Diffusive scaling and the high energy limit of DDIS

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Diffusive scaling and the high energy limit of
DDIS

• Yoshitaka Hatta
• (RIKEN BNL)

work done with E. Iancu, C. Marquet, G. Soyez, D.
Triantafyllopoulos Nucl.
Phys. A773 (2006) 95
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Outline

• Saturation in the BKJIMWLK equation
• DDIS in the context of saturation
• Beyond the mean field approximation
• Pomeron loop effects
• Application to DDIS, diffusive scaling

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QCD phase diagramLinear evolution
BFKL
DGLAP
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Gluon saturation
Saturation momentum
BFKL
DGLAP
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The B-JIMWLK equation
The dipole scattering amplitude
dipole kernel
An infinite hierarchy of coupled nonlinear
equations. Closed equation in the large Nc limit
(BK equation)
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Traveling wave solution
dipole size
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front
Geometric scaling
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Application to DIS
Dipole factorization
(Nikolaev Zakharov, 91)
integral dominated by
geometric scaling of
geometric scaling of
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Application to DDIS
minimal rapidity gap
satisfies the nonlinear Kovchegov-Levin equation
Note
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DDIS, Mean field results
The cross section involves the amplitude squared
Small size dipoles suppressed. Dominant
contributions come from the semihard region
slowly varying with
All dipoles equally absorbed (black disc limit)
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Beyond the BK-JIMWLK equation
Included in BK-JIMWLK
Gluon merging
Missing in BK-JIMWLK
merging splitting Pomeron loops
Gluon splitting
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Consequence of the gluon splitting Gluon
number fluctuation
Start with a single color dipole
boost
Salam, 96
The dipole (gluon) number fluctuates
event-by-event.
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BK equation with Gaussian noise

Iancu, Triantafyllopoulos, 04
BFKL merging splitting
The stochasticFKPP equation
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Universal behavior of the sFKPP equation
the Diffusive scaling
Front position (saturation scale ) becomes
a random variable
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Impact on DDIS
We have calculated the (one dipole),
and the (two dipoles) component at
Small dipoles not suppressed. Diffraction becomes
a hard process !

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Impact on DDIS (cont.)
Our result
valid for
dominates over even when
!
The fluctuations push up the saturation
physics to large
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Update on the (theory) phase diagram
Saturation (CGC)
cosmic ray, LHC ???
Diffusive scaling window
HERA ?
Geometric scaling window
BFKL DGLAP
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Summary

• We have presented the first analysis of the
  consequence
• of fluctuation in DIS/DDIS.
• Saturation momentum becomes a random variable.
• Cross-section is dominated by rare
  fluctuations
• (black spots) in the ensemble whose
  saturation momentum is
• Diffraction becomes a hard process.
  Cross-sections
• exhibit a new scalingthe diffusive scaling
  which eventually replaces the geometric scaling.