Vol. 48 (2017)

ACTA PHYSICA POLONICA B

No 10

FIRST RESULTS ON THE EXPERIMENTAL SEARCH
FOR η 0 -MESIC NUCLEI WITH THE 12 C(p, d)
REACTION∗
Y.K. Tanakaa , Y. Ayyadb , J. Benlliurec , K.-T. Brinkmannd
S. Friedrichd , H. Fujiokae , H. Geissela,d , J. Gellankif , C. Guog
E. Gutzd , E. Haettnera , M.N. Harakehf , R.S. Hayanoh
Y. Higashii , S. Hirenzakii , C. Hornungd , Y. Igarashij , N. Ikenok
K. Itahashil , M. Iwasakil , D. Jidom , N. Kalantar-NayestanakifR. Kanungon , R. Knöbeld,e , N. Kurza , V. Metagd , I. Mukhaa
T. Nagaee , H. Nagahiroi , M. Nanovad , T. Nishil , H.J. Ongb
S. Pietria , A. Prochazkaa , C. Rappolda , M.P. Reitera
J.L. Rodríguez-Sánchezc , C. Scheidenbergera,d , H. Simona
B. Sitaro , P. Strmeno , B. Sung , K. Suzukip , I. Szarkao ,M. Takechiq , I. Tanihatab,g , S. Terashimag , Y.N. Watanabeh
H. Weicka , E. Widmannp , J.S. Winfielda , X. Xua , H. YamakamieJ. Zhaog
η-PRiME/Super-FRS Collaboration
aGSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, GermanybRCNP, Osaka University, Ibaraki, Osaka, Japan
cUniversidade de Santiago de Compostela, Santiago de Compostela, SpaindUniversität Giessen, Giessen, Germany
eKyoto University, Kyoto, Japanf
KVI-CART, University of Groningen, Groningen, The Netherlands
gBeihang University, Beijing, China
hThe University of Tokyo, Tokyo, Japani
Nara Women’s University, Nara, Japan
jKEK, Tsukuba, Ibaraki, Japan
kTottori University, Tottori, JapanlNishina Center, RIKEN, Wako, Saitama, JapanmTokyo Metropolitan University, Hachioji, Tokyo, JapannSaint Mary’s University, Halifax, Nova Scotia, CanadaoComenius University Bratislava, Bratislava, Slovakiap
Stefan-Meyer-Institut für Subatomare Physik, Vienna, Austria
qNiigata University, Niigata, Japan(Received August 17, 2017)∗

Presented at the 2nd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Kraków, Poland, June 3–11, 2017.

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Y.K. Tanaka et al.

We performed a missing-mass spectroscopy experiment of the 12 C(p, d)reaction in order to search for η 0 -mesic nuclei. Excitation spectrum of
11
C around the η 0 -meson production threshold was successfully obtainedwith a high-statistical sensitivity and sufficiently good energy resolution.
Since no peak structure associated with the formation of η 0 -mesic nuclei
was observed, we set constraints on the formation cross sections of η 0 -mesic
states and on the η 0 –nucleus interaction.
DOI:10.5506/APhysPolB.48.1813

1. Introduction
The η 0 meson has a mass of 958 MeV/c2 , which is peculiarly large among
the light pseudoscalar mesons. This is theoretically attributed to the UA (1)anomaly in QCD with the spontaneous breaking of chiral symmetry [1, 2].
At finite nuclear density, chiral symmetry is expected to be partially restored[3–5], and the mass of the η 0 meson may be reduced. Theoretical calculations
based on the Nambu–Jona-Lasinio model [6, 7], linear sigma model [8], andquark–meson coupling model [9] predict η 0 mass reductions of −150, −80,
and −37 MeV at normal nuclear density, respectively. The mass reduction
then induces an attractive η 0 –nucleus potential, which leads to a possible
existence of η 0 meson–nucleus bound states (η 0 -mesic nuclei) [7, 10, 11].
Experimental information on the η 0 –nucleus interaction is still very limited. The CBELSA/TAPS Collaboration deduced an attractive η 0 –nucleus
potential of −39 ± 7(stat.) ± 15(syst.) MeV at the nuclear center fromη 0 -momentum distributions and excitation functions in η 0 photoproduction
off nuclear targets [12, 13]. They also evaluated the imaginary part of thepotential to be −13 ± 3(stat.) ± 3(syst.) MeV from measured transparency
ratios [14, 15]. Such a small imaginary part relative to the real part suggests possibilities of experimentally observing η 0 -mesic nuclei as narrow peakstructure. Another experimental information is the η 0 –proton scattering
length of Re(apη0 ) = 0 ± 0.43 fm and Im(apη0 ) = 0.37+0.40−0.16 fm [16] extracted
from a measurement of the pp → ppη 0 reaction close to its threshold. This
indicates a relatively weak attraction in the η 0 –nucleus system.
2. Experiment
In order to search for η 0 -mesic nuclei, we performed a missing-mass spectroscopy experiment of the 12 C(p, d) reaction [17–19]. A 2.5 GeV proton
beam extracted from the synchrotron SIS-18 at GSI impinged on a 4 g/cm2 thick carbon target. The deuterons emitted at 0◦ in the 12 C(p, d) reaction
were momentum-analyzed with the fragment separator (FRS) [20] used as ahigh-resolution spectrometer.

First Results on the Experimental Search for η 0 -Mesic Nuclei with . . .

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The experimental setup is schematically shown in Fig. 1. We employed aspecial ion-optical mode of the FRS with a momentum-achromatic focus at
F2 and a dispersive focus at F4. Multi-wire drift chambers (MWDCs) wereinstalled at the F4 dispersive focal plane to reconstruct the deuteron tracks
and thereby obtain their momenta. Scintillation counters (SC2H, SC2V,SC41, SC42) were used for time-of-flight measurements to distinguish thedeuterons from background protons. Moreover, Čerenkov counters (AC,TORCH) were installed to crosscheck the identification of the deuterons.
target10 mdipole magnet

F4F22.5 GeVproton

MWDC
quadrupolemagnet

SC2HSC2VACSC41SC42

AC TORCH

Fig. 1. A schematic view of the experimental setup with the FRS. A carbon target
was irradiated with a 2.5 GeV proton beam. The momentum of the deuteronemitted in the (p, d) reaction was measured by two sets of multi-wire drift chamber(MWDC) at the F4 dispersive focal plane. Scintillation counters (SC2H, SC2V,SC41, SC42) were used for time-of-fight measurements. Čerenkov detectors (AC,TORCH) were installed for confirmation of particle identification.

Data of the 12 C(p, d) reaction were accumulated for about 70 hours withseveral settings of the central momentum of the FRS spectrometer. The
excitation-energy region from −91 to +34 MeV relative to the η 0 -emission
threshold was investigated. In addition, the proton–deuteron elastic scattering was measured by using a 1.6 GeV proton beam and a CD2 target.
Mono-energetic deuterons emitted at 0◦ in this reaction were used as a reference to calibrate the ion-optical response of the spectrometer.
3. Results
Obtained excitation-energy spectrum is presented in Fig. 2. The horizontal axis gives the 11 C excitation energy (Eex ) relative to the η 0 -meson
emission threshold (E0 = 957.78 MeV). The spectrum shows a gradual increase from 4.9 to 5.7 µb/(sr × MeV), where the continuous component canbe understood by quasi-free meson production processes p + N → d + X(X = 2π, 3π, 4π, ω) [17]. The experimental resolution was evaluated to be
2.5 MeV (σ) from the width of the D(p, d)p peak in the calibration measure-1816

Y.K. Tanaka et al.

ment, as shown in the inset. A very high statistical sensitivity with ≤ 1%relative errors was achieved. However, no peak structure associated with theformation of the η 0 -mesic nuclei was observed.

Countsd 2σ/(d Ω dE ) [μb/(sr MeV)]

6.2

Deuteron momentum [MeV/c ]2920 2900 2880 2860 2840 2820 2800 2780

6.0
5.8

4000
4000
2000
200000D(p , d )p5.6
5.4
5.2
5.0
4.8
− 100

12C(p , d )

−80

−60

−40
−20
E ex − E 0 [MeV]

02040Fig. 2. Excitation spectrum of 11 C measured in the 12 C(p, d) reaction at 2.5 GeV.
The horizontal axis is the 11 C excitation energy Eex relative to the η 0 -meson production threshold E0 = 957.78 MeV. The gray curve shows a fit with a third-orderpolynomial. The inset displays a momentum spectrum of the deuterons in thecalibration D(p, d)p reaction at 1.6 GeV. This figure is adopted from Ref. [18].

Since no peak structure was seen in the excitation-energy spectrum, weevaluated upper limits of the formation cross sections of the η 0 -mesic nuclei
by statistically testing the existence of a Lorentzian-shaped peak at different
peak positions and widths. Thus obtained upper limits near the η 0 emission
threshold are 0.1–0.2 µb/sr for the assumed Lorentzian width of Γ = 5 MeV,
0.2–0.4 µb/sr for Γ = 10 MeV, and 0.3–0.6 µb/sr for Γ = 15 MeV at
the 95% confidence level [18]. These limits are as small as theoretically
predicted peak structures for a strongly attractive potential of the order ofV0 ∼ −150 MeV [11].
Furthermore, the obtained spectrum was directly compared with thetheoretically calculated spectra [11] for various strengths of the η 0 –nucleus
potential in −200 MeV ≤ V0 ≤ −50 MeV and −20 MeV ≤ W0 ≤ −5 MeV.
We introduced a scale parameter µ for the theoretical formation cross section, and evaluated upper limit of µ at 95% C.L. [18]. The resultant upper
limit (µ95 ) is shown in Fig. 3 as a contour plot on the real and imaginary
potential strengths (|V0 |, |W0 |) at nuclear saturation density. Here, we canexclude potential sets giving µ95 ≤ 1. Thus, a strongly attractive potential|V0 | ∼ 150 MeV is excluded under the present comparison for the imaginary
part of |W0 | ∼ 10 MeV [14, 15].

First Results on the Experimental Search for η 0 -Mesic Nuclei with . . .

|W 0 | [MeV]2016 8 42μ95 =1151/ 21/ 31/ 410550

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100150|V0 | [MeV]

200Fig. 3. The 95% C.L. upper limits (µ95 ) on the scale parameter µ, introduced for thetheoretically calculated formation spectra. The limits are given by the contours on
the real and imaginary potential plane (|V0 |, |W0 |). The dashed curves indicate thesystematic errors for the contour of µ95 = 1. The potential region giving µ95 ≤ 1
can be excluded by the present analysis. This figure is adopted from Ref. [18].

4. Summary and future prospects
We measured the excitation spectrum of 11 C around the η 0 -meson production threshold to search for η 0 -mesic nuclei. Although high statisticalsensitivity and sufficient energy resolution were achieved in the spectrum,
no distinct structure due to the formation of the η 0 -mesic nuclei was observed. We determined upper limits on the formation cross sections of theη 0 -mesic states. A comparison with theoretically calculated formation spectra excluded strongly attractive η 0 –nucleus potentials.
In the near future, we will perform a semi-exclusive measurement of
the 12 C(p, dp) reaction to improve the experimental sensitivity. One of the
expected decay modes of the η 0 -mesic nuclei is a two-nucleon absorption
process (η 0 N N →N N ) [21], where a high-energy proton with Tp ∼ 500 MeV
can be emitted. A coincidence measurement of the forward deuteron andthe decay proton can drastically improve the signal-to-background ratio.
Detailed consideration of the experimental setup is ongoing.
The authors would like to acknowledge the GSI staff for their support
in the experiment. This work is partly supported by a Grant-in-Aid for
JSPS Fellows (No. 258155), MEXT Grants-in-Aid for Scientific Research on
Innovative Areas (Nos. JP24105705 and JP24105712), JSPS Grants-in-Aidfor Scientific Research (S) (No. JP23224008) and for Young Scientists (A)(No. JP25707018), by the National Natural Science Foundation of China(Grant No. 11235002), and by the Bundesministerium für Bildung undForschung.

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