A Novel Heavy Quark Suppression Mechanism in the QGP

Ivan Vitev

A Novel Heavy Quark Suppression Mechanism in the QGP

Ivan Vitev, Nuclear Theory, T-16 , LANL

"Characterization of the Quark-Gluon Plasma with Heavy Quarks” Seminar

June 25 - 28, 2008, Bad Honnef, Germany

-mesons, -mesonsD B

Time evolution

cu

Ivan Vitev

2

Outline of the Talk

Jet tomography of the QGP• Success of jet quenching for light hadrons, QGP tomography • The heavy quark puzzle at RHIC. A space-time picture of hadronization

Collisional dissociation of hadrons in dense QCD matter• Dissociation: new approach to D- and B-mesons suppression in the QGP • Light cone wave-functions. Mesons propagation in matter• Phenomenological results for RHIC and the LHC

Heavy resonances and partial chiral symmetry restoration • Hadrons and symmetry. Formation time of resonances in the medium • Interaction and decay of heavy resonances in matter • Experimental detection techniques

Summary and outlook • Universal modification of fragmentation functions in the QGP

Talk based upon: A.Adil, I.Vitev, Phys. Lett. B649 (2007) Ch.Markert, R.Bellwied, I.Vitev, Phys. Lett. B to be submitted R. Sharma, I.Vitev, in progress

Ivan Vitev

3

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

Light Hadron Quenching

• Constrained by the gluon rapidity (entropy) density

• Nuclear modification factor

TNN

TAA

collTAA dpdd

dpdd

NpR

ησηση

//1

),( 2

2

⋅><

=

• Predictions of this formalism tested vsparticle momentum, C.M. energy, centrality

Ivan Vitev

4

S. Wicks et al., Nucl.Phys.A (2007)

• 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

ω ω

ω

−−

+⊥ ⊥

+⊥ ⊥

⎡ ⎤⎡ ⎤ → +⎢ ⎥⎣ ⎦

⎢ ⎥⎣ ⎦

→ = ≈+

+

+

K K

r r

r r

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

Proceed the same way to heavy flavor in A+A collisions

Ivan Vitev

5

The Space-Time Picture of Hadronization

In mesoscopic systems one has to account for the space-time evolution

τ form =τ 0

Em

=τ 0γ

QuickTime™ and a decompressor

are needed to see this picture.A. Bialas, M.Gyulassy, Nucl.Phys.B 291, (1987)

J.D. Bjorken, Lect.NotesPhys.56, (1987)

• Inside-outside cascade

• Outside-inside cascade

τ 0 ~1 fm

- Correctly accounts for the leading energy and mass dependence. Lack of control over t0

- Correctly points at the reduction of tform at large values of x. Specific for Lund string fragmentation. Mass dependence obscured

p + p

A + A

Ivan Vitev

6

Evaluating the Formation Times

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

• Problem: treated in the same way as light quarks

π D B

20 fm 1.5 fm 0.4 fmform ( 10 )Tp GeVτ =

PartonHadron

p+

zp+

(1 )z p+−

~ QCDk⊥ ΛB

D π

}QGP extent (~5 fm)

pq= p+ ,

Mq2

2p+ ,0⎡

⎣⎢⎢

⎤

⎦⎥⎥

2 2

, ,2

hh

k mp zp k

zp+ ⊥

⊥+

⎡ ⎤+=⎢ ⎥

⎣ ⎦

2

(1 ) , ,2(1 )g

kp z p k

z p+ ⊥

⊥+

⎡ ⎤= − −⎢ ⎥−⎣ ⎦

+

τ form = τ form (z,kT = ΛQCD; pT ,mh )0

1

∫ P(z)dz

Ivan Vitev

7

Collisional Dissociation of D / B Mesons

• Conceptually different approach to heavy flavor suppression

-mesons, -mesonsD B

Time evolution

cu

A. Adil, I. Vitev, Phys. Lett. B649, 139 (2007), hep-ph/0611109

Ivan Vitev

8

Light Cone Wave Functions

ψ (Δk⊥ ,x)2: Exp −

Δk⊥2 + 4mQ

2 (1−x) + 4mq2(x)

4Λ2x(1−x)

⎡

⎣⎢⎢

⎤

⎦⎥⎥

From general theory of LCWF for the lowest-lying Fock state

• Results for heavy flavor

• Models such as coalescence should useplausible wave functions, especially for heavy flavor

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

• Expansion in Fock components

ψ M ;P⊥ ,P+ =

i=2

n

∑ dxi

2xi

∫d2k⊥ i

2π( )3ψ i (k⊥ i ,xi )

×δ xii=2

n

∑ −1⎛

⎝⎜⎞

⎠⎟δ k⊥ i

i=2

n

∑⎛

⎝⎜⎞

⎠⎟ i;k⊥ i + xiP⊥ ,xiP

+

LO Fock component Mean Peaked at large xk⊥2 ~0.5 GeV

- Transverse momentum scale

- Longitudinal momentum fractions 2 2 22 2 2

j i ji i i

i i j j

m m km m k

x x x x⊥ ⊥⊥ ⊥

⎛ ⎞+⎛ ⎞+= =⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

=

Ivan Vitev

9

Medium-Modified Heavy Meson

• Heavy meson acoplanarity:

K⊥2 =2 2μ2 L

λq

ξ⎛

⎝⎜

⎞

⎠⎟

Initial distribution:

Resum using GLV the multiple scattering in impact parameter (B,b) space

• Broadening (separation) the q q-bar pair:

2 2

0

12 2 2 2 ( )

( )

L

q q

Ll dl

lμ ξ μ ξ

λ λ⎛ ⎞ ⎛ ⎞

≡⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∫

ψ f (Δk⊥, x)2

=e

−K⊥

2

4 χμ 2ξ

4χμ 2ξ

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

× Norm2 x(1 − x)Λ2

χμ 2ξ + x(1− x)Λ2e

−Δk⊥

2

4(χμ 2ξ + x(1− x )Λ2 )e−

m12 (1− x )+m2

2 x

x(1− x )Λ2⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

ψ i (Δk⊥, x)2

= δ 2 (K⊥)⎡⎣ ⎤⎦× Norm2e−

Δk⊥2

4 x(1− x )Λ2

e−

m12 (1− x )+m2

2 x

x(1− x )Λ2⎡

⎣⎢⎢

⎤

⎦⎥⎥

ψ f (Δk⊥, x) = aψ M (Δk⊥, x) + (1− a)ψqq dissociated

(Δk⊥, x)

?

K⊥

Δk⊥

2 22

surv. (* ( , ), )f iP L dxd k x kx kλ

ψμ ξ ψ⊥ ⊥⊥

⎛ ⎞= Δ⎜ ⎟

⎝ ⎠ΔΔ∫

Ivan Vitev

10

c g c g+ → + ( ) ( )c q q c q q+ → +

Initial Conditions (Hard Parton Spectra)

Simultaneous fragmentation and dissociation call for solving a systemof coupled equations

I.V.,T.Goldman,M.Johnson,J.W.Qiu, Phys.Rev.D74 (2006)

• Proposed back-2-back D / B triggered correlationsp p D X+ → +

f Q ( pT,t =0) =

dσdyd2 pT

(y, pT )

f H (pT ,t=0) =0

• Initial conditions

• Example: radioactive decay chain

dNi

dt=λi−1Ni−1 −λiNi

Ivan Vitev

11

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~ 15-20 GeV at the LHC

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

τ

τ

τ

φ

τ

∂ =− ∂

∂ =− ∂

∫

∫

( )1, 1x z< <

Unique feature

A. Adil, I. Vitev, Phys. Lett. B649, 139 (2007)

Ivan Vitev

12

Quenching of Non-Photonic Electrons

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

• Similar to light , however, different physics mechanism

2

2coll

/( )

/

eAA T

epp T

eAA T

d dyd p

d d dR

yp

N p

σσ

±

±

±

=

• Full semi-leptonic decays of C- and B- mesons and baryons included. PDG branching fractions and kinematics. PYTHIA event generator

0π

Note on applicability

(e++e-) to 25 GeVD-, B-mesons to RAA (D) =RAA(B)

Ivan Vitev

13

Areas of Improvement

( We wanted to solve this, the hierarchy problem, GUT, the baryon asymmetry, dark matter … but we couldn’t in the same paper )

• Main criticism: what are the modifications to a fragmentation process, modified fragmentation functions, coalscence, …

0π

0π

/E Eε =Δ

A+A

• Incorporate radiative and collisional energy loss at really high pT

A. Majumder, X.N.Wang (2008)

Dh /c (z)→ dε P(ε)1

1−ε∫ Dh/c

z1−ε

⎛⎝⎜

⎞⎠⎟

+ dεdNg

dε1ε∫ Dh/g

zε

⎛⎝⎜

⎞⎠⎟

These are not “modified fragmentation functions”

Ivan Vitev

14

A Possible Path

• The apparent duality between parton distribution functions and fragmentation functions is understandable

Definition of the fragmentation functions

D(z) ~dy−

2π∫ eip+y− 0 ap++ hX hX a

p+ 0

R. Sharma, I. Vitev, in prepration

0 → QGP = n(i)i∑ a+

i 0

From D(z) parameterizations or LCWF extract information aboutmatrix elements

We may gain insight of universal (T) modifications to fragmentation functions

Ivan Vitev

15

Effects of Partial Chiral Symmetry Restoration

Kaon

• Scale of chiral symmetry restoration QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

Phi meson

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

L. Holt, K.Haglin, J. Phys. G31, S245 (2005)

mρ ≤Λ ≤4π fπ

Mass shifts

Width broadening

Manifestation for baryons

- Includes approximately strange quarks

SU(N )L ×SU(N)R → SU(N)L+R

L =iψ N /Dψ N + 0ψ Nψ N + L g



G. Brown, M.Rho, Rev. Mod. Phys., (2001)

Lagrangian

L. Glozman, Phys.Lett. B475, 329 (2000)

- Evidence for possible chiral symmetry restoration

- Important to include baryons (Δ,Λ*) in experimental searches at finite T

mρ (T )mρ

=fπ (T )

fπ

Ivan Vitev

16

Motivation / Estimates - a Simple Case

• Mass of heavy resonances: falls in the right region to ensure early formation

τ coll = 2RA / γ τ o = 1 / pT



dsNN

h1h2

dy1dy

2d2p

T 1d2p

T 2

=d(Dj - p)

pT 1

pT 2

dz1

Dh1/c

(z1)

z1z1 min

1

Ú Dh2/d

(z2)

abcdÂ

f (xa)f (x

b)

xax

b

as2

S2M 2

abÆcd

dsNN

h1

dy1d2p

T 1

= dxa

xa min

1

ÚabcdÂ dx

b

xb min

1

Ú f (xa)f (x

b)

as2

(xax

bS)2

M 2

abÆcd

Dh1/c

(z1)

z1

• Cross sections and z distributions

pT1/ z1 =pT2

/ z2

- QGP formation (in the absence of dynamical calculation)

- Quick evaluation ( z = 0.7 )

Ivan Vitev

17

Formation Time of Resonances

LHC

• Distributions

RHIC

• One has to approximate fragmentation functions. Normalizations cancel in the ratio

P(z

i) =

dsNN

h1...hn

dy1...dy

nd2p

T 1...d2p

Tndz

i

/ds

NN

h1...hn

dy1...dy

nd2p

T 1...d2p

Tn

K *, φ, Δ, Λ*

τ form = τ form (z,kT = ΛQCD; pT ,mh )0

1

∫ P(z)dz

Ivan Vitev

18

In-medium Lifetime (Stronger Constraints)

Phi meson

• Spectral function: medium broadening



L. Holt, K.Haglin, J. Phys. G31, S245 (2005)

M.Bleicher et al., Phys. Lett. B530, 81 (2002)

• URQMD study: any signal in pT 0-2 GeV strongly affected by hadronic rescattering of decay products (lower pT limit)

cτ (K * ) =3.88 fm, cτ (Δ) =1.64 fm,

cτ (Λ) =12.6 fm, cτ (φ) =46.5 fm

Remember the dilation factor γ =E / m

Reduction if the lifetime is critical if any effects are to be observed in the resonancechannel (upper pT limit)

Ivan Vitev

19

Triggered Measurements

• Ensure maximum medium size without changing the formation times

pT trigger

pT associated

• There is always a time distribution ~ (1−et/τ )• Many of the resonances will be dissociated. We are concerned with those that survive .

Ivan Vitev

20

Summary of Open Heavy Flavor Suppression

Searches for chiral symmetry restoration• Identified the phase space and channels if those searches are to be done

experimentally wit heavy resonances.

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• This will certainly motivate us to improve the calculation: modified

fragmentation functions (really) and folding in energy loss.

Ivan Vitev

21

Outline of the Talk

Jet tomography of the QGP• Success of jet quenching for light hadrons, QGP tomography • The heavy quark puzzle at RHIC. A space-time picture of hadronization

Collisional dissociation of hadrons in dense QCD matter• Dissociation: new approach to D- and B-mesons suppression in the QGP • Light cone wave-functions. Mesons propagation in matter• Phenomenological results for RHIC and the LHC

Heavy resonances and partial chiral symmetry restoration • Hadrons and symmetry. Formation time of resonances in the medium • Interaction and decay of heavy resonances in matter • Experimental detection techniques

Summary and outlook • Universal modification of fragmentation functions in the QGP

Talk based upon: A.Adil, I.Vitev, Phys. Lett. B649 (2007) Ch.Markert, R.Bellwied, I.Vitev, Phys. Lett. B to be submitted R. Sharma, I.Vitev, in progress

Ivan Vitev

22

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

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

SPS RHIC LHC

0 0

' / ( ') ' ( ')

0 0

( ')

( )

r r

abs absdr r dr r r

I r I e I eλ σ ρ− −

= =∫ ∫

Determining the properties of the QGP: ,T ρ ε→

Jet Tomography

Ivan Vitev

23

Single inclusive pion suppression at the LHC

• High pT suppression at the LHC can be comparable and smaller than at RHIC

• LHC quenching follows the steepness of the partonic spectra

Reduced sensitivity to medium properties

Running Fixed α s α s

S.Wicks et al., in progress

Ivan Vitev

24

Direct photon at the LHC

• Direct photons also have limited sensitivity: isospin effects, cold nuclear matter e-loss

R =dσ / dyd2 pT ( fragmentation)

dσ / dyd2 pT (prompt)

Dγ /γ (z) =δ(z−1)

Dγ /q(z)Dγ /g(z)

Prompt photons

Fragmentation photons {+

• Direct photon tagging: can be compromised by fragmentation photons

• Better jet interaction measures?

Ivan Vitev

25

S. Wicks et al., (2005)

• Diffusion coefficient D and eventually

• Existence of heavy heavy resonances near Tc in the QGP

Non-Photonic Electron / Heavy Flavor Quenching

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

i ijiA p

f p tp f p tB p

t p pt t

⎛ ⎞∂ ∂ ∂= + ∂⎜ ⎟∂ ∂ ∂⎝ ⎠

Langevin simulation of heavy quark diffusion

N. Armesto et al., (2006)

H. van Hees, R. Rapp, (2005) G. Moore, D.Teaney (2005)

Radiative and collisional energy loss

η / s

• Ratio:

• Opacity of the QGP

ΔEcoll . / ΔErad .

L / λg

Ivan Vitev

26

The Path Forward

• An interesting idea valid physics explanation

A.Adil, I.Vitev, Phys. Lett. B (2006) W.Horowitz, M. Gyulassy, (2007)



≠• To understand heavy flavor modification in the QGP we need direct and separate measurements of D- and B-mesons, excellent statistics

Measurable at RHIC Measurable at the LHC

RAAc (pT )

RAAb (pT )

=1

Meson dissociation

String theoryAdS/CFT

PQCD,Transport

PT [GeV]10-15 50-100 Never

Ivan Vitev

27

Heavy Flavor Elliptic Flow and Suppression

Understand the structure of mesons light cone wave functionsc

A. Adil, I. Vitev, Phys.Lett.B (2007)

Sensitive to the opacity of the QGP and its formation time τ 0



D. Molnar (2004)



Test coalescence model fits to the v2 of

light hadrons via heavy flavor

Ivan Vitev

28

Heavy Quark Production and Correlations

D

, ,kπ η

D

D

• Possibility for novel studies of heavy quark-triggered (D and B) jets: hadron composition of associated yields

• Fast convergence of the perturbative series

Ivan Vitev

29

Scales in Thermalized QGP (GP)

3e

2exp

0

xp 0

1200

1( ) , 120

0

6

( ) 1

.

7

g

g

dN

dydN

A fmA dy

f

m

m

f

ρ ττ

τ

ρ τ

⊥⊥

−

=

=

=

=

⇒

=

• 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

ρ ςπ

ππ

ς

∞= ×=

−

= × =

∫

400T MeV=

• Energy density4

( )30 [3]

( )theory theory T TTπ ρες

= × ×3

exp 0318 . 1( ) 00 0.14 .GeV fm GeV fmε τ − −= ≥ ×

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

, 2 2.5 ( 0.3 0.5)4sD

gggTμ α

π= − = −≈ =

0.8 1D GeVμ = −2

2

9 1

2,gg s

Dg gg

π λσμ σ ρα

== } 2 29ˆ

2D

g

sqμλ

πα ρ== q̂ =1−2.5 GeV 2. fm−1

0.75 0.42g fmλ = −

• Define the average for Bjorken0

20

2ˆ( )ˆ

( )

L

zq z zdzq

L z=

− ∫ 2 10.35 0.8 .ˆ 5 GeVq fm−= −

3

2

chg d

d d

dN

y y

dN

d

ηη

;

Ivan Vitev

30

Langevin Simulation of Heavy Quark Diffusion

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

Input in a Langevin simulation of heavy quark diffusion

H. van Hees, I.V., R. Rapp, in preparation

• Drag coefficient:

1( , )i

i

i

Ap t

p tpδδ

=

1

2( , )ji

j ipp

pt

tB

δ δδ

=

• Diffusion coefficient:

gλ

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

i ijiA p

f p tp f p tB p

t p pt t

⎛ ⎞∂ ∂ ∂= + ∂⎜ ⎟∂ ∂ ∂⎝ ⎠

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

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

Ivan Vitev

31

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

32

P’xbP’

P

xaP

0π

0π

Pc

Pd

Pc / zc

Pd / zd

dsNN

h1h2

dy1dy

2d2p

T 1d2p

T 2

=d(Dj - p)

pT 1

pT 2

dz1

Dh1/c

(z1)

z1z1 min

1

Ú Dh2/d

(z2)

abcdÂ

f (xa)f (x

b)

xax

b

as2

S2M 2

abÆcd

d

d

pd

z∫ {

X

X

dsNN

h1

dy1d2p

T 1

= dxa

xa min

1

ÚabcdÂ dx

b

xb min

1

Ú f (xa)f (x

b)

as2

(xax

bS)2

M 2

abÆcd

Dh1/c

(z1)

z1

Hard Probes from Factorized PQCD

• Single and double inclusive hard production in PQCD - applicable from photons to heavy quarks


Power laws: dσd2 pT

=A

pT + p0( )n ≈

A

pT( )n

n =n( s, pT ,system) ln RAA =−(n−2)ε

Quenching factor

ε =ΔE

E

Ivan Vitev

33

Jet cross sections: comparison to LO and NLO PQCD

• Good comparison to the shape at LO. Meaningful K-factor

• Even better comparison at NLO.

I.V., S. Wicks, in preparation

Ivan Vitev

34

P’xbP’

P

xaP

0π

0π

Pc

Pd

Pc / zc

Pd / zd

dsNN

h1h2

dy1dy

2d2p

T 1d2p

T 2

=d(Dj - p)

pT 1

pT 2

dz1

Dh1/c

(z1)

z1z1 min

1

Ú Dh2/d

(z2)

abcdÂ

f (xa)f (x

b)

xax

b

as2

S2M 2

abÆcd

d

d

pd

z∫ {

X

X

dsNN

h1

dy1d2p

T 1

= dxa

xa min

1

ÚabcdÂ dx

b

xb min

1

Ú f (xa)f (x

b)

as2

(xax

bS)2

M 2

abÆcd

Dh1/c

(z1)

z1

Jets from Factorized PQCD


For jets: D

h1/c(z

1) Æ d(1- z)

• Jet cross sections are more inclusive and therefore more robust PQCD observables

Caveat: parton-hadron duality

CDF studies:( 50 ) 1.2p h

TC E GeV− = =

( 500 ) 1.0p hTC E GeV− = =

J.Collins, D.Soper, G.Sterman, Nucl.Phys.B (1983)

Date post:	12-Jan-2016
Category:	Documents
Upload:	missy
View:	33 times
Download:	2 times

A Novel Heavy Quark Suppression Mechanism in the QGP

Documents