Open Questions in Jet Quenching Theory

1

Open Questions in Jet Quenching Theory

Ivan Vitev

QCD Workshop, Brookhaven National Laboratory July 17-21, 2006 , Upton, NY

2

Outline of the Talk

Final state interactions in the QGP: Radiative energy loss Recursive solutions for multiple parton scattering Energy, system size dependence and QGP properties

Heavy versus light quarks in p+p and p+A: Heavy quark correlations Cold nuclear matter effects for heavy versus light quarks

Initial state energy loss: Evidence for energy loss in cold nuclei in p+A Differential distributions for medium-induced initial state gluon bremsstrahlung Phenomenological implications

I.V., Phys.Lett.B 639 (2006), I.V. in preparationBased on:I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200

Conclusions:

3

In-Medium Modification of the PQCD Cross Sections

• The way to understand medium effects on hadron cross sections in the framework of PQCD is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron wave function (FF)

Range of the interaction in matter

QGP: 2

22 2

2 / 94

1/ 2

9 / 8

s

q

Cold nuclear matter:

21( )

2 el q 21( )

2 el q 2eld

d q

Calculated in the Born approximation

2 2 2 16

fD

ng T

1~D

D

0 ~ 1.2r fm

Scattering in the medium

4

Understanding the LPM Effect• Bremsstrahlung is the most efficient way to lose energy since it carries a fraction of the energy

p

k xp k

2

2

1 1 ( )ln ln

2 2g k xp

yk k

• Acceleration: radiation

1q1q 2q 3q 4q 4q

5q 5q 6q 6q 7q

f

1

1

1

1 1

1 1

1 1

...2 2

( ... )( ... ) 2 2

...,

( ... )

... ...

( ... ) ( ... )

n

m

m

m n

m n

m n

i ii i

i i

i i j ji i j j

i i j j

k q qkH C

k k q q

k q q k q qB

k q q k q q

• Formation time: coherence effects

1

1

2 21 1

0

21

...

( ),

( ... )m

m

f i f

i ii i f

k k q

k k

k q q

k

• Onset of coherence • Full coherence1

f gD

1

gfD

L

LPM = Landau-Pomeranchuk-Migdal

5

Building up Multiple ScatteringApproximations that allow to treat many scatterings:

1 1( ... ) ( ... )

n ni i i ik q q k q qp k

k p

Single Born scattering Double Born scattering

1 1 1

1 1

1

0

1

0

... ..

(

.

...

...

) [ , ]

ˆ ( , ; ) ( , ; )

(

[

, ; )

1 ( )

2, ]

n n

n

n

n

v

n

n

nn i i i

i z

i z

n n

n

i

i i

N

n el i i

D A x k a

q

c A x k c

A x k

B T Aae

c a

c

e

1

0

1

0

1 1

1 1

1

... ...

.(

..

..

)

.

ˆ ( , ; ) ( , ; )

- ( , ; )

1 - ( )

2

2

[ , ]

2

n

n

n

n

n

v

n

n

n i i i i

i i

N

n el i

R A

n n

i

i z

i z

n

A

V A x k c A x k c

A x k

B

C C

a

cT

q c a

C

e

e A

6

Medium-Induced Radiation in the Final State

• Includes interference with the radiation from hard scattering

Coherence phases(LPM effect)

Color current propagators

1

... ...2 1

2 222 2 2

1 1

1... 1... ...

10

1

- cos c

( )( )

2 s

1

o

njj i el

n ng g R s

n n

L zi

g ii i

e

n m n

i

m

m m

k kk n

n

n

l

mn

i

kk k

d z

z

d dd q q

N dN Ck k

dk d k dk d k d q

B z zC

Number of scatterings Momentum transfers

nz

,n nq a

,n nq a

nznz

,n nq a

,n nq a

nz

,n nq a

,n nq a ++ˆ = R

1

1...1

1 1 1 1

1 1 1 1

......2

... ...... ...

† † ˆ

n

ni in

n n

n n

ng i i

i i

i i i ii i i i

dNk Tr A A

dk d k

A A AD D V V R A

M.Gyulassy,P.Levai,I.V., Nucl.Phys.B 594 (2001)

7

Analytic Approximations and Numerical Results

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

J.D.Bjorken, Phys.Rev.D 27 (1983)

0( ) ( )

2 2

f

L L LE

l

mean numberof scatterings

Landau-Pomeranchuk-Migdal (LPM) effect

0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb

8

Jets and Hadrons from PQCD

P’xbP’

P

xaP

0

0

Pc

Pd

Pc / zc

Pd / zd

1

2

2

1

1

2 21 2 1

11/

1 2/1min

2

222

2

1

( ) (( )

) ( )( ) h c

h d

a sb

abcd aT T b

ab cdN

T T z

hhN

D zdz D z

x x

p p x

d

dydyd p d p SM

z x

ffd j p as®

D -= å ò

d

d

pd

z {

X

X

11

2

1/1

1 1

12

2

2min min 1

( )(

()

))(

a b

sa ab b

ab

h

cd a bx x

ab c

T

dc

hNN

ddx d

D z

zx x x

x xSd pM

ydas

ff ®= å ò ò

Can also incorporate Cronin effect:

2 ( )T med Td k f k

Kinematic modifications

Nuclear medium

9

System Size Dependence of Jet Quenching

I.V., Phys.Lett.B 639 (2006)

• Absolute scale comparisons can and should be done at large pT

• Similar pT dependence (flat) in Au+Au and Cu+Cu

• In classes with the same we find numerically the same suppression

partNAAR

(For example central Cu+Cu and mid central Au+Au)

1' 2 2

/ /

0

12

/

0

(1 ),(1 )

1( , ) ,

1 1

1

( )

) + ,(

cc c c

vach q h q

vacg

h g

zp p z

zD z Q d D Q

zd D Q

P

dN

d

Reduction of the hard scattering cross section

1

i

i

E

E E

( )P Probability density -

0A A X

10

Tomographic Summary

SPS 2-3.5 0.8 210-240 1.5-2.5 1.4-2 200-350

RHIC 7-10 0.6 380-400 14-20 6-7 800-1200

LHC 17-28 0.2 710-850 190-400 18-23 2000-3500

SPS RHIC LHC

F.Karsch, Nucl.Phys.A698 (2002)

0[ ]fm [ ]T MeV [ ]tot fm3[ / ]GeV fm /gdN dy

36.8 , 175 , 1 /Au c cR fm T MeV GeV fm

*dE GeV

dz fm

D. d’Enterria, Eur.Phys.J C (2005)

11

Transport Coefficients in Thermalized QGP

3e

2exp

0

xp 0

1200

1( ) , 120

0

6

( ) 1

.

7

g

g

dN

dydN

A fmA dy

f

m

m

f

• Experimental: Bjorken expansion• Theoretical: Gluon dominated plasma2

/ 30

32

#( ) [

1 4#

1 (2 )

where # 2( ) 8( ), [3] 1.2

3]the Tory p

p dpDoF

e

DoF polarizati

D

on

oFT

colo

T

r

400T MeV• Energy density

4

( )30 [3]

( )theory theory T TT

3exp 0

318 . 1( ) 00 0.14 .GeV fm GeV fm

• Transport coefficients (not a good measure for expanding medium)2

, 2 2.5 ( 0.3 0.5)4sD

gggT

0.8 1D GeV 2

2

9 1

2,gg s

Dg gg

2 29ˆ

2D

g

sq

2 1ˆ 1 2.5 .GeVq fm

0.75 0.42g fm

• Define the average for Bjorken0

20

2ˆ( )ˆ

( )

L

zq z zdzq

L z

2 10.35 0.8 .ˆ 5 GeVq fm

12

• Initial state energy loss + HTS

• High twist shadowing only

2 2( , ) ,1

xx Q Q

1/3

min bias/ , 0.0175E E kA k

Implementation of initial state E-loss

S.S.Adler et al., nucl-ex/0603017

New Directions for Energy Loss Calculations • One possible discussion

• A new direction: energy loss in cold nuclear matter, initial state

Provide simulations including the geometry, combination of elastic and radiative E-loss, jet topologies …

0d Au X • It is a challenging theoretical problem that has not been solved (you will see the solution)

• Of immediate relevance to pQCD effects in cold nuclear matter p+A

13

High Twist Shadowing in DIS

222 ( ) 2 ( ) 2

2

1/

2

3( 1)( , ) , = 1 ,dynLT LTA

T T T

mxF x Q F

Ax Q F x Q

QA

QA

J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)

x = energy = mass

• Dynamical parton mass (QED analogy): 1/32 2dynm A

Final state coherent scattering

14

• Shadowing parameterizations: (not)

2( , )LT LTS S x Q

• Dynamical calculations of high twist shadowing: (not)

1 2ˆ( ( ); ( , ( )))HT HTS S q g t z z

• Energy loss: in combination with HTS (yes)

T.Alber et al., E.Phys.J.C 2 (1998)

Cold Nuclear Matter Energy Loss

• Circular arguments should be avoided

• Nigh statistics 200 GeV p+A measurements will certainly reduce error bars, however …

• Most useful measurement – low energy p+A run (only at RHIC II)

15

Medium-Induced Radiation in the Initial State

• Bertsch-Gunion case with interference

1

...22... 1... 2... 1... 2... 1..

2 2 21

. 1... ..

1 1

2 22

.

0

1

(( )

cos2

)

njj i el

i iel i

m

kkn n n n n nn m n m n

n ng g R

k

s

n n i

L zi

g i

dd q q

d q

dN dN Ck

B B B B

kdk d k dk

d

zk

z

d

z

2

n

m

1

...22... 1... 2... 1... 2... 1..

2 2 21

. 1... ..

1 1

2 22

.

0

1

(( )

cos2

)

njj i el

i iel i

m

kkn n n n n nn m n m n

n ng g R

k

s

n n i

L zi

g i

dd q q

d q

dN dN Ck

B B B B

kdk d k dk

d

zk

z

d

z

2... 1...

1

...2

2

cos2 n n

n

m

n

kk nkH B z

• Realistic initial state medium induced radiation

Asymptotic

,t t

Asymptotic t

Large Q2

Lt z L

I.V. in preparation

16

Energy Loss to First Order in Opacity

• Bertsch-Gunion Energy Loss

• Initial-State Energy Loss

• Final-State Energy Loss

2/ 4 2

2 2 2 2 2 20

2

2(

( ))g

g s effR sCdNd q

q

k k q

L

d d k q

2/ 4 2

2 2 20 2 2

2

2

2 2( )

2

( )

k -q sin

k -q

gs effR s

g

g

k q

k k q

k

k

CdNd

q

Lq

d d k

L

2/ 4 2

2 2 2 2 2

2

2 2

2 2

2 2 2

0

( )

2 2 n

(

)

si

(

)

g s

g

effR s

g

q

k k q

q k q kk

k

CdNd q

d d

L

L

k q k

k q

k

Qualitatively

0ln (1)g

QE Lconst

E

2 20ln /

g

E EE Lconst

E E

0ln (2)

(2) (1)

g

QE Lconst

E

const const

New

Old

17

Numerical Results For Quark Energy Loss

Fractional energy loss

At any order in opacity we require( )

21

0g in

i

dN

dyd k

• Energetic quark jets can easily lose 20-30% of their energy, gluon jets x / 9 / 4A FC C • Coherence effects lead to cancellation of the medium-induced radiation

Radiation intensity

• Initial state E-loss is much smaller than the incoherent Bertsch-Gunion limit

• Initial state E-loss is much larger than final state energy loss in cold nuclei

1 contribution to gdN

x xdx

2 2 2 2 2

0 qk k Q x M M.Djordgevic, M.Gyulassy, Nucl.Phys.A (2004)

18

Path Length Dependence of E-Loss

• Bertsch-Gunion – linear dependence on L by definition

• Final state E-loss – approaches quadratic dependence on L, important for the centrality dependence and elliptic flow

• Initial state E-loss – approaches linear dependence on L, important for the centrality dependence in p+A reactions

19

pQCD Calculations of Heavy Quarks

• The contribution of logarithms is small in measurable pT ranges

Schematic NLO and NNLLO, NLO, NNLO expansion

LL, NLL, NNLL expansion

m/pT, (m/pT)2 power corrections

1, 0T

m

p

Will return to power corrections

• The quarks are treated as “heavy” – in the fixed order calculation. Implies that NLO generates the PDF for charm and bottom (mostly)

( ), ( ) coefficient functionsA m B m

• The new scale, mass, implies large logarithms, but …

M.Cacciari, P.Nason, JHEP 9805 (1998)

20

Phenomenological Results

• Description of open charm at the Tevatron is within uncertainties but not perfect

M.Cacciari, P.Nason, JHEP 0309 (2003)

Scales:/ 2, , 2T TTmm m

Comparison to the Tevatron data Comparison to the RHIC data

R.Vogt et al., Phys.Rev.Lett.95 (2005)

• At RHIC perturbative calculations under predict the data by factor of 2 – 4. Whether it is experimental systematic, incomplete theory or both – open question

• Residual large scale uncertainties – should be careful with consistent choices

( ) ( ) 0 ln ( ) ln ( )s sH H

21

Numerical Results and Partonic Sub-Processes

• Meaningful K-factors (otherwise K>4)• Anti-correlation between K and the hardness of fragmentation r• If (LO,c-PDF) ~(NLO,no c-PDF) what are the corrections from (NLO,c-PDF)?

PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002) FFs: Braaten et al., Phys.Rev.D51 (1995)Partonic sub-processes

22

Hadron Composition of C (B) Triggered Jets

• Can constrain the hardness of D and B meson fragmentation

Possibility for new measurements of heavy flavor production at RHIC

D (B) meson

“Few” hadrons

“Many” soft hadrons

D (B) meson

• Can clarify the underlying hard scattering processes and open charm production mechanisms

2 2/ / ,~ ( , ) / ( , )D c h q gD z Q D z Q

Robust

23

HTS for Light Hadrons and Open Charm

• Very similar dynamical shadowing for light hadrons and heavy quarks

• Insufficient to explain the forward rapidity data

• Single and double inclusive cross sections are similarly suppressed

Single inclusive particles Away-side correlations

J.W.Qiu, I.V., Phys.Lett.B632 (2006)

2( )( ) b

b ab cdb

xF x M

xf

®=

21/3

2( ) ( 1)b b b d

d

F x F x x C At m

1 2ˆ( ( ); ( , ( )))HT HTS S q g t z z

I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200

24

Energy Loss and High Twist Shadowing

• Main difference is much more pT independent suppression as compared to high twist shadowing

Single inclusive particles Double inclusive yields (away-side)

Same• Very similar e-loss effects for light hadron and heavy quark spectra• Single and double inclusive cross sections are similarly suppressed


25

• Cancellation of collinear radiation – large angle soft gluons and correspondingly soft hadrons

• Beyond the cancellation region - well defined power dependence

• The importance – hard scattering has the same power dependence

I.V., Phys.Lett.B630 (2005)

Effects of Medium-Induced Radiation

2 4

1~

gdN

dyd k k

4

1~

d

dt p

26

Phenomenological Implications

• Suppression at forward rapidity – from energy loss of the incoming partons

• Enhancement at backward rapidity – comes from the redistribution of the lost energy

• Consistent pQCD code is still to be developed

Correlated!

PHENIX Collaboration, Phys.Rev.Lett. (2005)

27

Conclusions

In-medim interactions can be understood following the history of a jet in a hard scatter:

Coherent final state interactions:

Shadowing is dynamically generated and arises from the final state Shadowing for D mesons and light pions is similar Initial state interactions:

Transverse momentum diffusion and Cronin effect Energy loss and rapidity asymmetry in p+A – new theoretical results

Radiative energy loss in the QGP:

Predicted supession for Cu+Cu versus centrality and pT QGP suppression is consistent with perturbative interaction of jets in the medium

Modification of di-jets: Gluon feedback is important for di-hadrons at large angle Flow leads to deflection of the jet+gluons, so be exp. determined

28

Initial State Elastic Scatterings

Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system

t = ¥

nz

,n nq a

nznznz

,n nq a ++ ,n nq a

,n nq a

,n nq a

,n nq a

† †n n n n nR̂ ˆ ˆD D ˆ ˆV V

The approximate solution is that of a 2D diffusion(Neglect and )p3( ( ) )kO k

Unitarization of multiple scattering

2

22 2

2 / 94

1/ 2

9 / 8

s

q

=

0

21

-2

1

1- - ..( ) ( ).

!-

niel

n

in e ii

nf

l

dd qdN e d

nq

d qNp qpc s

sc¥

= =

= å Õò

=

2( ) ( )i k kdN d^ ^

=

2

2

2

1,( )

2

k

f edN k

cmx

mp xc

^-

^= /Lc l=

Initial condition Solution

22 2 1For 2 , 2

2k k

kcm cmx x

^= - =D D

PP

Mean number of scatterings

Elastic scattering cross section

Implemented in the PQCD approach as broadening of the initial state partonsk

a) Initial state elastic scattering

29

Cronin Effect

p W X

p Be X Default0d Au X

Good description at mid rapidity

Wrong sign at forward rapidity

Data


Cronin effect: enhancement of cross sectionsat intermediate transverse momenta relativeto the binary scaled p+p

A.Accardi, CERN yellow report, references therein

30

Heavy Quarks in p+p and p+A

• Anti-correlation between K and the hardness of fragmentation r• Non-trivial hadron composition of c and b triggered jets

PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002)

FFs: Braaten et al., Phys.Rev.D51 (1995)

Robust

New possibility: hadron compositionof heavy quark triggered jets

31

In-Medium Modification of the PQCD Cross Sections• The way to understand medium effects on hadron cross sections in the framework of PQCD is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron wave function (FF)

• Jet interactions in the medium result in kinematic modifications to the hard scattering cross section that are process dependent

d) Final state interactions in the QGP Jet quenching

e) Final state interactions in the QGP Large angle correlations, Di-Jet suppression, Deflection of jets by flow

a) Initial state interactions Elastic scattering and Cronin effect

c) Final state interactions Dynamical shadowing, Generalization to heavy quarks

Cold nuclear matter effects are present at times

b) Initial state interactions Energy loss and forward Y suppression

32

Process Dependence of Power Corrections

• Power corrections are process dependent and not separable in PDFs and FFs

• The function F(xb) contains the small xb dependence

Enhancement ( )

Suppression ( )ˆ 0t

ˆ 0s (For example DY)

(For example forward rapidity)

• Similar process dependence in single spin asymmetries S.Brodsky et al, Phys.Rev.D65 (2002)

S.Brodsky et al, Phys.Lett.B530 (2002)

• Shadowing is dynamically generated in the hadronic collision

33

Universal Features of Jet Quenching

2/3

22

2

2

( (1 ) /(1 )

( ) /

1

1 '

T TAA

T

pa

T

t

n

r

d p dyd pR

d p dyd p

N

20( ) nn

T T T

d a a

dyd p p p p

2 /3/ 23 ' part

gE L dNA k

E A dyN

Baseline:

Fractional energy loss:

I.V., Phys.Lett.B in press, hep-ph/0603010

Prediction: 2/3ln AA partR N

Natural variables1/31/3 2/3 2/3,part part

g

t

g

par

L dNL A A

A dy

dNA

dy

N N

N

Scalings:

Suppression:

Approximately universal behavior

34

Numerical Results for Jet E-Loss

• Small probability not to radiate

• Small fractional energy loss at large ET

0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb

1 1

0 0

( ') 1, ( ')E

d P d PE

0 1gNP e

1 1

0 0

( ') , ( ')g gg

dN dN Ed N d

d d E

0 ( ) ( ) gNP e

…

…

1

ni

i E

M.Gyulassy, P.Levai, I.V., Phys.Lett.B (2002)

3

2

chg d

d d

dN

y y

dN

d

• Scales in the QGP

1200

gdN

dy

0.8 1D GeV

0.75 0.42g fm

11 5 .ˆ 2. Gq eV fm

Initial parameters

35

0A A X

System Size Dependence of Jet Quenching

I.V., Phys.Lett.B in press, hep-ph/0603010

• Absolute scale comparisons can and should be done at large pT

• Similar pT dependence (flat) in Au+Au and Cu+Cu

• In classes with the same we find numerically the same suppression

partNAAR

For example central Cu+Cu and mid central Au+Au

• Future tests of high energy nuclear physics at the LHC

36

Energy Loss and Di-Jets

One way of incorporating energy loss:

Satisfies the momentum sum rule

0

0

/E E

A+A

• “Standard” quenching of leadinghadrons• Redistribution of the lost energy in “soft” hadrons

RHIC

LHC

Away-side yieldsSingle inclusive particles


e) QGP effects on di-jet production

37

Radiation Distribution and Flow Effects

2

2 2 2 20

1

( ( ) )

el

el

d

d q q q

Gluon number distribution without or with q0 = 1 GeV

• Mechanical analogy, Theoretical derivation

022 2

0 0

0

2

2

21

1

( )

( )cos

2

gmed el

el

k q qddNd q

d d k d q k q q

k q q z

• We cannot confirm the prescription

q0

N.Armesto et al., Phys.Rev.C (2005)

Result: same energy loss andshifted reference frame

Problem

02k qk0k q 0k q 02k q k

Solution: expand about 0k q Show that vanishes 0( )O q

02k qk0k q 0k q 02k q k

• Important for deflected jets, to be seen in experiment

38

39

Cancellation of collinear radiation

40

41

42





2/ 4 2

2 2 2 2 20

2/ 4 2

2 2 2 2 20

2

10

2

2 2

( )

( )

( )

gs effR s

gs effs

g

g

R

LCdNd q

d d k q

CdNd q

d

d

d k

qL

k k q

z

q

B

2/ 4 2

2 2 2 2 2

2

1 1

2

22 2

0 0

2/ 4 2

2 2 2 2 20

k -q2 1-cos

k -q2sin

( ) k -

( )

) q(

L

g

g s effR s

g s effR s

g g

CdNd q

d d k q

CdNd q

d d k

zC B

k

k q k

k k q

d

k

z

LL

q

2/ 4 2

2 2 2 2 20

2/ 4 2

2

22

1 1

2 2 2

2 2 2 2 2

0

220 2 2

| | 2 cos

22 sin

( ( )

( )

( ) )

gs effR s

gs effR

L

g

g

s

g

k zB H B

k

q q k q kk

CdNd q

d d k q

CdNd q

d d k q k k q k k

d z

L

q k

L

k

Qualitatively

2

(1)g

LEconst

E

2 20ln /

g

E EE Lconst

E E

2

(2)

(2) (1)

g

LEconst

E

const const

43

Non-Perturbative Scales• Chiral perturbation theory

• (Generalized) vector dominance model

2 2min max( ) ( ) 4Q pQCD Q PT f

2 2 2min ( ) max( , )A VQ pQCD m m

Implementation2 2 2 2 2

0 qk k Q x M

22 2 20 0.94 1/ 0.2NQ m GeV fm

92f MeV

J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)

• Coherent high twist shadowing 2 2 2

min ( ) 0.8NQ pQCD m GeV

2min ( ) 1.15Q pQCD GeV

2 20.12 GeV

• Bertsch-Gunion2 2 2

min ( ) 0.6Q pQCD m GeV

0.35 , 1gGeV fm

• QCD evolution of FFs and PDFs2 2 2

min 0( ) 0.4 2Q pQCD Q GeV

44

Numerical Results For Quark Energy Loss

Fractional energy loss

At any order in opacity we require( )

21

0g in

i

dN

dyd k

• Energetic quark jets can easily lose 20-30% of their energy, gluon jets x / 9 / 4A FC C

• Coherence effects lead to cancellation of the medium-induced radiation

Radiation intensity

• Initial state E-loss is much smaller than the incoherent Bertsch-Gunion limit

• Initial state E-loss is much larger than final state energy loss in cold nuclei

1 contribution to gdN

x xdx

II. Coherent Power Corrections

Data from: NMC

Shadowing

Ivan Vitev, LANL

Longitudinal size:

Transverse size: 1/Q

1/ 2 Nm xIf then 0z r 0.1x

If then exceedthe parton size

NQ m

Deviation from A-scaling: A A

What remains for theory: power corrections in DIS - suppression

FSI are always present:

S.Brodsky et al.

46

Medium-Induced Bremsstrahlung

2Vacuum DGLAP type

+

+ +

+ + +

+ +

+ ...

+

+

Calculate everything else

p

p

Example of hardscattering

• Calculating the multiple scatterings in the plasma

1~D

D

2 2 16

fD

ng T

Potential

02 2~ ( )s

D

V qq

M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001)

Reaction operator: (Cross section level )

Medium

†S SAdvantage: applicable for elastic, inelastic and coherent scattering controlled approach to coherent radiation (LPM)

47

Comparison to Other Models

• How do you build from T = 400 MeV2

2ˆ 14 /g

q GeV fm

LHC: from T = 1 GeV

22ˆ 100 /

g

q GeV fm

B.Cole, QM 2005 proceedings

Strong coupling used as a parameter• Find T = 370 MeV (OK)

S.Turbide et al., Phs.Rev.C. (2005)

I.V., M.Gyulassy, Phys.Rev.Lett. (2002)

I.V. Phys.Lett.B in press

• Find dNg/dy = 1200 (OK)

3

2

chg d

d d

dN

y y

dN

d

G.Paic et al., Euro Phys.J C (2005)

K.Eskola et al., Phys.Rev.D (2005)

• Find (NOT OK)2ˆ 14 /q GeV fm

• These are not equivalent descriptions – the medium properties differ by more thanan order of magnitude (sometimes close to two)

48

The Source of the Problem

2200 GeVˆ 14 GeV /fmq

25500 GeVˆ 100 GeV /fmq

2/ˆ 2Lqc Typical gluon energy

( 5 )c L fm

350 GeV

2650 GeV

• Note that the region of PT at RHIC is 10-20 GeV and at the LHC 100-200 GeV

cR L

R

~10000

~100000

Energy momentumviolation

Problem

Problem

Problem

Negative gluon number and jet enhancement from energy loss

Negative probability density

C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003)

2200 GeVˆ 0.4 GeV /fmq 11 GeV ~500

GLV

• Symptomatic of problems in the underlying model of energy loss

A useful table

Realistic

0 gNP e

49

Analytic Limits of Delta E

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

- transport coefficient

- effective gluon rapidity density

2ˆ /q /gdN dy

M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86 (2001)

00( ) ( )

v c

• Controlled approach to coherence GLV

,k

q

k q

Includes the fluctuations of the gluonmomentum and energy

• Average implementations in the largenumber of scatterings limit

22 1 2 1( )( )

cos cos2f

z z z z k q

l

2 2~k nBDMPS, AMY

• Calculate differential spectra in ,k • Calculate the energy loss

Static:

BJ expansion: BJ+2D

Different dynamics REQUIRES different solutions

50

Energy Loss and High Twist Shadowing

• Main difference is much more pT independent suppression as compared to high twist shadowing

Single inclusive particles Double inclusive yields (away-side)

Same• Very similar e-loss effects for light hadron and heavy quark spectra• Single and double inclusive cross sections are similarly suppressed


51

Future Directions of Jet Interaction Studies

• Self consistency of the description of interactions in cold nuclear matter

I.V., in preparation

• Regimes of initial state energy loss

Is there a full Reaction Operator (GLV-like) expression via a formal solution to recurrence relations?

Cronin effect

What is the energy loss for such momentum transfer from the medium?

2 22 / gQ L 2 2 1/3Q A

52





2/ 4 2

2 2 2 2 20

2/ 4 2

2 2 2 2 20

2

10

2

2 2

( )

( )

( )

gs effR s

gs effs

g

g

R

LCdNd q

d d k q

CdNd q

d

d

d k

qL

k k q

z

q

B

2/ 4 2

2 2 2 2 2

2

1 1

2

22 2

0 0

2/ 4 2

2 2 2 2 20

k -q2 1-cos

k -q2sin

( ) k -

( )

) q(

L

g

g s effR s

g s effR s

g g

CdNd q

d d k q

CdNd q

d d k

zC B

k

k q k

k k q

d

k

z

LL

q

2/ 4 2

2 2 2 2 20

2/ 4 2

2

22

1 1

2 2 2

2 2 2 2 2

0

220 2 2

| | 2 cos

22 sin

( ( )

( )

( ) )

gs effR s

gs effR

L

g

g

s

g

k zB H B

k

q q k q kk

CdNd q

d d k q

CdNd q

d d k q k k q k k

d z

L

q k

L

k

Qualitatively

2

(1)g

LEconst

E

2 20ln /

g

E EE Lconst

E E

2

(2)

(2) (1)

g

LEconst

E

const const

New

Meaning of the expansion in “n”

Documents

Open Questions in Jet Quenching Theory