Strong Chromofields and Baryon Stopping in Ultrarelativistic Heavy Ion Collisions

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Strong Chromofields and Baryon Stopping in
Ultrarelativistic Heavy Ion Collisions

• K. Lyakhov
• Frankfurt International Graduate School for
  Science (FIGSS)

Scientific advisor-Prof.Dr.I.N.Mishustin
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Motivation

• Goal to describe the space-time
• development of the HI reaction at RHIC and LHC
  energies.

• What are the mechanisms of baryon stopping?
• How QGP is produced and equilibrated?
• How do the data for d-Au and Au-Au collisions
  constrain models?

K.J.Eskola, hep-ph/9911350
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Outline

• Net-baryons are coming from the initial
  nucleus.
• In the initial stage of parton collisions
  net-baryons loose part of their energy.
• Chromofields are generated at the initial stage
  of collision
• It is demonstrated that strong chromofields can
  contribute significantly to rapidity loss of
  leading baryons

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The model
Assumptions

• Color charges are induced on nuclear sheets
• Chromofields are produced in the space between
  nucleus and they depend only on proper time
• The chromofield exerts a force acting on color
  charge of each slab
• At later times chromofields decay via partons
  production
• The initial energy density stored in the
  chromofield is assumed proportional to the number
  of nucleus nucleus collisions

• After the collision at t0 the trajectories of
  projectile and target slabs are affected by the
  energy-momentum loss due to generation of
  classical fields and production of massless
  partons.

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Evolution of produced plasma

• Plasma evolution is described by ideal
  hydrodynamics

• The energy-momentum tensor can be represented
  as
• where ,
• and partonic contribution is
• The equation of state was chosen for ideal
  relativistic gas of massless quarks and gluons
  where is the sound
  velocity
• Assuming Bjorken velocity field
• hydrodynamical equations simplify to
• where r.h.s corresponds to the decay rate of
  chromofield

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Chromofield decay
Schwinger mechanism

• The pair creation rate in uniform external
  electric field

• This leads to the power law of chromofield decay
• field relaxation time is taken of order 1
  fm/c

Gyulassy, Gatow
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Chromofield decay
Color Glass Condensate

• In the Color Glass Condensate model the gluon
  field evolution is governed by equations derived
  from QCD.
• Initial gluon distribution function can be
  described by classical fields.
• After collision this fields have not only
  transversal but also longitudinal component
• Fourier transform over the transverse coordinate
  of perturbative solution of classical Yang-Mills
  equations
• Therefore the field energy density is
• Saturation scale defines a
  border between perturbative and nonperturbative
  regimes of QCD

MacLerran, Venugopolan, Kajantie
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Time evolution of plasma and chromofield energy
density
The maximum value of the plasma energy density is
22 of the initial field energy density for power
field decay law and 43 for CGC.
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Time evolution of plasma with Joule heating
T.Matsui,PRD ,36, 114 (1987)
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Equations of motion of baryonic slabs

• In Glauber model the average number of
  participants is

• Distribution of baryon number in transverse
  plane is given by integration of Woods- Saxon
  distribution

• The average number of collisions is

• Baryon energy differs from nucleon mass due to
  internal excitation

• The energy-momentum of slabs is parameterized as
• where the initial slab mass is
  , and -collective slab rapidity

• From the energy-momentum conservation we get

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Slab equations of motion
where -slab momentum
in the local frame moving with rapidity
-slab energy in local frame
-plasma enthalpy density
-total pressure taken with negative sign

• the initial conditions for the slab rapidities
  

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At RHIC the mid-rapidity region is almost
net-proton free.
Linear Increase in rapidity seems to saturate at
RHIC.
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Baryon rapidity loss in nucleus nucleus
collisions.
plasma
no plasma
N
Net-baryon rapidity loss cab be explained by
action of chromofields with the initial energy
density of about To compare Bjorken estimate
for initial plasma energy density is
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Net-baryon rapidity distribution in Au-Au
collisions.
Net-baryons spectra are calculated by the
formula where weight function is gaussian with
width 0.4
no plasma
plasma
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Partonic rapidity distribution

• The invariant momentum spectrum of partons is
  given by Cooper-Frye formula
• where integration is carried out over the fluid
  hypersurface
• Local thermal equilibrium is assumed in fluid
• Therefore partonic yield is regulated by
  temperature
• where and

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Partonic rapidity distribution in Au-Au collisions
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Conclusions

• Strong chromofields should give rise to
  significant baryon stopping
• Our model allows to get information about the
  initial energy density of the chromofields
• Calculated partonic rapidity distribution can be
  used as a input for further hydrodynamical
  calculations

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Thank You for attention