1 D. Kharzeev Nuclear Theory Group @ BNL Alice Club, CERN TH, May 14, 2007 Non-linear evolution in...
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Transcript of 1 D. Kharzeev Nuclear Theory Group @ BNL Alice Club, CERN TH, May 14, 2007 Non-linear evolution in...
1
D. Kharzeev Nuclear Theory Group @ BNL
Alice Club, CERN TH, May 14, 2007
Non-linear evolution in QCDand hadron multiplicity predictions for the LHC
Based on work with E. Levin, M. Nardi, K. Tuchin
2
Two questions:
1. What is the mechanism of multi-particle production at high energies in QCD?
2. What are the implications for high-energy evolution and for the energy dependence?
A possible answer:strong semi-classical color fields
3
Strings vs partons in high energy QCD
string picture:
color string = longitudinal color fields
parton picture:
“Weizsacker-Williams” gluons = transverse color fields
4
€
Aμ =e
4π R − v→
R→ ⎛
⎝ ⎜
⎞ ⎠ ⎟(1,v
→
)
• Lienard-Weichert potential of a moving charge
€
R2 = (z − z(t '))2 + x⊥2 (1− v 2)
• Electro-magnetic fields:
€
E→
=e
4π
1− v 2
(R − R→
v→
)3R→
− v→
R ⎛ ⎝ ⎜
⎞ ⎠ ⎟+
e
4π (R − R→
v→
)3R→
× R→
− v→
R ⎛ ⎝ ⎜
⎞ ⎠ ⎟× a
→ ⎛
⎝ ⎜
⎞
⎠ ⎟
€
H→
=R→
× E→
R
a
vR
E
≈Ez
What is the structure of the classical fields?warm-up: electrodynamics
transverselongitudinal
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The space-time picture of high-energy interactions in QCD
1. Fast (large y) partons live for a long time;2. Parton splitting probability is ~ s y - not small!
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The origin of classical background field
Gluons with large rapidity and large occupation numberact as a background field for the production of slower gluons
static field sources
“Color Glass Condensate”
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What is the dynamics of non-linear evolution in QCD?
Parton splitting in the background of the color field? (generalization of the linear QCD evolution equations - BFKL, DGLAP)
GLR, MQ,JIMWLK,BK equations
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Renormalization group
Emitted partons become a part of the classical fieldfor slower partons; “slow” and “fast” are relative
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Mean field approach: BK equation
Let us compute an imaginary part of the gluon propagator in the background field:
where the S-matrix is related to the imaginary scattering amplitude
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Equivalent form:
where
is the BFKL splitting kernel;initial conditions are provided e.g. by MV model:
Is this evolution equation unique?
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What are the properties of the color field at high energies?
The field created by faster moving partons is seen by the slower produced partons as:
• Static
• Constant in space
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Why static?
The lifetime of a field configuration is
(y is the rapidity distance from the beam);The ratio is
for BFKL,>>1
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Why constant in space?
at rapidity y, the field is constant at distances up to
gluon production occurs at y-y, at distances
The ratio is “large”: BFKL yields R ~ 10
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What is the mechanism of gluon production in strong, constant, static
color field at weak coupling? Schwinger-like gluon pair production:
whereSU(3): G.Nayak,P.Nieuwenhuizen,hep-ph/0504070
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Integrated spectrum:
Average transverse momentum (saturation scale):
Saturation momentum is a measure of the field strength
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Towards the evolution equation
the energy density of the field
grows with rapidity:
this is just the energy conservation!
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The evolution equation
Sudakov-type factor neededto avoid double counting(no gluons produced between Y and Y’)
DK, E. Levin,to appear
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Properties of the solution
for moderate energies, power growth with the intercept (for s ~ 0.3) ~ 0.25;
at very high energies, a universal limit!