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

≠