Ivan Vitev&

New Theoretical Approachesto Heavy Flavor Suppression

Ivan Vitev, T-16 and P-25, LANL A. Adil and I.V., hep-ph/0611109, H. van Hees I.V. and R. Rapp, in progress

• Energy loss in QCD – application to light / heavy hadrons • Implementation in heavy quark diffusion simulations • Alternative theory of heavy flavor suppression in the QGP• Conclusions

Ivan Vitev&

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

Light Hadron Quenching in A+A

Establishing the E-loss mechanism

2q

0 3p p0 'p

3 'p

2q

0 3p p0 'p

3 'p

• Collisional:

• Radiative:

/ 4 2220

( )coll el

sdE ddq z

qE q

dz d

.( , )colldEconst E

dz

0

raddE E

dz X

min

1 22

1 1 1( , )

rad

R xq

dEC x dx d k f k q

dz x kE

Very important: Laldau-Pomeranchuk-Migdal effect

Important: mass dependence

Ivan Vitev&

S. Wicks et al., nucl-th/0512076

• Radiative Energy Loss using (D)GLV (both c + b)

• Radiative + Collisional + Geometry (both c + b) (overestimated)

• Deviation by a factor of two

• Is it accidental or is it symptomatic?

Non-Photonic Electron / Heavy Flavor Quenching

• Single electron measurements (presumably from heavy quarks) may be problematic

11

(1 ) (1 )

2

2 22

2 2

22

2

,g

n ngm x M

m

xE

k k k

x Mx

p Ek k

M.Djordjevic, M.Gyulassy, Nucl.Phys.A (2004)

Ivan Vitev&

Langevin Simulations of C- / B-Quark Diffusion

Fokker-Plank diffusion equation

• Expansion of gain / loss terms to second order

Equilibration is imposed by Einstein’s fluctuation-dissipation relation:

H. van Hees, R. Rapp, Phys.Rev.C71 (2005)

( , )( , )( ,( , ) )ii

i ijiA p

f p tp f p tB p

t p pt t

• Model of quark-resonance interaction near the QCD phase transition

( ) (), ,) ( )( iT t E tB Ap p pt

( , )iA p t - drag ~ equilibration1/

( , )jiB p t - diffusion ~ fluctuation1/

• Efficient at

• Include e-loss at high pT

resonances M

Ivan Vitev&

Collisional versus Radiative Energy Loss

Radiative energy loss is dominant except for b-quarks and very small systems

Input in a Langevin simulation of heavy quark diffusionH. van Hees, I.V., R. Rapp, in preparation• Drag coefficient:

1( , )i

i

i

Ap t

p tp

1

2( , )ji

j ipp

pt

tB

• Diffusion coefficient:

Two regimes (light partons):

jet coll radt L E E

jet coll radt L E E

g

Ivan Vitev&

Transport + Quenching Approach

• The suppression and v2 are large when e-loss and q-resonance interactions are combined

• Normal hierarchy: c quarks are significantly more suppressed than b-quarks

Numerical results for heavy quark diffusionH. van Hees, I.V., R. Rapp, in preparationResults are preliminary

Ivan Vitev&

Conceptually Different Approach to D / B

• Fragmentation and dissociation of hadrons from heavy quarks inside the QGP

• Problem: treated in the same way as light quarks

D B

20 fm 1.5 fm 0.4 fmform ( 10 )Tp GeV

PartonHadron

p

zp

(1 )z p

~ QCDk

B

D

QGP extent

2 2 2

form

(0.2 . ) 2 (1 )1

(1 ) (1 )

/(1 )

h q

Q

GeV fm z z py

p k z m z z M

y

2

, ,02

qq

Mp p

p

2 2

, ,2

hh

k mp zp k

zp

2

(1 ) , ,2(1 )g

kp z p k

z p

+

C.Y.Wong, Phys.Rev.C 72, (2005)

Ivan Vitev&

Light Cone Wave Functions

• Distribution of internal momenta

…and their distortion

A.Adil, I.V., hep-ph/0611109

S.Brodsky, D.S.Hwang, B.Q.Ma, I.Schmidt, Nucl.Phys.B 592 (2001)

2

32

; ,2 2

( ,

)

; ,

ni i

Mi i

i i i

i i i

dx d kP P

x

i k x P

k x

x P

2

2

222 (1 ) ( )

(

4 4

4

,1

( ))

Q qm mE

k x x

x xk x xp

2 2

surv. surv., 01 1q q

P L P L

• Heavy meson acoplanarity

• Distortion of the light cone wave function (meson decay)

2 22

surv. (* ( , ), )f iP L dxd k x kx k

2 22 2q

LK

Ivan Vitev&

Heavy Meson Dissociation at RHIC and LHC

Coupled rate equations

• The asymptotic solution in the QGP - sensitive to t0~0.6 fm and expansion dynamics

• Features of energy loss

• B-mesons as suppressed as D-mesons at pT~ 10 GeV (unique feature)

A.Adil, I.V., hep-ph/0611109

1

/20

1

/20

( , ) ( , )

( / , )

( / , )

( , )

( / , )

( , )

( / , )

1

1 1 + ( )

1

1 1

(

+ ( )

, ) ( , )

form T

diss T

diss T

for

t t

Q H

t t

m

H

H H

Q

T T

H

QT T

T

QT

T

Q

f

f p

p t

p x t

p t

p z

dx xx

dz

f p

t f

t f p t

p x t

f p z tzt

z

t

D

p

1, 1x z

Ivan Vitev&

Quenching of Non-Photonic Electrons

A.Adil, I.V., hep-ph/0611109• PYTHIA used to decay all B- and D-mesons / baryons into (e++e-)

Predictions also made for Cu+Cu (RHIC) and Pb+Pb (LHC)

• Suppression RAA(pT) ~ 0.25 is large

• B-mesons are included. They give a major contribution to (e++e-)

1

/( ; ) 1/n

ii

B b Df c

• Similar to light , however, different physics mechanism

0

2

2coll

(/

)/

ee

AAAA

TT

epp T

dN dyd p

N d dy pp

dR

Ivan Vitev&

Summary of Open Heavy Flavor Suppression

Langevin simulation of heavy quark diffusion • Calculated drag and diffusion from the collisional and radiative e-loss • Combined with a chiral model of quark-resonance interactions: obtained

large v2 and RAA . Work in progress• Normal suppression hierarchy: B- much less suppressed than D- mesons

Collisional QGP-induced B- / D-meson dissociation• Derived formation and dissociation times in the QGP. They are short • Solved the set of coupled rate equations. More sensitive to QGP properties and formation / expansion dynamics than e-loss• Found that suppression of non-photonic electrons from heavy mesons, including B, is large. Not inconsistent with light pions • B-mesons are as suppressed as D-mesons at pT ~ 10 GeV, unique

Toward experimental resolution of the B- / D- puzzle • Identify the B- and D-meson contribution to the inclusive electron spectra and the suppression factor RAA separately for Bs and Ds

Ivan Vitev&

Outline of the Talk

Energy loss in QCD

• Radiative and collisional energy loss, recent developments • Application to A+A collisions and p+A collisions

Applications to heavy quarks • Discrepancy between PQCD and c- and b-quark quenching• Transport+quenching approach to D- and B mesons

Alternative theory of heavy flavor suppression• In-medium formation and dissociation of D- and B- mesons• Suppression of non-photonic electrons

Conclusions

I.V., work in progressA.Adil and I.V., hep-ph/0611109H. van Hees I.V. and R. Rapp, work in progress

Based upon:

Ivan Vitev&

• Collisional: / 4 2220

( )coll el

sdE ddq z

qE q

dz d

Arises from the acceleration of the charges in the target. No significant mass dependence

2

0

1coll qdE

dz Q

/ 0EE E 2q

0 3p p0 'p

3 'p

Types of Energy Loss

• Radiative:min

1 22

1 1 1( , )

rad

R xq

dEC x dx d k f k q

dz x kE

0

raddE E

dz X

2q

0 3p p0 'p

3 'p

Arises from the acceleration of the incident charge.Can have significant mass dependence

/ 0EE E

/ EE E const Much more efficient

Ivan Vitev&

• 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 xpy

k k

• Acceleration: radiation

1q 1q 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 coherence1f g

D

1gf

D

L

LPM

Understanding the LPM Effect

Ivan Vitev&

• Bertsch-Gunion Energy Loss

• Initial-State Energy Loss

• Final-State Energy Loss

0

(1) lng

E L Econst

E Q

2 20ln /

(3)g

E QE Lconst

E E

0(2) ln

(2) (1)

g

QE Lconst

E

const const

I.V. in preparation

Regimes of QCD Radiative Energy Loss

Ivan Vitev&

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

Light Hadron Quenching in A+A

Establishing the E-loss mechanism

Centrality

C.M

. en

ergy

D. d’Enterria, Eur.Phys.J C (2005)

Theory (constrained) / Experiment

3

2

g chdN dN

dy dy

Ivan Vitev&

Nuclear Effects at Forward Rapidity

I.V., in preparation

• The most detailed calculation so far at forward rapidity

• Dynamical shadowing (FS)

• Cronin effect (IS)

• Initial state energy loss (IS)

• Consistency in the extracted cold nuclear matter properties

22

1/3( ) 2

2

( 1)( , ) ,LTA

T T

xF x Q FA Q

Ax

Q

2

2 2

2

2

For 2

med

tot vac med

k

k k k

cmx^

^ ^ ^

D =

D = D + D

2 2( , )1

,/

xx Q Q

E E

Ivan Vitev&

• Cancellation of collinear radiation

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

What Happens to Medium-Induced Radiation?

In A+A

+2Re

2

x

2 *2 Resin *

...gmed

a b c

dNM M M

d d d

0, / 0k k

Correlated!

2

2

1 1 ( )ln ln

2 2g k xpy

k k

How about p+A?

First quantitative PQCD calculation

Ivan Vitev&

I. Heavy Ion Theory Effort at LANL

Core theory staff• Terry Goldman (T-16, quark models, neutrinos, PQCD)• Rajan Gupta (T-8, energy future, LQCD)• Mikkel Johnson (P-25, energy loss, shadowing, PQCD)• Emil Mottola (T-8, gravity, black holes, non-equilibrium FT)

J.Robert Oppenheimer fellow• Ivan Vitev (P-25 & T-16, energy loss, shadowing, PQCD)

External Collaborators• Miklos Gyulassy (Columbia U.)• Boris Kopeliovich (Heidelberg U., Germany)• Peter Levai (KFKI, Hungary)• Jianwei Qiu (Iowa State U.)• Joerg Raufeisen (Heidelberg U., Germany)• Ivan Schmidt (Santa-Maria U., Chile)

Columbia university

Collaborating institution

Ivan Vitev&

Publications and Workshops

Publications.

• Ivan Vitev, LARGE ANGLE HADRON CORRELATIONS FROM MEDIUM- INDUCED GLUON RADIATION.

Phys.Lett.B630:78-84,2005. • Ivan Vitev, T. Goldman, Mikkel Johnson, Jian-Wei Qiu, NUCLEAR EFFECTS ON OPEN CHARM PRODUCTION IN

P+A REACTIONS. HEP-PH 0511220 • Ivan Vitev, JET QUENCHING AT INTERMEDIATE RHIC ENERGIES. Phys.Lett.B606:303-312,2005. . • Mikkel B. Johnson, PROPAGATION OF FAST PARTONS IN THE NUCLEAR MEDIUM. Eur.Phys.J.A19:2004. • B.Z. Kopeliovich, J. Nemchik, I.K. Potashnikova, M.B. Johnson, I. Schmidt, BREAKDOWN OF QCD

FACTORIZATION AT LARGE FEYNMAN X. Phys.Rev.C72:054606,2005. • Fred Cooper, Ming X. Liu, Gouranga C. Nayak, J / PSI PRODUCTION IN PP COLLISIONS AT S**(1/2) = 200-GEV

AT RHIC. Phys.Rev.Lett.93:171801,2004.

• Jian-Wei Qiu, Ivan Vitev, RESUMMED QCD POWER CORRECTIONS TO NUCLEAR SHADOWING,

Phys.Rev.Lett.93:262301,2004Conferences / Workshops• Emil Mottola, organizer, “QCD and Gauge Theory Dynamics in the RHIC Era”, April 2002, KITP• Rajan Gupta, organizer, “Modeling the QCD Equation of State at RHIC”, February 2006, LLNL• Ivan Vitev, organizer, “LHC workshop at PANIC’05” November 2005, Santa Fe• Terry Goldman, Mikkel Johnson, organizers, “PANIC’05” November 2005, Santa Fe (Martin Cooper, Joe Carlson, P-25, T-16 )

LANL - LLNL

Ivan Vitev&

II. Theory: Jet Quenching

Breakthrough theoretical work:

• Formalism for calculating the energy loss: GLV (Gyulassy-Levai-Vitev)

• Implementation of energy loss, Croninscattering in PQCD hadron production

TNN

TAA

collTAA dpdd

dpdd

NpR

/

/1),(

2

2

Nuclear modification

M.Gyulassy,P.Levai,I.Vitev Phys.Rev.Lett. 85 (2000);

Nucl.Phys.B571 (2000); Nucl.Phys.B594 (2001)

I.Vitev, M.Gyulassy, Phys.Rev.Lett. 89 (2002);

I.Vitev, Phys.Lett. B562 (2003); Phys.Lett. B630 (2005)

I.Vitev,M.Gyulassy,P.Levai,I.Vitev, in preparation

Ivan Vitev&

PQCD Factorization and Energy Loss Theory

11

2

/1 1 2

1 1

1

2min min 1

2( )(

()

))(

a b

sa b a b

ab

h

cd a bx x

ab cT

dc

hNNd

dx dD z

zx x x

x xSd pM

ydas

ff ®= å ò ò

(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• Bjorken expanding medium: 0

0( ) ( )

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

Challenge: connection

v c

Box of plasma

0p p X

Pio

n cr

oss

sect

ion

Ivan Vitev&

I.Vitev,in preparation; hep-ph/0511273

Results on Energy and Centrality Dependence

Establishing the E-loss mechanism

Centrality

C.M

. en

ergy

D. d’Enterria, Eur.Phys.J C (2005)

I.Vitev, M.Gyulassy, Phys.Rev.Lett. 89 (2002)I.Vitev, Phys.Lett.B 606 (2005)

Theory / Experiment

3

2

chg d

d d

dN

y y

dN

d

Experimentallymeasured

Pio

n su

ppre

ssio

n in

A+

A r

eact

ions

Pio

n su

ppre

ssio

n in

A+

A r

eact

ions

0A A X

Ivan Vitev&

E-loss in Back-to-Back Di-jets and Correlations

1 2

1 2

1 2(2) 1 2

1 2 1 2

h hAA

T Th hApp

T T

A

bin

d

dy dy dp dp

d

dy d pN

dp

R

y d

1

1

1

1

2/

1 / 2

/0 / 2

2

1

/ ( ) (1

( )

( )

)1 1

( ) ( )

h d med

T gh g g vac

g

h d

g

zD f

p dzD z d f

z

dN

D

z

z

d d

0

0

/E E

A+A

Tag

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

• Multi-particle modification• Angular gluon distribution

Tw

o pa

rtic

le s

uppr

essi

on /

enha

ncem

ent i

n A

+A

rea

ctio

ns

1 2A A h h X

See talk by M. Brooks

Ivan Vitev&

Theory: High Twist Shadowing Theory

Coherent final state scattering theory Shadowing is the ratio of DIS reduced cross sections – structure functions

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

2 2

2 20 0

2 00

3 ( ) 3 ( )( lim ()

8 2 8)x

i p ys sQ dy Qe p F F p y

r rxG x

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

Data from: NMC

*, *g

• QCD factorization approach, background color magnetic field

Shadowing

Twist Dimension Spin O

Power suppressed ~ 1/QT

Ivan Vitev&

A-, x- and Q2-Dependence: Numerical Results

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

• The scale of higher twist per nucleon is small: 2 20.1 0.12 GeV

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

• The nuclear effect is of power law nature: Q2 dependent

2 ) 22

2( 2 4

( , ) ( , ) ( , )A AL TLT

LF x Q x Q F QQ

A F x

Sup

pres

sion

in D

IS S

truc

ture

Fun

ctio

ns

Sup

pres

sion

in D

IS S

truc

ture

Fun

ctio

ns

Ivan Vitev&

Shadowing in Neutrino+A and p+A Reactions

2( )( ) b

ab cdbb

xF x M

x

f®=

21/ 3( 1( ) )b b b dx C A

tF x F x

J.W.Qiu, I. Vitev, Phys.Lett.B 587 (2004)

J.W.Qiu, I. Vitev, Phys.Lett.B 632 (2006)

p+A

STAR

• DIS-like t-channel FS scattering

g u sea u valS S S

Nuc

lear

sup

pres

sion

in p

+A

rea

ctio

ns

Str

uctu

re F

unct

ions

No nuclear effect

d A h X

• Dynamical shadowing for sea quarks, valence quarks and gluons

Ivan Vitev&

Theory: Energy Loss in Cold Nuclear Matter

M.B.Johnson et al., Phys.Rev.C72 (2005)

I.Vitev,T.Goldman,M.Johnson,J.W.Qiu, in preparation

• Evidence from low energy p+A reactions

( , , ) 0.25Ty y p A Eff. E-loss

( ) 2

2 2 2 2( )

BGg s

A

d qNC

qdyd k k k

(1 ) 1gN

F F FS x x Suppression

( 1) 1gN y

+ +2 2~ | |B

Nuc

lear

sup

pres

sion

in d

+A

rea

ctio

ns

Nuc

lear

sup

pres

sion

at f

orw

ard

rapi

dity

d A h X

See talk by M. Brooks

2 22

1 2 2 21

( ) /( , , )

( ) /

ABT

y T ABT

d y dyd pR p y y

d y dyd p

Ivan Vitev&

c g c g c q q c q q

+ ...+ ...

III. Heavy Quark Production and Modification

Gluon fusion is not the dominantprocess in open charm production

I.V.,T.Goldman,M.Johnson,J.W.Qiu, Phys.Rev.D74 (2006) • Proposed back-2-back charm triggered correlations

( ) 2

( ) 2

/

/

process iT

process iT

i

d dyd pR

d dyd p

p p D X

Ivan Vitev&

Nuclear Matter Effects on Charm Production

PHENIX data

(min. ) 0.25,y bias No Cronin Very similar behavior of charmquarks (D-mesons) to light hadronsE-loss seems to play a similarly

important role

I.Vitev,T.Goldman,M.Johnson,J.W.Qiu, in preparation hep-ph/0511220

Experimental y = 1.4-2.2

LDRD: “Heavy Quarks as a Probe of a New State of Matter”

Nuc

lear

sup

pres

sion

in d

+A

rea

ctio

ns

Nuc

lear

sup

pres

sion

in d

+A

rea

ctio

ns

0d A X d A D X

See talks by M. Brooks and P. McGaughey

Ivan Vitev&

2 2

q

E E FM

Reduce large theoretical spreadof "melting" temperatures of

Future / LDRD Research Directions

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

qq

• Lattice QCD equation-of-state and heavy quarkoniaFrom Nt=4 to Nt=6, 8 lattices Improved lattice actions

• E-loss of heavy quarks at

• Transport coefficients of the QGP

I.Vitev

0Y

Thermal and electrical conductivityNon-equilibrium field theory

Fra

ctio

nal q

uark

ene

rgy

loss

Ene

rgy

dens

ity

See talk by P. McGaughey

R. Gupta

I. Vitev

E. Mottola

Ivan Vitev&

Summary of Theory Effort / Directions

Heavy Ion Theory at Los Alamos • 4+1 staff, new external collaborations, extensive publication record.

Participated / organized HIT conferences / workshops

Recent Theoretical Progress • Establishing the jet quenching theory: verified predictions versus C.M.

energy, predictions versus centrality Cu+Cu, Au+Au• Understanding high twist shadowing: final state interactions. DIS structure

functions F1, F2, neutrino-nucleus reactions F3, p+A reactions • Energy loss in cold nuclear matter: understanding the p+A rapidity

asymmetry and verification at lower C.M. energies.

Future Theoretical Developments, LDRD• Heavy quark production / modification: charm on gluon scattering• Energy loss mechanism for heavy quarks: non-zero Y, novel e-loss• Transport coefficients: electrical and thermal conductivity of the plasma• Lattice QCD Equation-of-State and heavy quarkonia: improved simulations

Ivan Vitev&

Analytic Models of Jet Quenching

2 /2 23

1 1

1 '1

AA n

T part

n

T

RNp

p

20( ) nn

T T T

d a a

dyd p p p p

/ 2 /32 3par

g

t

L dNA

A dEN

y

E

PQCD baseline:

• Predictions

2/3

2/3

ln

exp

AA part

AA part

R N

R N

I.Vitev,in preparation; hep-ph/0511273

• Centrality dependence

Verified with PHENIX and STAR

GLV E-loss:

Quenched PQCD: 2 )/(1n nT TT T

d a

dy p p pd p

Comparison