Download Search for Chiral Magnetic Effects in Au + Au Collisions at STAR

Search for Chiral Magnetic Effects in
Au + Au Collisions at STAR
Hongwei Ke1, 2 for the STAR Collaboration 1. 
2. 
Mar. 15, 2013 Central China Normal University Brookhaven National Laboratory Moriond QCD and High Energy Interactions
1 Outline Ø Motivation
Ø STAR Experiment
Ø Observations
•  Three-particle correlation
•  Charge asymmetry dependency of pion
azimuthal anisotropy
Ø Summary
Mar. 15, 2013 Moriond QCD and High Energy Interactions
2 QCD Vacuum Transi;on Gluonic field
potential energy
NC
S
= 2
-1
instanton
0
1
sphaleron
2
•  Gluonic field energy is periodic in Chern–Simons number (NCS) direction
•  Winding number
QW = NCS (+1)
NCS ( 1)
•  Nonzero topological charge generates chirality imbalance
NLf
NRf = 2QW
•  QCD vacuum transition è nonzero topological charge è chirality imbalance
QW 6= 0 ! µA 6= 0
Mar. 15, 2013 Moriond QCD and High Energy Interactions
3 CME, CSE and CMW •  Chiral Magnetic Effect (CME): nonzero axial charge density induces a vector
(electric) current along external magnetic field.
jV =
Nc e
µA B
2⇡ 2
è
electric charge separation along B field
•  Chiral Separation Effect (CSE): nonzero vector charge density induces an axial
(chiral) current along external magnetic field.
Nc e
jA =
µV B è chiral charge separation
The Chiral
Magnetic
along
B fieldWave
2⇡ 2
DK, H.-U. Yee,
arXiv:1012.6026 [hep-th]
•  Chiral Magnetic Wave (CMW): CME and CSE
CMEinduce each
Chiralother;
separation
form density waves of electric and chiral charge
✓
@0 ⌥
Nc eB↵
@1
2⇡ 2
◆
0
DL @12 jL,R
=0
Chiral
Propagating chiral wave:
Electric
collective
mode Nuclear Physics A 803, 227 (2008)
D. Kharzeev, L. McLerran,Gapless
and H.
Warringa,
11
D. T. Son and A. R. Zhitnitsky, Phys. Rev. D 70, 074018
(2004)
D. Kharzeev and H.-U. Yee, Physical Review D 83, 085007 (2011)
Mar. 15, 2013 Moriond QCD and High Energy Interactions
4 Heavy Ion Collisions The existence of the background magnetic field is illustrated in figure 6.2. The
p
Au + Au
sN N = 200GeV
Nuclear Physics A 803, 227 (2008).
•  Chiral symmetry restoration
Figure 6.2: A non-central heavy-ion collision showing the magnetic field
•  Extremely strong magnetic field created in heavy ion collision, ~1015 Tesla!
n grid represents
the reaction
plane. Effect
The ovalè
orange/red
zone represents
•  Chiral
Magnetic
out-of-plane
electric the
charge
separation
sion participants
while the
blue partialEffect
spheresè
represent
the spectators.
•  Chiral
Separation
out-of-plane
chiral The
charge
separation
ctators are highly
charged
and are moving
at speeds
close
to that of light.
•  Chiral
Magnetic
Wave è
electric
quadrupole
moment
a mid-central collision with the impact parameter b ∼ .8 times the radius
15, 2013 each blue partial sphere
Moriond
and High
Energy Interactions
he GoldMar. nucleus,
will QCD
contain
on average
half of
5 Rela;vis;c Heavy-­‐Ion Collider Mar. 15, 2013 Moriond QCD and High Energy Interactions
6 STAR detector
STAR Experiment BEMC
TOF
Magnet
TPC
EEMC
BBC
upVPD
Large & Uniform acceptance for all energies
TPC: Full azimuthal angle and large pseudo-rapidity coverage
Mar. 15, 2013 Moriond QCD and High Energy Interactions
7 g magnetic field, induces a electric current along the diction of magnetic field. This
Chiral Magne;c Effect -plane electric charge separation manifests itself via preferential same-charge par-
emission along the diction of magnetic field and opposite-charge particles emission
itely along the diction of magnetic field. A P -odd sine term in the Fourier series
chargeØ 
particle
azimuthal
distribution
can be
used distribution
to describe such e↵ect.
Charge
particle
azimuthal
angle
• 
dN↵
∝1 + 2v1,↵ cos(
d
+ 2a1,↵ sin(
) + 2v2,↵ cos(2
) + 2a2,↵ sin(2
)+�
)+�
(4.17)
. (4.17), coefficients
a reflect the aPα-violating
e↵ect,
↵ represent the sign of electric
aβ can be
•  Correlations
measured
e of particles,• 
α,= (β =− +,RP-) is azimuthal angle with respect to the reaction plane
52
Ø  Three-particle correlation
= hcos ( ↵ +
• 
RP )i
= [hv1,↵ v1, i + Bin ] [ha↵ a i + Bout ]
•  Direct flow term v1,α v1,β is small and expected to be the same for SS and OS
•  In plane (Bin) and out-of-plane (Bout) correlations largely cancel out
•  aα aβ is sensitive to charge separation
os > 0, ↵ =
ss
< 0, ↵ =
S. A. Voloshin, Parity violation in hot qcd: How to detect it, Phys. Rev. C 70, 057901 (2004)
Mar. 15, 2013 Moriond QCD and High Energy Interactions
8 20
2.76 TeV Pb+Pb
200 GeV Au+Au
-2
62.4 GeV Au+Au
39 GeV Au+Au
27 GeV Au+Au
10
RP
) ] ×104
Centrality dependence of γos & γss Opposite Sign: =0
+
Same Sign: =
20
[ = cos(
19.6 GeV Au+Au
11.5 GeV Au+Au
7.7 GeV Au+Au
10
0
STAR preliminary
80
60
40
20
0
60
40
20
% Most Central
0
60
40
20
0
•  From 2.76 TeV to 7.7 GeV, changes start to show from the peripheral collisions.
ALICE Collaboration, Phys. Rev. Lett. 110, 012301 (2013)
Mar. 15, 2013 Moriond QCD and High Energy Interactions
9 Use γos - γss as signal 2.76 TeV Pb+Pb
200 GeV Au+Au
10
62.4 GeV Au+Au
39 GeV Au+Au
27 GeV Au+Au
0
-5
10
19.6 GeV Au+Au
11.5 GeV Au+Au
7.7 GeV Au+Au
[
OS
-
SS
] ×104
5
5
0
-5
80
STAR preliminary
60
40
20
0
60
40
20
% Most Central
0
60
40
20
0
•  The signal seems to be disappearing at 7.7 GeV.
ALICE Collaboration, Phys. Rev. Lett. 110, 012301 (2013)
Mar. 15, 2013 Moriond QCD and High Energy Interactions
10 are likely to mask or reverse this difference in the hadron
resonance ‘‘afterburner’’ phase of a heavy ion collision. On
the other hand, the smaller difference in the absorption
cross sections of negative and positive pions potentially
may make it possible to detect the electric quadrupole
moment of the plasma through the difference of elliptic
flows of pions, v2 ð!þ Þ < v2 ð!" Þ.
The effect can be estimated by noting that a strong radial
flow aligns the momenta of the emitted hadrons along the
direction of the radial flow (see Fig. 3). The asymmetry of
the electric charge distribution in the expanding plasma is
then translated into the asymmetry in the azimuthal distribution of the positive and negative hadrons:
Z
Nþ ð"Þ " N" ð"Þ / j0e ðR; "ÞRdR:
(8)
dN)
¼ N) ½1 þ 2v2 cosð2"Þ'
d"
* N! ) ½1 þ 2v2 cosð2"Þ + A) r cosð2"Þ':
Chiral M
agne;c W
ave An Electric Quadrupole of QGP
B
This asymmetry has a 0th Fourier harmonic (monopole)
originating from a nonzero net charge density:
Z
(9)
#! e ¼ RdRd"j0e;B¼0 ðR; "Þ:
In addition there is a 2nd harmonic (quadrupole) of the
form 2qe cosð2"Þ due to the CMW contribution:
Z
qe ¼ RdRd" cosð2"Þ½j0e ðR; "Þ " j0e;B¼0 ðR; "Þ': (10)
e
The ratio of the two r ( 2q
#! e can be used to parametrize the
asymmetry in the azimuthal distributions of positive and
negative hadrons:
Chiral Separation Effect
+
-
+ +
(12)
In the second line we assume that both v2 and the charge
asymmetry A) ( ðN! þ " N! " Þ=ðN! þ þ N! " Þ are small.
The elliptic flow therefore becomes charge dependent:
v)
2 ¼ v2 +
rA)
:
2
(13)
The magnitude of the effect: Numerical simulation.—As
described above, we have computed the evolution of the
right and left chiral components of the u and d quarks
according to Eq. (3) (at zero rapidity) in a static plasma.
For simplicity, we assume the temperature to be uniform
within the almond. At the boundary of the plasma, the
chiral symmetry is broken and therefore we set v$ ¼ 0.
In the transverse (with respect to the magnetic field) direction, we assume a diffusion with a diffusion constant
DT estimated [25] as DT ¼ ð2!TÞ"1 within the SakaiSugimoto model. The difference in the elliptic flows of
positive and negative pions is given, within our approximation, by Eq. (13). In Fig. 4 we present the ratio r ¼
2qe =#! e as a function of impact parameter b at different
times. In this computation we took the impact parameter
dependence of the magnetic field from [3], with the maximal value eBjmax ¼ m2! . To convert this ratio into the
difference of the elliptic flows of positive and negative
pions according to Eq. (13), we also have to estimate the
electric charge asymmetry A) in the quark-gluon plasma
that varies between 0 and 1. We do this using the baryon
chemical potential and temperature at freeze-out extracted
[30] from the data and evaluating the p
yields
of baryons
ffiffi
and charged mesons; for the energy of s ¼ 11 GeV we
B
Chiral Magnetic Effect
r
0.01
0.001
+ +
10
4
dN±
= N± [1 + 2v2 cos(2 )]
±
d
The QGP acquires a v2 = v2
⇡ N± [1 + 2v2 cos(2
) ⌥ Aquadruple
ch r cos(2 )] deformation
electric
r
⌥ Ach
2
+
✓ ◆
vdensity!
N to the Chiral
qe Magnetic Wave at finitevbaryon
due
2
2 = rAch
2
FIG. 3 (color online). Schematic demonstration of the CMWinduced electric quadrupole deformation carried by strong
radial flow.
4
6
8
b fm
FIG. 4 (color online). The normalized electric quadrupole moment r, eBjmax ¼ m2! , T ¼ 165 MeV.
052303-3
Ach =
N+
N+ + N
r=2
⇢¯e
What
would be
theKharzeev,
measurable
Y. Burnier,
D. E.
J. Liaoconsequence?
and H-U Yee, Phys. Rev. Lett. 107, 052303 (2011)
Mar. 15, 2013 Moriond QCD and High Energy Interactions
11 Integrated v2
× 10
STAR Preliminary
0.2
Au + Au 200GeV
30-40%
STAR Preliminary
2
Au + Au 200 GeV
30-40%
400
v2(π-) - v (π+) (%)
Counts
3
500
300
200
0.1
0
100
0
-0.4
-0.2
0
0.2
0.4
v2{2} (%)
observed A ch
Au + Au 200 GeV 30-40%
0.15 < p < 0.5 GeV/c
T
3.7
3.6
STAR Preliminary
-0.1
-0.05
0
0.05
0.1
<observed Ach>
Mar. 15, 2013 -0.05
0
0.05
<Ach>
π-+
π
3.8
-0.1
Ø  v2(π+) and v2(π-) integrated over 0.15 < pT <
0.5 GeV/c
Ø  v2(π+) and v2(π-) have linear dependency to Ach
Ø  v2(Ach) slopes of π+ and π- have
•  opposite sign
•  similar magnitude
Ø  v2 difference vs. Ach may have a non-zero
intercept
Moriond QCD and High Energy Interactions
12 Slope parameter r (%)
Slope vs. Centrality 5
STAR Preliminary
Au+Au 200 GeV
0.15 < p < 0.5 GeV/c
T
|η| < 1
0
STAR data
UrQMD
-5
0
20
CMW (DH)
τ = 6 fm/c
τ = 5 fm/c
τ = 4 fm/c
τ = 3 fm/c
40
60
% Most Central
•  Similar trends between data and theoretical calculations with CMW.
•  UrQMD cannot reproduce the slopes at √sNN = 200 GeV.
Y. Burnier, D. E. Kharzeev, J. Liao, and H.-U. Yee, arXiv:1208.2537
Mar. 15, 2013 Moriond QCD and High Energy Interactions
13 Energy Dependence Slope parameter r (%)
5
5
5
CMW (BS)
0
Au + Au 200GeV
STAR Preliminary
-5
5
0
20
40
60
0
0
0
-5
Au + Au 62.4 GeV
0.15 < p < 0.5 GeV/c, |η| < 1 -5
T
5
0
20
40
60
0
Au + Au 39 GeV
-5
0
20
40
0
20
40
60
0
Au + Au 27 GeV
-5
60
5
τ = 3.5 fm/c
τ = 3 fm/c
τ = 2.5 fm/c
τ = 2 fm/c
0
20
40
Au + Au 19.6 GeV
-5
60
0
20
40
60
% Most Central
•  The slope parameter r shows a rise and fall feature from central to peripheral collisions
•  Slope as a function of centrality shows weak energy dependency
•  Similar trend to the theoretical calculation based on CMW
Mar. 15, 2013 Moriond QCD and High Energy Interactions
14 Summary Ø  The three-particle correlation show charge separation with respect
to event plane. Signal has similar magnitude from √sNN = 2.76 TeV
to 11.5 GeV and seems to disappear at √sNN = 7.7 GeV.
Ø  The difference between v2(π-) and v2 (π+) shows a linear dependency
on charge asymmetry in Au + Au collisions at √sNN = 200, 62.4, 39
and 27 GeV.
Ø  As a function of collision centrality, the slope parameter r shows a
rise and fall feature from central to peripheral collisions and the
energy dependence seems weak. The UrQMD model calculations
cannot reproduce this feature at √sNN = 200 GeV.
Ø  Similar trends of slope vs. centrality to the calculations based on
CMW.
Mar. 15, 2013 Moriond QCD and High Energy Interactions
15