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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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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
Úabcd 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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
≠• 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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
D. Molnar (2004)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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
Úabcd 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
• 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
Úabcd 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
• Single and double inclusive hard production in PQCD - applicable from photons to heavy quarks
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)
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