Introduction to heavy Introduction to heavy ion physics (NPII_06)ion physics (NPII_06)lect.3lect.3
Edward ShuryakEdward ShuryakDepartment of Physics and AstronomyDepartment of Physics and Astronomy
State University of New YorkState University of New York
Stony Brook NY 11794 USAStony Brook NY 11794 USA
Why study the heavy ion physics?
• A ``Bang” like other magnificent explosions like Supernova or Big Bang
• New form of matter formed, the Quark-Gluon Plasma
• It is different from the QCD vacuum phase• New spectroscopy, in spite of deconfinement
and With restored chiral symmetry • Relation to other fields: plasma physics, strongly
coupled atoms, string theory
The theoretical tools we will need
• Finite T field theory
• Finite T QCD and lattice formulation
• Hydrodynamics
• Transport phenomena (freezeout) and coefficients (viscosity)
• Jet quenching: dE/dx and its origin
Cooling of the Universe (in the inverse order in time)
• T>1 ev ( or 10^4 K) time< 300000 years: atoms cannot exist. After atoms are created, the photons propagate unscattered till today, and we see them as T=2.7K “background radiation”
• T=1-0.05 MeV: time=few mins, size of Universe is about a Solar system. Light nuclei (d,He…Li^7) are created
• T>170 MeV: time 10^(-5) sec, Universe size about 3 km.
Before that there was no “elementary particles” such as protons, neutrons, pions,
and the matter was in a Quark-Gluon Plasma phase
•T>200 GeV quarks,leptons and W,Z get massless: the last phase transition we think we understand. We will not discuss electroweak phase transition in these lectures.
The Big vs the Little Bang
• Big Bang is an explosion which created our Universe.
• Entropy is conserved because of slow expansion
• Hubble law v=Hr for distant galaxies. H is
isotropic. • “Dark energy”
(cosmological constant) seems to lead to accelrated expansion
• Little Bang is an explosion of a small fireball created
in high energy collision of two nuclei.
• Entropy is also conserved• Also Hubble law, but H is
anisotropic • The ``vacuum pressure”
works against QGP expansion
(And that is why it was so difficult to produce it)
Two main phases ofQuantum Chromodynamics (QCD)
• The vacuum phase: Quarks and gluons cannot
propagate free but are confined into hadrons
(mesons and baryons) with zero total color.
• Color charges are “confined” Attempts to separate them lead to creation of a string between charges and a potential V=Kr
• Another feature of the vacuum: quark pairs are
• condensed, like Cooper pairs in superconductor => <qRqL>
Broken chiral symmetry by a ``quark condensate”
• In QGP phase quarks and gluons are deconfined
and they can propagate as “quasiparticles”. The color charges
are “screened” at large distances (ES,1978) , while also
being antiscreened at small ones (Politzer, Gross and Wilczek 1973)
• New spectroscopy: Recently we learned that
at not too high T=(1-4)Tc
quasiparticles can also be bound in pairs, but in this case
a nonzero color is allowed and such states in fact dominate
High density phases of color superconductivity we will not discuss
The vacuum vs QGP, continued
• The vacuum is very complicated, dominated by ``topological objects”
Vortices, monopoles and instantons
• Among other changes it shifts its energy down compared to an
“empty” vacuum, known asThe Bag terms:
p=#T4-B =3#T4+B
• The QGP, as any plasma, screens them, and is nearly free from them
• So, when QGP is produced, the vacuum tries to expel it
(recall here pumped out Magdeburg hemispheres
By von Guericke in 1656 we learned at school)
Magdeburg hemispheres 1656
We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma
Diquarks as a Feshbach resonance
• Point S has the maximal Tc/Mu
• Line of qq marginal stability befurkates
• Line with point D is de-binding of Cooper pairs
Our map: the QCD Phase Diagram
T
The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland)
Chemical potential mu
Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)
The zigzags on the phase diagram
• Both bar.charge and entropy are conserved: n_b/s=const(t)
• In resonance gas and QGP different formulae: curves do not meet at the critical line
• Of course they are connected inside the mixed phase –heating while expanding due to latent heat
A decade old plotFrom C.M.Hung and ES,hep-ph/9709264,PRC
Crude zigzags start to appear, but far from being accurate enough…
Effective eos along the line s/n_b=const also have aminimum at e=1 GeV/fm^3
Macro theory expects 3 special points in an energy scan, not 1!
(Macro theory=collision of very large nuclei, so hydro is valid without doubt…)
Focusing effect
See below
longest expansion, K/pi
V2 stops rising,
Elab about
5 GeV*A
The same thing in log(s)-log(n) coordinates (now the cooling lines are simple, but the
thermodynamics is tricky)
Black=true
RHIC: a view from space
A dedicated collider for
(i) Heavy ion collisions, AuAu 100+100 GeV/N
(ii) Polarized pp, 250+250 GeV
Relativistic Heavy Ion Collider
Two counter rotating beams in two rings,6 crossing points
Multiple magnets of the ring are all At the liquid HeTemperature – the main Expence during the runs
Two large experiments +2 small
PHENIX
2 e and 2 muon armsSTAR
Large tracking TPC
One of the first RHIC events at STAR detector,
The average multiplicity at AuAu 200 GeV/N
Is about 5000
Many measurements (up to high pT!)from all 4 detectors
Main findings at RHIC
• Partciles are produced from matter which seems to be well equilibrated (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T)
• Very robust collective flows, well described by ideal hydro withLattice-based Equation of state (EoS). This indicates very strong
interaction even at early time => sQGP
• Jet quenching: Quarks and gluons with high energy (jets) do not fly away freely but are mostly (up to 90%) absorbed by the matter .
The released energy partly go to hydrodynamical ``conical flow” or sound waves rather than gluons.
Most importantly, we definitely produced ``matter”:
(while many skeptics predicted otherwise) The main condition for that:l << L
(the micro scale) << (the macro scale)(the mean free path) << (system size)
(relaxation time) << (evolution duration)
I
the zeroth order in l/L is ideal hydro with a local stress tensor. Viscosity appears as a first order correction l/L, it has velocity gradients.
(Note that it is inversely proportional to the cross section and thus is the oldest strong coupling expansion)
If so, Hydrodynamics is simple!Static
•EoS from Lattice QCD•Finite T, field theory•Critical phenomena
Dynamic Phenomena •Expansion, Flow•Space-time evolution of thermodynamic variables
Once we accept localthermalization,life becomes very easy.
Why and when the equilibration takes place is a tough question
one has to answer
Local Energy-momentum
conservation:Conserved number:
Example of Hydro (with Jet Quenching)
Color: parton densityPlot: mini-jets
Au+Au 200AGeV, b=8 fmtransverse plane@midrapidityFragmentation switched off
hydro+jet modelHydro+Jet Hydro+Jet
modelmodel (T.Hirano (T.Hirano & Y.Nara (’02))& Y.Nara (’02))
x
y
How Hydrodynamics Works at RHIC
Explosion goes in all directionsExplosion goes in all directionsRadial and especiallyRadial and especially
Elliptic flowElliptic flow
The red almond-The red almond-shaped region is shaped region is where the dense where the dense matter is. Yellow matter is. Yellow
region shows region shows “spectators” which “spectators” which
fly by without fly by without interactioninteraction
The so called “jet tomography” of the initial shape of the matter
“elliptic flow” works as a barometer which measures the pressure of QGP
Origin: spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system spatial anisotropy momentum anisotropy
v2: 2nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane
Almond shape overlap region in coordinate space
y2 x2 y2 x2
2cos2 vx
y
p
patan
More on Elliptic Flow
See recent reviews, P.Huovinen (QM2002) , nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227
Hydro: P.Kolb et al.(’99)(Note: Hydro+RQMD
gives a better description.D.Teaney et al.(’01))
STAR, PRC66(’02)034904
Hydro: P.Huovinen et al.(’01)
PHENIX, PRL91(’03)182301.
Viscosity of QGPQGP at RHIC seem to be the most idealfluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made
• viscous corrections1st order correction to dist. fn.:
:Sound attenuation length
Velocity gradiants
Nearly ideal hydro !? D.Teaney(’03)
What is needed to reproduce themagnitude of v2?
Huge cross sections!!
How to get 50 times pQCD gg?
quark bound states don’t all melt at Tc
• all q,g have strong rescattering qqbar mesonResonance enhancements (Zahed and
ES,2003)
• Huge cross section due to resonance enhancement causes elliptic flow of trapped Li atoms
Elliptic flow with ultracold trapped Li6 atoms, a=> infinity regime
The system is extremely dilute, but can be put into a hydro regime, with an elliptic flow, if it is specially tuned into a strong coupling regime via the so called Feshbach resonance
Similar mechanism was proposed (Zahed and myself) for QGP, in which a pair of quasiparticles is in resonance with their bound state at the “zero binding lines”
The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a
Micro-Bang !
3 more strongly coupled systems
• N=4 Supersymmetric Yang-Mills
• Cold trapped atoms in Feshbach resonance (a=>1)
• Classical plasma with =(Ze)2/RT>>1 is a very good liquid, up to 300, with very small viscosity at » 10 where it has a deep minimum
