bfkl equation at finite temperature
DESCRIPTION
BFKL equation at finite temperature. Kazuaki Ohnishi (Yonsei Univ.) In collaboration with Su Houng Lee (Yonsei Univ.). arXiv:0707.1451 [hep-ph]. Introduction Color Glass Condensate at zero T BFKL Eq. at finite T Summary. 1. Introduction. Relativistic Heavy Ion Collision experiments. - PowerPoint PPT PresentationTRANSCRIPT
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BFKL equation at finite temperature
Kazuaki Ohnishi (Yonsei Univ.)
In collaboration with Su Houng Lee (Yonsei Univ.)
1.Introduction2.Color Glass Condensate at zero T3.BFKL Eq. at finite T4.Summary
arXiv:0707.1451 [hep-ph]
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1. IntroductionRelativistic Heavy Ion Collision experiments
QGP
Hadron gas
z
t
nucleus
(RHIC,LHC)
Quark-Gluon Plasma
light-cone
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Success of Hydrodynamic description• Ideal fluid with no dissipation
• Early thermalization: Just after collision?
(<1 fm/c at RHIC? Even earlier at LHC?)
What is Initial Condition for Hydrodynamic expansion?
Before Collision (Thermalization?) After (Expansion)
Relativistic Heavy Ion Collision experiments
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Small-x gluon distribution in Nucleon
Nucleon Structure DIS (Deep Inelastic Scattering)
Gluon distribution (Zeus data)
• BFKL eq.
• Unitarity violation
Saturation at small x
Color Glass Condensate
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McLerran & Venugopalan (1994)Jalilian-Marian, Kovner, Leonidov & Weigert (1997)Iancu, Leonidov & McLerran(2001)
CGC is a successful framework to explain saturation
small x partons short life time
large x partons (valence partons) long life time
“static” color charge at light-conegluon radiation
Separation of scale
Color Glass Condensate
(cf)
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“static” color charge at light-cone
small x
Recombination
Saturation regime
Color Glass Condensate
BFKL eq. JIMWLK eq.
(Jalilian-Marian,Iancu,McLerran,Wegert,Leonidov,Kovner)
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Color Glass Condensate
“Phase diagram” of high energy hadron
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Valence partons (large x partons) are intactand keep staying on light-cone
If thermalization takes place just after the collision, valence partonsradiate soft gluons into finite temperature medium.
CGC at finite temperature (Thermal BFKL & Thermal JIMWLK eq.)
Initial Condition for Hydrodynamic expansion
Bjorken picture:
Relativistic Heavy Ion Collision experiments (revisited)
Before Collision (Thermalization?) After (Expansion)
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Jet Quenching
Jet Quenching The energetic parton radiates soft gluons (Casalderrey-Solana & X.N.Wang: arXiv:0705.1352)
We need thermal BFKL (JIMWLK) eq.
High energy collision between jet and QGP
QGP
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2. CGC at zero temperature• Partition func. for CGC
Partition func for soft gluon at fixed
Averaging with weight func for
• Gluon distribution func.
1. Solve classical YM eq. at fixed
(cf. Coulomb potential for QED)
Static (time-independent) solution
2. Average over with
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• RG equation for
If we integrate out the hard modes of momentum shell ,
then the fluctuation is renormalized into
RG eq. for
BFKL eq. & JIMWLK eq.
BFKL eq.
:unintegrated gluon distribution
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3. BFKL eq. at finite temperature
Real-time formalism for finite T field theory (Alves,Das&Perez:PRD66(2002)125008)
C : complex time contour
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1. Classical solution
: time independent same as at zero temperature
2. RG eq. for
: induced charge
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• Evaluation of induced charge correlators
Virtual BFKL kernel
Real BFKL kernel
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Saturation regime is reached sooner than expected by vacuum BFKL eq.
Thermal BFKL eq.
Bose enhancement factor
de Vega & Lipatov: PLB578 (2004)335 (“BFKL pomeron at non-zero temperature and…”)
different from ours
Note
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4. Summary
• CGC at finite temperature Initial Condition for heavy ion collision
BFKL eq. at finite temperature
• Bose enhancement will increase soft gluons more rapidly than in vacuum.
• Thermal JIMWLK eq. will be interesting