Spectroscopy of eta'-nucleus bound states at GSI-SIS

The eta' meson mass may be reduced due to partial restoration of chiral symmetry. If this is the case, an eta'-nucleus system may form a nuclear bound state. We plan to carry out a missing-mass spectroscopy with the 12C(p,d) reaction at GSI-SIS. Peak structures corresponding to such a bound state may be observed even in an inclusive measurement, if the decay width is narrow enough.


Introduction
The U A (1) anomaly in QCD is considered to explain the peculiarly large mass of the η ′ meson (about 958 MeV/c 2 ) among the pseudoscalar meson nonet. It is known that the anomaly has an effect on the η ′ mass only through the spontaneous and/or explicit SU(3) chiral symmetry breaking [1,2]. Recently it has been suggested, if chiral symmetry is partially restored in nuclear matter, that the η ′ mass may be reduced in nuclei with a suppression of the magnitude of the quark condensate [1]. According to Nambu-Jona-Lasinio model calculations [3,4], the mass reduction at normal nuclear density amounts to around 150 MeV/c 2 . The significant in-medium mass reduction can be regarded as a strong attraction between the η ′ meson and the nucleus. Then, an η ′ -nucleus system may exist as a bound state [4,5].
It should be mentioned that the scattering length of the η ′ N interaction is evaluated to be of the order of 0.1 fm from the measurement of the near-threshold pp → ppη ′ cross section at COSY-11 [6], which means that the η ′ N interaction is very weak. While it seems that these two scenarios contradict each other, a reaction spectroscopy of η ′ -nucleus bound states will put a constraint on the strength of the η ′ -nucleus interaction [5].
As for the decay width, which is also an important property in discussing the feasibility of an experimental observation, a recent measurement on η ′ photoproduction from nuclei by the CBELSA/TAPS Collaboration revealed the absorption width of the η ′ meson [7]. Through the A-dependence of the transparency ratio, defined as the ratio of the cross section of γA → η ′ A ′ and that of γN → η ′ N ′ , the absorption width is found to be 15-25 MeV at normal nuclear density for an average η ′ momentum of 1050 MeV/c. Therefore, one can expect the decay width of η ′ bound states in nuclei could be small as well. Motivated by these latest theoretical and experimental improvements on the understanding of the η ′ -nucleus interaction, we proposed a missing-mass spectroscopy experiment of η ′ -nucleus bound states at GSI in 2011 [8,9].

Experimental Principle
We will make use of the 12 C(p,d) reaction for a missing-mass spectroscopy of η ′ -nucleus bound states. The incident proton beam with kinetic energy of 2.50 GeV will be supplied by the SIS synchrotron at GSI, and the ejectile deuteron will be momentum-analyzed by the fragment separator FRS (Fig. 1). With this experimental condition, a high-resolution and high-statistics spectroscopy will be enabled.
Another feature of the proposed experiment is to perform an inclusive measurement; we will detect only the outgoing deuteron in the (p,d) reaction, and not the decay particle of η ′ -mesic nuclei. Then, an unbiased spectrum can be obtained without assuming properties of the decay process despite a poorer signal-to-noise ratio. As shown later, a high sensitivity to observe a peak structure over a huge physical background is expected only if the decay width of η ′ -mesic nuclei is narrow enough. At present, this inclusive measurement for η ′ -nucleus bound states is considered only at GSI-SIS.
We will detect deuterons at the final focal plane S4 of FRS, as the FRS optics will be set to momentum-dispersive. Multi-wire drift chambers (MWDC) installed at S4 will serve for momentum measurement. For the particle identification, an AerogelČerenkov counter (AC) with a high refractive index around 1.20 [10] will be installed as a veto counter for the predominant background of protons from the (p,p ′ ) reaction on the target. Furthermore, time-of-flight between a set of segmented plastic scintillators (SC1 at S3 and SC2 at S4) will be used in the offline analysis. Another source of background, which consists of secondary particles from the beam pipe near S1 due to the intense proton beam, needs to be removed between S1 and S3, in order to decrease the particle rate at S4. One of the possible solutions for this is to set the optics of the first half of FRS (S0-S2) as the momentum compaction mode and to install a slit at S2.
The overall spectral resolution is estimated to be σ = 1.6 MeV, which is sufficiently smaller than the expected width of η ′ -mesic nuclei. Such a high resolution is an indispensable requirement in realizing an inclusive measurement.

Expected Spectrum
The formation cross section of the p + 12 C → d + 11 C ⊗ η ′ is calculated by the Green's function method [11], in which η ′ -nucleus optical potential V η ′ is assumed to be proportional to the nuclear density ρ(r), that is, V η ′ = (V 0 + iW 0 )ρ(r)/ρ 0 , where ρ 0 is the normal nuclear density. Although there is no experimental data available on the cross section of the elementary process pn → dη ′ , we have evaluated it to be around 3 µb in the following two ways.
Assuming an isotropic distribution in the pn → dη ′ reaction, the forward differential cross section in the laboratory frame is obtained as ∼ 30 µb/sr for incident kinetic energy of 2.5 GeV. The detail of the theoretical calculation with the Green's function method will be given in Ref. [11]. The background in the inclusive (p,d) spectrum mainly comes from the quasi-free process such as multi-pion production by the pp → dX or pn → dX reaction. The total background level is estimated to be around 4 µb/sr/MeV by using ω production data by COSY-ANKE [16] as a reference.
Combining the signal and background, we carried out a simulation with 3.24 × 10 14 protons on a 4 g/cm 2 -thick carbon target 1 . The result for various types of optical potentials is shown in Fig. 2. The signal-to-noise ratio is found to be of the order of 1/100 at most. In case that the real part |V 0 | is large and the imaginary part |W 0 | is small, clear peak structures corresponding to η ′ -mesic nuclei can be observed, especially near the η ′ production threshold. They could be a signature of an attractive η ′ -nucleus interaction.
It should be stressed that the Nambu-Jona-Lasinio calculations correspond to |V 0 | ∼ 150 MeV, and that the transparency ratio measurement by CBELSA/TAPS indicates |W 0 | 12.5 MeV. If so, we may be able to observe at least one peak structure due to an excited state of η ′ -mesic nuclei close to the threshold.