Theoretical Aspects of the Color Glass Condensate and Glasma
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Theoretical Aspects of the Color Glass Condensate and Glasma
CGC GlasmaInitial Singularity
sQGP Hadron Gas
Art due to S. Bass1
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Baryon:
3 quarks
3 quarks 1 gluon
…..
3 quarks and lots of gluons
The Hadron Wavefunction at High Energy
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Small x limit is high energy limit
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Where do all the gluons go?
Cross sections for hadrons rise very slowly with energy
But the gluon density rises
much more rapidly!The high energy limit is the high
gluon density limit.
Surely the density must saturate for fixed sizes of
gluons at high energy.
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What is the Color Glass Condensate?
Glue at large x generates glue at small x
Glue at small x is classical field
Time dilation -> Classical field is glassy
High phase space density -> Condensate
Phase space density:
Attractive potential Repulsive interactions
Density as high as it can be
Because the density is high is small
is big
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There must be a renormalization group
The x which separates high x sources from small x fields is arbitrary
Phobos multiplicity data High energy QCD “phase” diagram
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The CGC Path Integral:
The current source:
Rapidity:
The separation scale is in rapidity or longitudinal momentum
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The Renormalization Group Equation:
For strong and intermediate strength fields: H is second order in
It has no potential, and a non-linear kinetic energy term
Like diffusion
Wavefunction spreads for all time, and has universal limit: Universality at high energy 7
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What does a sheet of Colored Glass look like?
On the sheet is small
Independent of
small
big
Density of gluons per unit area
Lienard-Wiechart potentials
Random Color
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Fields in longitudinal space:
is a delta function on scales less than the inverse longitudinal cutoff
Gluon distribution is at scales larger than the
cutoff
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10CGC Gives Initial Conditions for QGP in Heavy Ion Collisions
Two sheets of colored glass collide
Glass melts into gluons and thermalize
QGP is made which expands into a mixed
phase of QGPand hadrons
“Instantaneously” develop longitudinal color E and B fields
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Before the collision only transverse E and B CGC fields
Color electric and magnetic monopoles
Almost instantaneous phase change to longitudinal E and B
The Glasma: 11
In forward light cone
generates correct sources on the light cone
Equal strength for magnetic and electric charge on average!
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Topological charge density is maximal:
Anomalous mass generation
In cosmology:
Anomalous Baryogenesis
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Different signs
Generate different chiralities and vorticity in the fluid.
Violates P and CP on an event by event basis
Integral vanishes initially
Classical equation do not generate net
topological charge.
Instabilities in these solutions will generate such charge, and can themalize the system
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Before collision, stability
After collisions, unstable
Quantum fluctuations can become as big as the classical field
Quantum fluctuations analogous to Hawking Radiation
Growth of instability generates turbulence => Kolmogorov spectrum
Analogous to Zeldovich spectrum of density fluctuations in cosmology
Topological mass generation
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Interactions of evaporated gluons with classical field is g x 1/g ~ 1 is
strong
Thermalization?
Wigner distribution of initial wavefunction gives seeds of
fluctuations.
These seeds grow when inserted into classical equations
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Fluctuation in saturated regions and 2-d Quantum Gravity?
What is the distribution of the sizes of saturated spots of
gluonic matter with size less than the saturation size
scale?
Such fluctuations can in principle dominate the
scattering out to very large momentum scales:
breakdown of factorization of hadron-hadron relative to
lepton hadronHow to compute scattering?
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2-d field theory: Dimensionless scalar theory
Liouville theory: 2-d conformal invariance:
Insert a source term:
Theory appears to be UV finite (unlike Liouville which is renormalizable) and conformal on distance scales
less than the saturation scale!
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16Summary
Successes:
Geometric scaling in DIS
Diffractive DIS
Shadowing in dA
Multiplicity in AA
Limiting fragmentation
Long range correlations
Total cross section
Pomeron, reggeon, odderon
CGC
Extended scaling
Perturbative