Bottomonium Suppression in Heavy Ion Collisions
Michael Strickland
Gettysburg College, Gettysburg, PA, USA
5th International workshop on heavy quark production in
heavy-ion collisions, Utrecht University, Nov 14 2012
Collaborators: Bazow, Dumitru, Guo, Margotta, McCarty, McGahan, Mocsy, and Yager-Elorriaga
References: 1112.2761, 1106.2571, 1101.4651, 1011.3056, 1007.0889, and 0903.4703
Michael Strickland, Gettysburg College
Why consider bottomonium?
• Bottom quark mass mB ≈ 4.2 GeV and ϒ(1s) has
mass ≈ 9.5 GeV
• As a result we can apply NRQCD and have some
hope that it is reliable
• Hard to produce thermally à production primarily
comes from initial hard scatterings
• Cold nuclear matter effects expected to decrease
as the mass of the state increases
(larger Bjorken x probed)
• Regeneration effects are also expected to be
smaller due to fewer bottom quarks
Michael Strickland, Gettysburg College
CMS Data (2012)
CMS Collaboration, arXiv:1208.2826
pp
Michael Strickland, Gettysburg College
PbPb
3
Perturbative/EFT Expectations
• Debye Screening à
quarkonium suppression in QGP
• Decrease in the real part of the binding energy (Ebind) as a
function of temperature
• Imaginary part of Ebind à thermal width (~ decay rate) which
increases as a function of temperature
• Real and imaginary parts of the heavy quark potential, V, are
known to leading order in an isotropic and a momentumspace anisotropic plasma
Isotropic Potential:
Laine, Philipsen, Romatschke, and Tassler, hep-ph/0611300
Anisotropic Potential: Dumitru, Guo, and MS, 0711.4722, 0903.4703
Burnier, Laine, Vepsalainen, 0903.3467
Philipsen and Tassler, 0908.1746
EFT Approach:
Brambilla, Ghiglieri, Petreczky, and Vairo, arXiv:0804.0993
Brambilla, Escobedo, Ghiglieri, and Vairo, arXiv:1109.5826
Michael Strickland, Gettysburg College
4
Heavy Ion Collision Timescales
Michael Strickland, Gettysburg College
5
Hadrons XII - April 23, 2012
QGP momentum anisotropy
CGC
Glasma
1-3 fm/c
Boltzmann-Vlasov Transport
~ 5-9 fm/c
Viscous Hydrodynamics
Anisotropic Hydrodynamics
1
Expansion rate is much faster
than the interaction time scale
1/t >> 1/t int
Expansion rate and isotropization
via interactions balance
0
-1
o ~ Qs
Michael Strickland, Gettysburg College
Processes
Plasma Instability
Inelastic Scattering
Elastic Scattering
Quark Pair Production
hydro
Decreasing η/S
(Longitudinal Pressure)/(Transverse Pressure)
0.1-0.3 fm/c
Computing medium suppression
• Formation times on the order of 0.2 - 1 fm/c à
states form inside in plasma
• We then need to understand the time evolution of
the surrounding medium starting at very early
times
• Use an “improved” viscous hydrodynamics frame
called anisotropic hydrodynamics
• Dynamical variables: average momentum of the
states (~T) and pressure anisotropy (PL ≠ PT)
Michael Strickland, Gettysburg College
7
Anisotropic Plasma
f (⌧, x, p) = fiso ([p2 + ⇠(⌧, x)p2z ]/p2hard (⌧, x))
⇠ = momentum space anisotropy parameter (ellipticity in LRF)
phard = typical transverse momentum of plasma constituents
PL > PT
prolate
PL = PT
PL < PT
oblate
Navier-Stokes Limit
Michael Strickland, Gettysburg College
8
Perturbative Anisotropic Potential
Using real-time formalism one can express potential in terms
of static advanced, retarded, and Feynman propagators
Z
⌘
⇣
3
d
p
1
⇤L
ip·r
⇤L
⇤L
+
D
+
D
V (r, ⇠) = g 2 CF
(e
1)
D
R
A
F
(2⇡)3
2
Real part can be written as
Re[V (r, ⇠)] =
g 2 CF
Z
p2 + m2↵ + m2
d3 p ip·r
e
3
(2⇡)
(p2 + m2↵ + m2 )(p2 + m2 )
m4
With direction-dependent masses, e.g.
Anisotropic potential calculation: Dumitru, Guo, and MS, 0711.4722 and 0903.4703
Gluon propagator in anisotropic plasma: Romatschke and MS, hep-ph/0304092
Michael Strickland, Gettysburg College
9
Imaginary Part of the Potential
1.0
0.8
f
0.6
0.0
0.4
y1
0.2
0.4
1.0
0.0
0
0.2
0.0
1.5
q
-0.1
y2
-0.2
-0.3
1.5
1.0
0
q
0.5
0
2
4
r`
6
8
10
`5
r
0.5
`5
r
10
0.0
10
0.0
Anisotropic potential calculation: Dumitru, Guo, and MS, 0711.4722 and 0903.4703
Michael Strickland, Gettysburg College
10
But … pQCD is not enough
• Need to supplement the perturbative (short range) potential
with an appropriate long range potential
• We use a generalization of the Karsch-Mehr-Satz (KMS)
potential which gives the internal energy (U) of the state
Isotropic potential
Mocsy and Petreczky, 0705.2559
• With α = 0.385 and string tension σ = 0.223 GeV2. Fixed to
lattice data.
KMS potential: Karsch, Mehr, and Satz, Z. Phys. C37, 617 (1988)
Isotropic case: Mocsy and Petreczky, 0705.2559
Anisotropic case: Dumitru, Guo, Mocsy, and MS, 0901.1998
Michael Strickland, Gettysburg College
11
Solve the 3d Schrodinger EQ
with complex-valued potential
Obtain real and imaginary parts of the binding
energies for the ϒ(1s), ϒ(2s), ϒ(3s), χb1, χb2
Michael Strickland, Gettysburg College
12
Results for the ϒ(1s) binding energy
0.9
Binding Energy [GeV]
0.8
= 0, (Real Part)
ϒ
0.7
= 0, -(Imaginary Part)
= 1, (Real Part)
0.6
= 1, -(Imaginary Part)
0.5
0.4
0.3
0.2
0.1
0
1
1.5
2
2.5
c c
pT/T
hard/T
3
3.5
4
Margotta, McCarty, McGahan, MS, and Yager-Elorriaga, 1101.4651
Michael Strickland, Gettysburg College
13
Results for the χb1 binding energy
Binding Energy [GeV]
0.4
= 0, (Real Part)
χb
= 0, -(Imaginary Part)
= 1, (Real Part)
0.3
= 1, -(Imaginary Part)
0.2
0.1
0
1
1.5
pT/T
hardc/Tc
2
2.5
Margotta, McCarty, McGahan, MS, and Yager-Elorriaga, 1101.4651
Michael Strickland, Gettysburg College
14
Sequential Suppression
Υ(1s)
0.5
Real Part
Imaginary Part
593 MeV
Binding Energy [GeV]
0.6
0.4
0.3
Excited states “melt” at lower temperatures.
Since they “feed down” (decay) to the
ground state this will result in a suppression
of the ground state.
Figure Courtesy CLEO Collaboration
0.2
0.1
0
200
300
400
500
T [MeV]
600
700
0.15
0.1
Υ(2s)
230 MeV
Binding Energy [GeV]
0.2
0.05
0
200
Real Part
Imaginary Part
300
400
500
T [MeV]
Michael Strickland, Gettysburg College
600
700
15
QGP Dynamical Evolution
Martinez, Ryblewski, and MS, arXiv:1204.1473; Ryblewski and Florkowski, arXiv:1204.2624
Tiso [GeV] at τ = 2.50 fm/c
Tiso [GeV] at τ = 0.50 fm/c
8
8
0.6
6
-2
0.3
0.07
0.21
0.28
y [fm]
0
0.2
• Can handle larger
momentum-space
anisotropies than
viscous hydro
Michael Strickland, Gettysburg College
-8 -6 -4 -2
0
2
4
6
0
0.2
-6
0
-8
0.1
0
-8 -6 -4 -2
2
4
6
8
PL/PT at τ = 2.50 fm/c
1
8
6
0.8
2
0.6
0.4
0.4
0.5
-4
0.2
0.37
1
0.2
0.8
4
y [fm]
4
-6
0
x [fm]
6
-2
0.3
0.15
-2
0.1
8
8
0
0.4
0.1
x [fm]
PL/PT at τ = 0.50 fm/c
y [fm]
• Fluctuating or
smooth initial
conditions
-8
2
-4
-4
-6
0.5
0.05
4
0.4
0.14
2
0.6
6
0.5
4
y [fm]
• “aHydro” provides
space-time evolution
of the temperature
and momentum
space-anisotropy
(PL/PT)
2
0.6
0
-2
0.4
0.4
0.6
0.8
-4
0.2
-6
-8
0
-8 -6 -4 -2
0
x [fm]
2
4
6
8
-8
0
-8 -6 -4 -2
0
2
4
6
8
x [fm]
16
Putting the pieces together…
• Have instantaneous decay rate as a function of
phard and ξ
• Take phard and ξ from anisotropic hydrodynamics
• Transverse and impact parameter dependence
using Glauber model.
• Radial dependence of temperature profile
à thermal width approaches zero at the edges
of the plasma
Michael Strickland, Gettysburg College
17
The suppression factor
• Resulting decay rate ΓΤ ≡ -2 Im[Ebind] is a function of τ, x⊥, and ς
(spatial rapidity). First we need to integrate over proper time
• From this we can extract RAA
• Using the overlap density as the probability distribution function
for quarkonium production vertices and geometrically averaging
Michael Strickland, Gettysburg College
18
State Suppression Factors,
i
RAA
D Bazow and MS, Nucl. Phys. A 879, 25 (2012); MS, PRL 107, 132301 (2011).
1
Potential Model B
sqrt(sNN) = 2.76 TeV
0.8
RAA
Υ(1s)
Υ(2s)
Υ(3s)
χb1
χb2
0.6
T0 = 580 MeV
0.4
0.2
0
0
Michael Strickland, Gettysburg College
100
200
Npart
300
400
19
Excited State “Feed Down”
• CDF pp measurements at 1.8 TeV find that only
[51 +/- 8.2 +/- 9]% of ϒ(1s) are produced directly
• The rest come from excited state decays.
• Based on CDF Data we use “feed down” fractions of
fi = {0.51, 0.107, 0.008, 0.270, 0.105} for the
{ϒ(1s), ϒ(2s), ϒ(3s), χb1, χb2} states
⌥ full
RAA
=
X
i
fi RAA
i2 states
Michael Strickland, Gettysburg College
20
Comparison with new Υ(1s) CMS data
D Bazow and MS, Nucl. Phys. A 879, 25 (2012)
MS, PRL 107, 132301 (2011).
(a)
Inclusive Υ(1s) RAA
1.2
CMS Stat Err
CMS Sys Err
1
4πη/S = 1
4πη/S = 2
4πη/S = 3
0.8
0.6
0.4
0.2
0 < |y| < 2.4
0 < pT < 20 GeV
0
0
100
200
300
400
Npart
Michael Strickland, Gettysburg College
21
Comparison with new Υ(2s) CMS data
MS arXiv:1207.5327
D Bazow and MS, Nucl. Phys. A 879, 25 (2012)
Inclusive Υ(2s) RAA
1.2
(b)
0 < |y| < 2.4
0 < pT < 20 GeV
1
CMS Stat Err
CMS Sys Err
4πη/S = 1
4πη/S = 2
4πη/S = 3
0.8
0.6
0.4
0.2
0
0
100
200
300
400
Npart
Michael Strickland, Gettysburg College
22
Compare with 2011 CMS data
D Bazow and MS, Nucl. Phys. A 879, 25 (2012); MS, PRL 107, 132301 (2011).
Full Υ(1s) RAA
1
Potential Model B
0.8
0.6
0.4
CMS 2011 Data
0.2
sqrt(sNN) = 2.76 TeV
0 - 100%
0 < pT < 20 GeV
0
-3
Michael Strickland, Gettysburg College
-2
-1
4πη/S = 1
4πη/S = 2
4πη/S = 3
0
y
1
2
3
23
RHIC sqrt(sNN) = 200 GeV
D Bazow and MS, Nucl. Phys. A 879, 25 (2012).
STAR data courtesy R. Reed
Υ(1s+2s+3s) RAA
1
0.8
0.6
0.4
0.2
0
0
Michael Strickland, Gettysburg College
STAR
4πη/S = 1
4πη/S = 2
4πη/S = 3
100
200
Npart
300
400
24
Conclusions and Outlook
• Heavy quark potential à thermal width which
determines suppression factor
• Need to carefully treat the edges of the plasma where
corrections to 2nd order viscous hydrodynamics are large
• Dynamical treatment guarantees positive pressures and
describes ideal hydro through free streaming.
• Transverse dependence of the temperature is important:
Large suppression in center, small at edges. Measured
suppression factor is geometrical average.
• In future we need to better constrain the long range part
of the potential and potential in general near Tc from first
principles.
Michael Strickland, Gettysburg College
25
~~~~ Backup Slides ~~~~
Michael Strickland, Gettysburg College
26
Initial State Effect at RHIC
<xd> ~ 0.35 - 0.7 <xd> ~ 0.05
Anti-Shadowing
<xd> ~ 0.008
Shadowing
Ferreiro et al, arXiv:1110.5047
STAR
Michael Strickland, Gettysburg College
27
ALICE Predictions
(b)
Gaussian
Boost Inv. Plateau + Ltd. Frag.
1.2
1
Inclusive Υ(2s) RAA
Inclusive Υ(1s) RAA
(a)
0.8
0.6
0.4
0.2
2.5 < |y| < 4
0 < pT < 50 GeV
0
0
100
1
0.8
0.6
2.5 < |y| < 4
0 < pT < 50 GeV
0.4
0.2
0
200
300
400
0
100
200
300
Npart
Npart
Michael Strickland, Gettysburg College
Gaussian
Boost Inv. Plateau + Ltd. Frag.
1.2
28
400
MS arXiv:1207.5327
Hadrons XII - April 23, 2012
LHC Rapidity Dependence
D Bazow and MS, Nucl. Phys. A 879, 25 (2012); MS, PRL 107, 132301 (2011).
CMS 2011 Data
Michael Strickland, Gettysburg College
29
Short/Medium Range Potential
• Short/medium
range potential welldescribed by an
efficient
parameterization.
Michael Strickland, Gettysburg College
0.4
0.2
a⇥ ⇧
1.0
0.8
0.8
0.6
0.4
0.2
0.1
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
V ⇤ Vvac
0.6
1.0
b⇥ ⇧
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
1.0
1.0
0.9
0.8
0.6
0.4
d⇥ ⇧
10
0.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
0.8
0.7
0.6
0.5
0.6
0.4
0.2
1
V ⇤ Vvac
V ⇤ Vvac
0.8
V ⇤ Vvac
Numerical, ⌅ 0
Model, ⌅ 0
Numerical, ⌅ ⇤⇤2
Model, ⌅ ⇤⇤2
V ⇤ Vvac
• Constrained by
analytic small and
large anisotropy
limits.
1.0
V ⇤ Vvac
• Parameterization is
based on a Debyescreened potential
with a directiondependent Debye
mass.
D Bazow and MS, Nucl. Phys. A 879, 25 (2012); MS, PRL 107, 132301 (2011)
e⇥ ⇧ 100
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
c⇥ ⇧
2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
f⇥ ⇧
1000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
30
V ⇤ Vvac
0.8
D Bazow and MS, Nucl. Phys. A 879, 25 (2012)
0.6
0.4
0.2
a⇥ ⇧
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
0.6
0.4
b⇥ ⇧
0.8
0.7
0.6
0.5
0.6
0.4
0.2
1
0.9
V ⇤ Vvac
V ⇤ Vvac
Michael Strickland, Gettysburg College
0.8
1.0
0.8
d⇥ ⇧ 10
0.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
0.8
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
1.0
0.4
1.0
0.2
0.1
0.6
1.0
V ⇤ Vvac
Numerical, ⌅ 0
Model, ⌅ 0
Numerical, ⌅ ⇤⇤2
Model, ⌅ ⇤⇤2
V ⇤ Vvac
1.0
V ⇤ Vvac
Anisotropic Debye Mass Parameterization
e⇥ ⇧ 100
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
c⇥ ⇧
2
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
f⇥ ⇧
1000
0.0 0.5 1.0 1.5 2.0 2.5 3.0
r⇥
31
Transverse Dynamics
M. Martinez, R. Ryblewski, and MS, arXiv:1204.1473.
Michael Strickland, Gettysburg College
Pb-Pb @ 2.76 TeV
T0 = 600 MeV
τ0 = 0.25 fm/c
b = 7 fm
32
Sequential Suppression
b1
RAA
b2
“Corona effect”
“Decay effect”
Critical Temperature
1
(3s)
Michael Strickland, Gettysburg College
(2s)
(1s)
T [MeV]
33
Sequential Suppression
b1
RAA
b2
“Idealized Case”
Critical Temperature
1
(3s)
Michael Strickland, Gettysburg College
(2s)
(1s)
T [MeV]
34
Sequential Suppression
b1
RAA
b2
“Corona effect”
Critical Temperature
1
(3s)
Michael Strickland, Gettysburg College
(2s)
(1s)
T [MeV]
35
Initial Condition Dependence
D Bazow and MS, Nucl. Phys. A 879, 25 (2012)
1
1
0.8
Full Υ(1s) RAA
Full Υ(1s) RAA
Potential Model B
0.6
0.6
4⇡⌘/S = 2
0.4
0.2
0
0
0.8
sqrt(sNN) = 2.76 TeV
|y| < 2.4
0 < pT < 20 GeV
sqrt(sNN) = 200 GeV
|y| < 2.4
0 < pT < 20 GeV
100
0.4
Wounded Nucleon
Two Component, α=0.145
200
Npart
300
1
nmix (x, y, b) = (1
2
↵ = 0.145
Michael Strickland, Gettysburg College
4⇡⌘/S = 2
0.2
400
Wounded Nucleon
Two Component, α=0.145
Potential Model B
0
0
100
200
Npart
300
400
↵) npart (x, y, b) + ↵ ncoll (x, y, b)
PHOBOS Au
Au @ 200 GeV
36
Formation Time Effect
• Formation time of a bound state in its local rest frame is
given by its inverse binding energy
• In the lab frame the formation time is time dilated
• In this study I assume that the formation time of the states
in the local rest frame is given by the inverse of the
vacuum binding energy which gives Υ(1s) and χb1
Michael Strickland, Gettysburg College
37
The suppression factor
• The suppression factor, RAA, is the ratio of the
number produced in a collision of two symmetric
nuclei (AA) to the amount produced in a protonproton (pp) collision scaled by the expected number
of nucleon collisions
N AA
RAA =
nbinary ⋅ N pp
Number produced in a
nucleus-nucleus collision
Number produced in a
proton-proton collision
Number of pp collisions per nucleus-nucleus collision
Michael Strickland, Gettysburg College
38
CMS Data (2011)
Michael Strickland, Gettysburg College
39
3
Free energy based
potential model
seems incapable of
explaining the data
Michael Strickland, Gettysburg College
40
4
0+1d - Hard Momentum vs Time
M. Martinez and MS, Nuclear Physics A 848, 183 (2010).
2T (⌧ )
2R1/4 (⇠)phard
=
=
5¯
⌘
5¯
⌘
[Strong Coupling]
[Weak Coupling]
[Very Weak Coupling]
Michael Strickland, Gettysburg College
41
0+1d Hydro vs AD : Strong Coupling
M. Martinez and MS, Nuclear Physics A 848, 183 (2010).
⌧0 = 0.2 fm/c
T0 = 350 MeV
⇠0 = 0
Michael Strickland, Gettysburg College
42
0+1d Hydro vs AD : Weak Coupling
M. Martinez and MS, Nuclear Physics A 848, 183 (2010).
⌧0 = 0.2 fm/c
T0 = 350 MeV
⇠0 = 0
Michael Strickland, Gettysburg College
43
0+1d Entropy Production
τ0 = 0.25 fm/c
T0 = 600 MeV
Tf = 150 MeV
τ0 = 0.25 fm/c
T0 = 400 MeV
Tf = 150 MeV
Michael Strickland, Gettysburg College
44
N=4 SUSY using AdS/CFT
• In 0+1 case there are now
numerical solutions of
Einstein’s equations to
compare with.
Fhydro known up
to 3rd order hydro
analytically
[Heller, Janik, and Witaszczyk, arXiv:1103.3452]
• They study a wide variety
of initial conditions and
find a kind of universal
lower bound for the
thermalization time
Red – 1st Order Hydro
Blue – 2nd Order Hydro
Green – 3rd Order Hydro
Grey – GR solution
w > 0.63
RHIC 200 GeV/nucleon:
T0 = 350 MeV, τ0 > 0.35 fm/c
LHC 2.76 TeV/nucleon:
T0 = 600 MeV, τ0 > 0.2 fm/c
Michael Strickland, Gettysburg College
45
N=4 SUSY using AdS/CFT
However, at that time the
system is not isotropic and
remains anisotropic for the
entirety of the evolution
How well does the
aHydro framework
compare?
1.2
Red – 1st Order Hydro
Blue – 2nd Order Hydro
Green – 3rd Order Hydro
Grey – GR solution
0.8
FHwLêw
=
1.0
0.6
0.4
= 0.31
Michael Strickland, Gettysburg College
0.2
0.0
0.0
Black - aHydro
Red – 1st Order Hydro
Blue – 2nd Order Hydro
Green – 3rd Order Hydro
0.5
1.0
w
1.5
2.0
46