Observation of a Be double-Lambda hypernucleus in the J-PARC E07 experiment

A double-$\Lambda$ hypernucleus, ${}_{\Lambda\Lambda}\mathrm{Be}$, was observed by the J-PARC E07 collaboration in nuclear emulsions tagged by the $(K^{-},K^{+})$ reaction. This event was interpreted as a production and decay of $ {}_{\Lambda\Lambda}^{\;10}\mathrm{Be}$, ${}_{\Lambda\Lambda}^{\;11}\mathrm{Be}$, or ${}_{\Lambda\Lambda}^{\;12}\mathrm{Be}^{*}$ via $\Xi^{-}$ capture in ${}^{16}\mathrm{O}$. By assuming the capture in the atomic 3D state, the binding energy of two $\Lambda$ hyperons$\,$($B_{\Lambda\Lambda}$) of these double-$\Lambda$ hypernuclei are obtained to be $15.05 \pm 0.11\,\mathrm{MeV}$, $19.07 \pm 0.11\,\mathrm{MeV}$, and $13.68 \pm 0.11\,\mathrm{MeV}$, respectively. Based on the kinematic fitting, ${}_{\Lambda\Lambda}^{\;11}\mathrm{Be}$ is the most likely explanation for the observed event.

Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan. 21 Department of Physics, University of Yangon, Myanmar 22 Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea 23  A double-Λ hypernucleus, ΛΛ Be, was observed by the J-PARC E07 collaboration in nuclear emulsions tagged by the (K − , K + ) reaction. This event was interpreted as a production and decay of 10 ΛΛ Be, 11 ΛΛ Be, or 12 ΛΛ Be * via Ξ − capture in 16 O. By assuming the capture in the atomic 3D state, the binding energy of two Λ hyperons (B ΛΛ ) of these double-Λ hypernuclei are obtained to be 15.05 ± 0.11 MeV, 19.07 ± 0.11 MeV, and 13.68 ± 0.11 MeV, respectively. Based on the kinematic fitting, 11 ΛΛ Be is the most likely explanation for the observed event. 1. Introduction A complete understanding of the baryon-baryon interaction requires (at least) the consideration of all octet baryons within the SU(3) f group. Compared to baryon pairs with zero or only one strange baryon, experimental information in the S = −2 sector is still very scarce. In particular, it is difficult to study the interaction between two hyperons by scattering experiments due to their short lifetimes. Therefore, double-Λ hypernuclei, which include two Λ hyperons in a nucleus, have been investigated. The ΛΛ interaction is expressed in terms of ∆B ΛΛ , which can be deduced from the mass of a double-Λ hypernucleus and which is defined as Here B Λ and B ΛΛ represent the binding energies of a Λ hyperon in single-Λ hypernuclei and two Λ hyperons in double-Λ hypernuclei, respectively. Emulsion detectors allow the detection of the weak decay products from double-Λ hypernuclei with sub-µm resolution, thus providing the most precise reconstruction of double-Λ hypernucleus masses as of today.
In the past, several experiments have successfully searched for double-Λ hypernuclear decays in nuclear emulsions [1][2][3][4]. The most impressive results were collected by the KEK-PS E373 experiment. Among seven double-Λ hypernuclear events, an event called "NAGARA" was uniquely identified as 6 ΛΛ He [3]. From this event, the ΛΛ interaction, especially its s-wave ( 1 S 0 ) interaction, was found to be weakly attractive (∆B ΛΛ = 0.67 ± 0.17 MeV) [4]. In order to understand ΛΛ and the related interaction systematically, more double-Λ hypernuclei need to be uniquely identified.
J-PARC E07 is an upgraded counter-emulsion hybrid experiment aiming at about a factor of 10 more identified double-Λ hypernuclei as compared to the E373 experiment. It is expected to detect approximately 100 double-Λ hypernuclear events among 1 × 10 4 Ξ − stopping events. This substantially improved statistics will allow us to explore not only the ΛΛ s-wave interaction but also ΞN -ΛΛ mixing, and the structure of the core nucleus, etc. Beam exposure of E07 was carried out in 2016 and 2017. A total of 118 modules produced from 2.1 tons emulsion gel were exposed to 1.13 × 10 11 particles of the K − beam. An impressive double-Λ hypernuclear event, "MINO", was observed after scanning 30% of all modules. In this paper, an interpretation of this event is discussed.

2.
Experimental setup Double-Λ hypernuclei were searched for by detecting Ξ − stopping events in an emulsion module. A Ξ − hyperon generated in the quasi-free (K − , K + ) reaction in a diamond target with 30 mm thickness (9.83 g/cm 2 ) was injected into the module and subsequently slowed down and captured in the atomic orbit of a nucleus in the emulsion material. Double-Λ hypernuclei are produced by the interaction between the Ξ − hyperon and nucleus with a probability of a few percents. In order to trace Ξ − tracks to the module and detect particle tracks from the module, two sets of SSD (Silicon Strip Detector) were installed so as to sandwich the module. Experimental setup around the target is shown in Fig. 1.
J-PARC E07 experiment was performed at K1.8 beam line in the J-PARC Hadron Experimental Facility with K − beams of 1.8 GeV/c momentum. This momentum was chosen to maximize the Ξ − stopping yield in the emulsion. Typical intensity and purity of the K − beam were 2.8 × 10 5 particles per spill of 2.0 s duration every 5.5 s and 82%, respectively. Incoming K − mesons and outgoing K + mesons were momentum analyzed by corresponding magnetic spectrometers, the beam line spectrometer [6] and the KURAMA spectrometer, respectively. Momentum resolution of each spectrometer was ∆p/p = 3.3 × 10 −4 (FWHM) and ∆p/p = 2.7 × 10 −2 (FWHM), respectively. The acceptance of the KURAMA spectrometer was 280 msr. 3/11 Each emulsion module consisted of eleven thick-type sheets sandwiched between two thintype sheets with an area of 345 mm [W] × 350 mm [H] [ Fig. 1(c)]. The thin-type sheets had emulsion layers with a thickness of 100 µm on both sides of 180 µm polystyrene base film and were used to connect tracks to the SSD's, because they have high deformation tolerance thus good angular resolution. The thick-type sheets had 450 µm thick layers on both sides of 40 µm polystyrene base film. The emulsion layers were made of "Fuji GIF" emulsion gel produced by FUJIFILM Corporation. The thirteen sheets were packed all together in a stainless case and fixed tightly by vacuum pumping.
The module was moved in the beam spill-off period to keep the beam particles density less than 1 × 10 4 particles/mm 2 in order to keep good efficiency for automated image tracking. Typical exposure cycle was 5 hours for one module.
Each SSD had a four layers configuration (XYXY) with a strip pitch of 50 µm. The thickness of a silicon sensor was 0.3 mm. The resolutions of SSD's were estimated to be 15 µm (σ) for position and 20 mrad (σ) for angle.

Analysis
Tracks of Ξ − were kinematically identified with the SSD by tagging the (K − , K + ) reaction. The candidate tracks of Ξ − hyperons were constructed from hits in four layers checking the consistency with the 'p'(K − , K + )Ξ − kinematics. In order to select Ξ − hyperons having high stopping probability, the Ξ − candidates with large energy deposit in the SSD were selected. The downstream SSD was used to reject Ξ − candidates which penetrated the module without nuclear interactions.
From the sets of the predicted positions and angles of the Ξ − hyperons based on the SSD hits, the tracks were traced through the emulsion with automated microscope systems [7]. At first, the most upstream sheet of the module was scanned to find Ξ − tracks in an area of about 200 µm × 200 µm for each Ξ − prediction. A relative position between the module and the SSD's was calibrated using p beam through events with a beam-pattern matching method. By calibrating four corners of the module, it was corrected with 20 µm accuracy. Prediction accuracy of Ξ − incident position was estimated to be about 50 µm for the thintype sheet. Then, the Ξ − tracks found in the first thin-type sheet were traced downstream through several emulsion sheets. When the tracing by the microscope system detected the end point of the track, the system took photographs around the stopping point and those were checked by human eyes.
For kinematic analysis, range-energy calibration and shrinkage correction were performed for each emulsion sheet by α tracks with the monochromatic energy of 8.784 MeV from the decay of 212 Po existing in the emulsion. The α track can be identified in the thorium series isotopes because it has the largest kinetic energy, i .e., the longest range. Such α decay chains were searched for around the observed event by using the so called Overall scanning method [8]. One hundred α tracks were scanned for calibration. Since the emulsion layers were shrunk along the beam direction due to photographic development, the ranges of particles were corrected for the shrinkage effect. The mean range of α tracks and the shrinkage factor were obtained to be 50.77 ± 0.12 µm and 1.98 ± 0.02, respectively. The relation between ranges and kinetic energies of charged particles was obtained by the range-energy formula given by Barkas et. al., [9,10]. The density of the emulsion sheet was determined to be 3.486 ± 0.013 g/cm 3 . Ranges of particles in polystyrene base films and SSD's were converted into corresponding emulsion ranges considering the energy loss ratio. Fig. 2 A photograph of the MINO event and its schematic drawing. The overlaid photograph is made by patching focused regions. Tracks #4, #5, #6, #8, and #9 are not fully shown in this photograph because these tracks are too long to be presented.

Interpretation of MINO event A new double-Λ hypernuclear event was observed in
the 7th sheet of a module. An overlaid photograph and a schematic drawing of the event are shown in Fig. 2. We named this event "MINO" 1 .
The Ξ − hyperon came to rest at vertex A, from which three charged particles (#1, #3, and #4) were emitted. The particle of track #1 decayed to three charged particles (#2, #5, and #6) at vertex B. The particle of track #2 decayed again to three charged particles (#7, #8, and #9) at vertex C. Measured ranges and angles are summarized in Table 1. If the Ξ − hyperon was captured in a heavy nucleus such as Ag or Br, a short track like #3 with a range of less than 32 µm could not be emitted due to the Coulomb barrier [2]. Therefore, we have concluded that the Ξ − hyperon was captured in a light nucleus such as 12 C, 14 N, or 16 O. The particles of tracks #6 and #9 escaped from the module into the downstream SSD after passing several emulsion sheets. These tracks could be connected to the SSD by extrapolating the tracks at the exit point from the last emulsion sheet. The particle of track #6 was found to be stopped in the SSD 4th layer and #9 penetrated all SSD layers. The ranges of #6 and #9 in the SSD were 4500 ± 200 µm and 2200 ± 20 µm in emulsion equivalent, respectively.
We began with checking vertex C. Three charged particles were emitted with a coplanarity of 0.001 ± 0.043. The coplanarity is defined as ( − → r 1 × − → r 2 ) · − → r 3 , where − → r i is a unit vector of a track angle. It shows that three particles were emitted in a plane; thus, neutron emission is unlikely. The possibility of neutron emission is discussed in the end of this section. From all 1 The name of the southern part of Gifu prefecture, Japan, where the event was found.  nuclide combinations for both mesonic and non-mesonic decays of known single-Λ hypernuclei, possible decay modes were selected using the following criteria. (1) An angular difference between #9 and the momentum sum of #7 and #8 should be back-to-back with 3 σ confidence. (2) Momenta and energies should be conserved with 3 σ by applying the kinematic fitting with degree of freedom (DOF) of 3 [11]. Here, the range of #9 was parameterized to conserve the total momentum and reconstruct the mass of a single-Λ hypernucleus. Possible decay modes at vertex C are listed in Table 2. When the chi-square value of the kinematic fitting was larger than 14.2, such decay modes were rejected. In this fitting case, such setting corresponds to a p-value of 0.27%, i .e., 3 σ cut condition. Taking this into account, the possible candidate of #2 was identified to be 5 Λ He in the case of no neutron emission. The lower limit of the range of #9 was obtained to be 7378 (in emulsion) + 2200 (in SSD) µm considering the track length in the SSD. The interpretation of 5 Λ He is consistent with this requirement.

5/11
Next, we checked vertex B. The particle of track #1 decayed to three charged particles including a very thin track (#6). The range of #6 was measured to be 23170 (in the emulsion) + 4500 (in the SSD) µm. If the particle of track #6 is π − , the total visible energy by decay daughters (#2, #5, and #6) is at least 47.7 MeV. Since this energy is larger than the Q value of any π − mesonic decay mode, the possibility of #6 to be π − was rejected. Thus, the charge of #1 should be more than three. The maximum charge of #1 is five by assuming Ξ − 6/11  However, this decay mode was also rejected because there was no electron track associated with the end point of track #5 as seen in Fig. 3, even though 6 He should decay to 6 Li + e − + ν with a half-life of 806.7 ms [12]. Thus, neutron(s) should be emitted at vertex B although the coplanarity is so small. Regarding decay modes with neutron(s) at vertex B, all nuclide combinations were checked for charged particles. In the kinematic analysis, the range of #6 was calculated by assuming a double-Λ hypernucleus with ∆B ΛΛ = 0, where the missing momentum was carried by unobserved neutron(s). In the case of multiple neutron emissions, all neutrons were treated as having the same momentum. This setting gives the minimum kinetic energy of neutrons and the maximum kinetic energy of #6, which corresponds to the maximum range of #6. If the maximum range was not consistent with the measurement, those assignments were rejected. Since non-mesonic decays have large Q values, many decay modes remained for the case of #1 being ΛΛ Be or ΛΛ B nuclides as summarized in Table 3.

7/11
Finally, we checked vertex A, where three tracks were observed. All nuclide combinations for #1 to be ΛΛ Be or ΛΛ B were checked. In case of the decay with neutron(s) emission, the momentum of neutron(s) was assumed to be the missing momentum. In the case of more than one neutron emission, only a lower limit of ∆B ΛΛ could be obtained. Possible decay modes are listed in Table 4. However, neutron(s) emission was unlikely because the coplanarity of vertex A was calculated to be 0.000 ± 0.099. Additionally, ∆B ΛΛ − B Ξ − should not be a large value considering the result of the NAGARA event.
In above analysis, it is assumed that no neutron was emitted at vertex C. The interpretation of vertex C is important because the analysis of vertex B is not effective in selecting possible candidates from the kinematics due to the large Q values of non-mesonic decays. If we assume neutron(s) emission, following decay modes are also accepted.
In these cases, interpretations of ΛΛ Li nuclides in vertex A are also remaining. However, this possibility is very unlikely: The branching ratio of 3 Λ H and 4 Λ H decays were measured in a past experiment [17]. Among about 2000 3 Λ H and 4 Λ H decays, less than 30 instances of decay mode (i) and 5 of (ii) have been observed. Theoretical calculation also supports this small possibility e.g., 0.6% for decay mode (i) [18].

Discussion
The newly observed double-Λ hypernuclear event is interpreted as the production of a 10 ΛΛ Be, 11 ΛΛ Be, or 12 ΛΛ Be nucleus. The present result was compared with the results of past experiments. Candidates of ΛΛ Be double-Λ hypernuclei which were observed in past experiments are listed in Table 7.
DEMACHIYANAGI event was interpreted as 10 ΛΛ Be * (most probable), an excited state of 10 ΛΛ Be, with a B ΛΛ value of 11.90 ± 0.13 MeV [4]. The present result of 10 ΛΛ Be interpretation 9/11 is consistent with DEMACHIYANAGI event when considering 10 ΛΛ Be was generated in the ground state. The energy difference of the excited (2 + 1 ) and ground (0 + 1 ) states of the core nucleus 8 Be is 3.03 MeV [19], although both states are particle unbound. The double-Λ hypernucleus 10 ΛΛ Be with B ΛΛ = 14.7 ± 0.4 MeV observed by Danysz is also consistent with the present result [20][21][22].
The present result of 11 ΛΛ Be interpretation is consistent with the past results given by HIDA and MIKAGE, in which B ΛΛ values were reported to be 22.15 ± 2.94 MeV, 23.05 ± 2.59 MeV, and 20.83 ± 1.27 MeV [4]. The present result has a small error on B ΛΛ because no neutron was emitted at the production vertex of the double-Λ hypernucleus.
In the case of 12 ΛΛ Be, the present analysis shows negative ∆B ΛΛ value (−2.7 ± 1.0 MeV ), which is not consistent with NAGARA. However, if 12 ΛΛ Be was produced in an excited state, ∆B ΛΛ of the ground state is increased by its excitation energy. Therefore, the interpretation of 12 ΛΛ Be can not be excluded. The core nucleus, 10 Be, has excited states 3.368-6.263 MeV [19]. The level of 12 ΛΛ Be is estimated to be similar to that of 10 Be [23]. Thus, ∆B ΛΛ for the ground state of 12 ΛΛ Be becomes positive. Three interpretations, 10 ΛΛ Be, 11 ΛΛ Be, and 12 ΛΛ Be * , are accepted from the above consideration. Among them, 11 ΛΛ Be is the most probable one from the analysis described in the previous section.
6. Summary An experiment to search for double-Λ hypernuclei with a counter-emulsion hybrid method, E07, was carried out at J-PARC. An impressive double-Λ hypernuclear event called "MINO" has been observed. Based on kinematic analysis, the nuclide of the double-Λ hypernucleus was uniquely identified as a ΛΛ Be. The event was interpreted as one of the three following candidates. 16 O + Ξ − → 10 ΛΛ Be + 4 He + t, 16 O + Ξ − → 11 ΛΛ Be + 4 He + d, 16 O + Ξ − → 12 ΛΛ Be * + 4 He + p.
B ΛΛ (∆B ΛΛ ) of these double-Λ hypernuclei was obtained to be 15.05 ± 0.11 MeV (1.63 ± 0.14 MeV), 19.07 ± 0.11 MeV (1.87 ± 0.37 MeV), and 13.68 ± 0.11 MeV (−2.7 ± 1.0 MeV), respectively by assuming the Ξ − capture in the atomic 3D state with B Ξ − of 0.23 MeV. Negative ∆B ΛΛ value of 12 ΛΛ Be indicates it was produced in the excited state. The most 10/11 probable interpretation was found to be the production and decay of the 11 ΛΛ Be nucleus from the kinematic fitting.
The emulsion scanning of the E07 experiment is ongoing. Twice the statistics for Ξ − stopping events than that of E373 has been scanned and more than ten events of doubleand twin-Λ hypernuclei have been observed up to the present. Further impressive events are expected to be observed in the near future.