F. Scardina INFN-LNS Catania, University of Messina V. Greco, M. Di Toro
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Transcript of F. Scardina INFN-LNS Catania, University of Messina V. Greco, M. Di Toro
F. Scardina INFN-LNS Catania, University of MessinaV. Greco, M. Di Toro
Sensitivity of the jet quenching observables to the temperature dependence of the energy loss
[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
• 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
dydp/Nddydp/Nd
N)p(R
Tpp
TAA
collTAA 2
21 22
22
2 2yx
yx
pppp
cosv
xy z
• Elliptic flow
Modelling jet quenchingOur 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.
Density profile r(t, r, f) for the
Bulk medium in the transverse plane (Glauber Model)
a) Initial condition
Hard partons distributions - space coordinates (Glauber Model Ncoll)
- momenta coordinates (pQCD)
transverse plane
( )( )
20
0
3 24
9tt
ftrtt
TsR Plog,r,CE 3s
( )TsConstant
( ) ( ) 204 QlnTs
with ( )22 2 TQ
b) Eloss on particles propagating in straight lines (path-length)
Ex. GLV
c) Hadronization by AKK fragmentation function
)z(Dpd
dNdz
pddN
hff
f
fh
h 22 z=ph/pf
Application of the model to evaluate RAA
RAA Integrated for pT> 6 GeV
π0 Au+Au at 200 AGeV
For pT<5 GeV there are non-perturbative mechanisms (coalescence)
RAA(pT), RAA(Npart) does not allow discrimination of Eloss(T)
Open issues
Azimuthal puzzle Simultaneous description of both RAA and V2 is still a theoretical challengeThe experimental data show V2 above theoretical prediction
High PT protons less suppressed than pions
R AA A
u+Au
cen
tral
0-
12%
protons
pions
because they come more from gluons…
…and gluons are more suppressed than quarks ΔE for gluons=9/4* ΔE for quarks
But protons should be more suppressed
RAA(q)/RAA(g)≤1
Flavor puzzle AA
pAA RR
RAA(q)/RAA(g)=9/4
Does it mean?
they are strongly correlated
20-30%
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
RAA (quark)/RAA(gluon) and T dependence of energy lossRAA 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 9/4The ratio is lower if quenching mainly occur close to Tc
Energy Loss
The sensitivity to the amount of Eloss is damped alreadyby a small percentage of partons that don’t lose energy
initial
The sensitivity to the amount of Eloss is damped alreadyby a small percentage of partons that don’t lose energy
If energy loss is predominant at high T particles near the surface lose a small amount energy
If energy loss occurs at low T all particles lose a large amount of energy
A solution to flavor puzzle: Jet q<g conversion
[Ko, Liu, Zhang Phys. Rev C 75][Liu, Fries Phys. Rev C 77]
We also have introduced this mechanism in our code:
results confirmed
conversion rate is given by the collisional width
( ) ( ) ( )( ) ( ) ( )
( ) ( )( )432144
23412432
434
3
333
3
23
23
2
1
2
11
22222221
pppp
Mfff
Ed
Ed
Edg
EKCC
ppp
ppp
RAA(q)/RAA(g)
Inelastic collisions cause a change in the flavor q<->g
without
conversion
with conversion
Eloss at high TGLVcGLV α(T)Eloss at low T
Exp
Correlation RAA (quark)/RAA (gluon) - V2(Wood-Saxon) RAA (PT) fixed on experimental data for pions
Lattice QCD EoS state moves V2 and RAA(q)/RAA(g) to the right
31 /T r )T(T r
To get close to experimental data: E stronger close to phase
transition is needed
But If E is stronger close to Tc deviations of r(T) from the free gas approximation become important -> use lQCD EoS
( )n
c
TTaT
31
a= 0.15; n=1.89
flavor conversion becomes more necessary
Eloss at low T EoS lattice QCD
Fit to Lattice QCD
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.
...II)p,x(fmmFpp *p
3222
Future Developments transport code takes into account collisional and radiative
energy loss joined to a dynamics consistent with the used EoS
[Greiner Group][Catania]
Initial condition Density profile for the bulkIn longitudinal direction evolves according to the Bjorken expansion at the velocity of light
1. Glauber Model partecipant distribution2. Sharp elliptic shape
Momenta space
High PT partons distribution
Coordinates space (Ncoll)
Dal profilo di densita otteniamo il profilo di T 31
rT Ideal gas
The initial transverse density profile can be modelled in two different way
The spectra are calculated in the NLO pQCD scheme
( ) fnfT
f
T BpA
pddN
12
[Ko, Liu, Zhang Phys. Rev C 75][Liu, Fries Phys. Rev C 77]The value of the parameters Af ,Bf and nf are taken from Ref.
Glauber Model
( ) AAAA dzz,y,bxˆy,xT̂
2
r
NNinelABcoll )b,y,x(T̂BA)b,y,x(N
NucleoniBroglieDe R<<
The trasverse density profile for the bulk is proportional to the partecipant distribution
The hard parton distribution in space coordinates scales with the number of binary Nucleon collision
PartN
( )
aRrexp
Cr1
0rr
)b,y,x(T̂)b,y,x(T̂)b,y,x(T̂ BAAB
)b,y,x(N part
Proiezione lungo l’asse x
Density profile for the bulkDensity profile for the jet
Hadronization
)z(Dpd
dNdz
pddN
hff
f
fh
h 22
z=ph/pp
[S. Albino, B. A. Kniehl, and G. Kramer, Nucl. Phys B597]
The parton distribution after the quenching are employed to evaluate the hadron spectrum by indipendent jet fragmentation using the AKK fragmentation function )z(D hf
Ts r Tpr
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
( ) ( )( )T
TTAA pf
EpfpR
( )( )
( )( )
( )( )( )Epfpf
pfEpf
gRqR
Tg
Tg
Tq
Tq
AA
AA
49
There is no reason why this ratio must be 9/4
Over simplified case: all quark lose the the same amount of energy and all gluons lose ΔEg =9/4*ΔEquarkMinimal realistic case: 2 classes of quarks undergoing different quenching, always with ΔEg =9/4*ΔEqThe ratio is dominated by the way the energy loss is distributed among partonsSharp Ellipse: direct relation T<->τ
Wood Saxon: No direct relation T<->τ(Surface -> low T also at early times)
quenching at high T • particles lose energy early;all particle lose energy (dotted line)
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
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 low T• DE is strong in a layer on the surface
-> all particles across this layer so all particles lose energy
≠
RAA (quark)/RAA(gluon): profile and T dependence of energy loss
≠