QCD Phase Transition - theorie.ikp.physik.tu-darmstadt.de · QCD Phase Transition(s) & The Early...

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


Part I:Aspects of 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

Quantumchromodynamics (QCD)Overview – QCD – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary


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 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


● Baryon: 3 (valence-)quarks

QCD degrees of freedom IIOverview – QCD: Degrees of Freedom – Finite Temperature QCD – Unsettled Issues – Early Universe - Summary


● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark



● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark● Interactions mediated by gluons



● Baryon: 3 (valence-)quarks● Meson: 1 quark and 1 antiquark● Interactions mediated by gluons● Gluons are also charged

– Pure glue theory: Yang-Mills Theory



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


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 1:1030-1040

● 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 1:1030-1040

● 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)

[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



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


Theoretical Methods● Lattice gauge theory

– Massive numerical calculations

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



– Massive numerical calculations● Functional methods

– Equations of motions, renormalization group





– 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



Finite Temperature QCD I● Can the properties of

QCD change?

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



QCD change?● Old Idea: QCD weakly

coupled at high temperature– Perturbation theory– Chiral restoration and

deconfinement






deconfinement● Phase diagram of QCD

– Phase transition at high temperature and densities






deconfinement● 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



Temperature from Experiment● Temperature and chemical potential cannot be measure

directly

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


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]



Experiments

[From CERN press release]



Experiments

SIS: ~1 GeV/A(Kaos, Fopi, Hades)Ongoing




Experiments AGS: 5 GeV/A(E802/864,E917,E810,E814/877,E864,E895)Completed





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





Experiments

RHIC: 200/130 GeV/A(Star, Phenix, Brahms, Phobos)Ongoing







ExperimentsLHC: 2700 GeV/A(Alice, CMS, Atlas)Under construction








ExperimentsLHC: 2700 GeV/A(Alice, CMS, Atlas)Under construction



FAIR: High density(CMB)Under construction






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,...



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

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

[From the STAR collaboration, 2002]


...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


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


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 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



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: Order of the phase transition – Unsettled Issues – Early Universe - Summary


The fate of hadrons● Hadrons broaden

– Observable inspectral function

● “Dissolving”?– Consequenceson (production)cross-sections

– Experimentalconsequences (?)


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


Part III:Unsettled issues

DeconfinementThe non-triviality of the high-temperature phase



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: Deconfinement – 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]

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


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]




● 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






● 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






● 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




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


Picture of the high-temperature phase● How does the high-temperature phase look?

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

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


Part IV:The Early Universe - t=+6µs



Physical situation● Unclear if a phase

transition

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



transition● Even if not a drastic

change occurs● Large jump in energy




transition● Even if not a drastic

change occurs● Large jump in energy● Practical very similar

effects● Assume a 1st order transition



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 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 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 Kapusta, 2001]


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


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]



“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



● 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



Summary● QCD describes strong interactions

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


Summary● QCD describes strong interactions● Non-perturbative theory – non-perturbative effects

– Chiral symmetry breaking and confinement




– Chiral symmetry breaking and confinement● Undergoes a phase change at high temperatures

– Details are yet unclear





– 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





– 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


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