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\title{Spectroscopy of $\eta^\prime$-mesic nuclei with WASA at GSI/FAIR %
\thanks{Presented at the 3rd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics}%
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}

\author{
Y.~K.~Tanaka$^{a}$, 
S.~Bagchi$^{a}$,
J.~Benlliure$^{b}$, 
T.~Dickel$^{a}$, 
V.~Drozd$^{a,c}$, 
H.~Ekawa$^{d}$,
H.~Fujioka$^{e}$,
H.~Geissel$^{a,f}$, 
F.~Goldenbaum$^{g}$,
C.~Guo$^{h}$,
E.~Haettner$^{a}$, 
M.~N.~Harakeh$^{c,a}$, %comment by muhsin
R.~S.~Hayano$^{i}$, 
Y.~He$^{j}$,
S.~Hirenzaki$^{k}$,   
C.~Hornung$^{f}$, 
Y.~Igarashi$^{l}$, 
N.~Ikeno$^{m}$, 
K.~Itahashi$^{d}$, 
M.~Iwasaki$^{d}$, 
D.~Jido$^{e}$, 
N.~Kalantar-Nayestanaki$^{c}$, 
R.~Kanungo$^{n}$, 
B.~Kindler$^{a}$,
R.~Kn\"{o}bel$^{a,f}$,
D.~Kostyleva$^{a}$,
N.~Kurz$^{a}$, 
N.~Kuzminchuk$^{a}$,
E.~Liu$^{j}$,
B.~Lommel$^{a}$, 
Y.~Ma$^{d}$,
S.~Y.~Matsumoto$^{o}$, 
V.~Metag$^{f}$, 
S.~Minami$^{a}$,
P.~Moskal$^{p}$, 
I.~Mukha$^{a}$, 
A.~Muneem$^{d}$,
T.~Nagae$^{o}$, 
H.~Nagahiro$^{k}$,
M.~Nakagawa$^{d}$,
H.~J.~Ong$^{q}$, 
H.~Outa$^{d}$, 
S.~Pietri$^{a}$, 
W.~R.~Plass$^{a}$,
A.~Prochazka$^{a}$,
S.~Purushothaman$^{a}$, 
X.~Qiu$^{j}$, 
C.~Rappold$^{a}$, 
J.~Ritman$^{g}$,
J.~L.~Rodr\'{i}guez-S\'{a}nchez$^{b}$, 
R.~Ruber$^{r}$,
O.~Rundel$^{p}$,
T.~R.~Saito$^{a,d}$,
C.~Scheidenberger$^{a,f}$,
R.~Sekiya$^{o}$,
V.~Serdyuk$^{g}$,
H.~Simon$^{a}$, 
B.~Sitar$^{s}$,
M.~Skurzok$^{p,t}$,
P.~Strmen$^{s}$, 
B.~Sun$^{h}$, 
B.~Sun$^{j}$, %take's group
I.~Szarka$^{s}$, 
M.~Takechi$^{u}$, 
I.~Tanihata$^{q,h}$, 
S.~Terashima$^{h}$,
H.~Weick$^{a}$, 
A.~Yamamoto$^{l}$,
J.~Zhao$^{h}$\\($\eta$-$\mathrm{PRiME}$/$\mathrm{Super}$-$\mathrm{FRS}$
$\mathrm{Experiment}$ 
$\mathrm{Collaboration}$)
\address{
$^{a}${GSI Helmholtzzentrum f\"ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany}\\
$^{b}$Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain\\
$^{c}$KVI-CART, University of Groningen, %Zernikelaan 25, 
9747 AA Groningen, the Netherlands\\
$^{d}$RIKEN, %2-1 Hirosawa, 
Wako, 351-0198 Saitama, Japan\\
$^{e}$Tokyo Institute of Technology, 
152-8550 Tokyo, Japan\\
$^{f}$Universit\"{a}t Giessen, %Heinrich-Buff-Ring 16, 
35392 Giessen, Germany\\
$^{g}$Forschungszentrum J\"{u}lich,  52425 J\"{u}lich, Germany\\
$^{h}$Beihang University, %Xueyuan Road 37, Haidian District, 
100191 Beijing, China\\
$^{i}$The University of Tokyo, %7-3-1 Hongo, Bunkyo, 
113-0033 Tokyo, Japan\\
$^{j}$Lanzhou University, Lanzhou, 730000 Gansu, China\\
$^{k}$Nara Women's University, %Kita-Uoya Nishi-Machi, 
630-8506 Nara, Japan\\
$^{l}$KEK, %1-1 Oho, 
Tsukuba, 305-0801 Ibaraki, Japan\\
$^{m}$Tottori University, 680-8551 Tottori, Japan\\
$^{n}$Saint Mary's University, %923 Robie Street, 
Halifax, Nova Scotia B3H 3C3, Canada\\
$^{o}$Kyoto University, 606-8502 Kyoto, Japan\\
$^{p}$Jagiellonian University, 30-348 Krak\'{o}w, Poland\\
$^{q}$RCNP, Osaka University, Ibaraki, 567-0047 Osaka, Japan\\
$^{r}$Uppsala University, 75120 Uppsala, Sweden\\
$^{s}$Comenius University Bratislava, 
842 48 Bratislava, Slovakia\\
$^{t}$INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy\\
$^{u}$Niigata University, %8050 Ikarashi 2-no-cho, Nishi-ku, 
950-2181 Niigata, Japan}
}

\maketitle
\begin{abstract}
We plan to conduct an experimental search for $\eta^\prime$-mesic nuclei 
in order to 
%aiming at investigating 
investigate
in-medium properties of the $\eta^\prime$ meson. 
A 2.5 GeV proton beam is employed to produce $\eta^\prime$-mesic $^{11}$C nuclei with the $^{12}$C($p$,$d$)$\eta^\prime \otimes ^{11}$C reaction. 
%We measure the ${}^{12}$C($p$, $dp$) reaction at the incident proton energy of 2.5 GeV.
Simultaneous measurements of the forward ejected deuterons 
%for missing-mass spectrometry 
and decay protons from $\eta^\prime$-mesic nuclei will allow us to achieve high experimental sensitivity. 
The experiment will be performed at GSI by making full use of the fragment separator FRS and the WASA detector system. The plan of this proposed experiment is described. 
\end{abstract}
\PACS{13.60.Le, 14.40.Be, 25.40.Ve, 21.85.+d}
     
\section{Introduction}
Possible existence of $\eta^\prime$-meson nucleus bound states ($\eta^\prime$-mesic nuclei) has recently attracted both theoretical and experimental interests, since such bound states reflect $\eta^\prime$ meson properties in finite nuclear density \cite{Metag2017,Bass2019}. 
The peculiarly large mass of the $\eta^\prime$ meson in vacuum is theoretically understood by an interplay between $U_A(1)$ anomaly and chiral symmetry breaking \cite{Jido2012,Lee1996}. Thus, the $\eta^\prime$ mass may be reduced 
in finite nuclear density due to
partial restoration of chiral symmetry \cite{Jido2012,Costa2005,Nagahiro2006,Sakai2013,Bass2006}. Such mass reduction would induce an attractive $\eta^\prime$-nucleus potential, leading to a possible existence of $\eta^\prime$-mesic nuclei \cite{Nagahiro2005,Nagahiro2013}.

We performed a first experiment to search for $\eta^\prime$-mesic nuclei by means of missing-mass spectroscopy of the $^{12}$C($p$,$d$) reaction near the $\eta^\prime$-meson production threshold \cite{Itahashi2012,Tanaka2016,Tanaka2018}.
Although good statistical sensitivity and energy resolution were achieved,
no significant peak structure due to the formation of the $\eta^\prime$-mesic states was observed in the measured excitation spectra.
We determined upper limits for the formation cross sections of $\eta^\prime$-mesic nuclei and deduced a constraint on the $\eta^\prime$-nucleus potential $(V_0 + iW_0)$ at normal nuclear density, as shown by the gray area in Fig.~\ref{tanaka_VWplane} \cite{Tanaka2016, Tanaka2018}. A relatively large real potential ($V_0 \sim -150$~MeV) is excluded in the analysis of this first experiment, while the experimental sensitivity is still not sufficient to find peak structures in the case of smaller real potentials.

\begin{figure}[htb]
\centerline{ \includegraphics[width=8.0cm]{fig1.pdf} }
\caption{Constraint on the $\eta^\prime$-nucleus potential 
$(V_0 + iW_0)$ at normal nuclear density obtained from the first experiment. This figure is taken from Ref.~\cite{Tanaka2018}. Theoretical predictions \cite{Costa2005,Nagahiro2006,Sakai2013,Bass2006,Nagahiro2012} and indications from the CBELSA/TAPS experiment \cite{Nanova2013,Nanova2016,Nanova2012,Friedrich2016} are shown as well. 
See Ref.~\cite{Tanaka2018} for details.
%Trajectories of the particles are measured by multi-wire drift chambers (MWDCs), and deuterons are identified by plastic scintillators (SCs) and aerogel Cherenkov detector (AC).
}
\label{tanaka_VWplane}
\end{figure}

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\section{Experiment with WASA at GSI/FAIR}

\subsection{Experimental Principle and Method}
We propose a measurement of the ${}^{12}$C($p$,$dp$) reaction 
%near the $\eta^\prime$ production threshold 
in order to search for $\eta^\prime$-mesic nuclei with further increased 
experimental sensitivity \cite{S457_proposal}. 
We employ a 2.5~GeV proton beam to produce $\eta^\prime$-mesic 
nuclei in the ${}^{12}$C($p$,$d$)$\eta^\prime \otimes ^{11}$C reaction. 
The excitation energy of $^{11}$C is obtained 
by precisely measuring the momentum of the ejectile deuteron.
In addition, protons emitted from decay of the $\eta^\prime$-mesic nuclei are
 identified to select events associated with the formation of $\eta^\prime$-mesic nuclei. A large amount of physical background processes in the ${}^{12}$C($p$,$d$) reaction, such as quasi-free 
    multi-pion production, are thus suppressed, leading to a better signal-to-background ratio of the excitation spectrum 
    than that in the first inclusive measurement. 

This experiment is feasible at GSI by combining the fragment separator (FRS) \cite{Geissel1992} and the WASA central detector system \cite{WASA1, WASA2}.
FRS is a versatile high-resolution spectrometer, as shown in Fig.~\ref{fig_setup_tanaka}, and suitable for the measurement of the ejectile deuterons at $0^\circ$. The WASA central detector system, consisting of a superconducting solenoid magnet, a mini drift chamber, plastic scintillator barrel, and CsI electromagnetic calorimeter, covers nearly the full solid angle and is ideal for the detection of the decay particles. 
%The combination of FRS and WASA enables this new type of measurement.

 Figure~\ref{fig_setup_tanaka} shows a schematic view of the detailed experimental setup.
A 2.5 GeV proton beam accelerated by the synchrotron SIS-18 is injected to a carbon target placed inside the WASA central detector at F2. Emitted deuterons in the $^{12}$C($p$,$dp$) reactions are momentum-analyzed by the F2-F4 section of FRS operated as a high-resolution spectrometer. Trajectories of the particles are measured by multi-wire drift chambers (MWDCs), and deuterons are identified by time-of-flight measurements with plastic scintillators (SCs) and by an aerogel Cherenkov detector (AC).  Protons emitted from the decay of $\eta^\prime$-mesic nuclei are 
    identified by the WASA central detector. 

\begin{figure}[htb]
\centerline{ \includegraphics[width=10.0cm]{fig2.pdf} }
\caption{A schematic view of the experimental setup with the fragment separator FRS and the WASA central detector. See the texts for details. 
}
\label{fig_setup_tanaka}
\end{figure}

%------------------

\subsection{Simulation Results}
In order to evaluate the experimental sensitivity with the proposed method, 
we performed simulations %of excitation spectra 
for two sets of 
$\eta^\prime$-nucleus potential parameters ($V_0$, $W_0$) = ($-90$, $-17$) MeV and ($-45$, $-5.5$) MeV.
  The formation cross sections of $\eta^\prime$-mesic nuclei
decomposed into different decay modes were taken from theoretical calculations \cite{Nagahiro2013, NagahiroNPA2013}. The cross section of the physical background in the ($p$,$d$) reaction has been measured in the first inclusive experiment \cite{Tanaka2016, Tanaka2018}. Emitted particles from the 
residual nuclei were simulated by using an intra-nuclear cascade code JAM \cite{JAM_Nara, higashi}.

Figure~\ref{fig_simulation} shows simulated excitation-energy spectra 
of $^{11}$C relative to the $\eta^\prime$-meson production threshold. 
A proton with a momentum larger than 1.0~GeV$/c$ and an emission angle $\theta_p$ in a range of $-0.9<\cos{\theta_p}<0.0$ was requested in the analysis of the simulation data. The black points show the simulated 
spectra, while the red and blue curves display the components of the signal process associated with $\eta^\prime$ mesons and the physical background process, respectively.
In the upper row, we assumed the acceptance of FRS for the forward deuterons and a data collection time of 4 days, which corresponds to the 
proposed experiment at GSI \cite{S457_proposal}. 
As seen in the figure, indications of peak structures
due to the formation of the $\eta^\prime$-mesic states 
can be expected for these two potential parameter sets. 
Furthermore, in the lower row, we assumed a 20-day beam time with 
Super-FRS \cite{superfrs} in the future facility FAIR.
In this case, prominent peak structures are expected, which enable precise measurements of $\eta^\prime$-mesic nuclei.

\begin{figure}[htb]
\centerline{ \includegraphics[width=12.0cm] {fig3.pdf} }
\caption{Simulated spectra for $\eta^\prime$-nucleus potential parameters of ($V_0$, $W_0$) = ($-90$, $-17$) MeV (left) and ($-45$, $-5.5$) MeV (right). The abscissa shows the excitation-energy $E_{\mathrm{ex}}$ of $^{11}$C relative to the $\eta^\prime$-meson production threshold $E_0$. The black points are the simulated spectra, whereas the red and blue curves are the signal and the physical background components, respectively. 
A 4 (20)-day beam time with FRS (Super-FRS) is assumed in the upper (lower) panels.
}
\label{fig_simulation}
\end{figure}

%------------------

\subsection{Preparation Status}
We have transported the WASA central detector from Forschungszentrum 
J\"{u}lich, where WASA had been operated from 2006 to 2015, to GSI in Darmstadt. 
The mini drift chamber has been set up again 
   at GSI and tested with cosmic-ray particles. 
The plastic scintillator barrel (PSB) will be updated by 
additionally attaching multi-pixel photon counters (MPPCs) 
to read out photons at both ends of the scintillator.  
We have developed a prototype of the new PSB and performed 
a systematic evaluation of its time resolution 
by using a 1.7 GeV proton beam at the cooler synchrotron COSY in Forschungszentrum J\"{u}lich. 
Preparations for operation of the superconducting solenoid magnet at GSI are currently underway. We are planning to assemble the full WASA central detector in 2020 and aim at starting the physics run in 2021.


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\section{Summary}
We plan to perform a semi-exclusive measurement of 
the $^{12}$C($p$,$dp$) reaction to search for 
$\eta^\prime$-mesic nuclei. 
The WASA central detector will be integrated with the fragment separator FRS to enable this new type of experiment. 
Preparations and developments on the integration of the 
WASA central detector into the FRS are currently ongoing. 
The first physics run is expected in 2021.


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