# Probing nuclear structure using elliptic flow of strange and multi-strange
hadrons in isobar collisions

Priyanshi Sinha (for the STAR collaboration)

###### Abstract

Isobar collisions, ${}^{96}_{44}$Ru+${}^{96}_{44}$Ru and
${}^{96}_{40}$Zr+${}^{96}_{40}$Zr, at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV have
been performed at RHIC in order to study the charge separation along the
magnetic field, called the Chiral Magnetic Effect (CME). The difference in
nuclear deformation and structure between the two isobar nuclei may result in
a difference in the flow magnitudes. Hence, elliptic flow measurements for
these collisions give direct information about the initial state anisotropies.
Strange and multi-strange hadrons have a small hadronic cross-section compared
to light hadrons, making them an excellent probe for understanding the initial
state anisotropies of the medium produced in these isobar collisions. The
collected datasets include approximately two billion events for each of the
isobar species and provide a unique opportunity for statistics hungry
measurements. In this proceeding, we will report the elliptic flow ($v_{2}$)
measurement of $K_{s}^{0}$, $\Lambda$, $\overline{\Lambda}$, $\phi$,
$\Xi^{-}$, $\overline{\Xi}^{+}$, $\Omega^{-}$, and $\overline{\Omega}^{+}$ at
mid-rapidity for Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200
GeV. The centrality and transverse momentum ($p_{T}$) dependence of $v_{2}$ of
(multi-)strange hadrons will be shown. System size dependence of $v_{2}$ will
be shown by comparing the $v_{2}$ results obtained from Cu+Cu, Au+Au, and U+U
collisions. The number of constituent quark (NCQ) scaling for these strange
hadrons will also be tested. We will also compare the $p_{T}$-integrated
$v_{2}$ for these two isobar collisions. Transport model calculations will be
compared to data to provide further quantitative constraints on the nuclear
structure.

##  1 Introduction

Relativistic heavy-ion collisions indicate the presence of a strongly
interacting medium called Quark Gluon Plasma (QGP). Studies of the elliptic
flow of produced particles in this medium provide insight into the early
anisotropy in the medium. Despite having the same number of nucleons, the
anisotropic flow coefficients of Ru+Ru and Zr+Zr were observed to be distinct
in the isobar collision run at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV at the
Relativistic Heavy Ion Collider (RHIC) [1]. This suggests that the difference
in nuclear structure may also leave imprints on the elliptic flow of
particles. Recent studies also discuss the use of $v_{2}$ ratios and
$v_{2}$-[$p_{T}$] correlations in isobar collisions to probe nuclear
structures. [2, 3]. Compared to light hadrons, (multi-)strange hadrons have a
smaller hadronic cross-section, making their $v_{2}$ an excellent probe of the
initial state anisotropies in these isobar collisions.

##  2 Analysis details

We report strange and multi-strange hadron $v_{2}$ in
${}^{96}_{44}$Ru+${}^{96}_{44}$Ru and ${}^{96}_{40}$Zr+${}^{96}_{40}$Zr
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV using the data collected by
the STAR experiment. Each isobar collision had roughly 650M events analysed.
The Time Projection Chamber (TPC) and Time-Of-Flight (TOF) have been used to
identify the decay daughters of these short-lived particles and reconstruct
them using invariant mass technique. Using their weak-decay topology, strange
particles $K_{s}^{0}$, $\Lambda(\bar{\Lambda})$, and
$\Xi^{-}(\overline{\Xi}^{+})$ are reconstructed. The combinatorial background
for these hadrons is constructed using rotational background method [4].
$\phi$-mesons are reconstructed using hadronic decay channel and event mixing
technique is used for combinatorial background estimate. The $v_{2}$ is
calculated using $\eta$-sub event plane method [5]. The maximum resolution for
the second order event plane is nearly 48% for both collision systems.

##  3 Results

Figure 1 shows the $v_{2}$ of strange and multi-strange hadrons as a function
of $p_{T}$ for minimum bias Ru+Ru and Zr+Zr collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. An approximate mass ordering at low
$p_{T}$ and a baryon-meson splitting at intermediate $p_{T}$ is observed. All
particles and anti-particles tend to follow the number of constituent quark
(NCQ) scaling within 10% as shown in Fig. 1, indicating partonic collectivity
as well as domination of quark coalescence mechanism for hadronization at
intermediate $p_{T}$ region.

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Figure 1: $v_{2}$ as a function of $p_{T}$ of (multi-)strange hadrons and NCQ-
scaled $v_{2}$ as a function of transverse kinetic energy for Ru+Ru and Zr+Zr
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. The vertical lines and
shaded boxes denote statistical and systematic uncertainties, respectively.

A clear centrality dependence of $v_{2}$ has been observed for $K_{s}^{0}$,
$\Lambda$ and $\Xi^{-}$ as shown in Fig. 2 and for other hadrons for the
isobar collision systems.

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---|---|---
|  |
Figure 2: Top panel: Centrality dependence of $v_{2}$ of $K_{s}^{0}$,
$\Lambda$ and $\Xi^{-}$ as a function of $p_{T}$ in Ru+Ru collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV; Bottom Panel: Same for Zr+Zr collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. The vertical lines and shaded boxes denote
statistical and systematic uncertainties, respectively.

The $p_{T}$-integrated $v_{2}$ for strange hadrons was also studied as a
function of the collision centrality as shown in Fig. 3. The ratios of $v_{2}$
between the two isobar collisions for $K_{s}^{0}$, $\Lambda$, and
$\bar{\Lambda}$ show clear deviation of nearly 2% from unity in mid-central
collisions, indicating a difference in nuclear structure and shape [1].

Figure 3: $p_{T}$-integrated $v_{2}$ as a function of centrality for
$K_{s}^{0}$, $\Lambda$, and $\bar{\Lambda}$ in Ru+Ru and Zr+Zr collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. The vertical lines on the ratio includes
statistical and systematic uncertainties. The dotted lines denotes the fitting
with a constant. Figure 4: $v_{2}$ of $K_{s}^{0}$, $\Lambda$ and
$\bar{\Lambda}$ in minimum bias Cu+Cu, Ru+Ru, Zr+Zr, Au+Au collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV and U+U collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 193 GeV [6, 7, 8].

We investigated the system size evolution of $v_{2}$ by comparing the
${}^{63}_{29}$Cu+${}^{63}_{29}$Cu, ${}^{96}_{44}$Ru+${}^{96}_{44}$Ru,
${}^{96}_{40}$Zr+${}^{96}_{40}$Zr, ${}^{197}_{79}$Au+${}^{197}_{79}$Au
collisions in 0-80% centrality at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV, and
${}^{238}_{92}$U+${}^{238}_{92}$U collisions at $\sqrt{s_{\mathrm{NN}}}$ = 193
GeV [6, 7, 8]. Figure 4 shows an approximate system size dependence of $v_{2}$
for $p_{T}$ $>$ 1.8 GeV/$c$, based on the nuclear size. The $v_{2}$ in U+U and
Au+Au is observed to be higher, whereas in Cu+Cu is slightly lower than those
in isobar collisions.

##  4 Conclusion

We presented the elliptic flow of $K_{s}^{0}$, $\Lambda$, $\bar{\Lambda}$,
$\phi$, $\Xi^{-}$, and $\overline{\Xi}^{+}$ particles in Ru+Ru and Zr+Zr
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. In these isobar collisions,
we noticed a mass ordering at low $p_{T}$ and a baryon-meson splitting at
intermediate $p_{T}$. The NCQ scaling representing the partonic degrees of
freedom and coalescence hadronization, is followed by all strange hadrons. The
hadron $v_{2}$ ratio exhibits a deviation from unity of around 2% when
integrated over $p_{T}$ indicative of different nuclear density and
deformation between the two isobar nuclei. The $v_{2}$ is observed to be
higher for larger colliding systems. These results when compared to model
calculations may shed light on structures of these nuclei.

## References

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