < 1