paul stankus oak ridge rhic/ags users’ meeting june 20, 05 hitchiker’s guide: qgp in the early...
TRANSCRIPT
Paul StankusOak Ridge
RHIC/AGS Users’ Meeting June 20, 05
Hitchiker’s Guide: QGP in the Early Universe
Paul StankusOak Ridge Nat’l Lab
APS 06 April Meeting
Contents Big Bang Basic Framework �
Nuclear Particles in the Early �Universe; Limiting Temperature?
Thermal Quarks and Gluons; �Experimental Evidence
If I can understand it, so can you!
Henrietta Leavitt American
Distances via variable stars
Edwin Hubble American
Galaxies outside Milky Way
The original Hubble Diagram“A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae” E.Hubble (1929)
USUS USUS
Now
Slightly Earlier
As seen from our position: As seen from another position:
Recessional velocity distance
Same pattern seen by all observers!
Original Hubble diagram
Freedman, et al. Astrophys. J. 553, 47 (2001)
1929: H0 ~500 km/sec/Mpc
2001: H0 = 727 km/sec/Mpc
Photons
t
x
UsGalaxies
?
vRecession = H0 d
1/H0 ~ 1010 year ~ Age of the Universe?
1/H
0
W. Freedman Canadian
Modern Hubble constant (2001)
H.P. Robertson American
A.G. Walker British
W. de Sitter Dutch
Albert Einstein German
A. Friedmann Russian
G. LeMaitre Belgian
Formalized most general form of isotropic and homogeneous universe in GR “Robertson-Walker metric” (1935-6)
General Theory of Relativity (1915); Static, closed universe (1917)
Vacuum-energy-filled universes “de Sitter space” (1917)
Evolution of homogeneous, non-static (expanding) universes “Friedmann models” (1922, 1927)
€
dτ 2 = −ds2 = dt 2 − a(t)[ ]2dχ 2
a(t) dimensionless; set a(now) =1
χ has units of length
a(t)Δχ = physical separation at time t
Robertson-Walker Metric€
dτ 2 = −ds2 = dt 2 − dx 2
H. Minkowski German
“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)
Minkowski Metric
t
t1
t2
Photons
Us Galaxies at rest in the “Hubble flow”
t
t=now
€
χ = constant
"At rest in the Hubble flow"
Galaxies
€
dτ = 0 ⇒dt
dχ= ±a(t)
Photons€
H(t) =velocity
distance=
d
dta(t)Δχ[ ]
a(t)Δχ=
˙ a (t)
a(t)
Hubble Constant
A photon’s period grows a(t)
Its coordinate wavelength is constant; its physical wavelength a(t) grows a(t)
(t2)/(t1) = a(t2)/a(t1) 1+z
Cosmological Red Shift
Robertson-Walker Coordinates
w=P/
-1/3
+1/3
-1
a(t)eHt
a(t)t1/2
a(t)t2/3t
now
acc
dec
Inflation, dominated by
“inflaton field” vacuum energy
Radiation-dominated thermal equilibrium
Matter-dominated, non-uniformities grow (structure)
Acceleration in a(t), domination by cosmological constant and/or vacuum energy.
a(t) depends on pressure/energy: The New Standard Cosmology in Four Easy Steps
€
dE = TdS − PdVBasic
Thermodynamics
Sudden expansion, fluid fills empty space without loss of energy.
dE = 0 PdV > 0 therefore dS > 0
Gradual expansion (equilibrium maintained), fluid loses energy through PdV work.
dE = -PdV therefore dS = 0Isentropic Adiabatic
Hot
Hot
Hot
Hot
Cool
Golden Rule 1: Entropy per co-moving volume is conserved
Golden Rule 3: All chemical potentials are negligible
Golden Rule 2: All entropy is in relativistic species
Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out)
€
Entropy S in co - moving volume Δχ( )3preserved
Relativistic gas S
V≡ s = sParticle Type
Particle Type
∑ =2π 2
45
⎛
⎝ ⎜
⎞
⎠ ⎟T 3
Particle Type
∑ =2π 2
45
⎛
⎝ ⎜
⎞
⎠ ⎟g∗S T 3
g∗S ≡ effective number of (Boson) relativistic species
Entropy density S
V=
S
Δχ( )3
1
a3=
2π 2
45g∗S T 3
€
T ∝ g∗S( )− 1
31
aGolden Rule 4:
g*S1 Billion oK 1 Trillion oK
Start with light particles, no strong nuclear force
g*S1 Billion oK 1 Trillion oK
Previous Plot
Now add hadrons = feel strong nuclear force
g*S1 Billion oK 1 Trillion oK
Previous Plots
Keep adding more hadrons….
How many hadrons?
Density of hadron mass states dN/dM increases exponentially with mass.
Prior to the 1970’s this was explained in several ways theoretically
Statistical Bootstrap Hadrons made of hadrons made of hadrons…
Regge Trajectories Stretchy rotators, first string theory
€
dN
dM~ exp M
TH
⎛ ⎝ ⎜ ⎞
⎠ ⎟
Broniowski, et.al. 2004TH ~ 21012 oK
Rolf Hagedorn GermanHadron bootstrap model and limiting temperature (1965)
€
E ~ E i gi
states i
∑ exp −E i /T( ) ~ EdN
dE∫ exp −E /T( ) dE
€
E ~ MdN
dM∫ exp −M /T( ) dM now add in
dN
dM~ exp M /TH( )
~ M∫ exp −M1
T−
1
TH
⎡
⎣ ⎢
⎤
⎦ ⎥
⎛
⎝ ⎜
⎞
⎠ ⎟ dM
Ordinary statistical mechanics:
For thermal hadron gas (crudely set Ei=Mi):
Energy diverges as T --> TH
Maximum achievable temperature?
“…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)
Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556,2003
/T4
g*S
D. GrossH.D. PolitzerF. Wilczek
American
QCD Asymptotic Freedom (1973)
“In 1972 the early universe seemed hopelessly opaque…conditions of ultrahigh temperatures…produce a theoretically intractable mess. But asymptotic freedom renders ultrahigh temperatures friendly…” Frank Wilczek, Nobel Lecture (RMP 05)
QCD to the rescue!
Replace Hadrons (messy and numerous)
by Quarks and Gluons (simple
and few)
Ha
dro
n g
as
Thermal QCD ”QGP” (Lattice)
Kolb & Turner, “The Early Universe”
QC
D T
rans
ition
e+e- A
nnih
ilatio
n
Nuc
leos
ynth
esis
D
ecou
plin
g
Mes
ons
free
ze o
ut
Hea
vy q
uark
s an
d bo
sons
free
ze o
ut
“Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today…since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel Lecture (RMP 05)
Thermal QCD -- i.e. quarks and
gluons -- makes the very early universe tractable; but where is the experimental
proof?
g*S
National Research Council Report (2003)
Eleven Science Questions for the New
Century
Question 8 is:
Also: BNL-AGS, CERN-SPS, CERN-LHC
BNL-RHIC Facility
Low High
Low High
Density, PressurePressure Gradient
Initial (10-24 sec) Thermalized Medium Early
Later
Fast
Slow
€
v2 =px
2 − py2
px2 + py
2
Elliptic momentum anisotropy
PHENIX Data
Fluid dynamics predicts momentum anisotropy correctly for 99% of particles
produced in Au+Au
• Strong self-re-interaction
• Early thermalization (10-24 sec)
• Low dissipation (viscosity)
• Equation of state P/ similar to relativistic gas
What does it mean?
Beam energy
• High acceleration requires high P/ pressure/energy density. Hagedorn picture would be softer since massive hadrons are non-relativistic.
• Increase/saturate with higher energy densities. In Hagedorn picture pressure decreases with density.
Momentum anisotropy increases as we increase beam energy & energy density
What does it mean?
Thermal photon radiation from
quarks and gluons?
Ti> 500 MeV
Direct photons from nuclear collisions suggest initial temperatures > TH
1. B violation2. C,CP violation
3. Out of equilibrium
Sakharov criteria for baryogenesis
Most of the early universe is QCD!
Dissipation could be relevant here:
Mean Free Path ~ de Broglie
€
η Shear viscosity
s Entropy density< ~ 0.1
Quantum Limit! “Perfect Fluid”
Ideal gas Ideal fluidLong mfp Short mfp
High dissipation Low dissipation
Data imply (D. Teaney, D. Molnar):
Conclusions•The early universe is straightforward to describe, given simplifying assumptions of isotropy, homogeneity, and thermal equilibrium.
•Strong interaction/hadron physics made it hard to understand T > 100 MeV ~ 1012 K.
•Transition to thermal QCD makes high temperatures tractable theoretically; but we are only now delivering on a 30-year-old promise to test it experimentally.
References
Freedman & Turner, “Measuring and understanding the universe”, Rev Mod Phys 75, 1433 (2003)
Kolb & Turner, The Early Universe, Westview (1990)
Dodelson, Modern Cosmology, Academic Press (2003)
Weinberg, Gravitation and Cosmology, Wiley (1972)
Weinberg, The First Three Minutes, Basic (1977, 1993)
Schutz, A First Course in General Relativity, Cambridge (1985)
Misner, Thorne, Wheeler, Gravitation, W.H.Freeman (1973)
Backup material
Side-to-beam view
Along-the-beam view
Hot Zone
Au+Au at √sNN = 200 GeV
STAR Experiment at RHIC
€
dτ 2 = −ds2 = dt( )2 − dx( )
2 − dy( )2 − dz( )
2
= d ′ t ( )2 − d ′ x ( )
2 − d ′ y ( )2 − d ′ z ( )
2
€
dx 0 ≡ dt dx1 ≡ dx dx 2 ≡ dy dx 3 ≡ dz
dτ 2 = −ds2 = gμν dx μ dxν
gμν =
1 0 0 0
0 −1 0 0
0 0 −1 0
0 0 0 −1
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
Metric
Tensor
Complete coordinate freedom! All physics is in g(x0,x1,x2,x3)
H. Minkowski German
“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)
x
t
t’
x’
Photons
Photons
E1
E1
E2
E2
E0
E0
B. Riemann German
Formalized non-Euclidean geometry (1854)
a(t) a Friedmann-Robertson-Walker (FRW) cosmology
Three basic solutions for a(t):
1. Relativistic gas, “radiation dominated”
P/ = 1/3 a-4 a(t)t1/2
2. Non-relativistic gas, “matter dominated”
P/ = 0 a-3 a(t)t2/3
3. “Cosmological-constant-dominated” or “vacuum-energy-dominated”
P/ = -1 constant a(t)eHt “de Sitter space”
€
T00 = ρ Energy density (in local rest frame)
€
˙ a
a
⎛
⎝ ⎜
⎞
⎠ ⎟2
= H 2 =8π
3Gρ −
1
r02a2
Curvature
€
Critical ≡3H 2
8πGρ
ρ Cr≡ Ω Ω =1⇒ Flat
Q: How does change during expansion?
Friedmann Equation 1 (=0 version)
€
˙ ̇ a
a= −
4πG
3ρ + 3P( )
Friedmann Equation 2 (Isen/Iso-tropic fluid,=0)
However, this cannot describe a static, non-empty FRW Universe.
Ac/De-celeration of the Universe’s expansion
€
If ρ (t) ≥ 0 and P(t) ≥ 0 then
˙ a (t) ≥ 0 and ˙ ̇ a (t) ≤ 0, and then
a(t) = 0 for some t
Necessity of a Big Bang!
Over-
€
Something
about space- time
curvature
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
=
Something
about
mass- energy
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
€
Metric Tensor gμν
Riemann Tensor Rαβγδ
Ricci Tensor Rμν = Rαμαν
Ricci Scalar R = Rαα
€
Stress- Energy Tensor Tμν
€
Rμν −1
2Rgμν
For continuity
≡ Gμν Einstein Tensor
1 2 4 4 3 4 4 − Λ
Unknown{ gμν = 8πGNewton
To match Newton
1 2 4 3 4 Tμν
€
Gμν = 8πTμν Einstein Field Equation(s)
B. Riemann GermanFormalized non-Euclidean geometry (1854)
G. Ricci-Curbastro Italian Tensor calculus (1888)
€
˙ ̇ a
a= −
4πG
3ρ + 3P( )
€
˙ a
a
⎛
⎝ ⎜
⎞
⎠ ⎟2
= H 2 =8π
3Gρ −
1
r02a2
With freedom to choose r02 and , we can arrange
to have a’=a’’=0 universe with finite matter density
Einstein 1917 “Einstein Closed, Static Universe”
disregarded after Hubble expansion discovered
- but -
“vacuum energy” acts just like
Friedmann 1 and 2:
€
Gμν − Λgμν = 8π Tμν rearrange Gμν = 8π Tμν + Λgμν
Gμν = 8π
ρ M +Λ
8π0 0 0
0 PM −Λ
8π0 0
0 0 PM −Λ
8π0
0 0 0 PM −Λ
8π
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
≡ 8πT Effμν
Re-introduce “cosmological constant”
Generalize (t)=Matter(t) +/8 P(t)=PMatter(t)
-/8
Cosmological constant acts like constant energy density, constant negative pressure, with EOS P/ = -1
T(t)
a(t)(t)
t
How do we relate T to a,? i.e. thermodynamics
The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting
Weinberg (1972): Considers Hagedorn-style limiting-temperature model, leads to a(t)t2/3|lnt|1/2; but concludes “…the present contents…depends only on the entropy per baryon…. In order to learn something about the behavior of the universe before the temperature dropped below 1012oK we need to look for fossils [relics]….”
Kolb & Turner (1990): “While we will not discuss the quark/hadron transition, the details and the nature (1st order, 2nd order, etc.) of this transition are of some cosmological interest, as local inhomogeneities in the baryon number density could possible affect…primordial nucleosythesis…”
Weinberg, Gravitation and Cosmology,
Wiley 1972
Golden Rule 5: Equilibrium is boring!Would you like to live in thermal equilibrium at 2.75oK?
Example of e+e- annihilation transferring entropy to photons, after neutrinos have already decoupled (relics).