EEvveenntt  ggeeoommeettrriiccaall  aanniissoottrrooppyy  aanndd  fflluuccttuuaattiioonn  vviieewweedd  bbyy  HHBBTT  iinntteerrffeerroommeettrryy

Takafumi Niida
University of Tsukuba

WPCF2014, Gyöngyös, Hungary

Event shape engineering with HBTat the PHENIX experiment
CCoonntteennttss
Event twist selection with HBTwith AMPT model2

EEvveenntt  sshhaappee  eennggiinneeeerriinngg  wwiitthh  HHBBTTaatt  tthhee  PPHHEENNIIXX  eexxppeerriimmeenntt

EEvveenntt  sshhaappee  eennggiinneeeerriinngg
2,alower 5%

3

10

0.6
102

(a) 0.474
2000

10
0.4

1500

1

0.2 0

1000

0.05

0.1

0.15

0.2

0.25

0.3

v2500
0
0

0.2

0.4

0.6

Centrality 20-25%
J.Jia et al., arXiv:1403.6077

∈B2

104
0.6

no cuts
q3,a upper 5%(c) 0.640

q3,a lower 5%

4000

103
3000

0.42
10

More accurate connection between initial
and ﬁnal source eccentricity ?
Azimuthal HBT w.r.t Ψ2

B

∈F2

!

2,a

q

B

!
Q2,x = ⌃wi cos(2 )!
Q2,y = ⌃wi sin(2 )
Ψ2
q
!
p
2
2
! Q2 = Q2,x + Q2,y / ⌃wi! 2 = tan 1 ( Q2,y )Q2,x!
!
Possibly control the initial geometry

no cuts
q upper 5%

104

F

Selecting e-b-e v2 by the magnitude of ﬂow vector

Centrality 20-25%∈F2

J. Schukraft et al., arXiv:1208.4563

initial shapeε2number of events

Event shape engineering (ESE)number of events

J.Schukraft et al., arXiv:1208.4563

2000

10
0.2
AMPT
Pb+Pb 2.76TeV

1
00
0

0.05

0.1
0.1

0.15

qF

0.2
0.2

0.25 0.3
0.3

2

ﬂow vector qv3(e) online)
0.354Actual (true) v2 and v23 distributions
FIG. 3. (color
in the event
samples selected by di↵erent cuts on the corre2
sponding qn -vector magnitude indicated in the plot compared
2000
to that extracted from the BG fits to qn,b distribution shown
B
2* )

4

1000

MMeeaassuurreemmeenntt  aatt  PPHHEENNIIXX
Event plane & ﬂow vector determination
Reaction Plane Detectors (RxNP) (1<|η|<2.8)
Res(Ψ2)~75%!
Charged pion Identiﬁcation
Electromagnetic calorimeter (EMCal) (|η|<0.35)
using time-of-ﬂight at EMCal

HBT measurement
ππ-correlation
Core-halo picture with out-side-long frame

beam

Rs

Rl
Ro

~kT = (~
pT 1 + p~T 2 )/2~qo k ~kT , ~qs ? ~kT

C2 =C2core + C2halo=[ (1 + G)Fcoul ] + [1G =exp( Rs2 qs2

5

Ro2 qo2]

Rl2 ql22
2Ros
qs qo )

HHooww  ttoo  aappppllyy  tthhee  EESSEE
1. Q2 distribution measured by RxNP
2. Fitted with the Bessel-Gaussian functionxx0 x(x20 + x2 )fBesselGaus = I0 ( 2 ) exp()
2
2
3. Select higher or lower Q2 events

Resolutions of event planes were
estimated by 3-sub method using
RxNP(1<|η|<2.8) and BBC(3<|η|<3.9)
applying Q2 selection.

6

CChhaarrggeedd  hhaaddrroonn  vv22  wwiitthh  EESSEETest of the event shape engineering for v2 in Au+Au 200GeV collisions
v2 measured at mid-rapidity (|η|<0.35)
Q2 and EP determined at 1<|η|<2.8

Conﬁrmed that higher(lower) Q2 selects larger(smaller) v2

7

HHBBTT  rraaddiiii  ww..rr..tt  Ψ22  wwiitthh  EESSEE  

Applying the ESE to azimuthal HBTcharged ππ-correlation measured at mid-rapidity (|η|<0.35)
Q2 and EP determined at 1<|η|<2.8

Oscillations of Rs and Ro become larger when selecting higher Q2

8

HHBBTT  rraaddiiii  ww..rr..tt  Ψ22  wwiitthh  EESSEE((RRll  aanndd  RRooss))

Oscillation of Rl doesnʼt change, while Ros increases when selecting
higher Q2 events as well as Rs and Ro9

εﬁnal ~ 2Rs,22/Rs,02
F. Retiere and M. A. Lisa, PRC70.044907
at the limit of kT=0!

2Rs,22 / Rs,02

FFrreeeezzee--oouutt  eecccceennttrriicciittyy  vvss  NNppaarrtt  wwiitthh  EESSEE!

ε2finalHigher Q2 selection increases themeasured εﬁnal
Selected more elliptical source at freeze-out?
might be originated from εinit with larger Q2(v2)
Or just v2 eﬀect?

10

2Ro,22 / Ro,02

Rside modulation 
Rout modulation 

ε2final

EEvveenntt  ttwwiisstt  sseelleeccttiioonn  wwiitthh  HHBBTT

wwiitthh  AAMMPPTT  mmooddeellTTwwiisstteedd  ssoouurrccee??

33

we should expect the following relation to hold:

we should expect the following relation to hold:

Twisted ﬁreball due
ﬂuctuation
F the density
B
B (1 − α(η))⃗⃗ncn(η)≈ cnϵFn(η)
ϵnϵ+
ϵn ]
v⃗n (η) ≈v(η) [α(η)⃗+ (1[α(η)⃗− α(η))⃗n]⃗geo(η)+δ⃗geo (η) ++δ⃗δdyn, + δ⃗dyn (η) , (10)(η)

of wounded nnucleons
going to (10)forwardnnnwhere thecn (η)
is thehydrodynamic
response function,
where
the
cn (η)
is the hydrodynamic
response function,and the three additional terms in the form of δ⃗n = δn einσn ⃗
inσn
and
the
three
additional
terms
in
the
form
of
δ
=
δ
e
n
n
represent additional
initial oret
final
state
eﬀects. The term
P. Bozekal.,
PRC83.034911
geo⃗
represent
additional
initialoreﬀects. The termδn (η) represents additional geometric final
eﬀectsstate
not acgeo
δ⃗nfor(η)
representscountedby theeccentricity,additionalsuch as the geometricdetails in theeﬀects not acradial distribution
thetheenergydensity profile
counted forofby
eccentricity,
such[15,
as 39]
the details in theand thediﬀerencefromanalternative
definitionof
ecradialK.
distribution
the energy density profile [15, 39]
Xiao
et of
al.,
The
last termδ⃗ndyn PRC87.011901
represents additional
centricity [20].
andthediﬀerencefroman alternative
definition of ecdynamical fluctuations [40, 41] generated
duringthehylast increases
term δ⃗ndyn represents
additional
centricity[20].andThedecorrelation
with increasing
η-gap
drodynamic
evolution
hadronization.
F
B
dynamical[40, 41]
generated
Secondly,ϵ⃗n and fluctuationsϵ⃗n fluctuate strongly
event
to event, during the hyF
both indrodynamic
their magnitude
and orientation.
If ϵn ≠ ϵBevolutionand hadronization.
n , theF
distributionsof flow ϵ⃗coeﬃcientsvn (η) are expected to
Secondly,⃗Bn and ϵn fluctuate strongly event to event,show strong forward-backward asymmetry. Similarly, if
F
B
both
in
their
magnitudeandorientation.
If
ϵ
≠
ϵ
∗F
∗B
n
n , theΦn ≠ Φn , the event-plane angle Φn is expected to rotate
distributionsof flow coeﬃcients vn (η)
are expected togradually
rapidnfrom backward rapidity to the forward
show strong
forward-backward
asymmetry.
Similarly, if
ity. However
since α(η)
is a non-linear function,
these
F
∗F
∗B
FIG. 1: Schematic illustration of the forward-backward flucchangesΦnmay≠ alsolinear, especiallyΦn not, thebeevent-planeanglewhenΦn isNexpected
to rotatepartB
tuation of second-order eccentricity and participant plane, inand Npartvalues are
verybackward
diﬀerent suchas in Cu+Au
graduallyfrom
rapidity
to theor forward rapidtransverse plane (a) B
and along rapidity F
direction (b) in A+A
p+Pb collisions.
ity. However since α(η) is a non-linear function, thesecollisions. The dashed-lines indicate the particle production
A simple monte-carlo Glauber model [42] is used to
part
part
F
for forward-going
and backward-goingparticipants, flucFIG.profiles
1: Schematic
illustrationof the forward-backwardB linear, especially when Nchanges
may also not
Ψ2be
part
estimatetheFB
eccentricity
fluctuations
in
Pb+Pb
colF
F
B
B
f (η)N
part , respectively.
part and f (η)NB
tuationof second-ordereccentricity
and participant plane, inare verydiﬀerentsuch as in Cu+Au or
B
Flisions.andThe N
results
as a functionof Npart
are summarizedpart values
F
B
transverse plane (a) and along rapidity direction (b) in A+A
2. The valuesof ϵ2 and ϵ2 are found to be always
in Fig. p+Pb
collisions.
nncollisions. The dashed-lines indicate the particle production
larger thanover themonte-carlofull centrality range(Figure2(a)),[42]Ψ2F is used toA ϵ2simple
Glaubermodel
where
profilesfor2 forward-goingandbackward-goingparticipants,
BF
and this diﬀerence is due to the fact that the center-ofestimate the FB eccentricity fluctuations in Pb+Pb colF
F
B
B
f (η)Npart and fpart,n(η)Npart , respectively.
mass of the wounded nucleons in each nucleus is not atpart,nFlisions.
The
results
as abutfunctionof Npart are summarizedf F (η)Npart⟨rn ⟩Fthe centerof theoverlap
regionis shifted
towardsz"dirFBα(η) = F
,
(9)
c(o
2.
The
values
of
ϵ
and
ϵ
are
found
to
beealways
in
Fig.
the
centerofthecorresponding
nucleus(see
discussion
F
B
n
F
B
n
B
2
2
f (η)Npart ⟨r ⟩ + f (η)Npart ⟨r ⟩
12
n
F
B
in Appendix
In contrast,
the valuesof ϵ3 and ϵrange
largerA).
than
ϵ2 over thefull centrality
3 are (Figure 2(a)),

and backward directions

Also known as “event plane decorrelation"!
!
v may be underestimated, which mightlead to overestimating η/s

N

6= N

" 6= "
6=

0.6

0.6

0.6
3000

0.4

0.4

0.2

0.1

qF

0.2

0
0

0.3

0.1

(a)

2

(e) 0.354

0.5

2

0.2

1000

1000

0
0

∈F3

2000

S
F
q2 bin = 24,q

0.2

J.Jia et0 al., arXiv:1403.6077

0.3
cut

0

(f)

1.05
3

F
B
2(
Ψ
Ψ
)
2
2B
F

4
-2

2

2(Φ * -Φ * ) 0
F2∆ φ2(Ψ2 -Ψ2 ) final twist

C(

2 0

B

2

0.15

∆ η∈ [5,6]∆ η∈ [-4,-3](e) 0.125∆ η∈ [3,4]∆ η∈ [-2,-1]∆ η∈ [1,2]

0

10

-2

1

AMPT Pb+Pb 2.76TeV

1

-5

0

∆η

1.05

-0.5
-2

C(∆ φ)
1

C(∆ φ)∈F2-∈B2

0

0

-2

5

1000

102

0.1

qF3
∆ η∈ [-6,-5]

2

10

2000

0

0.05

(b)

top 10% of Ψ2

3(Φ3*F-Φ3*B)

0.2

initial twist
B*B)
2(Φ22*F*F
-Φ-Ψ
2(Ψ
2* )2

0.4

EEvveenntt  ttwwiisstt  sseelleeccttiioonn
2000

∈B2

∈F2

3000

-2

0

23(Ψ F3-Ψ B
3)

0

2

2
4

∆φ

a correlationb
rotcorrelation function in di↵erent ⌘ s
8: The 2D
function (left), 1D,B ⌘) /FIG.
1
+
2⌃v
v
cos(n
n
rot
F innthe)fourth q S bin with largest cut valu
B
n ∗FB
n
nF n for n = 2–5(right),for events selected
22

FIG. 4: Correlation of ϵ2 vs. ϵ2 (a), 2∆Φ2
vs. ϵ2 (b), ϵ2
FIG. 5: Correlation of ϵ3
F
F
∗FB
FB
B
F
F
−
ϵ
(e),
and
ϵ
vs. q2Bon(d),
2∆Φ
vs.
2∆Ψ
vs.
q
(d),
vs. q2F Twist(c), ϵF
vs.
q
(c),
ϵ
2
2
2
2eﬀect3
3
3
2
anisotropic
ﬂow&2PC
studied
with
AMPT
∗FB
q bin = 10, top 10% of Ψ(a)(b)∆ η∈ [-6,-5]∆ η∈ [5,6]vs. 2∆Φ∗FB
(f)
for
AMPT
Pb+Pb
events
with
b
=
8
fm.
The
vs.
3∆Φ
(f) for
AMPT
2
3
B
F
∆ η∈ [-4,-3]∆ η∈ [3,4]Requiring ﬁnite diﬀerence b/w forward and backward EPs (Ψ2 -Ψ2 )bars around the circles in panel-(b) indicates the RMS widthbars aroundthe circlesin∆ η∈ [-2,-1]∆ η∈ [1,2]1.1∗FB eﬀect appears as a phase shift in Δφ-Δη correlation∗FBof 2∆ΦTwist
at
given
ϵ
value,
andthefour
regionsdelineatedof3∆Φat given ϵ3 va
2
23initialintwist
survives
as a ﬁnal
state
ﬂow
momentumspace by the boxes in panel-(f)by the boxes
panel-(f)indicate
thecuts
forinthefour eventclassesHow
definedin Tableclasses defined in Table I
I. Thecoordinate
numbers inspace?
some panels indiabout
in spatial
1
cates the correlation coeﬃcients of 1.1
the distributions.
cates the correlation coeﬃ
13
cut
2

∆η

C(∆ φ)

5

0

1

C(∆ φ)S
2

HHBBTT  ssttuuddyy  iinn  AAMMPPTT  AMPT modelver.2.25 (string melting)
Pb+Pb 2.76 TeV collisions, b=8fm
initial ﬂuctuation based on Glauber model and ﬁnal state interaction via
transport model

EP determination at 4<|η|<6

!
!

HBT!
"3.5<η<3.5!
Δη=1!step

!

!"6!!"5!!"4!!"3!!"2!!"1!!!0!!!1!!!2!!!3!!!4!!!5!!!6

←twist!cut!
←a!reference!angle!of!HBTη

HBT analysis
Add HBT correlation (1+cos(ΔrΔq)) between two pion pairs
Allowing to take π+π- pairs to increase statistics
conﬁrmed a good agreement between π+π+ and π-π-

No EP resolution correction
Bowler-Sinyukov C2

C2 = 1 + exp( Rs2 qs2Ro2 qo2

Rl2 ql2
14

2
2Ros
qo qs

2
2Rol
qo ql

2
2Rsl
qs ql )

9

7

bbaacckkwwaarrdd
15

R 2l [fm2]

AMPT Pb+Pb 2.76TeV
b=8fm

R 2o [fm2]R 2s [fm2]

HHBBTT  rraaddiiii  ww..rr..tt  bbaacckkwwaarrdd  Ψ22
(ΨB2- ΨF2)>0.6

6

Ψ2B

10

Ψ2F

8
5
-3.5<η<-2.5-2.5<η<-1.5

1

2

4 0

3

∆ φ [rad]1

Selected events with (Ψ2B-Ψ2F)>0.6
R 2ol [fm2]R 2os [fm2]05

1.5<η<2.5

2

3∆ φ [rad]1

2

3∆ φ [rad]2

AMPT Pb+Pb 2.76TeV π π -HBT
Phase shift can be seen, and data are ﬁtted with cosine(sine)
0.2<k T<1 GeV/c, EP: -6<η<-41
1
1function including a phase shift parameter α

022Rµ2 = Rµ,0
+ 2Rµ,2cos(202Rµ2 = 2Rµ,2
sin(2

-1

+ ↵)

0

+ ↵)
-1

15

-1



ffoorrwwaarrdd
0

R 2sl [fm2]

7

z"dir
ec(
on

2.5<η<3.5-3.5<η<-2.5-2.5<η<-1.5-1.5<η<0.5

2.5<η<3.5
1.5<η<2.5
0.5<η<1.5

97bbaacckkwwaarrdd
15

R 2l [fm2]R 2o [fm2]R 2s [fm2]  
HHBBTT  rraaddiiii  ww..rr..tt  ffoorrwwaarrdd  Ψ22

(ΨB2- ΨF2)>0.6

6

Ψ2B

10

Ψ2F

8
5
-3.5<η<-2.5-2.5<η<-1.5

1

2

4 0

3

∆ φ [rad]1

Selected events with (Ψ2B-Ψ2F)>0.6
R 2ol [fm2]R 2os [fm2]05

1.5<η<2.5

2

3∆ φ [rad]

ffoorrwwaarrdd
0

R 2sl [fm2]

7

z"dir
ec(
on

2.5<η<3.5

1

2

3∆ φ [rad2

AMPT Pb+Pb 2.76TeV π π -HBT
Phase shift can be seen, and data are ﬁtted with cosine(sine)
0.2<k T<1 GeV/c, EP: 4<η<61
11function including a phase shift parameter α

022Rµ2 = Rµ,0
+ 2Rµ,2cos(202Rµ2 = 2Rµ,2
sin(2

-1

+ ↵)

0

+ ↵)
-1

16

-1

-3.5<η<-2.5-2.5<η<-1.5-1.5<η<0.5

2.5<η<3.5
1.5<η<2.5
0.5<η<1.514

R2long [fm2]R2out [fm2]R2side [fm2]BB((FF))  
HHBBTT  rraaddiiii  ww..rr..tt  Ψ22
((η<<00))
10

12

8

AMPT Pb+Pb 2.76TeV

10

10
6
8
5

4

2

0
0 0.5

1 1.5 22.5

3

∆ φ [rad]1 1.5 2

2.5

3

0 0.5

∆ φ [rad]2

R2sl [fm2]R2os=04

0 0.5

R2ol [fm2]R2os [fm2]

6 0 0.5 1 1.5 2 2.5 3∆ φ [rad]1

1 1.5 2

w.r.t Ψ B (-6<η<-4)-3.5<η<-2.5-2.5<η<-1.5
1-1.5<η<-0.5-0.5<η< 0.5

0-1-1 w.r.t Ψ F (4<η<6)

0 0.5

1 1.5 22.5

3

∆ φ [rad]3∆ φ [rad]0.2<kT<1[GeV/c]

2

0

-2

2.5

-3.5<η<-2.5-2.5<η<-1.5-1.5<η<-0.5-0.5<η< 0.5-2
0 0.5 1 1.5 2 2.5 3∆ φ [rad]22
Rµ2 = Rµ,0
+ 2Rµ,2cos(2Selected events with (Ψ2B-Ψ2F)>0.6

2
Rµ2 = 2Rµ,2
sin(2

+ ↵)

+ ↵)

Phase diﬀerence between Ψ2B and Ψ2F can be seen in Rs, Ro, and Ros
17η--ddeeppeennddeennccee  ooff  pphhaassee  sshhiifftt
22
Rµ2 = Rµ,0
+ 2Rµ,2
cos(2

0.4
0.2

0.6

αos [rad]0.6

αout [rad]αside [rad]2Rµ2 = 2Rµ,2
sin(2

0.4

AMPT Pb+Pb 2.76TeV
0.4
0.2

0

0

0

-0.2

-0.2

-0.2

-0.6

-0.4

-3

-2

-1

0

1

2

-0.6

3

w.r.t ΨB2
w.r.t ΨF2

-0.4

Ψ22BB

Ψ22FF
-3

-2

-1

0

1

2

η

-0.6

3

+ ↵)

0.6

0.2

-0.4

+ ↵)

-3

-2

-1

0

1

η

2

3

η

Phase shifts become larger with going far from η of a reference EP(-6<η<-4 or 4<η<6)Source at freeze-out might be also twisted as well as EP angles
It may include the eﬀect from twisted ﬂow

This twist eﬀect could be measured experimentally18

SSuummmmaarryy
Event shape engineering at PHENIX
Azimuthal HBT measurement with the event shape engineering have been
performed in Au+Au 200GeV collisions
Higher Q2 selection enhances the measured εﬁnal as well as v2
More accurate relation between initial and ﬁnal eccentricity!
Event twist selection with AMPT model
A possible twisted source have been studied via HBT measurement with
AMPT Pb+Pb 2.76TeV collisions
Phase shifts of HBT oscillations are seen as a function of η, possibly
indicating the twisted source at ﬁnal stateThis eﬀect might be measured in RHIC and the LHC, especially in ATLAS
or CMS

19

BBaacckk  uupp

EEvveenntt--bbyy--eevveenntt  vvnn  aatt  AATTLLAASS
2102

pT>0.5 GeV, |h|<2.5

pT>0.5 GeV, |h|<2.5

Pb+Pb

ATLAS Pb+Pb

ATLAS Pb+Pb

sNN=2.76 TeV

sNN=2.76 TeV-1Lint = 7 µb-1

ATLAS

10

sNN=2.76 TeV
Lint = 7 µb

-1

10Lint = 7 µb

pT>0.5 GeV, |h|<2.5

4

p(v )

p(v 3)

2

p(v )

1
10

1
-1

10

10-2
0

centrality:
0-1%
5-10%
20-25%
30-35%
40-45%
60-65%

10-1
0.1

0.2

0

v2

centrality:
0-1%
5-10%
20-25%
30-35%
40-45%

centrality:
0-1%
5-10%
20-25%
30-35%
40-45%

0.05

v3

0.1

1
0

0.01

0.02

0.03

0.04

0.05

v4

dN
∝1+ 2∑ v n cos n φ − ΦFigure
10. The probability density distributions of the EbyE vn in several centrality intervals fondφnn = 2 (left panel), n = 3 (middle panel) and n = 4 (right panel). The error bars are statisticaΦn)?

ear) dynamics?

mics?

(

)

uncertainties, and the shaded bands are uncertainties on the vn -shape. The solid curves are distri
butions calculated from the measured ⟨vn ⟩ according to eq. (1.6). The solid curve is shown only fo
0–1% centrality interval for v2 , but for all centrality intervals in case of v3 and v4 .

from ref. [31]. However, the uncertainties from ref. [31] for the vn -scale (table 2) andvn -shape, are well within the total systematic uncertainties derived from the data analysis
21

OOsscciillllaattiioonn  aammpplliittuuddeess  aass  aa  ffuunnccttiioonn  ooff  NNppaarrtt

wwiitthh  EESSEE22

R 2o [fm2]12

R 2s [fm2]1412

R 2l [fm2]BB
HHBBTT  rraaddiiii  ww..rr..tt  Ψ22
(ΨB2- ΨF2)>0.6

15

10

10

8

8

10

6

6

5

4
2

3

0

∆ φ [rad]

1

0

1

2

3

1

0

-1
1

2

3

∆ φ [rad]1

2

3∆ φ [rad] [GeV/c]
0.2<kT<1
0.2<kT<1 [GeV/c]

2
1

AMPT Pb+Pb 2.76TeV π π -HBT
0.2<k T<1 GeV/c, EP: -6<η<-40-3.5<η<-2.5-2.5<η<-1.5-1.5<η<0.5-0.5<η<0.5

-1

-1
0

0

∆ φ [rad]R 2sl [fm2]1

R 2ol [fm2]R 2os [fm2]

4 0

0

1

2

3

∆ φ [rad]

-2

0

1

2.5<η<3.5
1.5<η<2.5
0.5<η<1.5

2

3∆ φ [rad]Selected events with (Ψ2B-Ψ2F)>0.6
Phase shift can be seen, and become larger with going far from ηof EP for a reference angle (-6<η<-4)23

14

R2long [fm2]R2out [fm2]R2side [fm2]BB((FF))  
HHBBTT  rraaddiiii  ww..rr..tt  Ψ22
((η>>00))
10

12

8

AMPT Pb+Pb 2.76TeV

10

10
6
8
5

4
6 0 0.5 1 1.5 2 2.5 3∆ φ [rad]

0 0.5

1 1.5 2

2.5

3

0 0.5

∆ φ [rad]1 1.5 22.5

3

∆ φ [rad]R2os=0

4

2

0
0 0.5

1 1.5 22.5

3

∆ φ [rad]2

R2sl [fm2]R2ol [fm2]R2os [fm2]0.2<kT<1 [GeV/c]

1

2

w.r.t Ψ B (-6<η<-4)-0.5<η< 0.5
0.5<η< 1.5
1
1.5<η< 2.5
2.5<η< 3.5

0

0

-1

-1 w.r.t Ψ F (4<η<6)

-2

0 0.5

1 1.5 22.5

3

∆ φ [rad]-0.5<η< 0.5
0.5<η< 1.5
1.5<η< 2.5
2.5<η< 3.5-2
0 0.5 1 1.5 2 2.5 3∆ φ [rad]Selected events with (Ψ2B-Ψ2F)>0.6
Phase diﬀerence between Ψ2B and Ψ2F can be seen in Rs, Ro, and Ros

24