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February 6-11, 2017, Chicago, IL, USA
XXVI international conference on ultrarelativistic heavy-ion collisions: Quark Matter 2017
Prithwish Tribedy
Disentangling flow and signals of Chiral Magnetic Effect in U+U and Au+Au
collisions
(for the STAR Collaboration)
February 6-11, 2017, Chicago, IL, USA
XXVI international conference on ultrarelativistic heavy-ion collisions: Quark Matter 2017
Prithwish Tribedy
Disentangling flow and signals of Chiral Magnetic Effect in U+U and Au+Au
collisions
(for the STAR Collaboration)
2
Motivation : Separation of flow and CMESTAR Experiment at RHIC
Large Coverage: 0 < φ < 2π, |η| < 1.0 Uniform acceptance: transverse momentum (pT) and rapidity (y) Excellent particle identification capabilities (TPC and TOF)
5
Year √sNN (GeV)
Minimum Bias
Events(106)
2010 62.4 67
2010 39 130
2011 27 70
2011 19.6 36
2014 14.5 20
2010 11.5 12
2010 7.7 4
BES-I Dataset TPC MTD Magnet BEMC BBC EEMC TOF
HFT @ Maria & Alex Schmah
• M. Anderson et al., Nucl. Instrum. Meth. A 499 (2003) 659 • W. J. Llope., Nucl. Instrum. Meth. A 661 (2012) S110–S113
12/02/16
Time-Projection Chamber (used for this analysis)
STAR Detector
v2{2}2 = �cos(2(�1 � �2))��a,b � �cos((�a1 + �b
2 � 2�3))�v2{2}
Observables :
LPV correlator :
C112 = ⟨cos(φ1+φ2−2φ3)⟩
,
Three particle correlator :
CME : QCD anomaly driven chirality imbalance leads to current along B-field 3
Axial charge Vector charge j0
v
j0a
x
yz
FIG. 1. Illustration of real-time dynamics of the chiral magnetic wave for light quarks (mrsph ⌧ 1 ). Contour lines representthe distribution of axial and vector charges at times t/tsph = 0.6, 0.9, 1.1, 1.3, 1.6, 1.9 of the evolution. Simulations wereperformed on a 24⇥ 24⇥ 64 lattice.
the magnetic screening length (see e.g. [13, 43, 44]) a con-version to physical units can be achieved by assigning avalue of about 200�500 MeV to r�1
sph. If not stated other-wise we use a lattice spacing of rsph/a = 6, the durationof the sphaleron transition is chosen as tsph = 3/2rsph
(corresponding to ⇠ 0.6 � 1.5 fm/c) and the magneticfield strengths considered in this work is qB = 3.5r�2
sph
(corresponding to a few m2⇡
).Non-equilibrium dynamics of axial and vector
charges We will now analyze the dynamics of the axialand vector charges during and after a sphaleron transi-tion, and first focus on the anomalous transport of lightquarks with mrsph ⌧ 1, where dissipative e↵ects due to afinite quark mass can be neglected over the time scale ofa sphaleron transition. Our results for the time evolutionof the axial and vector densities j0
v/a
(t, x) in the presenceof an external magnetic field are compactly summarizedin Fig. 1 where we show contour lines of the distributionsat various stages of the time evolution.
We observe that during the sphaleron transition, a lo-cal imbalance of axial charge j0
a
is generated according tothe axial anomaly; at the same time the chiral magnetice↵ect induces a vector current jz
v
with a similar profilein coordinate space. Conservation of the vector current@
µ
jµ
v
= 0, implies that longitudinal gradients of the cur-rent @
z
jz
v
, lead to separation of electric charges alongthe direction of ~B; over time electric charge accumulatesat the edges of the sphaleron, resulting in a dipole likestructure of the vector charge density j0
v
observed e.g. att/tsph = 0.6, 0.9 in Fig. 1.
Since the local imbalance of vector charge j0v
in turninduces an axial current ~j
a
/ j0v
~B due to the chiral sep-aration e↵ect (CSE) [45], the combination of CME andCSE ultimately leads to the formation of a chiral mag-netic wave [18, 46]. We observe from Fig. 1, that the
chiral magnetic wave manifests itself as the propagationof a soliton-like wave-packet associated with the non-dissipative transport of axial and vector charges alongthe direction of magnetic field. We note that this is thefirst time that the emergence of such a collective exci-tation is confirmed in non-perturbative real-time latticegauge theory simulations.Chiral magnetic wave: The dynamics of the chiral
magnetic wave can be further investigated by integratingout the transverse coordinates to study the propagationof the wave-packet along the longitudinal direction. Thisallows us to compare the results of our microscopic simu-lations with a macroscopic description within the frame-work of anomalous hydrodynamics in a straightforwardway. In anomalous hydrodynamics [18–21], the coupleddynamics of axial and vector charges is described in termsof conservation laws and the constitutive relations of thecurrents, which to leading order in gradients and in pres-ence of an external magnetic field Bµ = (0, 0, 0, B) takethe form [19]
jµ
v,a
= nv,a
uµ + Dv,a
Oµnv,a
+ �B
v,a
Bµ . (7)
Specifically, for a system of non-interacting fermions, thedi↵usion constant D
v,a
, vanishes and the anomalous con-ductivities are simply given by �B
v,a
= na,v
/B when the
magnetic field strength is su�ciently large B � r�2sph, m2
[2]. In the local rest-frame uµ = (1, 0, 0, 0), the anoma-lous hydrodynamic equations of motion for the integratedquantities j0,z
v,a
(t, z) =R
d2x? j0,z
v,a
(t, x?, z) then take theform,
@t
✓j0v
(t, z)j0a
(t, z)
◆= �@
z
✓j0a
(t, z)j0v
(t, z)
◆+
✓0
S(t, z)
◆(8)
with the sphaleron induced source term given as S(t, z) =
� g
2
8⇡
2
Rd2x?Tr Fµ⌫ F̃
µ⌫
. The solutions for the vector and
Fig: Muller, Schlichting, Sharma, PRL 117 142301 (2016)
B→
Goal : Search for signals of CME & suppress flow driven background Voloshin, PRC 70 (2004) 057901
Prithwish Tribedy, QM 2017, Chicago
Prithwish Tribedy, QM 2017, Chicago
31
v2
Δγ
B-field driven
0
v2
Δγ
If Background dominates
All Bkg
B-field
Total
Δγ ~0
v ~02
min
Δγmax
v2,max
Chatterjee, Tribedy PRC 92, 011902 (2015)
v2
Δγ
If B-field dominates
All Bkg
B-fieldTotal
Δγ ~0
v ≠02
Δγmax
0min
v2,max
Signal and background of CME
v2
Δγ
0
Voloshin PRC 70 (2004) 057901, Schlichting, Pratt, PRC 83 014913 (2011), Wang PRC 81 064902 (2010),Bzdak, Koch, Liao PRC 83 014905 (2011)
Flow driven
3
Signal & Backgrounds of charge separation
HBT, Coulomb
Flowing resonance
Charge conservation
Momentum conservation
v2
Background
Charge separation(central-events)
�a,b =�cos(�a1 + �b
2�2�2)�
Δγ→0, v2→0
(γOS − γSS)Background ≈ v2{2}N
≥ 0
Prithwish Tribedy, QM 2017, Chicago
31
v2
Δγ
B-field driven
0
v2
Δγ
If Background dominates
All Bkg
B-field
Total
Δγ ~0
v ~02
min
Δγmax
v2,max
Chatterjee, Tribedy PRC 92, 011902 (2015)
v2
Δγ
If B-field dominates
All Bkg
B-fieldTotal
Δγ ~0
v ≠02
Δγmax
0min
v2,max
Signal and background of CME
v2
Δγ
0
Voloshin PRC 70 (2004) 057901, Schlichting, Pratt, PRC 83 014913 (2011), Wang PRC 81 064902 (2010),Bzdak, Koch, Liao PRC 83 014905 (2011)
Flow driven
4
Signal & Backgrounds of charge separation
HBT, Coulomb
Flowing resonance
Charge conservation
Momentum conservation
v2
Background
Magnetic fieldSignal
Ψ2
Charge separation(central-events)
�a,b =�cos(�a1 + �b
2�2�2)�
Δγ→0, v2→0
Δγ→0, v2 ≠ 0
(γOS − γSS)Background ≈ v2{2}N
≥ 0
≈ ⟨B2cos(2(ΨB−Ψ2))⟩
Prithwish Tribedy, QM 2017, Chicago
31
v2
Δγ
B-field driven
0
v2
Δγ
If Background dominates
All Bkg
B-field
Total
Δγ ~0
v ~02
min
Δγmax
v2,max
Chatterjee, Tribedy PRC 92, 011902 (2015)
v2
Δγ
If B-field dominates
All Bkg
B-fieldTotal
Δγ ~0
v ≠02
Δγmax
0min
v2,max
Signal and background of CME
v2
Δγ
0
Voloshin PRC 70 (2004) 057901, Schlichting, Pratt, PRC 83 014913 (2011), Wang PRC 81 064902 (2010),Bzdak, Koch, Liao PRC 83 014905 (2011)
Flow driven
5
Signal & Backgrounds of charge separation
HBT, Coulomb
Flowing resonance
Charge conservation
Momentum conservation
v2
Background
Magnetic fieldSignal
Ψ2
Charge separation(central-events)
�a,b =�cos(�a1 + �b
2�2�2)�
(γOS − γSS)Background ≈ v2{2}N
≥ 0
≈ ⟨B2cos(2(ΨB−Ψ2))⟩
Strategy : look for vanishing Δγ when v2 is still non-zero
Δγ→0, v2→0
Δγ→0, v2 ≠ 0
Prithwish Tribedy, QM 2017, Chicago 6
Analysis details
— Data Set used : U+U 193 GeV (Year 2012), Au+Au 200 GeV (Year 2011), p+Au 200 GeV (Year 2015)
— Acceptance cuts : 0<φ<2π, |η|<1, pT > 0.2 GeV/c
— Centrality : Time Projection Chamber & Zero Degree Calorimeter
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
Uncorrected multiplicity in |η|<0.5
Multiplicity binning Spectator binning
Neutron response of ZDCs
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
esZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
STAR preliminary
STAR preliminary
Centrality Selection
12
0.1
1
10
100
1000
10000
0 100 200 300 400 500 600 700 800
U+U 193 GeV
Entri
es
Refmult
Min-bias0-2%2-4%4-6%6-8%8-10%
-Method 1 (using RefmultCorr)
1
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
U+U 193 GeV
Entri
es
ZDCUnAttenuated (East+West)
Min-bias8-10
6-84-62-40-2
-Method 2 (using ZDCs)
8
Body-Tip (0-1%)
Body-Tip Collisions (U+U)
Different trend than conventional centrality binning
0.026
0.027
0.028
0.029U+U 193 GeV
0-1%
v 2 {
2}
-0.1
0
0.1
0.2
0 1 2 3 4 5
(γO
S -γSS
) × 1
04
|L-R| bin
STAR preliminary
STAR preliminary
STAR preliminary
Binning in spectator asymmetry → independent from centrality binning
Body-Tip
0
0.1
0.2
0.3
0.4
0.02 0.03 0.04U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Global-DataBody-Tip
Asymmetry percentile %
Prithwish Tribedy, QM 2017, Chicago
γab– v2 correlation plot (multiplicity & spectators)
14
Observations in 0-10%:
• Strong correlation linear in central events : universal curve
Dominance of fluctuations of participants and spectators
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
0.025 0.035 0.045
U+U 193 GeV 0-10%∆η>0.025
(γO
S -γSS
) × 1
04
v2 {2}
RefMult binningZDC binning
7
0
0.1
0.2
0.3
0.4
0 0.01 0.02 0.03 0.04
U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Multiplicity binningSpectator binning
Results : Central and Ultra-central Collisions
U+U Au+Au
0
0.5
1
0 0.01 0.02 0.03 0.04 0.05
Au+Au 200 GeV
(γO
S -γSS
) × 1
04v2 {2}
Run 4 (0909.1717)Run 7 (1302.3802)Run 11 Cumulant (0-1%)
STAR preliminary
STAR preliminary
Prithwish Tribedy, QM 2017, Chicago
γab– v2 correlation plot (multiplicity & spectators)
14
Observations in 0-10%:
• Strong correlation linear in central events : universal curve
Dominance of fluctuations of participants and spectators
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
0.025 0.035 0.045
U+U 193 GeV 0-10%∆η>0.025
(γO
S -γSS
) × 1
04
v2 {2}
RefMult binningZDC binning
8
0
0.1
0.2
0.3
0.4
0 0.01 0.02 0.03 0.04
U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Multiplicity binningSpectator binning
Results : Central and Ultra-central Collisions
U+U Au+Au
0
0.5
1
0 0.01 0.02 0.03 0.04 0.05
Au+Au 200 GeV
(γO
S -γSS
) × 1
04v2 {2}
Run 4 (0909.1717)Run 7 (1302.3802)Run 11 Cumulant (0-1%)
STAR preliminary
STAR preliminary
Data :- Show vanishing charge separation for non-zero values of v2 {2}- Show linear growth with v2 {2}- Show larger v2 {2} offset (Δγ=0) for U+U than Au+Au
Prithwish Tribedy, QM 2017, Chicago 9
Data
0
0.1
0.2
0.3
0.4
0 0.01 0.02 0.03 0.04
U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Multiplicity binningSpectator binning
γab– v2 correlation plot (multiplicity & spectators)
14
Observations in 0-10%:
• Strong correlation linear in central events : universal curve
Dominance of fluctuations of participants and spectators
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
0.025 0.035 0.045
U+U 193 GeV 0-10%∆η>0.025
(γO
S -γSS
) × 1
04
v2 {2}
RefMult binningZDC binning
STAR preliminary
Central and Ultra-central Collisions
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
10
Data
MC-Glauber
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
Projected B-field
0
1
2
3
4
5
0 0.05 0.1 0.15
U+U 193 GeV0-10 %
-⟨|eB
2 |cos
(2(Ψ
B-Ψ
2)) ⟩
(fm
)-4
Ellipticity ε2
Multiplicity binningSpectator binning
Chatterjee, Tribedy, PRC 92, 011902 (2015)
0
0.1
0.2
0.3
0.4
0 0.01 0.02 0.03 0.04
U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Multiplicity binningSpectator binning
γab– v2 correlation plot (multiplicity & spectators)
14
Observations in 0-10%:
• Strong correlation linear in central events : universal curve
Dominance of fluctuations of participants and spectators
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
0.025 0.035 0.045
U+U 193 GeV 0-10%∆η>0.025
(γO
S -γSS
) × 1
04
v2 {2}
RefMult binningZDC binning
STAR preliminary
Projected B-field vs ε2 can provide a natural explanation to the data
Central and Ultra-central Collisions
{x,y}=〈x〉, 〈y〉
Prithwish Tribedy, QM 2017, Chicago 11
Data
0
0.1
0.2
0.3
0.4
0 0.01 0.02 0.03 0.04
U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Multiplicity binningSpectator binning
γab– v2 correlation plot (multiplicity & spectators)
14
Observations in 0-10%:
• Strong correlation linear in central events : universal curve
Dominance of fluctuations of participants and spectators
0 0.05
0.1 0.15
0.2 0.25
0.3 0.35
0.4
0.025 0.035 0.045
U+U 193 GeV 0-10%∆η>0.025
(γO
S -γSS
) × 1
04
v2 {2}
RefMult binningZDC binning
STAR preliminary
We need to see if a background model can explain data
Central and Ultra-central Collisions
STAR preliminary
Data & Background expectations
∆γBackground = (γOS − γSS)Background ≈ v2{2}N
0
0.005
0.01
0.015
0.02
0 0.02 0.04
0-20%(Background-model)
U+U 193 GeV
∆γ
× N
part
v2 {2}
Data∆γ ∝ v2 /Npart
⇒ ∆γBackground ×N ≈ v2{2}
Prithwish Tribedy, QM 2017, Chicago 12
Body-Tip (0-1%)
Body-Tip Collisions (U+U)
STAR preliminary
STAR preliminary
Binning in spectator asymmetry → independent from centrality binning
0.026
0.027
0.028
0.029
U+U 193 GeV0-1%v 2
{2}
-0.1
0
0.1
0.2
0 20 40 60 80 100
(γO
S -γSS
) × 1
04
Symmetry Percentile %
Provides a way to trigger even smaller v2 {2}
8
Body-Tip (0-1%)
Body-Tip Collisions (U+U)
Different trend than conventional centrality binning
0.026
0.027
0.028
0.029U+U 193 GeV
0-1%
v 2 {
2}
-0.1
0
0.1
0.2
0 1 2 3 4 5
(γO
S -γSS
) × 1
04
|L-R| bin
STAR preliminary
STAR preliminary
STAR preliminary
Binning in spectator asymmetry → independent from centrality binning
Body-Tip
0
0.1
0.2
0.3
0.4
0.02 0.03 0.04U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Global-DataBody-Tip
Asymmetry percentile %
Chatterjee, Tribedy, PRC 92, 011902 (2015)
Prithwish Tribedy, QM 2017, Chicago 13
Body-Tip (0-1%)
Body-Tip Collisions (U+U)
Different trend than conventional centrality binning
STAR preliminary
STAR preliminary
STAR preliminary
Binning in spectator asymmetry → independent from centrality binning
Body-Tip
0
0.1
0.2
0.3
0.4
0.02 0.03 0.04U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Global-DataBody-Tip
8
Body-Tip (0-1%)
Body-Tip Collisions (U+U)
Different trend than conventional centrality binning
0.026
0.027
0.028
0.029U+U 193 GeV
0-1%
v 2 {
2}
-0.1
0
0.1
0.2
0 1 2 3 4 5
(γO
S -γSS
) × 1
04
|L-R| bin
STAR preliminary
STAR preliminary
STAR preliminary
Binning in spectator asymmetry → independent from centrality binning
Body-Tip
0
0.1
0.2
0.3
0.4
0.02 0.03 0.04U+U 193 GeV
(γO
S -γSS
) × 1
04
v2 {2}
Global-DataBody-Tip
Asymmetry percentile %
0.026
0.027
0.028
0.029
U+U 193 GeV0-1%v 2
{2}
-0.1
0
0.1
0.2
0 20 40 60 80 100
(γO
S -γSS
) × 1
04
Symmetry Percentile %
Provides a way to trigger even smaller v2 {2}
-0.43±0.03 +(17±1)xv2
-2.9±0.1 +(93±4)xv2
Prithwish Tribedy, QM 2017, Chicago
31
v2
Δγ
B-field driven
0
v2
Δγ
If Background dominates
All Bkg
B-field
Total
Δγ ~0
v ~02
min
Δγmax
v2,max
Chatterjee, Tribedy PRC 92, 011902 (2015)
v2
Δγ
If B-field dominates
All Bkg
B-fieldTotal
Δγ ~0
v ≠02
Δγmax
0min
v2,max
Signal and background of CME
v2
Δγ
0
Voloshin PRC 70 (2004) 057901, Schlichting, Pratt, PRC 83 014913 (2011), Wang PRC 81 064902 (2010),Bzdak, Koch, Liao PRC 83 014905 (2011)
Flow driven
14
Signal & Backgrounds of charge separation
HBT, Coulomb
Flowing resonance
Charge conservation
Momentum conservation
v2
Background
Magnetic fieldSignal
Ψ2
Charge separation(central-events)
�a,b =�cos(�a1 + �b
2�2�2)�
Δγ→0, v2→0
Δγ→0, v2 ≠ 0
Jet-fragmentation Ψ2 ?
Prithwish Tribedy, QM 2017, Chicago 15
Anatomy of three-particle correlationsSearch of early time charge separation → should be long-range in Δη
STAR preliminary
-0.002
-0.001
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
(All-charge) U+U 193 GeV (30-40%)
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
∆η12
fitShort-range-positive
Residualpedestal
C112(∆η12) = A+
SRe−(∆η)2/2σ2
SR −A−
IRe−(∆η)2/2σ2
IR +ALR
Prithwish Tribedy, QM 2017, Chicago 44
t
z
Δη1
τ3τ2τ1
Δη
2Δη
3
-
--
+
++
Prithwish Tribedy, QM 2017, Chicago 16
Anatomy of three-particle correlationsSearch of early time charge separation → should be long-range in Δη
Short-range-positive
Short-range limit : C112 = ⟨cos(φ1(η1)+φ2(η2)−2φ3)⟩ ≥ 0∆φ → 0,∆η → 0 :
STAR preliminary
-0.002
-0.001
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
(All-charge) U+U 193 GeV (30-40%)
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
∆η12
fitShort-range-positive
Residualpedestal
C112(∆η12) = A+
SRe−(∆η)2/2σ2
SR −A−
IRe−(∆η)2/2σ2
IR +ALR
Prithwish Tribedy, QM 2017, Chicago 44
t
z
Δη1
τ3τ2τ1
Δη
2Δη
3
-
--
+
++
Prithwish Tribedy, QM 2017, Chicago 17
Anatomy of three-particle correlationsSearch of early time charge separation → should be long-range in Δη
ResidualShort-range-positive
Short-range limit : C112 = ⟨cos(φ1(η1)+φ2(η2)−2φ3)⟩ ≥ 0∆φ → 0,∆η → 0 :
STAR preliminary
-0.002
-0.001
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
(All-charge) U+U 193 GeV (30-40%)
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
∆η12
fitShort-range-positive
Residualpedestal
C112(∆η12) = A+
SRe−(∆η)2/2σ2
SR −A−
IRe−(∆η)2/2σ2
IR +ALR
Prithwish Tribedy, QM 2017, Chicago 44
t
z
Δη1
τ3τ2τ1
Δη
2Δη
3
-
--
+
++
Prithwish Tribedy, QM 2017, Chicago
-0.002
0
0.002
0.004
0.4 0.8 1.2 1.6
70-80%
U+U 193 GeV
opposite-sign
∆η12
-0.001
0
0.001 30-40%
U+U 193 GeV
opposite-sign
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
fitShort-range-positive
Residual
-0.0002-0.0001
0 0.0001 0.0002 0-5%
U+U 193 GeV
opposite-sign
-0.002
0
0.002
0.4 0.8 1.2 1.6
70-80%
U+U 193 GeV
same-sign
∆η12
-0.003
-0.001
0.001 30-40%
U+U 193 GeV
same-sign
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
fitShort-range-positive
Residual
-0.0004-0.0002
0 0.0002 0-5%
U+U 193 GeV
same-sign
18
Comparison between U+U centralities
STAR preliminary STAR preliminary
Opposite-signSame-sign
Peripheral
Central
Very different trend between central and peripheral events
Prithwish Tribedy, QM 2017, Chicago 19
ResidualShort-range-positive
Comparison between U+U centralities
STAR preliminary
STAR preliminary
Central
Peripheral
-0.004
-0.002
0
0 0.4 0.8 1.2 1.6
70-80%
U+U 193 GeV
∆η12
-0.004
-0.002
030-40%
U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
opposite-signsame-sign
-0.004
-0.002
00-5%
U+U 193 GeV
0
0.001
0.002
0.003
0 0.4 0.8 1.2 1.6
70-80%
U+U 193 GeV
∆η12
0
0.001
0.002
0.003
30-40%
U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
opposite-signsame-sign
0
0.001
0.002
0.003
0-5%
U+U 193 GeV
Prithwish Tribedy, QM 2017, Chicago 20
Centrality dependence of charge separation
STAR preliminary
�a,b � �cos((�a1 + �b
2 � 2�3))�v2{2} � �� = �OS��SS
After short-range-positive subtraction, Δγ → 0 for small & large Npart
Short-range positive component: Likely HBT, Coulomb & jet-fragmentation in peripheral eventsOnly HBT, Coulomb in central events.
Residual component:May still have short-range backgrounds in mid-central events
Charge separation :
STAR preliminary
Widths of different componentsMagnitudes of different components
0.01
0.1
1
10
0 100 200 300 400
U+U 193 GeV
σ∆η
Npart
Short-range-positiveResidual
0
0.01
0.02
0.03
0 100 200 300 400 500
U+U 193 GeV
∆γ
× N
part
Npart
TotalResidual
Short-range-positive
Prithwish Tribedy, QM 2017, Chicago 21
Opposite-signSame-signComparison between U+U and p+Au
STAR preliminary
STAR preliminary
p+A
Peripheral
Central
A+A
A+A
Min-bias
p+Au data are consistent with peripheral U+U
-0.002
0
0.002
0.004
0.4 0.8 1.2 1.60-100% p+Au 200 GeV
opposite-sign
∆η12
fitShort-range-positive
Residual
-0.002
0
0.002
0.004
70-80% U+U 193 GeV
opposite-sign
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
-0.001
0
0.001
30-40% U+U 193 GeV
opposite-sign
-0.002
0
0.002
0.004
0.4 0.8 1.2 1.60-100% p+Au 200 GeV
same-sign
∆η12
fitShort-range-positive
Residual
-0.002
0
0.002
0.004 70-80% U+U 193 GeV
same-sign
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
-0.002
0
0.002 30-40% U+U 193 GeVsame-sign
Prithwish Tribedy, QM 2017, Chicago 22
Short-range-positive
Comparison between U+U and p+Au
STAR preliminary
STAR preliminary
Short-range subtracted component vanishes in p+Au
p+A
Peripheral
Central
A+A
A+A
Min-bias
Residual
-0.004
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.004
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
opposite-signsame-sign
-0.004
-0.002
030-40% U+U 193 GeV
0
0.001
0.002
0.003
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
U+U 193 GeV
∆η12
0
0.001
0.002
0.003
70-80% U+U 200 GeV
U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt
0
0.001
0.002
0.003
30-40% U+U 200 GeV
U+U 193 GeV
opposite-signsame-sign
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
23
Data (short-range-positive subtracted)
Comparison between U+U and p+Au
Ultra-Central A+A
STAR preliminary
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
Projected B-field in A+A
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
{x,y}=〈x〉, 〈y〉
MC-Glauber Chatterjee, Tribedy,
PRC 92, 011902 (2015)
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
24
Comparison between U+U and p+Au
Ultra-Central A+A
STAR preliminary
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
Projected B-field in A+A
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
{x,y}=〈x〉, 〈y〉
Peripheral A+A
Data (short-range-positive subtracted)
MC-Glauber Chatterjee, Tribedy,
PRC 92, 011902 (2015)
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
25
Projected B-field in A+A
Comparison between U+U and p+Au
Ultra-Central A+APeripheral A+ABelmont, J.L. Nagle 1610.07964
p+A
0<Ψ2<2π
B
STAR preliminary-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
{x,y}=〈x〉, 〈y〉
Data (short-range-positive subtracted)
MC-Glauber Chatterjee, Tribedy,
PRC 92, 011902 (2015)
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
26
Projected B-field in A+A
Comparison between U+U and p+Au
Ultra-Central A+APeripheral A+AShort-range-positive
component subtracted charge separation vanishes the same
way as projected B-field
Belmont, J.L. Nagle 1610.07964
p+A
0<Ψ2<2π
B
STAR preliminary-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
{x,y}=〈x〉, 〈y〉
Terra Ignota (Need Isobars)
Data (short-range-positive subtracted)
MC-Glauber Chatterjee, Tribedy,
PRC 92, 011902 (2015)
Prithwish Tribedy, QM 2017, Chicago
— Ultra-central U+U and Au+Au show Δγ ~0, v2≠0
• Δγ vs v2 consistent with B-field vs ε2, constrain for background models of charge separation
—Short-range-positive component (ASR) subtracted charge separation vanishes in central & peripheral events
— p+Au data show no ASR subtracted charge separation, consistent to peripheral A+A
• ASR subtracted signal follow projected B-field in central, peripheral A+A & in p+Au
27
Summary
Current data helped to disentangle signal/background in the limits of vanishing projected B-field. Isobar collisions at RHIC will help clarify the origin of charge separation in the regime of finite B-field.
0
0.2
0.4
0 0.02 0.04
∆γ
× 10
4
v2 {2}
Multiplicity binningSpectator binning
U+UAu+A
uSTAR preliminary
STAR preliminary
-40
-20
0
0 0.4 0.8 1.2 1.6
p+Au 200 GeV
C11
2 ×
Npa
rt
×
104
∆η12
opposite-signsame-sign
-40
-20
0
0 0.4 0.8 1.2 1.6
U+U 193 GeV (70-80%)
C11
2 ×
Npa
rt
×
104
∆η12
opposite-signsame-sign
STAR preliminary
+
+
+
Prithwish Tribedy, QM 2017, Chicago
backup slides
28
Prithwish Tribedy, QM 2017, Chicago
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
Components of LPV correlator
0
0.01
0.02
0.03
0 100 200 300 400
U+U 193 GeV
(γO
S -γSS
)× N
part
Npart
TotalLong-rangeShort-range
STAR preliminary
MC-Glauber
Projected B-fieldData
0
5
10
15
20
0 100 200 300 400-⟨ B2 c
os(2
(ΨB
- Ψ2)
) ⟩ [
fm-4
]
Npart
U+U 193 GeV
Ψ2
B
0<Ψ2<2π0<Ψ2<2π 0<ΨB<2π
BB
29
Projected B-field in A+A
Comparison between U+U and p+Au
Ultra-Central A+APeripheral A+AShort-range-positive
component subtracted charge separation vanishes the same
way as projected B-field
Belmont, J.L. Nagle 1610.07964
p+A
0<Ψ2<2π
B
STAR preliminary-0.002
0
0 0.4 0.8 1.2 1.6
0-100% p+Au 200 GeV
∆η12
-0.002
070-80% U+U 193 GeV
⟨cos
(φ1
+ φ 2
- 2φ
3)⟩ ×
Npa
rt -0.002
00-1% U+U 193 GeV
opposite-signsame-sign
Terra Ignota (Need Isobars)
Data (short-range-positive subtracted)
0
0.4
0.8
1.2
0 100 200 300 400
U+U 193 GeV
Y/⟨Y⟩ m
ax
Npart
Y=-⟨ B2 cos(2(ΨB - Ψ2)) ⟩Y=v2 {2}
Prithwish Tribedy, QM 2017, Chicago 30
Outlook for Isobar collisions at RHIC
Zr +Zr Ru +Ru Au +Au
Idea is to change B-field without changing background
Single collision in IP-Glasma model (b=0)
Ru4496
Ru4496+ Zr40
96Zr40
96+
Different B-field with same flow background is expected √s =200 GeV
% Most central0 20 40 60 80
part
* N
γ∆
0
0.01
0.02
Ru+RuZr+Zr
(a)
= 200 GeVNNs
80% bgprojection with 1.2B events
% Most central0 20 40 60 80
(Ru+
Ru
- Zr+
Zr)
γ∆
Rel
. dif.
in
0.1−
0.05−
0
0.05
0.1 = 200 GeVNNs
(b)
)2∈ from σ rel. dif. (5γ∆
rel. dif. (case 1)2∈ rel. dif. (case 2)2∈
3.5 weeks of running with about 1.2 B events can provide about 5σ confidence of signal/bkg.
Gang Wang, QCD Chirality workshop ‘2016, Deng et al PRC 94, 041901 (2016), Skokov et al, 1608.00982
31
v2
Δγ
B-field driven
0
v2
Δγ
If Background dominates
All Bkg
B-field
Total
Δγ ~0
v ~02
min
Δγmax
v2,max
Chatterjee, Tribedy PRC 92, 011902 (2015)
v2
Δγ
If B-field dominates
All Bkg
B-fieldTotal
Δγ ~0
v ≠02
Δγmax
0min
v2,max
Signal and background of CME
v2
Δγ
0
Voloshin PRC 70 (2004) 057901, Schlichting, Pratt, PRC 83 014913 (2011), Wang PRC 81 064902 (2010),Bzdak, Koch, Liao PRC 83 014905 (2011)
Flow driven