Title: Phase transitions in the early universe
1 Phase transitions in the early
universe
2Cosmological phase transition
- when the universe cools below 175 MeV
- 10-5 seconds after the big bang
Quarks and gluons form baryons and mesons
before simply not enough volume per particle
available
3Heavy ion collision
Seen in experiment ?
Phase transition ?
4 Cosmological relics ?
- Only if transition is first order
- Out of equilibrium physics is crucial
- 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
5Cosmological phase transitions
- QCD phase transition T175 MeV
- Electroweak phase transition T150 GeV
- baryogenesis ?
- GUT phase transition(s) ? T1016 GeV
- monopoles,cosmic strings ?
- inflation
T1015 GeV - primordial density fluctuations !
- primordial magnetic fields ?
6Order of the phase transition is crucial
ingredient for cosmological phase transition
and experiments ( heavy ion collisions )
7Order ofthephasetransition
temperature dependence of order parameter
8Second order phase transition
9 First order phase transition
10Electroweak phase transition ?
- 10-12 s after big bang
- fermions and W-,Z-bosons get mass
- standard model crossover
- baryogenesis if first order
- ( only for some SUSY models )
- bubble formation of our vacuum
Reuter,Wetterich 93
Kuzmin,Rubakov,Shaposhnikov 85 , Shaposhnikov 87
11Electroweak phase diagram
M.Reuter,C.Wetterich Nucl.Phys.B408,91(1993)
12Masses of excitations (d3)
small MH
large MH
O.Philipsen,M.Teper,H.Wittig 97
13Continuity
14Higgs phase and confinement
- can be equivalent
- 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 -
15QCD at high temperature
- Quark gluon plasma
- Chiral symmetry restored
- Deconfinement ( no linear heavy quark potential
at large distances ) - Lattice simulations both effects happen at the
same temperature
16Chiral symmetry restoration at
high temperature
Low T SSB ltfgtf0 ? 0
High T SYM ltfgt0
at high T less order more symmetry examples
magnets, crystals
17QCD phase transition
- Quark gluon plasma
- Gluons 8 x 2 16
- Quarks 9 x 7/2 12.5
- Dof 28.5
- Chiral symmetry
- Hadron gas
- Light mesons 8
- (pions 3 )
- Dof 8
- Chiral sym. broken
Large difference in number of degrees of freedom
! Strong increase of density and energy density
at Tc !
18Understanding the phase diagram
19Phase diagram for ms gt mu,d
quark-gluon plasma deconfinement
quark matter superfluid B spontaneously broken
vacuum
nuclear matter B,isospin (I3) spontaneously
broken, S conserved
20Order parameters
- Nuclear matter and quark matter are separated
from other phases by true critical lines - Different realizations of global symmetries
- Quark matter SSB of baryon number B
- Nuclear matter SSB of combination of B and
isospin I3 - neutron-neutron condensate
21Phase diagram for ms gt mu,d
quark-gluon plasma deconfinement
quark matter superfluid B spontaneously broken
vacuum
nuclear matter B,isospin (I3) spontaneously
broken, S conserved
22 minimal phase diagram for
equal nonzero quark masses
23 Endpoint of critical line ?
24 How to find out ?
25 Methods
- Lattice You have to wait until chiral
limit - is properly implemented !
- Models Quark meson models cannot work
- Higgs picture of QCD ?
- Experiment Has Tc been measured ?
- Indications for
- first order transition !
26Lattice
27Lattice results
- e.g. Karsch,Laermann,Peikert
- Critical temperature in chiral limit
- Nf 3 Tc ( 154 8 ) MeV
- Nf 2 Tc ( 173 8 ) MeV
- Chiral symmetry restoration and deconfinement at
same Tc
28 pressure
29realistic QCD
- precise lattice results not yet available
- for first order transition vs. crossover
- also uncertainties in determination of critical
temperature ( chiral limit ) - extension to nonvanishing baryon number only for
QCD with relatively heavy quarks
30Models
31Analytical description of phase
transition
- 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.
32Universe cools below 175 MeV
- Both gluons and quarks disappear from
- thermal equilibrium mass generation
- Chiral symmetry breaking
- mass for fermions
- Gluons ?
- Analogous situation in electroweak phase
transition understood by Higgs mechanism - Higgs description of QCD vacuum ?
33Higgs phase and confinement
- can be equivalent
- 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?
34Higgs picture of QCD
- spontaneous breaking of color
- in the QCD vacuum
- octet condensate
- for Nf 3 ( u,d,s
)
C.Wetterich, Phys.Rev.D64,036003(2001),hep-ph/0008
150
35Quark antiquark condensate
36Octet condensate
- lt octet gt ? 0
- Spontaneous breaking of color
- Higgs mechanism
- Massive Gluons all masses equal
- Eight octets have vev
- Infrared regulator for QCD
37Flavor symmetry
- for equal quark masses
- octet preserves global SU(3)-symmetry
- diagonal in color and flavor
- color-flavor-locking
- (cf. Alford,Rajagopal,Wilc
zek Schaefer,Wilczek) - All particles fall into representations of
- the eightfold way
- quarks 8 1 , gluons 8
38Quarks and gluons carry the observed quantum
numbers of isospin and strangenessof the baryon
and vector meson octets !They are integer
charged!
39Low energy effective action
?f?
40accounts for masses and couplings of light
pseudoscalars, vector-mesons and baryons !
41Phenomenological parameters
- 5 undetermined parameters
42Chiral perturbation theory
- all predictions of chiral perturbation theory
- determination of parameters
43Chiral phase transition at high temperature
- High temperature phase transition in QCD
- Melting of octet condensate
- Lattice simulations
- Deconfinement temperature critical temperature
for restoration of chiral symmetry - Why ?
44 Simple explanation
45Higgs picture of the QCD-phase transition
- A simple mean field calculation gives roughly
reasonable description that should be improved. - Tc 170 MeV
- First order transition
46Experiment
47Has the critical temperature of the QCD phase
transition been measured ?
48 Heavy ion collision
49 Chemical freeze-out temperature
Tch 176 MeV
hadron abundancies
50 Exclusion argument
hadronic phase with sufficient production of O
excluded !!
51Exclusion argument
- Assume T is a meaningful concept -
- complex issue, to be discussed later
- Tch lt Tc hadrochemical equilibrium
- Exclude Tch much smaller than Tc
- say Tch gt 0.95 Tc
- 0.95 lt Tch /Tc lt 1
52Has Tc been measured ?
- Observation statistical distribution of hadron
species with chemical freeze out temperature
Tch176 MeV - Tch cannot be much smaller than Tc hadronic
rates for - Tlt Tc are too small to produce multistrange
hadrons (O,..) - Only near Tc multiparticle scattering becomes
important - ( collective excitations ) proportional to
high power of density
TchTc
P.Braun-Munzinger,J.Stachel,C.Wetterich,
Phys.Lett.B (2004)
53 Tch Tc
54 Phase diagram
ltfgt0
ltfgt s ? 0
55 Temperature dependence of chiral
order parameter
- Does experiment indicate a first order phase
transition for µ 0 ?
56Second order phase transition
- for T only somewhat below Tc
- the order parameter s is expected to
- be close to zero and
- deviate substantially from its vacuum value
- This seems to be disfavored by observation of
chemical freeze out !
57Temperature dependent masses
- Chiral order parameter s depends on T
- Particle masses depend on s
- Chemical freeze out measures m/T for many species
- Mass ratios at T just below Tc are
- close to vacuum ratios
58 Ratios of particle masses and
chemical freeze out
- at chemical freeze out
- ratios of hadron masses seem to be close to
vacuum values - nucleon and meson masses have different
characteristic dependence on s - mnucleon s , mp s -1/2
- ?s/s lt 0.1 ( conservative )
59 first order phase transition seems to be
favored by chemical freeze out
or extremely rapid crossover
60conclusion
- Experimental determination of critical
temperature may be more precise than lattice
results - Rather simple phase structure is suggested
- Analytical understanding is only at beginning
61end
62 How far has first order line been measured?
quarks and gluons
hadrons
63Exclusion argument for large density
hadronic phase with sufficient production of O
excluded !!
64 First order phase transition line
quarks and gluons
µ923MeV transition to nuclear matter
hadrons
65Phase diagram for ms gt mu,d
quark-gluon plasma deconfinement
quark matter superfluid B spontaneously broken
vacuum
nuclear matter B,isospin (I3) spontaneously
broken, S conserved
66Is temperature defined ?Does comparison with
equilibrium critical temperature make sense ?
67Prethermalization
J.Berges,Sz.Borsanyi,CW
bulk quantity
mode quantity
Scalar fermion model with Yukawa coupling
68Vastly different time scales
- for thermalization of different quantities
- here scalar with mass m coupled to fermions
- ( linear quark-meson-model )
- method two particle irreducible non-
equilibrium effective action ( J.Berges et al )
69 Prethermalization equation
of state p/e
similar for kinetic temperature
70 different temperatures
71Mode temperature
np occupation number for momentum p late
time Bose-Einstein or Fermi-Dirac distribution
72(No Transcript)
73 Kinetic equilibration before
chemical equilibration
74Once 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
75Key argument
- Two particle scattering rates not sufficient to
produce O - multiparticle scattering for O-production
dominant only in immediate vicinity of Tc
76Mechanisms for production of multistrange hadrons
- Many proposals
- Hadronization
- Quark-hadron equilibrium
- Decay of collective excitation (s field )
- Multi-hadron-scattering
- Different pictures !
77Hadronic picture of O - production
- Should exist, at least semi-quantitatively, if
Tch lt Tc - ( for Tch Tc Tchgt0.95 Tc is fulfilled
anyhow ) - e.g. collective excitations multi-hadron-scatter
ing - (not necessarily the best and simplest
picture ) - multihadron -gt O X should have sufficient rate
- Check of consistency for many models
- Necessary if Tch? Tc and temperature is defined
-
- Way to give quantitative bound on Tch / Tc
78Energy density
- Lattice simulations
- Karsch et al
- even more dramatic
- for first order
- transition
79Production time for O
- multi-meson scattering
- pppKK -gt
- Op
- strong dependence on pion density
P.Braun-Munzinger,J.Stachel,CW
80extremely rapid change
- lowering T by 5 MeV below critical temperature
- rate of O production decreases by
- factor 10
- This restricts chemical freeze out to close
vicinity of critical temperature - 0.95 lt Tch /Tc lt 1