QCD Phase Transition(s)&
The Early Universe
6th of January 2005RHI Seminar WS 2004/2005
Axel Maas
QCD Phase Transition(s) & The Early Universe/Axel Maas
Overview● Aspects of QCD● QCD at finite temperature
– Theoretical ideas– Experimental investigations
● Unsettled issues● QCD phase transition in the early universe● Summary
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Part I:Aspects of QCD
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
● (Quantized) Theory of strong interactions● Describes the structure of hadrons and (ultimately) nuclei
● Elementary degrees of freedom are quarks and gluons– Carry new charge: Color charge– Quarks come in red, green, blue, and anti-colors
Quantumchromodynamics (QCD)Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
QCD degrees of freedom IDOF # Mass Bound state mass Spin El.chargeUp quark 3 0-5 MeV 300 MeV ½ 2/3Down quark 3 5-10 MeV 300 MeV ½ -1/3Strange quark 3 90-150 MeV450 MeV ½ -1/3Charm quark 3 1500 MeV 1800 MeV ½ 2/3Bottom quark 3 4500 MeV 4800 MeV ½ -1/3Top quark 3 175000 MeVNo bound states ½ 2/3Gluon 8 0 MeV Not applicable 1 0
Overview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
QCD degrees of freedom IDOF # Mass Bound state mass Spin El.chargeUp quark 3 0-5 MeV 300 MeV ½ 2/3Down quark 3 5-10 MeV 300 MeV ½ -1/3Strange quark 3 90-150 MeV450 MeV ½ -1/3Charm quark 3 1500 MeV 1800 MeV ½ 2/3Bottom quark 3 4500 MeV 4800 MeV ½ -1/3Top quark 3 175000 MeVNo bound states ½ 2/3Gluon 8 0 MeV Not applicable 1 0
● Quark species (“flavor”) conserved in strong and electromagnetic but not in weak interactions● Existence of quarks and gluons experimentally established● Quarks in ep-scattering and gluons by event topologies
Overview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
● Baryon: 3 (valence-)quarks
QCD degrees of freedom IIOverview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark
QCD degrees of freedom IIOverview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark● Interactions mediated by gluons
QCD degrees of freedom IIOverview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark● Interactions mediated by gluons● Gluons are also charged
– Pure glue theory: Yang-Mills Theory
QCD degrees of freedom IIOverview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD● Weakly interacting at high energies (> a few GeV)– Asymptotic freedom– Accessible by perturbation theory
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD● Weakly interacting at high energies (> a few GeV)– Asymptotic freedom– Accessible by perturbation theory
● Strongly interacting at low energies– Perturbation theory fails– Genuine non-perturbative effects– Seem to be generated by gluon interaction
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD II● Chiral symmetry
– Connection of left- and right-handed quarks– Exact symmetry if quarks are massless– (Weak) explicit breaking by quark masses
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD II● Chiral symmetry
– Connection of left- and right-handed quarks– Exact symmetry if quarks are massless– (Weak) explicit breaking by quark masses
● Chiral symmetry spontaneously broken– Nucleon mass of ~1 GeV although bare quark masses ~5-10 MeV
– “Constituent” or bound state quark masses larger by ~300 MeV
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD III● Confinement
– Free quarks and gluons not observed– In general: No colored objects observed– Measured for quarks at 1:1030-1040
● Unique signature due to fractal electric charge
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD III● Confinement
– Free quarks and gluons not observed– In general: No colored objects observed– Measured for quarks at 1:1030-1040
● Unique signature due to fractal electric charge● Not yet understood (“millennium problem”)● Recent progress
– Collective (topological) gluon excitations?
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD IV● Inter-quark potential confining (“Cornell potential”): V=a/r+σr (σ string tension)
[Figures from Sommer et al., 2001]
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Properties of QCD IV● Inter-quark potential confining (“Cornell potential”): V=a/r+σr (σ string tension)– Flattened by string breaking
[Figures from Sommer et al., 2001 (left) and from Greensite, 2003 (right)]
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Chiral symmetry and confinement● Connection between chiral symmetry and confinement
● Removal of confining properties removes also chiral symmetry breaking
● Seem to be linked by collective (topological) excitations
● Not understood– But some progress in the last years
Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Formulation of QCD● Gauge Theory with classical Lagrangian
– : Quarks– : Gluons– Upon quantization commonly auxiliary fields to described quantum fluctuations (“Ghosts”) are introduced
L=−14
F a F , aiD
−m
F a =∂ A
a−∂ Aagf abc A
b Ac
D=∂−ieAa a
Aa
,
Overview – QCD: Formulation – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Theoretical Methods● Lattice gauge theory
– Massive numerical calculations
Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Theoretical Methods● Lattice gauge theory
– Massive numerical calculations● Functional methods
– Equations of motions, renormalization group
Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Theoretical Methods● Lattice gauge theory
– Massive numerical calculations● Functional methods
– Equations of motions, renormalization group● Effective theories
– Systematic expansion, e.g. Chiral perturbation theory– Ad hoc models
Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Theoretical Methods● Lattice gauge theory
– Massive numerical calculations● Functional methods
– Equations of motions, renormalization group● Effective theories
– Systematic expansion, e.g. Chiral perturbation theory– Ad hoc models
● Many other methods and attempts
Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Theoretical Methods● Lattice gauge theory
– Massive numerical calculations● Functional methods
– Equations of motions, renormalization group● Effective theories
– Systematic expansion, e.g. Chiral perturbation theory– Ad hoc models
● Many other methods and attempts● No method yet successful alone – combinations
needed
Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Part II:Finite Temperature
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD I● Can the properties of
QCD change?
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD I● Can the properties of
QCD change?● Old Idea: QCD weakly
coupled at high temperature– Perturbation theory– Chiral restoration and
deconfinement
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD I● Can the properties of
QCD change?● Old Idea: QCD weakly
coupled at high temperature– Perturbation theory– Chiral restoration and
deconfinement● Phase diagram of QCD
– Phase transition at high temperature and densities
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD I● Can the properties of
QCD change?● Old Idea: QCD weakly
coupled at high temperature– Perturbation theory– Chiral restoration and
deconfinement● Phase diagram of QCD
– Phase transition at high temperature and densities
[Figure from Karsch et al., 2003]
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD II
● Relevant for the early universe and neutron-stars (?)
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature QCD II[Figure from Andronic et al., 2004]
● Relevant for the early universe and neutron-stars (?)● Experimentally investigated in heavy-ion collisons
Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Temperature from Experiment● Temperature and chemical potential cannot be measure
directly
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Temperature from Experiment● Temperature and chemical potential cannot be measure
directly● Indirect extraction from a fit of the hadron production
ratios– Idealized model of a free hadron gas
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Research centers for Heavy-Ion physics
[Earth picture from NASA]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Research centers for Heavy-Ion physics
[Earth picture from NASA, research center picture from the homepage]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Research centers for Heavy-Ion physics
[Earth picture from NASA, research center pictures from their respective homepages]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Research centers for Heavy-Ion physics
[Earth picture from NASA, research center pictures from their respective homepages]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experiments
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experiments
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experiments AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experiments
SPS: <17 GeV/A(WA80/98, NA35/49, NA 38/50/60, NA 44,CERES, WA97, NA57,NA52)Nearly completed
AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experiments
RHIC: 200/130 GeV/A(Star, Phenix, Brahms, Phobos)Ongoing
SPS: <17 GeV/A(WA80/98, NA35/49, NA 38/50/60, NA 44,CERES, WA97, NA57,NA52)Nearly completed
AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
ExperimentsLHC: 2700 GeV/A(Alice, CMS, Atlas)Under construction
RHIC: 200/130 GeV/A(Star, Phenix, Brahms, Phobos)Ongoing
SPS: <17 GeV/A(WA80/98, NA35/49, NA 38/50/60, NA 44,CERES, WA97, NA57,NA52)Nearly completed
AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
ExperimentsLHC: 2700 GeV/A(Alice, CMS, Atlas)Under construction
RHIC: 200/130 GeV/A(Star, Phenix, Brahms, Phobos)Ongoing
SPS: <17 GeV/A(WA80/98, NA35/49, NA 38/50/60, NA 44,CERES, WA97, NA57,NA52)Nearly completed
FAIR: High density(CMB)Under construction
AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed
SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing
[From CERN press release]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Hevay-Ion Experiments I● NA45/CERES, fixed target @ CERN SPS
– Second generation, special purpose detector
[From the CERES homepage]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Heavy-Ion Experiments II● ALICE, collider @ CERN LHC
– Fourth generation, omnipurpose detector
[From the ALICE homepage]
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experimental signatures...● Many observables available
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experimental signatures...● Many observables available
– Hard probes● Perturbative QCD applicable, e.g. Jet quenching
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experimental signatures...● Many observables available
– Hard probes● Perturbative QCD applicable, e.g. Jet quenching
– Hadronic probes● Strangness or charm enhancement/suppression
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experimental signatures...● Many observables available
– Hard probes● Perturbative QCD applicable, e.g. Jet quenching
– Hadronic probes● Strangness or charm enhancement/suppression
– Leptonic probes● Dilepton or (direct) photon spectra enhancement
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Experimental signatures...● Many observables available
– Hard probes● Perturbative QCD applicable, e.g. Jet quenching
– Hadronic probes● Strangness or charm enhancement/suppression
– Leptonic probes● Dilepton or (direct) photon spectra enhancement
– Many other observables● HBT interferometry, hadron yields, event-by-event fluctuations of observables,...
Overview – QCD – Finite Temperature QCD: Experiment – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Jet quenching● Jets are a collimated spray of hadrons● Originated from a (hard) production of two colored objects
Overview – QCD – Finite Temperature QCD: Experiement – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Jet quenching● Jets are a collimated spray of hadrons● Originated from a (hard) production of two colored objects● One can be stooped by the medium
Overview – QCD – Finite Temperature QCD: Experiement – Unsettled Issues – Early Universe - Summary
[From the STAR collaboration, 2002]
QCD Phase Transition(s) & The Early Universe/Axel Maas
...and theoretical problems● Euqilibrium properties of the quark-gluon plasma
● Bound state physics of hadrons● Hadron formation in a medium● Phase transition: Non-equilibrium● Heavy-Ion collision: Finite size etc.● Propagation of probes in a heavy-ion collision
Overview – QCD – Finite Temperature QCD: Theory – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature on the Lattice I● Numerical calculation in a finite volume
– Thermodynamic limit reached by extrapolation– Phase transition deduced from peaks in susceptibilities
Overview – QCD – Finite Temperature QCD: Chiral transition – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature on the Lattice I● Numerical calculation in a finite volume
– Thermodynamic limit reached by extrapolation– Phase transition deduced from peaks in susceptibilities
● Main observables are the chiral condensate and thermodynamic quantities– Energy density, pressure,
entropy,...– Calculated directly from
the partition sum[Figure from Karsch, 2001]
Overview – QCD – Finite Temperature QCD: Chiral transition – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Finite Temperature on the Lattice II
[Figure from Karsch et al., 2003]
● First order phasetransition or crossover– Yang-Mills Theory: First order at 269 MeV
● Approaches Stefan-Boltzmann limit slowly
● Strong residual interactions at least up to several times Tc
Overview – QCD – Finite Temperature QCD: Chiral transition – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Order of the phase transition● Order of the phase transition depends on the quark
masses– Currently not possible to calculate at physical quark masses
[Figure from Karsch et al., 2003]
Overview – QCD – Finite Temperature QCD: Order of the phase transition – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
The fate of hadrons● Hadrons broaden
– Observable inspectral function
● “Dissolving”?– Consequenceson (production)cross-sections
– Experimentalconsequences (?)
[Figure from Karsch et al., 2003]
Overview – QCD – Finite Temperature QCD: Hadrons – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Part III:Unsettled issues
DeconfinementThe non-triviality of the high-temperature phase
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Deconfinement I
● String tension vanishes at phase transition● Not observable in full QCD
[From Karsch et al., 2003]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Deconfinement – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Deconfinement II● Polyakov line order
parameter in pure glue– Well defined?
● Not well defined
with quarks● Used anyway● Same transition temperature
as for chiral transition● Not understood – as in the vacuum
[From Karsch, 2001]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Deconfinement – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Trace anomaly● θ=ε-3p=0 for a Stefan-Boltzmann gas● Significantly different from 0 at phase transition and
beyond [Left: From Karsch et al. 2000, Right: From Karsch 2001]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Trace anomaly – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Origin of the Trace Anomaly ● Only one independent thermodynamic quantity
p=TV
ln Z =T 2 ∂∂T
pT
=−3 p=T 5 ∂∂T
pT 4
[Following Zwanziger, 2004]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Trace anomaly – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Origin of the Trace Anomaly ● Only one independent thermodynamic quantity
● Re-express everything by trace anomaly
p=TV
ln Z =T 2 ∂∂T
pT
=−3 p=T 5 ∂∂T
pT 4
pT 4=cSB−∫T
∞dT
T 5
T 4=3cSB−∫T
∞dT
1T 3
∂∂T
T
[Following Zwanziger, 2004]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Trace anomaly – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Origin of the Trace Anomaly ● Only one independent thermodynamic quantity
● Re-express everything by trace anomaly
● Only a term linear in T can contribute to p but not to ε
p=TV
ln Z =T 2 ∂∂T
pT
=−3 p=T 5 ∂∂T
pT 4
pT 4=cSB−∫T
∞dT
T 5
T 4=3cSB−∫T
∞dT
1T 3
∂∂T
T
[Following Zwanziger, 2004]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Trace anomaly – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Origin of the Trace Anomaly ● Only one independent thermodynamic quantity
● Re-express everything by trace anomaly
● Only a term linear in T can contribute to p but not to ε
● Perturbation theory cannot provide such a term
p=TV
ln Z =T 2 ∂∂T
pT
=−3 p=T 5 ∂∂T
pT 4
pT 4=cSB−∫T
∞dT
T 5
T 4=3cSB−∫T
∞dT
1T 3
∂∂T
T
[Following Zwanziger, 2004]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Trace anomaly – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Non-trivial High-Temperature Phase● Perturbation theory fails● Infrared divergences
– Similar to the vacuum● Most problems for
chromomagnetic sector● Also spatial string tension
cannot be explained by
perturbation theory● High temperature phase cannot be perturbative● Likely not even at infinite temperature
[Figure from Rischke, Prog.Part.Nucl. 2004]
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Failure of perturbation theory – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Picture of the high-temperature phase● How does the high-temperature phase look?
● Strongly interacting (“ionic”) liquid with delocalized quarks and gluons
Overview – QCD – Finite Temperature QCD – Unsettled Issues: Picture – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Part IV:The Early Universe - t=+6µs
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Physical situation● Unclear if a phase
transition
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Phase transition - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Physical situation● Unclear if a phase
transition● Even if not a drastic
change occurs● Large jump in energy
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Phase transition - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Physical situation● Unclear if a phase
transition● Even if not a drastic
change occurs● Large jump in energy● Practical very similar
effects● Assume a 1st order transition
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Phase transition - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
QCD inflation● Chiral symmetry restoration similar to inflation transition● Allows in principle for an inflationary era with reheating
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Inflation - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
QCD inflation● Chiral symmetry restoration similar to inflation transition● Allows in principle for an inflationary era with reheating● QCD phase transition not strong enough to give a
measurable effect – too small surface tension (0.03-0.5?)
[Figure from Kämpfer, 2000]
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Inflation - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
QCD inflation● Chiral symmetry restoration similar to inflation transition● Allows in principle for an inflationary era with reheating● QCD phase transition not strong enough to give a
measurable effect – too small surface tension (0.03-0.5?)
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Inflation - Summary
[Figure from Kapusta, 2001]
QCD Phase Transition(s) & The Early Universe/Axel Maas
Impact on Nucleosynthesis I● Baryon-to-photon ratio is influenced by QCD phase transition– Quarks electrically charged
● Baryon distribution can also be influenced– Baryon density in the high-temperature phase higher
– Light quarks vs. heavy baryons● 1st order phase transition leads to bubble formation
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Nucleosynthesis - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Impact on Nucleosynthesis II● Baryon number conservation requires highest baryon
density in the last bubbles to freeze: High nucleon density– Neutrons diffuse faster due
to electric neutrality:
Isopsin inhomogeneities● Spatial inhomogeneities in
nucleosynthesis
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Nucleosynthesis - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Impact on Nucleosynthesis II● Baryon number conservation requires highest baryon
density in the last bubbles to freeze: High nucleon density– Neutrons diffuse faster due
to electric neutrality:
Isopsin inhomogeneities● Spatial inhomogeneities in
nucleosynthesis● Effect starts at ~150 m initial
average bubble separation
– Likely only ~0.01 m[Figure from Kainulainen, 1999]
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Nucleosynthesis - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
“Exotic” Consequences● Much stronger nucleations: Primordial black hole formation– Hawking flashes, gravitational micro-lensing, dark matter candidate
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Exotics - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
“Exotic” Consequences● Much stronger nucleations: Primordial black hole formation– Hawking flashes, gravitational micro-lensing, dark matter candidate
● Strangelets: Nuggets of strange matter– Unlikely as strange matter is likely not stable
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Exotics - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
“Exotic” Consequences● Much stronger nucleations: Primordial black hole formation– Hawking flashes, gravitational micro-lensing, dark matter candidate
● Strangelets: Nuggets of strange matter– Unlikely as strange matter is likely not stable
● Large scale chromomagnetic walls– Similar to cosmic walls– Would be observable in CMB for l>1000
Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Exotics - Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Summary● QCD describes strong interactions
Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Summary● QCD describes strong interactions● Non-perturbative theory – non-perturbative effects
– Chiral symmetry breaking and confinement
Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Summary● QCD describes strong interactions● Non-perturbative theory – non-perturbative effects
– Chiral symmetry breaking and confinement● Undergoes a phase change at high temperatures
– Details are yet unclear
Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Summary● QCD describes strong interactions● Non-perturbative theory – non-perturbative effects
– Chiral symmetry breaking and confinement● Undergoes a phase change at high temperatures
– Details are yet unclear● Can in principle have significant impact on the evolution of
the early universe– QCD parameters lead only to a weak effect– Strong and cosmological scales have already been to
different
Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary
QCD Phase Transition(s) & The Early Universe/Axel Maas
Summary● QCD describes strong interactions● Non-perturbative theory – non-perturbative effects
– Chiral symmetry breaking and confinement● Undergoes a phase change at high temperatures
– Details are yet unclear● Can in principle have significant impact on the evolution of
the early universe– QCD parameters lead only to a weak effect– Strong and cosmological scales have already been to
different● QCD directly not relevant – but indirectly: Nucleosynthesis
Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary