The High Energy Limit of QCD

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The High Energy Limit of QCD
The high energy limit is E -gt infinity at fixed
momentum transfer Not short distance limit which
is E -gt infinity at fixed angle
Related Questions
How do gluons and quarks arise in hadrons?
What are the possible forms of high density
matter?
Claim The high energy limit is controlled by a
universal, high energy density form of gluonic
matter The Color Glass Condensate In collisions,
this matter produces a Glasma with interesting
topolgical and dynamical properties
Lecture I The Color Glass Condensate Lecture
II The Glasma
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How do we think about a high energy hadron?
Work in fast moving frame
High Energy Limit is Small x Limit
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The Gluon Wall
Wavefunction has 3 quarks 3 quarks plus 1
gluon 3 quarks plus 2 gluon . 3 quarks plus
many gluons
Important matrix elements at high energies have
lots of gluons in them
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In RHIC Collisions Au-Au at 100GeV/Nucleon in
each beam About 1000 slow moving (small x)
particles are made in central collisions
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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 -gt
Classical field is glassy High phase space
density -gt 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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Why is the Color Glass Condensate Important?
It is a new universal form of matter Matter
Carries energy Separation of gluons is small
compared to size of system Number of gluons is
large
New Can only be made and probed in high energy
collsions
Universal Independent of hadron,
renormalization group equations have a universal
solution. Universality ltgt Fundamental
It is a theory of Origin of glue and sea quarks
in hadrons Cross sections Initial conditions for
formation of Quark Gluon Plasma in heavy ion
collisions
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What does a sheet of Colored Glass look like?
On the sheet
is small
Independent of
big
small
Lienard-Wiechart potentials Random Color
Density of gluons per unit area
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The Color Glass Condensate Explains Growth of
Gluons at Small x
Renormalization group equation predicts
Gluon pile up at fixed size until
gluons with strength
act like a hard sphere
Once one size scale is filled Move to smaller
size scale Typical momentum scale grows
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The CGC Explains Slow Growth of Total Cross
Section
Transverse distribution of gluons
Transverse profile set by initial conditions
Size is determined when probe sees a fixed number
of particles at some transverse distance
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CGC Explains Qualitative Features of
Electron-Hadron Scattering
Q is resolution momentum of photon, x is that of
struck quark

• Function only of a particular combination of Q
  and x
• Scaling relation

Works for
Can successfully describe quark and gluon
distributions at small x and wide range of Q
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CGC 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
Mystery The QGP is very strongly
interacting Arnold and Moore suggest heating may
be due to instabilities in melting CGC
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CGC predicted particle production at RHIC
Proportionality constant can be computed.
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CGC provides a theory of shadowing (modification
of quark and gluon distributions in nuclei)
Two effects Multiple scattering more particles
at high pT CGC modification of evolution
equations gt less particles
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Data from dA collisions at RHIC Consistent with
CGC
Look for fragments of deuteron since they measure
them smallest x properties of the nucleus
Back to back jet correlations seen in STAR?
Detailed studies of x dependence?
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Future studies of CGC at RHIC, LHC, and eRHIC
At RHIC Systematic pA studies Many exciting
possibilities Study and discover the QGP
Discover the CGC
LHC Can study at very small x with very high
resolution Study the CGC
eRHIC Precision experiments and tests Careful
and systematic study of CGC
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Glasma
Definition The matter which is produced by the
Color Glass Condensate immediately after the
collision It is not a glass, evolving on a
natural time scale It has components which are
highly coherent,
Components which are particle like
Components of strength in between
Initially it has large longitudinal color
electric and color magnetic fields, and maximal
topological charge density
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Choose A 0 in backward light cone. In left and
right halves, pure gauge. Discontinuity across
light cone to match color charge sources on light
cone Field is not pure gauge in forward lightcone
Physical motivation Renormalization group
description. In center of mass frame, degrees of
freedom with
are coherent fields. Larger y are sources
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Before the collision, two sheets of mutually
transverse color electric and color magnetic
fields. Boosted Coulomb fields Random in
color Thickness of sheets is
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Initial fields
In radial gauge,
the fields in the forward light cone are
Assume boost invariant solution
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Boundary conditions are determined by solving
equations across the light cone Infinitesmally
after the collision there are No transverse
fields Longitudinal magnetic and electric fields
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These fields have a local topological charge
density Chern-Simons charge
The Chern-Simons charge density is maximal!
and has a transverse correlation length
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How do the sources of color magnetic and color
electric field arise?
In forward light cone, the vector potential from
one nucleus can multiply the CGC field from the
other. Equal and opposite densities of charge
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However Glasma fields are initial conditions,
not a solution to time independent equation of
motion
Unlike the constant field where there is no
magnetic field
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The Glasma has three components Coherent
classical fields Hard particles Degrees of
freedom which can be described as either hard
particles or coherent fields
The Glasma has mostly evaporated by a time
During this time, scattering among the hard modes
(parton cascade) is not important
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Interactions in the coherent fields takes place
on a scale of order 1/Qs Because of coherence,
interactions of hard particles with the classical
fields, g x 1/g 1 Also take place on a time
scale 1/Qs Very rapid strongly interacting system
But boost invariance is a problem, as this does
not allow longitudinal momentum to become
thermalized Important for two reasons Almost
certainly instabilities of the hard-soft coupled
system under boost non-invariant
perturbations Can these instabilities generate
either rapid thermalization or isotropization of
momentum?
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Consequence of nonzero Chern-Simons Charge
Vorticity Generation
Positively charged particle accelerates along E,
rotates in clockwise direction Negatively charged
particle accelerates along -E, Rotates in
anticlockwise direction Net vorticity generation
Physical origin of t Hooft anomaly
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Exciting times for theory
Beginning of a complete description of high
energy limit of QCD Must understand the
collective excitations of the CGC pomerons,
reggeons, odderons Need to understand
interactions of these collective excitations
ploops or Pomeron loops
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