Elliptic flow for multistrange hadrons as
penetrating probes at RHIC
Hiroshi Masui / University of Tsukuba
High Energy Strong Interactions: A school for Young Asian Scientists,
Wuhan, Sep. 22-26, 2014

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

1 /18

Outline• Introductions‣ Elliptic flow

‣ Why multi-strange hadrons ?

• Latest STAR results in Au + Au collisions at √s

NN = 200 GeV‣ Number of constituent quark (NCQ) scaling‣ Violation of mass ordering between φ meson and proton• Hybrid hydrodynamical model calculations• Summary!

I would like to thank Shiori Takeuchi and Tetsufumi Hirano forallowing me to present their recent hydrodynamical model
calculations

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

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Azimuthal anisotropydN⇠ 1 + 2v1 cos (dv2 = hcos (2[2 ])i1 ) + 2v2 cos (2[2 ]) + 2v3 cos (3[3 ]) + · · · ,• Azimuthal anisotropy‣ Fourier expansion of azimuthal distribution with respect to thereaction plane‣ Fluctuation of constituents (nucleons or partons) → participant plane- Reaction plane ≠ participant plane• Elliptic flow - v

2‣ Final state momentum anisotropy, 2nd harmonic coefficient‣ not necessary to describe collective hydrodynamic flow

‣ 2 particle correlation is the most popular method
v2robs
v2 = hcos (22 r )i = v2 · hcos (2 r 2 2 )ievent planeobs
v2 = hcos (22 2 )i = v2 · hcos (2 2 2 2 )i resolution
High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

3 /18

Mass ordering of v2 - radial flow
AZIMUTHAL ANISOTROPY IN AU+AU COLLISIONS AT
STAR: Phys. Rev. C72, 014904 (2005)

0.3√

PHYSICAL REVIEW C 72, 014904 (2005)

sNN = 200 GeV

Te↵ = Tfo + m0 h T i

Hydro model
π
K
p
Λ

v2

0.2

FIG. 10. (Color online) v2 vs. pt for strange
particles from minimum bias collisions. The
STAR KS0 and ! + ! values are from Ref. [20].
The PHENIX data are from Ref. [32]. The hydrocalculations are from Ref. [60].

0.1
PHENIX Data
π++πK++Kp+p

0
0

2

4

2

STAR Data
h++hK0S
Λ+Λ

participant
plane Ψ2
6

pt (GeV/c)• Radial flow pushes heavier hadrons to higher p

be explained by the momentum resolution of the FTPCs. To
3. High pt
quantify the influence of the momentum resolution a MonteT
Hadron yields at sufficiently high transverse momentum
Carlo simulation of v2 (pt ) based on the measurements at
in Au+Au collisions are believed to contain a significant
spectraweremidrapidity
was
done,
but
the
input
η
and
p
t
fraction originating from the fragmentation of high-energy‣effTobtained from measurements of the Au+Au minimum bias
partons resulting from initial hard scatterings. Calculations
data at forward rapidities. Results of embedding charged pions
based on perturbative QCD predict that high-energy partons(neglecting‣protons) in real Au+Au events up to 5% of thetraversing nuclear matter lose energy through induced gluon
total multiplicity in the FTPCs were used to estimate theradiation [36]. Energy loss (jet quenching) is expected tomomentum resolution as a function of η and pt . At η = 3.0
depend strongly on the color charge density of the createdthe momentum resolution goes from 10% at low pt to 35%
system and the traversed path length of the propagating‣GeV/c,at pt = 2.0
2 but gets about a factor of two worse
T atparton. Consistent with jet-quenching calculations, strongη = 3.5. In Fig. 17 the MC simulation v2 (pt ), including the
suppression of the inclusive high-pt hadron production [10,37]
momentum➡resolution of the FTPCs, seems to explaintheand back-to-back high-pt jetlike correlation [38] compared2
observed flattening by smearing low pt particles to higher pt .
to the reference p+p and d+Au systems was measured inThus we cannot conclude that the shape of the pt dependence
central Au+Au collisions at RHIC. In noncentral heavy-ion
of elliptic flow at forward rapidities is different from that atcollisions, the geometrical overlap region has an almondHigh Energy
midrapidity, even though the values integrated overpt are Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

Inverse slope (T ) of p spectra depends on mass linearly

Due to the geometry deformation, hadrons around participant plane
are pushed more than those around out-of-planev decreases at low p , and the effect is stronger for heavier hadrons
Mass ordering of v

4 /18

0

π, K, p, !, ", and #.

Why multi-strange hadrons ?
0

1

2

3

4

5

6 70 1p (GeV/c)

2

3

4

5

6

7

T

STAR Collaboration / Nuclear Physics A 757 (2005) 102–183
STAR White paper: Nucl. Phys. A757 (2005) 102-183

131
STAR: Phys. Rev. C77, 054901 (2008)

v2 /nq

0.15

(a)0

KS
Λ+Λ

0.1

+

-

Ξ +Ξ
+
Ω +Ω

φ

(b)

Polynomial Fit

0.05

π+ + π-0Data/Fit

1.5 (c)

0.3

p+p

(d)

1
0.5

1.5 (e)Data/Fit

9(b) are the corresponding scaled results. It appears that thescaling works better when the data are plotted as a functionof transverse kinetic energy KT , as in Fig. 9(b). The idealhydrodynamic results are also shown in both presentations.
Clearly, the hydrodynamic distributions are also better scaled
when plotted versus KT . Polynomial fits were made for all
hadrons. The results are shown as dot-dot-dashed lines in
Figs. 9(a) and 9(b). The ratios of the data and the hydrodynamiclines over the polynomial fit are shown in Figs. 9(c) and
9(d). For all data, there is scaling at pT /nq ! 0.7 GeV/cor KT /nq ! 0.2 GeV/c2 . The errors from the multistrange
hadrons φ [16] and # are large, see Figs. 9(e) and 9(f),but are consistent with the scaling. This observed nq -scaling
provides strong evidence that these hadrons are formed via
a coalescence process at the end of the partonic evolution[11,13]. Compared with the light nonstrange hadrons, strange
hadrons participate much less in later stage hadronic rescat-

(f)

1
0.5
0

0.5

1

1.5

20

0.5

1

1.5

2

The χ 2 contours, extracted from
0.2 thermal + radial flow fits (without allowance for resonance feed-down),(m - m)/n q
p /n qiously produced hadrons π , K and p and multi-strange hadrons φ and πΩ.
Onp +thetop of the plot, theT+πpT
0.1 selection. For π , K and p, 9 centrality Kbins (fromΛ + Λ top 5% to 70–80%)
cal labels indicate the centrality
√
Ξ +Ξ
Ω +Ω
FIG. 9.For(Color online) Number-of-quark scaled v2 (v2 /nq ) of
ed for sN N = 200 GeV Au + Au collisions [87]. The results from p + p
collisions
are also shown.
T0(a) 0%-80%(b) 40%-80%
identified
particles vs pT /nq in (GeV/c) (left column) and (mT −Ω, only the most central results [86] are presented. Dashed and solid lines are the 1-σ and 2-σcontours,
2(c) 10%-40%(d) 0%-10%
vely.
0.3
fo
ch m)/nq in (GeV/c ) (right column). Dot-dot-dashed lines are the
+

0
S
-

+

Blast-wave model fit for p spectra support early freeze-out ofmulti-strange hadrons: T ~ T results of sixth-order polynomial fits to K , !, ", and #. The ratios
-

+

v2

•

-

0
S

of the data points over the fit are shown in panels (c) and (d) for
KS0 , π, p, !, and ", and in panels (e) and (f) for # and φ [16].
t RCP = 1. This conditionisnearlyachievedforbaryons
near
p
≈
2.5
GeV/c,but
T
0.1
The error bars are shown only for the statistical uncertainties. Ideal
er reached for mesons. The initial results for φ-mesons and Ω-baryons included
in calculations for π, K, !, ", and # are presented byhydrodynamic
0
dashed lines, dot-dashed lines, dot-long-dashed lines, and5 suggest that the difference
is not very sensitive to the mass of the hadron,solid
but lines,
rather0 1 2 3 4 5 6 70 1 2 3 4 5 6 7
dot-dot-dot-dashed lines, respectively. The ratio of hydrodynamic
ds primarily on the number of valence quarks contained
within it. The mesonand2calculations over the fit are also shown for comparison in panels
m T - m (GeV/c )n values appear to merge by pT ≈ 5 GeV/c, by which point RCP ≈ 0.3. (c) and (d). The data are from minimum bias (0–80%) Au+Au√
collisions
e origin of this significant
shortfallin central
hadronwill atbe sNN = 200 GeV.
FIG. 8. (Color
online) Sameas Fig. 7,high-p
but as a Tfunctionof mTproduction
− m.
0.2

‣ probe to collectivity in early partonic stage of heavy ion collisions• Statistics is limited in previous data to study the number of
constituent quark (NCQ) scaling

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

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Motivations• v for multi-strange hadrons is a good probe to partonic
2

collectivity‣ Multi-strange hadrons freeze-out earlier than others➡ less hadronic rescattering (less radial flow effect)➡ penetrating probe to study partonic stage!

‣ Powerful tool to study NCQ scaling of v2‣ We can also study the effect of hadronic rescattering on v2 bycomparing φ meson with proton• Statistics is limited in previous data set‣ We have huge amount of data in year 2010 & 2011
‣ In addition, particle identification will be improved with fully installed

MRPC-TOF detector

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

6 /18

STAR experiment
TOF

TPC
VPD

BBC

• Large acceptance at midrapidity‣ Full azimuth, |η| < 1• Excellent particle identification‣ TPC + TOF

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

7 /18

Particle identifications
TPC

TOF

p

K
π

⌅!⇤+⇡

⌦!⇤+K

! K+ + K• Topological reconstruction of Ξ and Ω weak decay‣ reduce combinatorial backgrounds• Calculate invariant mass

‣ Combinatorial background is estimated by rotational background fromthe same event
High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

8 /18

Centrality & pT dependenceSTAR, QM2012

STAR preliminary
PHYSICAL REVIEW LETTERSPRL 99, 112301 (2007)
φ (40%-80%)
φ (10%-40%)
φ (0%-5%)0.3

2tracting the v2 !pT " values is also included in the systematic
error. Nonflow effects [27,28] are not included in thesystematic error. As expected, v2 !pT " increases with increasing eccentricity (decreasing centrality) of the initial
overlap region. This trend is also illustrated in Table I
which presents the pT -integrated values of !-meson elliptic flow, hv2 i, calculated by convoluting the v2 !pT " with therespective pT spectrum for three centrality bins. It should
be noted that the centrality dependence of the hv2 i of!-mesons is consistent with that of charged hadrons [28].
The lower panel of Fig. 1 shows the minimum bias (0%–80%) result compared to parameterizations for number-ofquark scaling for mesons (NQ $ 2) and baryons (NQ $ 3)
whose free parameters have been fixed by fitting to the !
and KS0 results simultaneously [29]. In this case, for pT <2 GeV=c, the ! v2 follows a mass-ordered hierarchy
where the values of v2 , within errors, fall between thoseof the heavier ! (open circles) and lighter KS0 (opensquares). However, at intermediate pT , between
2–5 GeV=c, the ! v2 appears to follow the same trend
as KS0 . When we fit the v2 !pT " of !-mesons with the quark
number scaling ansatz [29], the resulting fit parameter
NQ $ 2:3 % 0:4. The fact that the ! v2 !pT " is the sameas that of other mesons indicates that the heavier s quarks
flow as strongly as the lighter u and d quarks. As previously mentioned, !-mesons are not formed through kaon
coalescence [8] and do not participate strongly in hadronicinteractions. Therefore the results provide evidence forpartonic collectivity at RHIC.
Figure 2 shows the pT distributions of !-mesons fordifferent centrality bins. The central-triggered dataset wasused to obtain the most central spectrum while the other
distributions were obtained using the minimum bias dataset. The error bars shown in Fig. 2 are statistical only. In the
figure, the errorsHigh
are smaller
than thesize of thedata points. A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba
EnergyStrongInteractions:• Clear centrality dependence - initial geometry• Similar p dependence with light hadrons

0.2

Elliptic flow parameter v

week ending
14 SEPTEMBER 2007

0.1

T

0

!

‣ Event plane method with Δη=0.1 gap

0

KS
Λ
NQ=2
NQ=3
φ (0%-80%)

0.3

0.2

‣ Improve statistical error φ for meson- compare with left figure

0.1‣ 2 centrality bins for Ω baryon

0

STAR: Phys. Rev. Lett. 99, 112301 (2007)
0

1

2

3

4

Transverse momentum p (GeV/c)
T

9 /18

Results

Transverse kinetic energy scaling
STAR, QM2012• Mass ordering is almost vanished in terms of transversepgure 1: (Color online) v2 vs. mT m0 of identified hadrons for Au + Au collision at sNN = 200 GeV with |y| < 1.00r centrality a)
0-80% b)energy
0-30% and c)
kinetic
m30-80%.
T - m0Systematic errors on KS , ⌅, and ⌦ are shown by shaded band and forby cap symbol. The vertical lines are the statistical errors.
Clear baryon and meson splitting above 1-2 GeV/c2•
The v ofidentified hadrons(⇡, K, p,seemK , ⇤, to⌅, ⌦) as a functionof transverse
kinetic
Multi-strange
hadronsbeand
smallerthan otherhadrons•p
nergy mm at s = 200 GeV for various centralities are shown in figure 1. We observed
2

T

0
NN
in 30-80%

0S

splitting between baryon and meson v2 at intermediate mT2

m0 for centrality 0-30%. HoweverHigh Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

10 /18

v2 mostly reflect collectivity from partonic phase, therefore our observation may indicate smal
contribution to the collectivity from the partonic phase in the peripheral collisions.

NCQ scaling for multi-strange hadrons

STAR, QM2012

p
Figure 2: (Color online) v2 /nq vs. (mT m0 )/nq in Au + Au collisionsat
sNN = 200 GeV |y| < 1.0 for centrality a) 00
Measuredeviation
relativetoKs% b) 0-30 % and c) 30-80 %. Systematic errors on KS0 , ⌅, and ⌦ are shown by shaded band and for ⇤ by cap symbol. T
vertical lines
are the statisticalerrors. Dottedblack linethan
is polynomial‣ deviation
at 30-80%
is larger
0-30%fit?to Ks0 v2 and yellow band represent uncertain
due to fit.

•High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

11 /18Mass ordering violation, prediction
PHYSICAL REVIEW C 77, 044909 (2008)

MASS ORDERING OF DIFFERENTIAL ELLIPTIC FLOW . . .

0.2

0.25

π
φ
p

0.2

0.25

π
φ
p

0.2

0.15
v2

0.15
v2

hydro. + JAM

0.1
0.05

(a)

0

0.1
0.05

(b)

0

0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8 2

pT (GeV/c)hydro. onlyπ, hydroφ, hydrop, hydro

0.15
v2

0.25

at chemical freeze-out

0.1
0.05

(c)

0

0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8 2

pT (GeV/c)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
pT (GeV/c)

FIG. 9. (Color online) Transverse-momentum dependence of the elliptic flow parameters for pions (dotted blue), protons (dashed green),and φ mesons (solid red), for Au+Au collisions at b = 7.2 fm. (a) Before hadronic rescattering. (b) After hadronic rescattering. (c) Idealhydrodynamics with Tth = 100 MeV. The results for pions and protons are the same as shown in Fig. 5.

• Prediction: v (φ) > v (p) at low p

T pT < 500 MeV/c). Instead, it decreases over almost
to ideal hydrodynamics with Tth2= 169 MeV)2and for the ideal
lowhydrodynamic model with Tth = 100 MeV, that (i) the ratio
the entire range of transverse kinetic energy shown in theless hadronic rescattering on
φ meson‣ Duefigure.
This decrease is due to the flattening of the proton
increases
with pto
T or KET due to radial flow effects and thatspectrum by hadronically generated radial flow in which the(ii) the rate of increase drops when the freeze-out temperature‣ decreased,baseddue
ontoideal
JAMφ mesons
hadronic
cascade,builduphydrodynamicalof additional radial flow. model
weakly+coupleddo not participate.
The comparison
Tth is
Surprisingly, the ratio increases even in pp collisions, butwith pp collisions and hydrodynamic model simulations insingle
shot
hydro
(no
initialfluctuations),
ideal gas equation of stateFig. 8 shows that the observation of such a decreasing φ/p
for entirely different reasons, unrelated to collective flow: theratio would be an unambiguous signature for early decoupling
φ spectrum from pp collisions shown in Fig. 10 below isof φ mesons from the hadronic rescattering dynamics.
considerably flatter than the proton spectrum, leading to the
We now proceed to the discussion of dissipative effects
prominent rise of the φ/p ratio with pT . The most interesting
during the hadronic rescattering stage on the differential
feature of Fig. 8 is that the φ/p ratio from the hybrid model
StrongatInteractions:
School forflow
Young
12 /18v Asiandoes not at all increase with p or HighKE Energy(except
very Aelliptic(p ).Scientists,
Figure H.
9 Masuishows/ Univ.
v (pof Tsukuba) from the hybrid

v2 at low pTSTAR, QM2012•

p low pv2(φ)for>Auv2+(p)in dataat at
gure 3: (Color online) v2 vs. pT of ⇡, K, p and -meson
Au collisionsNN = 200TGeV with |y| < 1.0
ntrality a) 0-80 % b) 0-30 % and c) 30-80 %.

‣ The effect is stronger in central collisions

Consistent with the scenario•
ee from figure 3 for 0-30% centrality that at low p (p < 1 GeV/c) -meson v is either highTT2

predicted in hydro. + hadronr similar to that of proton v2 although mass of -meson (1.019 GeV/c2 ) is greater than massmodel
roton (0.938 GeV/c2 ). This observation iscascadeconsistent withthe scenario of hadronic re-scatteri•↵ect as predicted in the theoretical model Systematic[11].
& quantitative
Summary

comparison is necessaryHigh Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

13 /18

pT distributions
Results
Recent update of hydro. model

Centrality dependences of pT distributions forhybridSTAR104

dN/2/pTdpTdy(c2/GeV2)

Results - pT distributions

10|⌘| < 0.5

2100

Centrality dependences of pT distributions for ⇡ , K and p

10-2

10-6

10-4

⇡+

10-8
0

1

+
K
(b) K

10-6

(a) /+

2

3

pT(GeV/c)

4

5

10-8

+

0

0.5

pT(GeV/c)

1.5

10-2
10-4
10-6
10-8

¯(a) +
R+ R
⇤
⇤

10

10-4
10-6
10-8

p

2

!
! 0
0
10
!
10
! -1
10
! -2

0

1

1

2

3

4

pT(GeV/c)2

3

4pT(GeV/c)

5

6

-10

0

1

10-1

hybridSTAR|⌘| < 0.75

3

4

5

hybridSTAR|⌘| < 0.75

10-3
10-4

-5

10-5

10-6

Integrated dynamical model well reproduces STAR data!
10-7
10-8
! ◆ in particular in low pT region!
++-9! ◆ deviation in high pT region due to absence of components10!-10 ⌅(b) U++U⌅
10
0
1
2
3
! for mini-jets/recombinationp (GeV/c)

10-6
10-7

4

5

10-8

+ +
+1 ⌦
⌦(c) 1-+

0

1

T

•

2

pT(GeV/c)

10-2

10-4
10

10

5

peripheral
10-3

(a) p

10-10
1

|⌘| < 1.0

dN/2/pTdpTdy(c2/GeV2)

100

10-4

10-10

10

central!
(b) q
-8

$

2
2

-2

2

10

10-6

|⌘| < 0.5

-2

-2

10-4

hybridSTAR0

dN/2/pTdpTdy(c2/GeV2)

10

10

4

10

|⌘| < 0.1

106|⌘| < 0.50hybridSTAR

dN/2/pTdpTdy(c2/GeV2)

102
10

108

hybridSTAR

dN/2/pTdpTdy(c /GeV )dN/2/pTdpTdy(c2/GeV2)

104

10

hybridSTAR100

dN/2/pTdpTdy(c2/GeV2)

S. Takeuchi,
ATHIC 2014, ⇤, ⌅ATHIC 2014, Osaka, August 5-8, 20142

3

pT(GeV/c)

B.I

4

5

B.I. Abelev et al., Phys. Rev. Lett. 97, 153201 (2006) !

Integrated dynamical model - hydro. + hadron cascade
J. Adams et al., Phys. Rev. Lett. 92, 112301 (2004)

ATHIC 2014, Osaka, August 5-8, 20148

‣ Initial geometry fluctuation by MC Glauber model‣ Lattice equation of state• Spectra are reproduced well at low p

THigh Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

14 /18

J. A

Results - elliptic flow
Results - elliptic flowv2(pT)v (p ) compared with STAR data
and
!v (p
! for ) comparedwith STAR data for
T

0.35

2

0.35
0.35

hybrid 0-5%
hybrid 10-40%
hybrid 40-80%
STAR 0-5%STAR 10-40%
STAR 40-80%

0.3

0.3
0.3

0.18

hybridhybrid0-10%
0-10%hybridhybrid10-40%
10-40%
hybridhybrid40-80%
40-80%STAR
STAR0-10%
0-10%
STAR
STAR10-40%
10-40%STAR
STAR40-80%
40-80%|⌘| < 1.0

0.2
0.2

vv22

0.2
0.15

⌅ and ⌦S. Takeuchi,
ATHIC 2014

hybrid 0-10%
hybrid 0-80%
STAR 0-10%
STAR 0-80%

0.16
0.14

0.25
0.25

0.25

v2

⇤

T

0.12

|⌘|
|⌘| <
< 1.0
1.0

|⌘| < 1.0

0.1

0.15
0.15

v2

2

0.08
0.06

0.1

0.1
0.1

0.04

0.05

0.05
0.05

0.02
0

0
-0.05

00

(a) q
0

0.5

1

1.5

pT(GeV/c)

2

2.5

3

-0.05
-0.050
0

(c)
⌅
(b)
⇤UR
0.5
0.5

11

1.5
1.5

22

ppTT(GeV/c)(GeV/c)

2.5
2.5

33

-0.04

• Compared with previous published STAR data
• Reasonable agreement with the data
• Some deviations at peripheral collisions

THIC 2014, Osaka, August 5-8, 2014

(d)
⌦1

-0.02
0

0.5

1

1.5

pT(GeV/c)

2

2.5

3

B.I. Abelev et al., Phys. Rev. Lett. 99, 112301 (2007) !

B.I. Abelev et al., Phys. Rev. Lett.

B.I. Abelev et al., Phys. Rev. C 77, 54901 (2008)

B.I. Abelev et al., Phys. Rev. C 77

ATHIC 2014, Osaka, August 5-8, 201411

‣ due to the difference between event plane method (data) and reaction

plane method (model)High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

15 /18

Results - Hadronic rescattering
effects
Results- Hadronic rescatt

Effectofhadronic
rescattering
pT
/pT
v
/v
1.04
1.02

(fluid)(final)⇡pK

2 (fluid)⇤ ⌅hybridmT scaling

0.98

mT scaling 1.04 ⇡

K

p

⇤ ⌅

If all the particles
1.02 !
- move with common
flow velocity v!f1
Tfo- freeze out at
0.98⌦

hybrid◇ !⇡~ 20%in the!

✓◆0.96◇ the o
dN
mT
0.94
/ exp
hadr
0.94
pT dpT 0.92
Te↵
cont
0.92
1
0.9
T
=
Tfo + mvf2
0.9
e↵
0.88
2
0.88
✓
◆
0.86
dN
mT
(a)
(b)
0.86 p dp / exp T
0.84
T
T
e↵
Multi-strange hadrons ( , ⌅ and ⌦ )!
Multi s0.84 T = T + 1 m v2
0.82
e↵
0
0 f
!
→
deviationfrom mT scaling!
2
→
li
0.82
0.8
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 !
0 0.2 effects
0.4 0.6 0.8
1 T i1.2 1.4 1.6 1.8
hp→
littlerescatteringon2
m (GeV/c )m (GeV/c2)
v2(fluid)/v2(final)<pT>(fluid)/<pT>(final)

1⌦

S. Takeuchi,
ATHIC 2014

2 (final)

0.96

→p

|y| < 1.0, minimum bias collision
ATHIC 2014, Osaka, August 5-8, 2014|y| < 1.0, minimum bias collision
16
ATHIC 2014, Osaka, August 5-8, 2014

• Less rescattering effect on multi-strange hadrons‣ Mean pT for multi-strange hadrons deviate from mT scaling‣ v2 almost unchanged between fluid and final stages
High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

16 /18

v!2 (p! T ) for ⇡ , p and !

v!2 (p! T ) for ⇡ , p and !

v2(φ)! vsv2on/off(p) hadronic rescatterings! - switch on/off hadronic rescatterings- switch
0.14
0.12

without rescatterings

S. Takeuchi,
ATHIC 2014

with rescatterings

0.14 /m⇡ < mp pq< m
0.12⇡
v2 (pT ) > v2p (pT ) > v2 (pT )
0.1

/
p
q

0.1

v2⇡ (

Mass ordering

0.08

v2

v2

0.08

m⇡ < m

0.06

0.06

0.04

0.04

0.02

0.02

0

(a)
0

0.5

1
1.5
pT (GeV/c)

0

2

v2⇡ (

0

• Compare v below ~1 GeV/c in p|⌘| < 1.0 , minimum bias collision

2

ATHIC 2014, Osaka, August 5-8, 2014

Vio

(b)

T

0.5

1
1.5
pT (GeV/c)

2

!

→d

|⌘| < 1.0 , minimum bias collision

ATHIC 2014, Osaka, August 5-8, 2014

‣ v2(π) > v2(p) ≥ v2(φ) without rescattering20‣ v2(π) > v2(φ) > v2(p) with rescattering• Confirmed violation of mass ordering‣ ~20% effect around 0.5 GeV/c in minimum bias events
High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

17 /18

Summary• Multi-strange hadrons can be used as penetrating probes tounderstand medium properties in heavy ion collisions• We have confirmed NCQ scaling for multi-strange hadrons
with high precision data set‣ partonic collectivity for light quark sectors (u, d, s)• Violation of mass ordering has been predicted, and observedby the comparison of φ meson and proton v2‣ The effect is stronger in central collisions• Recent hybrid hydrodynamical model provides realistic (initialstate fluctuations + lattice EoS) calculation‣ which will allow us to make quantitative and systematic comparison

with the data

High Energy Strong Interactions: A School for Young Asian Scientists, H. Masui / Univ. of Tsukuba

18 /18