F. Scardina INFN-LNS Catania, F. Scardina INFN-LNS Catania, University of MessinaUniversity of Messina

V. Greco, M. Di V. Greco, M. Di ToroToro

Jet quenching Dynamics

[Based on arXiv:1009.1261 (today) ]

OutlineOutline Our simple modelOur simple model Quenching observables :Quenching observables :• Nuclear modification factorNuclear modification factor

• RRAAAA(quarks)/R(quarks)/RAAAA(gluons)(gluons) linked to the flavour linked to the flavour dependence of dependence of ΔΔEE

Open questions Open questions

• Simultaneous description of both Simultaneous description of both RRAAAA and and VV22 is yet theoretical challenge – is yet theoretical challenge – “azimuthal puzzle”“azimuthal puzzle”

• High PHigh PTT protons less suppressed than pions protons less suppressed than pions - - flavor puzzleflavor puzzle

Conclusion and future developmentsConclusion and future developments

dydp/Nd

dydp/Nd

N)p(R

Tpp

TAA

collTAA 2

21 22

22

2 2yx

yx

pp

ppcosv

xy z

• Elliptic flowElliptic flow

Modelling jet quenchingModelling 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. Initial conditionInitial condition

Hadronization with Hadronization with AKK fragmentation AKK fragmentation function D(z)function D(z)

Density profile for the Bulk medium

Hard partons distributions in momenta coordinates (pQCD) in space (Ncoll) Energy loss (gluon Energy loss (gluon

bremsstrahlung,GLV) bremsstrahlung,GLV)

20

0

3 2

4

9

TsR P

log,r,CE

0 ,r,Glauber Model (Wood Saxon)Sharp Ellipse

3s

TsConstant

204 QlnTs with 22 2 TQ

Application of the model to evaluate Application of the model to evaluate AAR

AAR Integrated for pT> 6 GeV

For there are non-perturbative mechanisms (coalescence)

GeVPT 5

π0 Au+Au at 200 AGeV

Open questions Open questions

Azimuthal puzzle Azimuthal puzzle Simultaneous description of both RSimultaneous description of both RAAAA and V and V22 is yet a theoretical is yet a theoretical challengechallengeThe experimental data show V2 above theoretical prediction

High PHigh PTT protons less protons less suppressed than suppressed than pionspions

RA

A Au

+A

u c

en

tral

0-1

2%

protons

pions

because they come more from gluons…

…and gluons are more suppressed than quarks ΔΔE for E for gluons=9/4*gluons=9/4* Δ ΔE E for quarksfor quarks

But protons should be more But protons should be more suppressed suppressed

RAA(q)/RAA(g)≤1

Flavor puzzleFlavor puzzle AA

pAA RR

RAA(q)/RAA(g)=9/4

Does it mean?

One solution to azimuthal puzzle: Energy One solution to azimuthal puzzle: Energy loss near Tcloss near Tc

Sharp Ellipse

Wood Saxon

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 they are strongly

related

20-30% 20-30%

RRAAAA (quark)/ (quark)/RRAAAA(gluon) and Temperature dependence of (gluon) and Temperature dependence of energy lossenergy loss

The ratio is related to temperature dependence of energy loss it is not necessarely 9/4The ratio is lower if quenching mainly occur close to Tc

RAA fixed on experimental data for pions (RAA=0.2)

Sharp Ellipse

4

9

RRAAAA (quark)/ (quark)/ R RAAAA (gluon) (gluon) profile dependence profile dependence Wood Saxon

The two profiles show opposite behavior

Rigid case is not adequate

Sharp Ellipse

Over simplified case: all quarks lose the same amount of energy and all

gluons lose ΔEgluon =9/4*ΔEquark

Minimal realistic case: 2 classes of quarks quenched + unquenched,

always with ΔEg =9/4*ΔEq

The ratio is dominated by those The ratio is dominated by those particles which do not lose energyparticles which do not lose energy

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 (red dot dash line)

quenching at low T• E is strong in a layer on the surface -> all particles must cross this layer so all particles lose energy

≠

RRAAAA (quark)/R (quark)/RAAAA(gluon): profile and T dependence of (gluon): profile and T dependence of energy lossenergy loss

One solution to flavor puzzle:Jet conversionOne solution to flavor puzzle:Jet 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

To solve it inelastic collisions that cause a change of the flavor have been invoked[See Ko talk]The conversion rate is given by the collisional width

432144

2

3412432

434

3

333

3

23

23

2

1

2

11

2222222

1

pppp

Mfff

E

d

E

d

E

dg

EKCC

ppp

ppp

RAA(q)/RAA(g)

without conversion Kc=0conversion kc=6

Eloss at high T

GLVcGLV α(T)Eloss at low T

Exp

Correlation RCorrelation RAAAA (quark)/R (quark)/RAAAA (gluon)-V (gluon)-V22

(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 )T(T

To get close to experimental data: DE stronger close to phase transition is need

But If E is stronger close to Tc deviations of (T) from the free gas approximation become important -> use lQCD EoS

n

c

T

TaT

3

1

a= 0.15; n=1.89

flavor conversion becomes more necessary

Eloss at low T EoS lattice QCD

20-30%

Conclusions and Conclusions and PerspectivePerspective

If one goes beyond RAA, a realistic profile for the fireball is needed

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 + a strong flavor conversion

Sensitive to deviation from the free gas expansion (EoS) for Eloss (T~Tc)

What goes on for LHC conditions?

Future DevelopmentsFuture Developments transport code takes into account collisional and radiative energy loss joint 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

T 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 Bp

A

pd

dN

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,b

xˆy,xT̂

2

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

aRr

expCr1

0

)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

pd

dNhf

f

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 Tp

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

Epf

pf

pf

Epf

gR

qR

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 ratio is dominated by the way the energy loss is distributed the energy loss is distributed among partonsamong 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

≠

RRAAAA (quark)/R (quark)/RAAAA(gluon): profile and T dependence of (gluon): profile and T dependence of energy lossenergy loss

≠