This is the accepted manuscript made available via CHORUS. The article has been
published as:

Missing-mass spectroscopy of the ^{12}C(p,d) reaction
near the η^{′}-meson production threshold
Y. K. Tanaka et al. (η-PRiME/Super-FRS Collaboration)
Phys. Rev. C 97, 015202 — Published 12 January 2018
DOI: 10.1103/PhysRevC.97.015202

Missing-mass spectroscopy of the 12 C(p, d) reaction
near the η ′-meson production threshold
Y. K. Tanaka,1, ∗ K. Itahashi,2 H. Fujioka,3 Y. Ayyad,4 J. Benlliure,5 K.-T. Brinkmann,6 S. Friedrich,6
H. Geissel,6, 7 J. Gellanki,8 C. Guo,9 E. Gutz,6 E. Haettner,7 M. N. Harakeh,8 R. S. Hayano,1 Y. Higashi,10
S. Hirenzaki,10 C. Hornung,6 Y. Igarashi,11 N. Ikeno,12 M. Iwasaki,2 D. Jido,13 N. Kalantar-Nayestanaki,8
R. Kanungo,14 R. Knoebel,6, 7 N. Kurz,7 V. Metag,6 I. Mukha,7 T. Nagae,3 H. Nagahiro,10 M. Nanova,6 T. Nishi,2
H. J. Ong,4 S. Pietri,7 A. Prochazka,7 C. Rappold,7 M. P. Reiter,7 J. L. Rodrı́guez-Sánchez,5 C. Scheidenberger,6, 7
H. Simon,7 B. Sitar,15 P. Strmen,15 B. Sun,9 K. Suzuki,16 I. Szarka,15 M. Takechi,17 I. Tanihata,4, 9 S. Terashima,9Y. N. Watanabe,1 H. Weick,7 E. Widmann,16 J. S. Winfield,7 X. Xu,7 H. Yamakami,3 and J. Zhao9(η-PRiME/Super-FRS Collaboration)
1

The University of Tokyo, 7-3-1 Hongo, Bunkyo, 113-0033 Tokyo, Japan
Nishina Center for Accelerator-Based Science, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan
3
Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, 606-8502 Kyoto, Japan
4
RCNP, Osaka University, 10-1 Mihogaoka, Ibaraki, 567-0047 Osaka, Japan
5
Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
6
Universität Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany
7
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany
8
KVI-CART, University of Groningen, Zernikelaan 25, 9747 AA Groningen, the Netherlands
9
Beihang University, Xueyuan Road 37, Haidian District, 100191 Beijing, China
10
Nara Women’s University, Kita-Uoya Nishi-Machi, 630-8506 Nara, Japan
11
KEK, 1-1 Oho, Tsukuba, 305-0801 Ibaraki, Japan
12
Tottori University, 4-101 Koyamacho-minami, 680-8551 Tottori, Japan
13
Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, 192-0397 Tokyo, Japan
14
Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada
15
Comenius University Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
16
Stefan-Meyer-Institut für subatomare Physik, Boltzmangasse 3, 1090 Vienna, Austria
17
Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, 950-2181 Niigata, Japan(Dated: October 23, 2017)

2

Excitation-energy spectra of 11 C nuclei near the η ′ -meson production threshold have been measured by missing-mass spectroscopy using the 12 C(p,d) reaction. A carbon target has been irradiatedwith a 2.5 GeV proton beam supplied by the synchrotron SIS-18 at GSI to produce η ′ meson boundstates in 11 C nuclei. Deuterons emitted at 0◦ in the reaction have been momentum-analyzed by thefragment separator (FRS) used as a high-resolution spectrometer. No distinct structure due to theformation of η ′ -mesic states is observed although a high statistical sensitivity is achieved in the experimental spectra. Upper limits on the formation cross sections of η ′ -mesic states are determined,
and thereby a constraint imposed on the η ′ -nucleus interaction is discussed.
PACS numbers: 13.60.Le, 14.40.Be, 25.40.Ve, 21.85.+d

I.

INTRODUCTION

Understanding hadron masses is one of the major subjects in contemporary hadron physics. Studies of thelight pseudoscalar mesons are of particular importance,since they have close relations to fundamental symmetries in quantum chromodynamics (QCD). The flavoroctet mesons are considered to be Nambu-Goldstonebosons associated with spontaneous breaking of chiralsymmetry, leading to relatively small masses of the π, K,and η mesons. In contrast, the η ′ meson has an exceptionally large mass of 958 MeV/c2 , which has attracted
interest known as the “U(1) problem” [1]. Theoretically,∗ E-mail:y.tanaka@gsi.de; Present address: GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291
Darmstadt, Germany

the large η ′ mass can be explained by the explicit breaking of UA (1) symmetry owing to quantum anomaly effects in QCD [2, 3]. This anomaly effect on the η ′ mass
is expected to manifest itself under the presence of chiralsymmetry breaking [4, 5].
In finite baryon density, properties of the mesons may
be modified from those in the vacuum due to partial
restoration of chiral symmetry [6–8]. For the η ′ meson,
the reduction of the mass is expected through a weakening of the anomaly effect [5] and also predicted in various
theoretical models. For example, about 150 MeV/c2 reduction at the nuclear saturation density is predicted by
the Nambu–Jona-Lasinio (NJL) model [9, 10], 80 MeV/c2
by the linear sigma model [11], and 37 MeV/c2 by thequark meson coupling (QMC) model [12]. Investigationof such a modification would yield novel insights into themechanism of the meson mass generation as well as thevacuum structure of QCD.

2Meson-nucleus bound states open a unique possibilityof directly probing in-medium meson properties. A wellestablished example of such systems is the deeply-boundπ − states in heavy nuclei, where a π − meson is boundnear the nuclear surface by the superposition of the attractive Coulomb interaction and the repulsive s-wave
strong interaction. These states have been discoveredand studied in missing-mass spectroscopy of the (d,3 He)
reaction [13–15]. A large overlap between a π − mesonand a nucleus in well-defined quantum bound states allows the extraction of information on a modification of
the isovector part of the s-wave pion-nucleus potential,
leading to a quantitative evaluation of partial restorationof chiral symmetry at finite nuclear density [16–19].
In the case of neutral mesons [8], bound states may beformed only via the strong interaction, if the attraction
between a meson and a nucleus is strong enough. Inmedium meson properties, the mass shift ∆m(ρ0 ) andwidth Γ(ρ0 ) at the nuclear saturation density ρ0 , areincorporated in the meson-nucleus potential as U (r) =(V0 + iW0 )ρ(r)/ρ0 by relations V0 = ∆m(ρ0 ) and W0 =−Γ(ρ0 )/2, where ρ(r) denotes the nuclear density distribution. A small imaginary potential compared with thereal part, i.e., |W0 | < |V0 |, is required for the existenceof bound states as discrete levels. This condition may besatisfied for the η ′ meson, as described below.
Very limited information on the η ′ -nucleus interaction is currently available. On the theoretical side,
the predictions for the η ′ -mass reduction [9–12] suggest the real part of the potential V0 in the range from−150 MeV to −37 MeV. On the experimental side, the
CBELSA/TAPS collaboration deduced the real part as
V0 = −(39 ± 7(stat) ± 15(syst)) MeV from η ′ momentum distributions and excitation functions in η ′ photoproduction on nuclear targets [20, 21]. They also evaluated the imaginary part of W0 = −(13 ± 3(stat) ±3(syst)) MeV by measuring transparency ratios as a function of the mass number of the target nuclei [22] and as
a function of η ′ momentum [23]. Such a small imaginary
part relative to the real part implies the possibility ofobserving a bound state as a distinct peak structure. In
the meantime, the real part of the scattering length forthe η ′ -proton interaction has been extracted from measurements of the pp → ppη ′ reaction close to its thresholdto be 0.00 ± 0.43 fm [24], corresponding to an η ′ -nucleus
potential depth of |V0 | < 38 MeV at the nuclear densityof 0.17 fm−3 within the low-density approximation.
Experimental programs to search for η ′ -mesic nuclei
have recently been started, aiming at directly studying the in-medium properties of the η ′ meson. A onenucleon pickup reaction, for example (p, d) or (γ, p), at
forward angles is preferable to produce the η ′ -nucleus
bound states, because the momentum transfer of such areaction can be rather small. Spectroscopy experimentsof the 12 C(γ, p) reaction [25] using high-energy photon
beams were proposed by the LEPS2 collaboration at theSPring-8 facility [26] and by the BGO-OD collaboration
at the ELSA accelerator [27]. The results of these exper-

iments are thus far not available.
We proposed an experimental search for η ′ -mesic nuclei
with missing-mass spectroscopy of the 12 C(p,d) reaction
near the η ′ production threshold [28]. The kinetic energyof the proton beam was chosen to be 2.5 GeV, slightly
above the threshold energy for the elementary processn(p, d)η ′ of 2.4 GeV. The momentum transfer of this reaction at 0◦ is moderate (∼ 500 MeV/c) at 2.5 GeV. An
inclusive measurement of the forward-emitted deuterons
allows the analysis of the overall (p,d) spectrum without
any assumption on decay processes of η ′ -mesic nuclei.
The formation cross section of the η ′ -mesic nuclei via
the 12 C(p, d)11 C⊗η ′ reaction has been theoretically calculated in Ref. [29] for various sets of (V0 , W0 ), the realand imaginary parts of the η ′ -nucleus potential. Population of η ′ -mesic states coupling with neutron hole stateshas been predicted, depending on the assumed potential.
Distinct peak structures are expected in the excitation
spectra particularly near the η ′ production threshold because of the enhanced excited states due to the finite
momentum transfer of the reaction [29].
Physical background such as quasi-free meson production, pN → dX (X = 2π, 3π, 4π, ω), also contributes tothe experimental spectrum as a continuum. The crosssection of the above background process was estimatedto be 2–3 orders of magnitude larger than that of theformation of the η ′ -mesic states [28]. To overcome sucha small signal-to-background ratio, we aimed at achieving an extremely high statistical sensitivity with relative
errors of < 1% in the spectrum. An inclusive simulation has shown that observing peak structures near thethreshold is feasible under a realistic experimental condition for a strongly attractive potential V0 . −100 MeV[28].
We carried out the experiment in 2014. While its results have been briefly reported elsewhere [30], in thispaper a full description of the experiment and analysis including discussions based on additional theoretical calculations is presented. First, the experimental method andperformed measurements are introduced (Sec. II), andnext the data analysis to obtain the excitation-energy
spectra is described in detail (Sec. III). The results of astatistical analysis for the obtained spectra are explained(Sec. IV), followed by discussions of the η ′ -nucleus interaction and future plans for a follow-up experiment withhigher sensitivity (Sec. V). Finally, a conclusion is given
in Sec. VI.

II.

EXPERIMENT

A missing-mass spectroscopy experiment using theC(p,d) reaction was performed near the η ′ production
threshold at GSI, Darmstadt, Germany. A 2.5 GeV proton beam impinged on a carbon target, and the emitted
deuterons at 0◦ were momentum-analyzed to obtain missing masses in the reaction. In addition, elastic protondeuteron scattering was measured for the calibration of12

3
the experimental system.

Proton beams were supplied by the synchrotron SIS18. Two kinetic energies were employed: 2499.1 ± 2.0
MeV for the measurement of the 12 C(p,d) reaction and1621.6±0.8 MeV for the calibration with proton-deuteronelastic scattering. These energies were determined bymeasuring precisely the revolution frequencies of thebeams in the synchrotron. The accelerated beams wereextracted in a slow extraction mode with a spill lengthof 4 (1) seconds and a cycle of 7 (4) seconds for 2.5 (1.6)
GeV. The beams were focused at the experimental target, where a typical spot size was ∼ 1 mm (horizontal)
× 3 mm (vertical).
The beam intensity was ∼ 1010 /s, measured in frontof the target by the SEETRAM detector [31] inserted
on the beam axis. This detector was used only during ashort dedicated measurement for an absolute normalization of the cross sections to avoid unnecessary material
near the beam axis. Plastic scintillation counters placed
off axis around the target continuously monitored relativechanges in the luminosity by counting scattered particles
from the target.

B.

TargetThree targets were mounted on a movable ladder at theentrance position of the spectrometer. A natural carbon
target with an areal density of 4115 ± 1 mg/cm2 was used
for the measurement of the 12 C(p,d) reaction. Deuterated polyethylene (CD2 ) targets with areal densities of1027 ± 2 mg/cm2 and 4022 ± 9 mg/cm2 were used forthe calibration via the proton-deuteron elastic D(p, d)preaction. These targets had a cylindrical shape with adiameter of 2 cm.
C.

Spectrometer and detector system

The fragment separator (FRS) [32] was used as a highresolution magnetic spectrometer to precisely analyze themomenta of deuterons emitted at 0◦ in the (p,d) reactions. The FRS has four stages, as schematically depicted in the top panel of Fig. 1. Each stage consistsof a 30◦ -bending dipole magnet, quadrupole doublet andtriplet magnets. Such a configuration provides considerable flexibility to realize various ion-optics modes withhigh momentum resolving powers.
We developed a special ion-optical mode of the FRS,
which is momentum-achromatic at the central focal plane(F2) and dispersive at the final focal plane (F4), as illustrated in the middle and bottom panels of Fig. 1. The
achromatic section from the target to F2 was used to
select particles originating from reactions in the target.

DipolemagnetCarbontarget Quadrupole
magnet

MWDC, AC,TPC TORCH
SC2H, SC2V
TPC
AC
F2

SC41
SC42
F4

100
X [mm]

Proton beam

‒100
80
dispersion[mm/%]

A.

2.5 GeV
proton

‒ 80

0

73.2
[m]

FIG. 1. (Top panel) A schematic view of the experimental setup with the FRS. A 2.5 GeV proton beam impinged
on a carbon target. Deuterons emitted in the 12 C(p,d) reaction were momentum analyzed at F4 and the tracks werereconstructed from measurements by multi-wire drift chambers (MWDCs). Sets of 5 mm-thick plastic scintillation counters (SC2H, SC2V, and SC41) and a 20 mm-thick one (SC42)
were installed at F2 and F4 for time-of-flight (TOF) measurements. Čerenkov detectors (ACs and TORCH) and time
projection chambers (TPCs) were installed but not used in
the present analysis. (Middle panel) Horizontal beam trajectories with the specially-developed optics mode based on
calculated third-order transfer matrices. Initial positions andangles are taken from {−1, 1} mm × {−8, −4, 0, 4, 8} mrad,and a momentum at the central value. (Bottom panel) A
momentum-dispersion curve of this optics mode.

Secondary background produced by the non-interacting
primary beam dumped near the exit of the first dipole
magnet was thus rejected. The momenta of the deuterons
were then analyzed in the dispersive section from F2
to F4, where a designed momentum resolving power
was about 3.8 × 103 . The dispersion was kept relatively small throughout the whole spectrometer to havea wide momentum acceptance. At F4 the dispersion was
35.1 mm/%.
The detection system is depicted in the top panel ofFig. 1. Two sets of multi-wire drift chambers (MWDCs)
were installed at F4 to reconstruct the deuteron tracks
and obtain their momenta. A MWDC had eight layers ofdetection planes, each consisting of 48 anode wires with aspacing of 5 mm. The active area of each layer was 24 cm(horizontal) × 14 cm (vertical). The wires in the first
four layers were aligned vertically, while those in the next
two and the last two layers were inclined by −15◦ and+15◦ , respectively. The wire positions in the neighboringlayers with the same wire angle were shifted from eachother by a half length of the spacing. These MWDCs
were operated with a gas mixture of 76% argon, 20%
isobutane, and 4% dimethoxymethane. The signals fromthe anode wires were processed by preamplifier-shaper-

4

D.

Trigger condition for data acquisition

In the measurements of the 12 C(p,d) reaction, the total
rate of charged particles at F4 was ∼ 250 kHz. The
top panel of Fig. 2 shows a histogram of TOF between
SC2H and SC41 versus one between SC41 and SC42 for
all particles reaching F4, obtained with a data-acquisition
system triggered by the SC41 signal. Concentration of
events corresponding to deuterons and protons are seenat the expected locations and clearly identified. The ratioof the number of deuterons to that of protons is about 1
to 200, indicating that the deuteron and proton rates at
F4 were ∼ 1 kHz and 250 kHz, respectively.
In order to reject the background protons at the hardware level, we employed a TOF-based trigger for thedata-acquisition system by requiring a coincidence of theSC2H and SC41 signals within 15 ns around a relative
timing of the deuterons. A TOF histogram with thistrigger is shown in the middle panel of Fig. 2, demonstrating efficient rejection of the background protons at
the trigger level. The main source of the remaining
background events was accidental multiple-hit protons at
SC2H, which are randomly distributed in TOF between
SC2H and SC41. The multiple-hit protons are actuallyobserved in the recorded signal waveforms of SC2H, asTOF (SC41-SC42) [ns]TOF (SC41-SC42) [ns]

4

10
30

deuteron

protonSC41
trigger

3

10

25

2

20

10

15

30

10

multiple-hit proton

10

4

130

140 150 160 170
180
TOF-based
TOF (SC2H-SC41) [ns]trigger

10

3

25

10

20

10

2

15

10

10
120

SC2H signal [arb. units]

discriminator chips, and the resulting timing information
was recorded by time-to-digital convertors.
Plastic scintillation counters (SC2H, SC2V, SC41, andSC42) were installed for time-of-flight (TOF) measurements to distinguish signal deuterons with a velocity∼ 0.84 c from background protons with ∼ 0.95 c. SC2H
and SC2V had an active area of 6 cm (horizontal) ×
6 cm (vertical) and a thickness of 5 mm, whereas SC41
had 24 cm (horizontal) × 6 cm (vertical) and the same
thickness. A plastic scintillator with an area of 50 cm(horizontal) × 35 cm (vertical) and a thickness of 2 cm
was adopted for SC42, which was located at 5.16 m
downstream of SC41. Each of these scintillators was
equipped with two photomultipliers. The anode signals
were recorded by a 1-GHz sampling digitizer, and the discriminated timing information by a time-to-digital convertor.
In addition, aerogel Čerenkov detectors (ACs) anda total-reflection Čerenkov detector (TORCH) were installed for confirmation of the particle identification. The
ACs had silica aerogel with a refractive index of 1.17
[33] as a radiator, corresponding to a threshold velocityof 0.85c. TORCH was equipped with a quartz radiatorwith a refractive index of 1.5, hence the maximum detection velocity of ∼ 0.89 c due to designed insensitivity tototally-reflected photons [34]. Time projection chambers(TPCs) [35], the standard beam diagnostics devices of
the FRS, were also placed at F2 and F4 for the purposeof the online beam tuning. These Čerenkov detectors and
TPCs are not used in the offline analysis described in thispaper.

130

140 150 160 170
TOF (SC2H-SC41) [ns]

1
180

0

−1000

deuteron−2000
0

20 40 60 80 100 0time [ns]multiple-hit proton
20 40 60 80 100 120
time [ns]FIG. 2. TOF between SC2H and SC41 and between SC41
and SC42 recorded with a data acquisition system triggeredby the SC41 signals (top) and by the TOF-based coincidence
between the SC2H and SC41 signals (middle). Typical signal
waveforms of SC2H are shown for the deuteron (bottom left)
and the multiple-hit proton (bottom right) events based on
the TOFs.

shown in the bottom panels of Fig. 2, and are rejected
later in the data analysis (Sec. III A). The live rateof the acquisition system varied typically between 30%–
40%, and the data were recorded with a rate of about
103 events/s.

E.

Summary of measurements

The experimental conditions are summarized in Table I. Three types of measurements have been performed,
which are explained as follows.
The production measurements of the 12 C(p,d) reaction
were carried out by using the 2.5 GeV proton beam impinging on the carbon target. The emitted deuterons had
a momentum of 2814.4 ± 2.4 MeV/c at the η ′ production
threshold after the energy loss in the target. To cover awide excitation-energy region, measurements were conducted at seven central momenta of the FRS by scaling
the whole magnetic field with factors from f = 0.980 to5
TABLE I. Experimental conditions of the performed measurements. The first seven rows show production runs of the 12 C(p,d)
reaction at the proton energy of 2.5 GeV with seven momentum settings of the FRS. The next nine rows are calibrations using
the elastic D(p,d)p reactions at 1.6 GeV with nine FRS settings. One set of the calibration took about 0.5 hours, and thenumber of repetitions is given in the last column. The last row shows measurements of the elastic D(p,d)p scattering at 2.5
GeV.
ReactionC(p,d)

Proton energy(MeV)
2499.1 ± 2.0

C (4115 ± 1 mg/cm2 )D(p,d)p1621.6 ± 0.8

CD2 (1027 ± 2 mg/cm2 )D(p,d)p2499.1 ± 2.0

CD2 (4022 ± 9 mg/cm2 )12

Targetf = 1.020. In particular, a region near the η ′ production
threshold was intensively measured, as distinct narrow
structures of η ′ -mesic states were theoretically predicted
most strongly near the threshold [29].
The momentum calibration of the spectrometer was
performed by measuring the elastic D(p,d)p reaction at
1.6 GeV using a CD2 target. Nearly monochromatic
deuterons with the momentum of 2828.0 ± 1.0 MeV/c
were emitted from the target, which defined the central
momentum of the FRS at f = 1.000. These deuterons
were measured with various scale factors to analyze theion-optical response of the FRS. One calibration run took
about half an hour, and it was repeated every ∼ 8 hours
to check the stability of the whole spectrometer system.
The elastic D(p,d)p scattering was measured with a
CD2 target and a proton beam of 2.5 GeV in order tocrosscheck the normalization of the differential cross section. The obtained value was then compared with thosereported in Ref. [36], as explained in Sec. III D. During a part of the measurement, solid angles were tightly
limited to 2.35 × 10−2 msr and 3.94 × 10−2 msr by using slits directly behind the target. A comparison of theyields with and without the slits provided the effective
solid angle covered by the FRS.

III.

ANALYSIS

The goal of the data analysis described in this section
is to obtain excitation-energy spectra of 11 C near the η ′production threshold. The analysis procedure consistsof the following steps. First, the deuteron events are

Central momentumof FRS (MeV/c)
2771.42779.92785.62799.72828.02856.32884.62771.42779.92785.62799.72813.92828.02842.12856.32884.63809.3

Scaling factor f
for magnets
0.980
0.983
0.985
0.990
1.000
1.010
1.020
0.980
0.983
0.985
0.990
0.995
1.000
1.005
1.010
1.020
1.347

Duration
9.7 hour9.3 hour9.9 hour
10.9 hour23.0 hour
5.9 hour2.0 hour
5 set
2 set
1 set
5 set
1 set
8 set
1 set
3 set
1 set
1.2 houridentified (Sec. III A), and next the deuteron momenta
are reconstructed from the measured tracks (Sec. III B).
The excitation energies of 11 C are then kinematically calculated (Sec. III C), and finally the normalization of thecross section is performed (Sec. III D).
A.

Selection of deuteron events

Data of the plastic scintillation counters are analyzed
in order to identify deuterons at the F4 focal plane. As
explained in Fig. 2, major background particles in therecorded data are the accidental multiple-hit protons at
F2. Thus, signal waveforms of photomultipliers reading
SC2H are firstly analyzed to select single-hit events at
F2. TOF between F2 and F4 is analyzed as well to further reject remaining background protons. SC42 is not
used in the following analysis to avoid position-dependenttransmission from SC41 to SC42 caused by material inhomogeneity found in the Čerenkov detectors behind SC41.
The waveforms of SC2H signals are fitted by an empirical function(t − p3 )2
f (t) = p0 + p1 t − p2 · exp −, (1)2(p4 + p5 t)2
where the first two terms represent a baseline and thethird a pulse with a negative polarity. Signals are fitted
within a time window of 70 ns around a typical deuterontime, treating p1 , . . . , p5 as free parameters. The sum of
the squared residual (SSR) given by the fit is then used toquantify the multiplicity of the particles. Figure 3 shows
SSR against the height parameter p2 obtained for both

6

7

4000

4000

single3000 hit

single3000 hit

2000

2000

1000

1000

10

6

10

5

10

4

10

3

10

106
Counts / 40 ps

Fitted height p2 [arb. units]

two photomultipliers (left and right) of SC2H. Singlehit events are clearly identified around SSR ≈ 100. By
taking into account the correlation between SSR and p2 ,events in the regions indicated by the arrows are selected
as single-hit events and used in the following analyses.

f = 0.980

105

TOF
selection

104
103
102
10
145
150
155
160
TOF (SC2H-SC41) with corrections [ns]

2

10

10
0

06
2
3
4
5
2
3
4
5
6 1
10 10 10 10 10 10 10 10 10 10 10 10
SSR (left) [arb. units]
SSR (right) [arb. units]

FIG. 3. Fit results of SC2H waveforms with a single-pulse
function. SSR and the height parameter p2 obtained in the
fit are plotted for both of the two photomultipliers (left andright) of SC2H. The solid curves are used as boundaries toselect single-hit events.

Next, TOF between F2 and F4 is analyzed, by introducing corrections for time-walk effects and dependence
on ion-optical variables. The corrected TOF spectrum
for the data set at the scaling factor f = 0.980 is presented in Fig. 4 as an example. The unshaded spectrum
shows the total recorded events, where a peak for the
deuteron is observed above a constant component due tothe multiple-hit proton background. The achieved time
resolution for the deuteron peak is σ = 1.7 × 102 ps.
The shaded spectrum displays the single-hit events selected by the waveform analysis, demonstrating efficient
rejection of the multiple-hit background by 2–3 orders ofmagnitude. Finally, events within the dashed lines (±5σregion around the peak) are selected as deuteron events
to further reject remaining proton background.
The efficiency of the deuteron identification is discussed in three steps as follows. First, properly measured times and pulse heights of the SC2H and SC41
signals and reconstructed tracks at F4 are required forthe analysis of the particle identification. This first condition leads to 0.6–0.9% rejection of the deuteron. Second, rejection of the deuteron by selecting the single-hit
waveform is considered using a TOF spectrum for those
events rejected in the waveform selection. The spectrum
shows a small enhancement at the TOF value for the
deuteron, indicating 2–3% rejection. Third, probabilityof deuteron rejection by the TOF selection is estimated tobe 0.2–0.3% from the tail structure of the deuteron peakobserved in the TOF spectrum. The longer tail on theright side is due to accidental particles almost coincident
with the deuteron at F2 where the timing information
measured by a leading-edge discriminator deviated only
to the earlier side. Combining the above three contributions, the deuteron identification efficiency is evaluated

FIG. 4. Corrected TOF spectra between F2 and F4 at the
FRS scale factor of f = 0.980. The unshaded histogram shows
the total number of events, while the shaded one corresponds
to the single-hit events selected by the SC2H waveforms. The
dashed lines indicate the ±5σ region around the deuteronpeak used for the TOF selection. The region between thedotted lines is used to estimate the proton contamination fraction.

to be 96–97% for all the data sets of the 12 C(p,d) reaction.
The contamination of background protons in eventswith identified deuteron is evaluated in the TOF spectrum with the single-hit selection. The spectrum showsan almost constant background on the shorter TOF sideof the deuteron peak, where a tail structure of the peakis not significant. The amount of the contamination in
the TOF window (dashed lines) can be estimated by integrating the constant region between the dotted lines
with the same interval. The contamination fraction thus
evaluated is ∼ 2 × 10−4 , making only a negligible contribution in the subsequent spectral analysis.

B.

Momentum analysis

The deuteron momentum is obtained from the reconstructed track by MWDCs at the F4 dispersive focal
plane. The momentum Pd can be written as
Pd = PFRS (1 + δ),(2)

where δ denotes a momentum deviation relative to the
FRS central momentum, PFRS = f · 2828.0 MeV/c. The
deviation δ can be derived from the horizontal track (position X and angle X ′ ) regardless of the scaling factor f ,since ion-optical properties remain unchanged by scaling
the central momentum in a small range.
In order to obtain a calibration function converting a
track (X, X ′ ) to δ, the mono-energetic deuteron from theelastic D(p, d)p reaction at the proton energy of 1.6 GeV
is analyzed. A deuteron emitted in this reaction has amomentum of 2828.0 MeV/c, corresponding to a deviation of δ = 1/f − 1 for the FRS scaling factor f . Thus,
the ion-optical response for δ between −2% and 2% can

7

X′ at F4 [mrad]be evaluated from the calibration settings listed in Table I. Examples of the reconstructed horizontal position
X and angle X ′ are shown in the left panel of Fig. 5, overlaid for f = 0.980, 0.990, 1.000, 1.010, 1.020. An elasticscattering locus for each scaling factor is observed above
a continuum from reactions with carbon. We fit the position X by a polynomial function of both X ′ and δ using all the data sets, and thereby construct a calibration
function for δ, as demonstrated in the right panel.
An uncertainty associated with the calibration of δ isderived from deviations between the repeated measurements. Thus the estimated systematic error of δ is 0.02%
in a region of |X ′ | < 18 mrad, which is later used in theanalysis of the 12 C(p,d) reaction.
30

500

20

400

10

300

0

‒10

200

‒20

100

‒30
50 100 ‒3 ‒2 ‒1 0 1 2‒100 ‒50 0
Calibrated δ [%]X at F4 [mm]30FIG. 5. Calibration data with the elastic proton-deuteronscattering for the FRS scale factors f = 0.980, 0.990, 1.000,
1.010, 1.020. (Left panel) Horizontal position X and angle X ′at F4 reconstructed by MWDCs. (Right panel) Calibrated δ,
the momentum deviation relative to the FRS central momentum, is shown against the angle X ′ .

C.

Excitation energy
1.

Calculation

The excitation energy of 11 C has been calculated fromthe proton kinetic energy Tp and the deuteron momentum Pd . First, the relativistic energies of the proton (Ep′ )and the deuteron (Ed′ ) are calculated at the center of thereaction target, after correcting the energy losses, as
Ep′ = Tp + Mp c2 − ∆Ep ,q
Ed′ = Pd2 c2 + Md2 c4 + ∆Ed .

respectively. Here, the reaction angle is assumed to be0◦ because of the ion-optical restrictions on angle reconstruction. Finally, the excitation energy Eex is defined
relative to the η ′ production threshold E0 = 957.78 MeV
asEex − E0 = (MX − M11 C − Mη′ ) c2 ,(6)where M11 C and Mη′ denote the 11 C and η ′ masses, respectively.

2.

Systematic error

The systematic errors in the excitation-energy calculation have been evaluated by considering the following
three sources.
(a) Beam energy. Uncertainties in the absolute beamenergies (2499.1 ± 2.0 MeV and 1621.6 ± 0.8 MeV) cause
systematic errors of 1.9 MeV and 0.8 MeV in the excitation energy, respectively. Note here that the lower beamenergy also affects the excitation energy, as the deuteron
momentum in the D(p, d)p calibration at 1.6 GeV is used
to define the FRS central momentum. Considering thatthe two errors are mostly correlated because of theircommon source in the circumference of the SIS-18 synchrotron, we obtain the combined systematic error of 1.4
MeV in the excitation energy.
(b) Reaction angle. A systematic error originating in
the uncertainty of the reaction angle, which is assumed
to be 0◦ in the kinematical calculation of the production
and calibration reactions, is evaluated to be 0.8 MeV in
the excitation energy. The possible maximum systematic
error caused by neglecting the finite reaction-angle distribution (. 1◦ ) in the acceptance of the FRS is adopted.
(c) Optics calibration. The systematic error of the relative momentum deviation δ has been evaluated to be
0.02%. This corresponds to an error of 0.5 MeV in thescale of the excitation energy.
By taking a square root of the quadratic sum of all
the above contributions, a total systematic error in the
excitation energy is estimated to be 1.7 MeV.

3.

Experimental resolution

(3)
(4)

∆Ep and ∆Ed represent the energy losses in half of thetarget thickness based on a calculation with atima [37].
The missing mass MX in the 12 C(p,d)X reaction is thenobtained by
s


 ′

Ep′ − Ed′ 2
Pp − Pd′ 2
M12 C +
MX =
, (5)
−
c2
c
where M12 C is the mass of 12 C, and Pp′ and Pd′ are the proton and deuteron momenta corresponding to Ep′ and Ed′ ,The experimental resolution is evaluated using themono-energetic deuterons in the D(p, d)p calibration at
1.6 GeV. Figure 6 shows a spectrum of the deuteron
momentum at the FRS scaling factor of f = 1.000 analyzed in the same procedure as the production runs.
The spectrum is fitted well with a function given by
the gray solid line, summing a Gaussian function for
the elastic peak (dotted line) and a second-order polynomial for the carbon contribution (dashed line). The
Gaussian component yields the overall momentum resolution of 2.79 ± 0.09 MeV/c (σ), where the uncertainty includes deviations between the different data sets.

8This resolution corresponds to an energy resolution of
σcal = 2.20 ± 0.07 MeV in the scale of Eex shown in thelower axis.
In order to evaluate the experimental resolution in the
production runs from the above estimate for the calibration runs, two corrections for the different target andbeam energy in the calibration measurements are necessary. First, a Monte-Carlo simulation based on atima[37] shows that the energy straggling in the targets makes
targ
targ
contributions of σprod= 1.15 MeV and σcal
= 0.39 MeV
in the production and calibration runs, respectively, inthe scale of Eex . Second, an estimated relative momentum spread of the beams of ≤ 1.7 × 10−4 accounts forbeam
resolutions of σprod≤ 0.52 MeV in the production runs
beam
and σcal ≤ 0.34 MeV in the calibration in the scaleof Eex . By introducing the corrections quadratically i.e.,targ 2
targ 22
2
beam 2
beam 2σE= σcal+ {(σprod) − (σcal) } + {(σprod) − (σcal) },the excitation-energy resolution in the production measurements is obtained as σE = 2.4–2.6 MeV.

Counts [arb. units]

5000
4000

CD2(p , d )Tp = 1.6 GeV

3000
2000
1000
0

2860 2850 2840 2830 2820 2810 2800 2790
Pd [MeV/ c ]−40 −30 −20 −10
01020
E ex − E 0 [MeV] for 12C(p, d) at Tp = 2.5 GeV

FIG. 6. Momentum spectrum of deuterons in the CD2 (p, d)calibration measurement with the 1.6 GeV proton beam. The
lower axis shows the excitation energy for the production run
corresponding to the deuteron momentum. The gray solid line
displays a fit with a function consisting of a Gaussian peak
(dotted line) and a second-order polynomial (dashed line).

A(δ) ∝ 1 + (0.07 ± 0.03)δ/%, and the excitation spectraat the seven FRS settings are thus corrected with thisfunction.
To normalize the absolute scale of the double differential cross section, we analyze a short production run with
the SEETRAM detector directly monitoring the beam intensity. The double differential cross section is calculated
by
 2 
d σ
(dY /dE)ref=(7)dΩdE lab Np · nt · ∆Ωref · ε
at one reference energy Eex − E0 = −7.0 MeV, where
the solid angle covered by the FRS is separately evaluated as ∆Ωref = 1.16 ± 0.13 msr. (dY /dE)ref is themeasured yield density per unit excitation energy at thereference, Np is the number of the incident protons obtained by SEETRAM, and nt is the number density ofthe target. ε denotes the overall efficiency estimated tobe (25.2±0.1)%, taking into account the trigger efficiency(26.2%), the deuteron identification efficiency (96–97%),
and the tracking efficiency (99.8–99.9%). As a result, thedouble differential cross section of 5.4 ± 0.7 µb/(sr MeV)
is obtained at the reference energy.
Spectral normalization is then performed as follows.
First, the acceptance-corrected excitation spectrum at
the FRS scale factor of f = 0.990 is normalized, according to the analyzed cross section at the reference energy
Eex − E0 = −7.0 MeV. Next, the spectra at the neighboring FRS settings (f = 0.985 and 1.000) are scaled sothat they have consistent overlap in the common energy
region with the f = 0.990 spectrum. Spectra at the othersettings are sequentially normalized in the same manner.
The differential cross section of the elastic D(p, d)p reaction at 2.5 GeV is analyzed as well in a similar way inorder to confirm the analyses on the beam intensity at
this energy and on the normalization of the cross section.
The obtained value is 0.98 ± 0.11 µb/sr in the center-ofmass frame, which is consistent with known cross sections
around this energy, 1.10 ± 0.10(stat) ± 0.09(syst) µb/sr
at 2.4 GeV and 1.18 ± 0.03(stat) ± 0.09(syst) µb/sr at
2.55 GeV [36], within the experimental errors.
IV.

D.

RESULTS

Normalization of spectra

Excitation-energy spectra need to be corrected for theacceptance of the spectrometer, which can be expressed
as a function of the momentum parameter δ. For spectral
analysis, events with the horizontal angle at F4 in |X ′ | <18 mrad and δ in 0% ≤ δ ≤ 1.5% are selected, where theacceptance curve is assumed to be linear. The slope of
the acceptance function is then deduced by two methods:(i) measuring the δ-dependence of deuteron yields at one
fixed absolute momentum by scaling the FRS magnetic
fields, and (ii) a Monte Carlo simulation of the ion-opticaltransport in the FRS using the code mocadi [38]. These
two estimations result in a consistent acceptance curve ofExcitation-energy spectra of 11 C obtained with theC(p,d) reaction are presented in Fig. 7 for the seven
momentum settings of the spectrometer. The excitation energy Eex relative to the η ′ production threshold
E0 = 957.78 MeV is shown in the lower horizontal axis,
while the scale of the corresponding deuteron momentum
is given in the upper one. The systematic error associated with the excitation energy has been estimated to be
1.7 MeV. The ordinate gives the double differential crosssection, with an uncertainty of ±13% on the absolute
scale.
These seven spectra are combined into one spectrum
by averaging the data points of different FRS settings
12

9

5.4
100f = 0.983
80

60

40

20

0

20

405.8

d 2σ /(d ΩdE ) [μb/(sr MeV)]

5.6
5.8
100f = 0.985
80
5.6

60

40

20

0

20

5.4
40

5.4
5.2

5.4

5.6

f = 0.990

5.2
f = 1.000

f = 1.000

5.6

f = 1.010
5.4

f = 1.020

5.2

f = 0.980
f = 0.983

5.0

100
0.1

f = 0.985

5.4

f = 1.010

5.0

f = 1.020

5.0
4.8
− 100

−80

80

60

−80

−60

40

20

0

20

40

−40
−20
E ex − E 0 [MeV]

0

20

40

0

−100

5.2

5.2

f = 0.990

− 0.1

5.2
5.0

5.8

4.8
5.4

5.6

d 2σ/(d ΩdE ) [μb/(sr MeV)]

5.6

Residue

5.8

Deuteron momentum [MeV/c ]2920 2900 2880 2860 2840 2820 2800 2780
f = 0.980−60−40 −20E ex − E 0 [MeV]

020

FIG. 8. (Top panel) Combined spectrum of the 11 C excitation energy Eex near the η ′ production threshold E0 =957.78 MeV. A third-order polynomial fit is given by the solid
gray curve. The horizontal bars indicate excitation-energy
regions covered by each FRS momentum setting. (Bottom
panel) Residues of the polynomial fit. The dashed lines display envelopes of 2 standard deviations.

40

FIG. 7. Excitation-energy spectra of 11 C measured in the
12
C(p,d) reaction with seven momentum settings (f = 0.980–
1.020) of the FRS. The lower abscissa is the excitation energy
Eex relative to the η ′ production threshold E0 = 957.78 MeV,
and the upper axis shows the corresponding deuteron momentum. The gray solid curves display a third-order polynomial
simultaneously fitted to the seven spectra.

at each excitation energy. The resulting excitation spectrum is shown in Fig. 8 (top panel). Note that this averaging reduces the degrees of freedom originating in therelative spectral normalization between the neighboring
settings. Therefore, the following analyses are performed
for both the individual spectra (Fig. 7) and the combinedone (Fig. 8), where only minor differences are found as
shown later.
The obtained spectra show no distinct narrow structure, although a good statistical sensitivity at a level of< 1% is achieved together with a sufficiently good experimental resolution of σE = 2.4–2.6 MeV. The spectra
exhibit a smooth increase from about 4.9 to 5.7 µb/(srMeV) in the measured region of the excitation energy.
This continuous component can be understood within anorder of magnitude by quasi-free meson production processes pN → dX (X = 2π, 3π, 4π, ω), where N denotes anucleon in the target nucleus, as simulated in Ref. [28].
The spectra are fitted by a third-order polynomial
function over the whole measured energy region. The

seven spectra in Fig. 7 are simultaneously fitted, by sharing the polynomial parameters between the settings. In
addition, a multiplying factor is introduced as a free parameter to each spectrum except for the one at f = 0.990
in order to take into account a possible error correlation
with the relative normalization of the spectra. The fit
results are shown by the gray solid curves in both Figs. 7
and 8. χ2 /(n.d.f.) is 221/225 in Fig. 7 and 125/121 inFig. 8, where n.d.f. denotes the number of degrees of
freedom. Residues of the fit are also displayed in Fig. 8(bottom panel) with envelopes of 2 standard deviations.
We determine upper limits for the formation cross section of η ′ -mesic nuclei. Here, a Lorentzian function at an
excitation energy Eex with a width Γ (FWHM) is tested
as a signal shape. The measured spectrum is assumed to
be described by the following function: dσ· Voigt(E; Eex , Γ, σE )f (E; Eex , Γ) =dΩ+(p0 + p1 E + p2 E 2 + p3 E 3 ).

(8)

The first term includes a Voigt function, which is theLorentzian function folded by a Gaussian function accounting for the experimental resolution (σE ). The signaldσ). The seccross section to be tested is represented by ( dΩond term is the third-order polynomial accounting for thecontinuous component. The combined spectrum (Fig. 8)
is fitted by this function within a region of ±35 MeV
around the Lorentzian center, by treating both the signal cross section and the polynomial coefficients as free10
parameters. The upper limit of the cross section at the
95% confidence level is then determined by assuming a
Gaussian probability density function based on the fit
result and normalizing it in the physical non-negative redσ
≥ 0).
gion ( dΩIn order to obtain the upper limit as a function of theLorentzian position Eex and width Γ, the above analysis has been repeated for each set of (Eex − E0 , Γ) in{−60, −59, . . . , +20} × {5, 10, 15} MeV. In Fig. 9, the fitted values and errors of the Lorentzian cross section are
shown by the solid dots, and the resulting upper limits
are summarized by the solid curves. These values are
given in the differential cross section dσ/dΩ by the left
ordinate and in the Lorentzian peak height d2 σ/(dΩdE)by the right one. Moreover, analysis based on simultaneous fitting of the seven spectra (Fig. 7) is conducted inorder to check effects of possible error correlations withthe relative normalization of the spectra. Thus evaluated limits are given by the dashed curves, exhibiting no
significant difference between the two analysis methods.

Γ = 5 MeV

95% C.L. Upper limit

0

0
− 50

− 0.5
50MeV
− 40 − 30 − 20 − 10 0
1.0 − 60
Γ =−10d σ/d Ω [μb/sr]

50

10

20

50
0

0

− 50

−1.0

−60
50MeV
−40 −30 −20 −10
Γ =−15

0

10

20

1.0

50

0

0

−1.0

−50
−60 −50 −40 −30 −20 −10 0
E ex − E 0 [MeV]d 2σ/(d Ω d E ) [nb/(sr MeV)]

0.5

calculation (±1.7 MeV), (3) the uncertainty in the slopeof the momentum acceptance, (4) the uncertainty in theexperimental resolution, (5) different fit regions (10 MeV
wider or narrower), and (6) a choice of fitting of the
combined spectrum (Fig. 8) or simultaneous fitting of
the seven spectra (Fig. 7). The upper limit is analyzed
by changing each of these conditions, and then the total systematic error on the limit is evaluated by taking
the square root of the sum of the squared deviations. In
Fig. 9, the thus-evaluated systematic errors are displayedby the shaded areas.
V.

DISCUSSION

The 95% C.L. upper limits for the formation cross section of η ′ -mesic nuclei have been obtained as a function of
the position and width of the assumed Lorentzian peak.
The upper limits are particularly stringent near the η ′production threshold: 0.1–0.2 µb/sr for Γ = 5 MeV, 0.2–
0.4 µb/sr for Γ = 10 MeV, and 0.3–0.6 µb/sr for Γ =15 MeV. These are as small as ∼ 20 nb/(sr MeV) in theLorentzian peak height, and therefore exclude the existence of prominent peak structures theoretically expected
near the threshold for strongly attractive potentials, likea peak with ∼ 40 nb/(sr MeV) for V0 = −150 MeV shownin Fig. 10 (top) [29]. On the other hand, the obtained
limits are not in conflict with small peak structures predicted for shallow potentials, as in Fig. 10 (bottom) for
V0 = −50 MeV where a peak height is < 10 nb/(sr MeV).
(V0, W0) = ‒ (150, 10) MeV(V0, W0) = ‒ (50, 10) MeV

10 20

FIG. 9. Fitted values (solid dots) and resulting 95% C.L. upper limits (solid curves) of the Lorentzian-shaped formation
cross section of η ′ -mesic nuclei plotted as a function of the assumed peak position Eex for the widths of Γ = 5, 10, 15 MeV.
Upper limits evaluated by simultaneous fitting of the seven
spectra (Fig. 7) are shown by the dashed curves. The shaded
areas indicate the systematic errors on the upper limits.

To evaluate systematic errors on the upper limits, thefollowing contributions are considered: (1) the systematic
error on the absolute scale of the measured cross section(±13%), (2) the systematic error in the excitation-energy

FIG. 10.
Theoretically-calculated spectra of the
12C(p, d)11 C⊗η ′ reaction at 2.5 GeV [29]. The η ′ -nucleus potential parameters are taken as (V0 , W0 ) = (−150, −10) MeV(top) and (−50, −10) MeV (bottom). Total formation crosssections are shown by the thick lines, and major configurations of the η ′ -mesic states ℓη′ coupling with the neutron
hole states (nℓj )−1
n are shown by the thin lines.

In order to make further quantitative comparisons with

11

F (E; V0 , W0 ) = µ · S(E; V0 , W0 , σE )+(p0 + p1 E + p2 E 2 + p3 E 3 ),(9)where S(E; V0 , W0 , σE ) denotes the theoretical formation
spectrum (e.g., Fig. 10) [29, 39] for the real and imaginary
potentials of (V0 ,W0 ) folded by the Gaussian function for
the experimental resolution (σE ). The parameter µ is
introduced to test an allowed scale for S(E; V0 , W0 , σE ).
The remaining term is a third-order polynomial for thecontinuous part of the spectrum. A 95% C.L. upper limitof µ for given (V0 ,W0 ) is analyzed in the similar procedure, by fitting the measured spectrum with this function
within the region of −40 MeV ≤ Eex − E0 ≤ +30 MeV
and assuming a Gaussian probability density function ofµ in the physical region (µ ≥ 0).
The analysis has been repeated for the potential parameter sets listed in Table II, including W0 = −25 MeV
where theoretical spectra were newly calculated [39]. Fitted values and resultant 95% C.L. upper limits of thescale parameter µ are given by µfit and µ95 , respectively.
For each (V0 ,W0 ), the existence of the theoreticallycalculated peak structure with the strength multipliedby µ95 is excluded at the 95% C.L. The upper limits µ95
are then linearly interpolated between the calculated potentials, and presented as a contour plot on the real andimaginary potential plane (V0 ,W0 ) in Fig. 11. Smallerµ95 is deduced for larger |V0 | and smaller |W0 |. Systematic errors on µ95 are estimated by taking into accountthe same six sources as for the Lorentzian upper limits.
A band of the systematic error on the µ95 = 1 contour isshown by the dashed curves.
In Fig. 11, one can exclude a region of the potentialparameter set giving µ95 ≤ 1 at the 95% C.L. within
the present comparison with the theoretical calculations. Note here that the magnitude of the theoreticallycalculated spectra has an estimated uncertainty of a factor ∼ 2 [30, 40], originating in the assumed cross sectionof 30 µb/sr for the elementary reaction pn → dη ′ [28].
Thus, if the theoretical cross sections were overestimatedby a factor of 2, for example, one can reject a potential
region with µ95 ≤ 1/2 at the 95% C.L.
Figure 12 summarizes the obtained constraint and currently known information on the η ′ -nucleus potential.
The shaded region shows the excluded region (µ95 ≤ 1)
in the present analysis. The rectangular box displays
an evaluated region by the η ′ photoproduction experiments: the real part of −(39 ± 7(stat) ± 15(syst)) MeV
from the excitation function and the η ′ momentum distribution [20, 21], and the imaginary part of −(13 ±3(stat) ± 3(syst)) MeV from the transparency ratios[22, 23]. Theoretical expectations with the NJL model(V0 = −150 MeV) [9, 10], the linear sigma model (V0 =−80 MeV) [11], the QMC model (V0 = −37 MeV) [12],and the chiral unitary approach [41] are shown by the

TABLE II. Fitted values (µfit ) and resulting 95% C.L. upper
limits (µ95 ) for the scale of the theoretical formation spectra.
The analysis is performed at the listed sets of the real andimaginary potentials (V0 , W0 ).
V0
(MeV)
−50
−50
−50
−50
−50
−60
−60
−60
−80
−80
−80
−100
−100
−100
−100
−100
−150
−150
−150
−150
−150
−200
−200
−200
−200
−200

W0
(MeV)
−5
−10
−15
−20
−25
−5
−10
−15
−5
−10
−15
−5
−10
−15
−20
−25
−5
−10
−15
−20
−25
−5
−10
−15
−20
−25

µfit

µ95

0.04 ± 1.44
0.22 ± 2.88
1.07 ± 5.29
3.10 ± 9.11
6.74 ± 14.75
0.36 ± 0.79
0.75 ± 1.54
1.49 ± 2.83
0.13 ± 0.36
0.20 ± 0.63
0.19 ± 1.09
−0.24 ± 0.20
−0.32 ± 0.35
−0.43 ± 0.56
−0.60 ± 0.90
−0.85 ± 1.39
−0.01 ± 0.10
0.01 ± 0.15
0.03 ± 0.23
0.06 ± 0.35
0.09 ± 0.51
−0.05 ± 0.07
−0.04 ± 0.11
−0.03 ± 0.16
−0.03 ± 0.23
−0.04 ± 0.31

2.85
5.78
11.10
20.01
33.69
1.80
3.55
6.61
0.79
1.38
2.26
0.27
0.50
0.86
1.41
2.22
0.18
0.31
0.48
0.72
1.06
0.11
0.20
0.30
0.43
0.59

−5
− 10 1/ 4
W 0 [MeV]

the theoretical predictions, we evaluate constraints on thescales for the theoretically-calculated formation spectra.
Here, the following function is assumed to describe themeasured excitation spectrum,

1/ 3
− 15
1/ 2
− 20
− 25
− 200

μ95=1
− 150

2

4 8 16− 100
V 0 [MeV]−50

FIG. 11. A contour plot of µ95 (solid curves), the 95%
C.L. upper limit of the scale parameter µ for the theoreticalformation spectra, on the real and imaginary potential plane(V0 , W0 ). The limits have been analyzed at the potential setslisted in Table II and linearly interpolated in-between. The
systematic errors on the µ95 = 1 contour are shown by thedashed curves. The region with µ95 ≤ 1 is excluded by thepresent analysis. See the text for further explanation.

dashed lines.
Here, a strongly attractive potential of the order of12linear sigma

QMC

Distribution [arb. units]

NJL
0chiral unitary
W 0 [MeV]−5− 10

CBELSA/TAPS

μ 95 −
<1

− 15

0.08

− 150

− 100
V 0 [MeV]−50

0

FIG. 12. Obtained constraint and currently known information on the η ′ -nucleus potential (V0 + iW0 ) at normal nuclear density. The shaded region (µ95 ≤ 1) represents theregion excluded within the present analysis. The rectangular box shows real and imaginary potentials evaluated in η ′photoproduction experiments by the CBELSA/TAPS collaboration [20–23]. Theoretical predictions based on the NJL
model [9, 10], the linear sigma model [11], the QMC model[12], and the chiral unitary approach [41] are indicated by thedashed lines.

V0 ≈ −150 MeV, as predicted by the NJL model, is rejected within the present analysis for the region of theimaginary potential of |W0 | ≤ 24 MeV. The current experiment has very limited sensitivity in a shallower potential region where some small peak structures are predicted in the theoretical formation spectra [29], as shownin Fig. 10 (bottom), for example. Therefore, an improvement of the experimental sensitivity is necessary for further investigating the existence of η ′ -mesic nuclei.
One of the possible approaches for the next step isa semi-exclusive measurement by simultaneously detecting the forward deuteron in the 12 C(p, d) reaction for
missing-mass spectrometry and decay particles from η ′ mesic nuclei for event selection. A large amount of thecontinuous background dominating the present spectrum
in Fig. 8, which is understood as quasi-free multi-pion
production, will be suppressed by tagging the decay particles. As discussed in Ref. [42], major decay modes of theη ′ -mesic nuclei are expected to be one- and two-nucleon
absorption: η ′ N → ηN , η ′ N → πN , and η ′ N N → N N .
Among them the two-nucleon absorption process has adistinguishing feature in the emitted proton (or neutron)
energy of ∼ 300–600 MeV, as simulated in Fig. 13 assuming the Fermi motion of nucleons in the nucleus [43]. A
simulation based on an intra-nuclear cascade model [44]has shown that the signal-to-background ratio will be
increased by two orders of magnitude compared to thepresent experiment by selecting energetic protons in the
backward angular range (θplab ≥ 90◦ ) in the laboratory[45].
The semi-exclusive measurement will be performed in
the near future. This experiment is feasible with the
FRS at GSI and the next-generation Super-FRS [46] atηʼN → π N
ηʼN N → N N

0.04
0.02

− 20
− 25
− 200

ηʼN → η N

0.06

0

0

100 200 300 400 500 600 700
Proton kinetic energy [MeV]

FIG. 13. Simulated kinetic energy distributions of protons
emitted in the decay of η ′ -mesic nuclei. Three decay modes
are considered: η ′ N → ηN (thin gray), η ′ N → πN (thinblack), and η ′ N N → N N (thick). The integral of each distribution is normalized to unity.

FAIR, as the excellent performance of the FRS for theforward (p, d) spectroscopy has been demonstrated in thepresent experiment. A large-acceptance detector, such as
the WASA central detector [47, 48], will be additionallyinstalled surrounding the reaction target. An experimental setup combining the FRS and the WASA systems is
illustrated in Fig. 14. We will also consider possibilities ofusing other reaction channels such as the (π, N ) reaction.
WASA central
detector

FRS F2
beam-line
detectors

01m

carbon target

quadrupole
magnetprotonbeampdFIG. 14. A schematic view of an experimental setup forthe semi-exclusive measurement. A 2.5 GeV proton beam
impinges on a carbon target. The forward deuteron is
momentum-analyzed by the downstream FRS section. The
proton emitted backward in the decay of η ′ -mesic nuclei is
identified by the WASA central detector [47, 48].

VI.

CONCLUSION

A missing-mass spectroscopy experiment of theC(p,d) reaction was performed at a proton energy of
2.5 GeV aiming at the search for η ′ -mesic nuclei. The
excitation-energy spectra of 11 C nuclei were successfully
obtained around the η ′ -meson production threshold withhigh statistical sensitivity and sufficient experimental res12

13
olution. As no distinct peak structure has been observedin the excitation-energy spectra, upper limits on the formation cross sections of the η ′ -mesic nuclei have been
determined. A comparison with theoretically-predicted
formation spectra sets a stringent constraint on the η ′ nucleus potential.
The present work has established the applicability ofthe missing-mass spectroscopy of the (p,d) reaction forstudying in-medium properties of the η ′ meson. The application to other mesons will be considered. The experimental search for η ′ -mesic nuclei will further proceedwith the semi-exclusive measurement by simultaneously
detecting the decay particles.

the FRS engineering group, and the target laboratory.
We are grateful to staffs of Institut für Kernphysik,
Forschungszentrum Jülich for their support in a detector test at COSY. We also thank Dr. M. Tabata
for specially developed aerogel. Y.K.T. acknowledges
financial support from Grant-in-Aid for JSPS Fellows(No. 258155) and H.F. from Kyoto University Young
Scholars Overseas Visit Program. This work is partly
supported by a MEXT Grants-in-Aid for Scientific
Research on Innovative Areas (Nos. JP24105705 andJP24105712), JSPS Grants-in-Aid for Scientific Research(S) (No. JP23224008) and for Young Scientists (A) (No.
JP25707018), by the National Natural Science Foundation of China (No. 11235002) and by the Bundesministerium für Bildung und Forschung.

ACKNOWLEDGMENTS

The authors would like to acknowledge the support
from the GSI staffs, particularly the accelerator group,[1] S. Weinberg, Phys. Rev. D 11, 3583 (1975).
[2] E. Witten, Nucl. Phys. B 156, 269 (1979).
[3] G. Veneziano, Nucl. Phys. B 159, 213 (1979).
[4] Su H. Lee and T. Hatsuda, Phys. Rev. D 54, 1871 (1996).
[5] D. Jido, H. Nagahiro, and S. Hirenzaki, Phys. Rev. C 85,
032201(R) (2012).
[6] R. S. Hayano and T. Hatsuda, Rev. Mod. Phys. 82, 2949
(2010).
[7] S. Leupold, V. Metag, and U. Mosel, Int. J. Mod. Phys.
E 19, 147 (2010).
[8] V. Metag, M. Nanova, E. Ya Paryev, Prog. Part. Nucl.
Phys. 97, 199 (2017).
[9] P. Costa, M. C. Ruivo, C. A. de Sousa, and Yu. L.
Kalinovsky, Phys. Rev. D 71, 116002 (2005).
[10] H. Nagahiro, M. Takizawa, and S. Hirenzaki, Phys. Rev.
C 74, 045203 (2006).
[11] S. Sakai and D. Jido, Phys. Rev. C 88, 064906 (2013).
[12] S. D. Bass and A. W. Thomas, Phys. Lett. B 634, 368(2006).
[13] T. Yamazaki et al., Z. Phys. A 355, 219 (1996).
[14] H. Gilg et al., Phys. Rev. C 62, 025201 (2000) and
K. Itahashi et al., ibid., 025202.
[15] H. Geissel et al., Phys. Rev. Lett. 88, 122301 (2002).
[16] K. Suzuki et al., Phys. Rev. Lett. 92, 072302 (2004).
[17] E. E. Kolomeitsev, N. Kaiser, and W. Weise, Phys. Rev.
Lett. 90, 092501 (2003).
[18] D. Jido, T. Hatsuda, and T. Kunihiro, Phys. Lett. B 670,
109 (2008).
[19] T. Yamazaki, S. Hirenzaki, R. S. Hayano, and H. Toki,
Phys. Rep. 514, 1 (2012).
[20] M. Nanova et al., Phys. Lett. B 727, 417 (2013).
[21] M. Nanova et al., Phys. Rev. C 94, 025205 (2016).
[22] M. Nanova et al., Phys. Lett. B 710, 600 (2012).
[23] S. Friedrich et al., Eur. Phys. J. A 52, 297 (2016).
[24] E. Czerwiński et al., Phys. Rev. Lett. 113, 062004 (2014).
[25] H. Nagahiro and S. Hirenzaki, Phys. Rev. Lett. 94,
232503 (2005).

[26] N. Muramatsu et al., arXiv:1307.6411 (2013).
[27] V. Metag et al., approved proposal ELSA/03-2012-BGOOD (unpublished).
[28] K. Itahashi et al., Prog. Theor. Phys. 128, 601 (2012).
[29] H. Nagahiro et al., Phys. Rev. C 87, 045201 (2013).
[30] Y. K. Tanaka et al., Phys. Rev. Lett. 117, 202501 (2016).
[31] B. Jurado, K.-H. Schmidt, and K.-H. Behr, Nucl. Instrum. Methods Phys. Res., Sect. A 483, 603 (2002).
[32] H. Geissel et al., Nucl. Instrum. Methods Phys. Res.,
Sect. B 70, 286 (1992).
[33] M. Tabata et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 623, 339 (2010).
[34] T. Yoneyama, Master thesis, Tokyo Institute of Technology, 2001 (unpublished).
[35] R. Janik et al., Nucl. Instrum. Methods Phys. Res., Sect.
A 640, 54 (2011).
[36] P. Berthet et al., J. Phys. G 8, L111 (1982).
[37] T. Schwab, Ph.D. thesis, Universität Giessen, GSI Report No. GSI-91-10, 1991 (unpublished).
[38] N. Iwasa et al., Nucl. Instrum. Methods Phys. Res., Sect.
B 126, 284 (1997).
[39] H. Nagahiro (private communication, 2017).
[40] V. Yu. Grishina et al., Phys. Lett. B 475, 9 (2000).
[41] H. Nagahiro, S. Hirenzaki, E. Oset, and A. Ramos, Phys.
Lett. B 709, 87 (2012).
[42] H. Nagahiro, Nucl. Phys. A 914, 360 (2013).
[43] E. J. Moniz et al., Phys. Rev. Lett. 26, 445 (1971).
[44] Y. Nara et al., Phys. Rev. C 61, 024901 (2000).
[45] Y. Higashi, Master thesis, Nara Women’s University,
2015 (unpublished).
[46] H. Geissel et al., Nucl. Instrum. Methods Phys. Res.,
Sect. B 204, 71 (2003).
[47] C. Bargholtz et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 594, 339 (2008).
[48] H.-H. Adam et al., arXiv:nucl-ex/0411038 (2004).