Transcript Sensitivity of the jet quenching observables to the temperature dependence of the energy loss F.

Sensitivity of the jet quenching
observables to the temperature
dependence of the energy loss
F. Scardina INFN-LNS Catania,
University of Messina
V. Greco, M. Di Toro
[Phys. Rev. C 82:054901, 2010]
International School on “Quark-Gluon Plasma and Heavy Ion Collisions:
past, present, future” Torino 08/03/2011
Outline
 Our simple model
 Quenching observables :
• Nuclear modification factor
1 d 2 N AA / dpT dy
RAA( pT ) 
N coll d 2 N pp / dpT dy
• Elliptic flow
v2  cos2 
p x2  p y2
p x2  p y2
• RAA(quarks)/RAA(gluons)
linked to the flavour dependence of ΔE
Open question
• Simultaneous description of both RAA and V2
is still a theoretical challenge – “azimuthal puzzle”
• High PT protons less suppressed than pions - flavor puzzle
 First results for LHC
Conclusion and future developments
z
y
x
Modelling jet quenching
Our model is based on the approximation by which jets lose energy in a bulk
medium that is expanding and cooling independently from the jets energy loss.
a) Initial condition
 Density profile r(t, r, f) for the
Bulk medium in the transverse
plane (Glauber Model)
 Hard partons distributions
- space coordinates (Glauber Model Ncoll)
- momenta coordinates (pQCD)
transverse plane
b) Eloss on particles propagating in straight lines (path-length)
3
 2 PT 0 
E 9 CR s3s


t r (t , r ,f0 )log
2 
t
4
 t(t ) 
Ex.
GLV
 s (T ) 
Constant
 s (T )  4 0 ln( Q2 )
with
Q2  (2T )
2
c) Hadronization by AKK fragmentation function
dN f
dNh
   dz 2 D f h ( z )
2
d ph
d pf
f
z=ph/pf
Application of the model to evaluate RAA
Au+Au at 200 AGeV
π0
RAA Integrated for pT> 6 GeV
 For pT<5 GeV there are non-perturbative mechanisms (coalescence)
 RAA(pT), RAA(Npart) does not allow discrimination of Eloss(T)
Open issues
p

 Flavor puzzle RAA
 RAA
RAA Au+Au central 0-12%
High PT protons less
suppressed than pions
RAA(q)/RAA(g)≤1
But protons should be more suppressed
because they come more from gluons…
…and gluons are
more suppressed
than quarks
ΔE for gluons=9/4*
ΔE for quarks
Does it mean?
RAA(q)/RAA(g)=9/4
 Azimuthal puzzle
Simultaneous description of both RAA and V2 is still a theoretical challenge
The experimental data show V2 above theoretical prediction
One solution to azimuthal puzzle: Eloss near Tc
Predominant energy loss at low T
[Liao, Shuryak Phys. Rev. Lett. 102 (2009)]
Solution of azimuthal puzzle?
We analyze relation between T dependence of
quenching and v2, with RAA fixed on data
20-30%
they are strongly correlated
RAA (quark)/RAA(gluon) and T dependence of energy loss
RAA fixed on experimental data for pions (RAA=0.2)
ΔEgluon =9/4*ΔEquark
The ratio is related to T dependence of energy loss, it is not necessarily 9/4
The ratio is lower if quenching mainly occur close to Tc
Energy Loss
The sensitivity to the amount of Eloss is damped already
by a small percentage of partons that don’t lose energy
The sensitivity to the amount of Eloss is damped already
by a small percentage of partons that don’t lose energy
If energy loss occurs at low T all particles lose
a large amount of energy
If energy loss is predominant at high T particles
near the surface lose a small amount energy
A solution to flavor puzzle: Jet q<g conversion
Inelastic collisions cause a change
in the flavor q<->g
conversion rate is given by the collisional
width
d 3p3
1
g 2 d 3p 2
d 3p 4
C  K C
2 E1  (2 )3 2 E2 (2 )3 2 E3 (2 )3 2 E4
 f (p 2 )1  f (p3 )1  f (p 4 ) M 1234
 (2 )  (4 ) ( p1  p2  p3  p4 )
4
[Ko, Liu, Zhang Phys. Rev C 75]
[Liu, Fries Phys. Rev C 77]
We also have introduced this
mechanism in our code:
results confirmed
RAA(q)/RAA(g)
2
Correlation RAA (quark)/RAA (gluon) - V2
(Wood-Saxon) RAA (PT) fixed on experimental data for pions
To get close to experimental data:
 E stronger close to phase
transition is needed
 flavor conversion becomes more
necessary
Eloss at high T
GLVc
GLV α(T)
Eloss at low T
Eloss at low T
EoS lattice QCD
Exp
But If E is stronger close to Tc
deviations of r(T) from the free gas
approximation become important ->
use lQCD EoS
T r
1/ 3
T r
(T )
Fit to Lattice QCD
Lattice QCD EoS state moves
V2 and RAA(q)/RAA(g) to the right
 Tc 

T 
 (T )   a
1
3
n
a= 0.15; n=1.89
First results for LHC
We use less extreme T
dependencies of the energy loss
V2 for RHIC and LHC
First results for LHC RAA(gluon)/RAA(quark)
The rises are due to the changes in
the slope of the partons spectra
Conclusions and Perspective
 Different ΔE(T) generate very different RAA(q)/RAA (g) and v2
 Observed v2 and RAA(q)/RAA(g) seem to suggest a ΔE stronger near Tc and
a strong flavor conversion
 Sensitive to deviation from the free gas expansion (EoS) for Eloss (T~Tc)
 Our first results for LHC seem to confirm these indications.
Future Developments
 transport code takes into account collisional and radiative energy loss
joined to a dynamics consistent with the used EoS
p


 
   p F   m  m  p* f ( x, p )  I 22  I 23  ...
[Catania]
[Greiner Group]
Initial condition
 Density profile for the bulk
In longitudinal direction evolves according to the Bjorken expansion at the velocity of
light
The initial transverse density profile can be modelled in two different way
1. Glauber Model partecipant distribution
2. Sharp elliptic shape
Dal profilo di densita otteniamo il profilo di T
T r
1
3
 High PT partons distribution
 Momenta space
The spectra are calculated
in the NLO pQCD scheme
Af
dN

2
d pT (1  pT B f )n f
The value of the parameters Af ,Bf and nf are taken from
Ref. [Ko, Liu, Zhang Phys. Rev C 75][Liu, Fries Phys. Rev C 77]
 Coordinates space (Ncoll)
Ideal gas
Glauber Model
De Broglie << RNucleoni
r (r )  C
r0
rR
1  exp

 a 
b
ˆ A  x  , y , z A  dzA
Tˆ A (x , y )   r
2


TˆAB( x, y ,b )  TˆA( x, y ,b )TˆB ( x, y ,b )
NN
Ncoll ( x, y,b )  A B TˆAB( x, y,b ) inel
N part ( x, y ,b )
 The trasverse density profile for the bulk
is proportional to the partecipant
distribution N Part
 The hard parton distribution in space
coordinates scales with the number of binary
Nucleon collision
Proiezione lungo l’asse x
Density profile for the bulk
Density profile for the jet
Hadronization
The parton distribution after the
quenching are employed to
evaluate the hadron spectrum by
indipendent jet fragmentation
using the AKK fragmentation
function D
(z)
f h
z=ph/pp
[S. Albino, B. A. Kniehl, and G. Kramer, Nucl. Phys B597]
dN f
dNh
   dz 2 D f h ( z )
2
d ph
d pf
f
r  s  T
r p T
Ratio RAA(q)/RAA(g)
We consider a simplified case in which all
quarks lose the the same amount of energy DE
and all gluons lose their energy according to
DE=9/4*DE
Spectra are shifted by a quantity equal to
the energy lost
Partons that finally emerge with an energy pT
Are those which before quenching had an
energy pT+e*η where η=1 for quarks and 9/4
for gluons
RAA ( pT ) 
f ( pT  E )
f ( pT )
f g ( pT )
RAA (q ) f q ( pT  E )
There is no reason why this ratio must be

RAA (g )
f q ( pT ) f g ( pT  (9 4)E ) 9/4
RAA (quark)/RAA(gluon): profile and T dependence of energy loss
Over simplified case: all quark lose the the
same amount of energy and all gluons lose
ΔEg =9/4*ΔEquark
Minimal realistic case: 2 classes of quarks
undergoing different quenching, always
with ΔEg
=9/4*ΔEq
The ratio is dominated by the way the
energy loss is distributed among partons
Sharp Ellipse: direct relation T<->τ
Wood Saxon: No direct relation T<->τ
(Surface -> low T also at early times)
quenching at low T (later tau)
• Many particles escape without Eloss;
those in the inner part must be strongly
quenched  blue thin line)
quenching at high T
• particles lose energy early;
all particle lose energy (dotted line)
≠
≠
quenching at low T
• DE is strong in a layer on the surface -> all
particles across this layer so all particles
lose energy
quenching at high T
• No DE at the surface but only in the inner
part of the fireball (strong DE); particles in
the surface escape almost without Eloss