QCD phase transition in the early universe - Theory Center

QCD Phase Transition(s) 

& 

The Early Universe 

Axel Maas 

6 th of January 2005 

RHI Seminar WS 2004/2005

Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary 

Overview 

● Aspects of QCD 

● QCD at finite temperature 

– Theoretical ideas 

– Experimental investigations 

● Unsettled issues 

● QCD phase transition in the early universe 

● Summary 

QCD Phase Transition(s) & The Early Universe/Axel Maas


Part I: 

Aspects of QCD 



Quantumchromodynamics (QCD) 

● (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 


Overview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary 

QCD degrees of freedom I 

DOF # Mass Bound state mass Spin El.charge 

Up quark 3 0-5 MeV 300 MeV ½ 2/3 

Down quark 3 5-10 MeV 300 MeV ½ -1/3 

Strange quark 3 90-150 MeV450 MeV ½ -1/3 

Charm quark 3 1500 MeV 1800 MeV ½ 2/3 

Bottom quark 3 4500 MeV 4800 MeV ½ -1/3 

Top quark 3 175000 MeVNo bound states ½ 2/3 

Gluon 8 0 MeV Not applicable 1 0 



QCD degrees of freedom I 

DOF # Mass Bound state mass Spin El.charge 

Up quark 3 0-5 MeV 300 MeV ½ 2/3 

Down quark 3 5-10 MeV 300 MeV ½ -1/3 

Strange quark 3 90-150 MeV450 MeV ½ -1/3 

Charm quark 3 1500 MeV 1800 MeV ½ 2/3 

Bottom quark 3 4500 MeV 4800 MeV ½ -1/3 

Top quark 3 175000 MeVNo bound states ½ 2/3 

Gluon 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 



QCD degrees of freedom II 

● Baryon: 3 (valence-)quarks 





● Meson: 1 quark and 1 antiquark 






● Interactions mediated by gluons 






● Interactions mediated by gluons 

● Gluons are also charged 

– Pure glue theory: Yang-Mills Theory 


Overview – QCD: Properties – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary 

Properties of QCD 

● Weakly interacting at high energies 

(> a few GeV) 

– Asymptotic freedom 

– Accessible by perturbation theory 



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 



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 



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 



Properties of QCD III 

● Confinement 

– Free quarks and gluons not observed 

– In general: No colored objects observed 

– Measured for quarks at 1:10 30 -10 40 

● Unique signature due to fractal electric charge 



Properties of QCD III 

● Confinement 

– Free quarks and gluons not observed 

– In general: No colored objects observed 

– Measured for quarks at 1:10 30 -10 40 

● Unique signature due to fractal electric charge 

● Not yet understood (“millennium problem”) 

● Recent progress 

– Collective (topological) gluon excitations? 



Properties of QCD IV 

● Inter-quark potential confining 

(“Cornell potential”): V=a/r+σr (σ string tension) 

QCD Phase Transition(s) & The Early Universe/Axel Maas 

[Figures from Sommer et al., 2001]


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)]


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: Formulation – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary 

Formulation of QCD 

● Gauge Theory with classical Lagrangian 

, 

L=− 1 

4 F 

– : Quarks 

a 

A – : Gluons 

– Upon quantization commonly auxiliary fields to 

described quantum fluctuations (“Ghosts”) are 

introduced 


a F , a iD −m 

F 

a 

=∂ 

A 

a 

−∂ 

A D =∂ −ieA 

a 

 

a 

 

a 

gf 

abc b c 

A A

Overview – QCD: Theoretical Methods – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary 

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 











● Many other methods and attempts 

● No method yet successful alone – combinations 

needed 




Part II: 

Finite Temperature

Overview – QCD – Finite Temperature QCD: Introduction – Unsettled Issues – Early Universe - Summary 

Finite Temperature QCD I 

● Can the properties of 

QCD change? 






● Old Idea: QCD weakly 

coupled at high 

temperature 

– Perturbation theory 

– Chiral restoration and 

deconfinement 








temperature 




● Phase diagram of QCD 

– Phase transition at high temperature and densities 








temperature 




● Phase diagram of QCD 

– Phase transition at high temperature and densities 


[Figure from Karsch et al., 2003]


Finite Temperature QCD II 

● Relevant for the early universe and neutron-stars (?) 



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: Experiment – Unsettled Issues – Early Universe - Summary 

Temperature from Experiment 

● Temperature and chemical potential cannot be measure 

directly 



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 



Research centers for Heavy-Ion physics 


[Earth picture from NASA]




[Earth picture from NASA, research center picture from the homepage]




[Earth picture from NASA, research center pictures from their respective homepages]




[Earth picture from NASA, research center pictures from their respective homepages]


Experiments 


[From CERN press release]


Experiments 


[From CERN press release] 

SIS: ~1 GeV/A 

(Kaos, Fopi, Hades) 

Ongoing


Experiments AGS: 5 GeV/A 

(E802/864,E917, 

E810,E814/877, 

E864,E895) 

Completed 


[From CERN press release] 

SIS: ~1 GeV/A 

(Kaos, Fopi, Hades) 

Ongoing


Experiments 

SPS:


Experiments 

RHIC: 200/130 GeV/A 

(Star, Phenix, Brahms, 

Phobos) 

Ongoing 

SPS:


Experiments 

LHC: 2700 GeV/A 

(Alice, CMS, Atlas) 

Under construction 



Phobos) 


SPS:


Experiments 

LHC: 2700 GeV/A 

(Alice, CMS, Atlas) 

Under construction 



Phobos) 


SPS:


Hevay-Ion Experiments I 

● NA45/CERES, fixed target @ CERN SPS 

– Second generation, special purpose detector 


[From the CERES homepage]


Heavy-Ion Experiments II 

● ALICE, collider @ CERN LHC 

– Fourth generation, omnipurpose detector 


[From the ALICE homepage]


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 









– 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: Experiement – Unsettled Issues – Early Universe - Summary 

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 

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 


[From the STAR collaboration, 2002]

Overview – QCD – Finite Temperature QCD: Theory – Unsettled Issues – Early Universe - Summary 

...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: Chiral transition – Unsettled Issues – Early Universe - Summary 

Finite Temperature on the Lattice I 

● Numerical calculation in a finite volume 

– Thermodynamic limit reached by extrapolation 

– Phase transition deduced from peaks in susceptibilities 



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]


Finite Temperature on the Lattice II 

● First order phase 

transition or crossover 

– Yang-Mills Theory: 

First order at 269 MeV 

● Approaches 

Stefan-Boltzmann 

limit slowly 

● Strong residual 

interactions at least 

up to several times T c 



Overview – QCD – Finite Temperature QCD: Order of the phase transition – Unsettled Issues – Early Universe - Summary 

Order of the phase transition 

● Order of the phase transition depends on the quark 

masses 

– Currently not possible to calculate at physical quark masses 



Overview – QCD – Finite Temperature QCD: Hadrons – Unsettled Issues – Early Universe - Summary 

The fate of hadrons 

● Hadrons broaden 

– Observable in 

spectral function 

● “Dissolving”? 

– Consequences 

on (production) 

cross-sections 

– Experimental 

consequences (?) 





Part III: 

Unsettled issues 

Deconfinement 

The non-triviality of the high-temperature phase

Overview – QCD – Finite Temperature QCD – Unsettled Issues: Deconfinement – Early Universe - Summary 

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 

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: Trace anomaly – Early Universe - Summary 

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] 



Origin of the Trace Anomaly 

● Only one independent thermodynamic quantity 

p= T 

V ln Z =T 2 ∂ 

∂T 

p 

T 


=−3 p=T 5 ∂ 

∂T 

[Following Zwanziger, 2004] 

p 

T 4




p= T 

V ln Z =T 2 ∂ 

∂T 

● Re-express everything by trace anomaly 

p 

p 

T 


∞ 

T 4 =c SB −∫ T 

dT 

T 5 

 

=−3 p=T 5 ∂ 

∂T 

∞ 

T 4 =3c SB −∫ T 


dT 1 

T 3 

p 

T 4 

∂ 

∂T 

 

T




p= T 

V ln Z =T 2 ∂ 

∂T 


p 

● Only a term linear in T can contribute 

to p but not to ε 

p 

T 


∞ 

T 4 =c SB −∫ T 

dT 

T 5 

 

=−3 p=T 5 ∂ 

∂T 

∞ 

T 4 =3c SB −∫ T 


dT 1 

T 3 

p 

T 4 

∂ 

∂T 

 

T




p= T 

V ln Z =T 2 ∂ 

∂T 


p 

● Only a term linear in T can contribute 

to p but not to ε 

p 

T 

● Perturbation theory cannot provide such a term 


∞ 

T 4 =c SB −∫ T 

dT 

T 5 

 

=−3 p=T 5 ∂ 

∂T 

∞ 

T 4 =3c SB −∫ T 


dT 1 

T 3 

p 

T 4 

∂ 

∂T 

 

T

Overview – QCD – Finite Temperature QCD – Unsettled Issues: Failure of perturbation theory – Early Universe - Summary 

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: Picture – Early Universe - Summary 

Picture of the high-temperature phase 

● How does the high-temperature phase look? 





















● Strongly interacting (“ionic”) liquid with 

delocalized quarks and gluons 




Part IV: 

The Early Universe - t=+6µs

Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Phase transition - Summary 

Physical situation 

● Unclear if a phase 

transition 






● Even if not a drastic 

change occurs 

● Large jump in energy 






● Even if not a drastic 

change occurs 

● Large jump in energy 

● Practical very similar 

effects 

● Assume a 1 st order transition 


Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Inflation - Summary 

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]





● QCD phase transition not strong enough to give a 

measurable effect – too small surface tension (0.03-0.5?) 


[Figure from Kapusta, 2001]

Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe: Nucleosynthesis - Summary 

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 

● 1 st order phase transition leads to bubble 

formation 



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 



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: Exotics - Summary 

“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 








● 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 


Introduction – QCD – Vacuum Results – QCD Phase Diagram – Finite Temperature Results – Summary 

Summary 

● QCD describes strong interactions 



Summary 


● Non-perturbative theory – non-perturbative effects 

– Chiral symmetry breaking and confinement 



Summary 




● Undergoes a phase change at high temperatures 

– Details are yet unclear 



Summary 






● 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 



Summary 






● 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

QCD phase transition in the early universe - Theory Center

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