Search for the deeply bound $K^-pp$ state from the semi-inclusive forward-neutron spectrum in the in-flight $K^-$ reaction on helium-3

An experiment to search for the $K^-pp$ bound state was performed via the in-flight $^3$He($K^-,n)$ reaction using 5.3 $\times$ $10^9$ kaons at 1 GeV/$c$ at the J-PARC hadron experimental facility. In the semi-inclusive neutron missing-mass spectrum at $\theta_{n}^{lab}=0^\circ$, no significant peak was observed in the region corresponding to $K^-pp$ binding energy larger than 80 MeV, where a bump structure has been reported in the $\Lambda p$ final state in different reactions. Assuming the state to be isotropically decaying into $\Lambda p$, mass-dependent upper limits on the production cross section were determined to be 30--180, 70--250, and 100--270 $\mu$b/sr, for the natural widths of 20, 60, and 100 MeV, respectively, at 95\% confidence level.


Introduction
The existence of a strongly-attractive force between antikaons (K) and nucleons in isospin 0 channels leads, in some models, to the prediction of formation of deeply * corresponding author.
2 Deceased bound kaonic-nuclei [1,2]. The investigation of such exotic states will provide unique information to reveal the sub-thresholdKN interaction, which cannot be directly probed either by x-ray measurements [3,4,5] or by the low-energyKN scattering experiments [6]. The properties of kaonic nuclei are also of great interest, since they might open a door way to high-density nuclear matter [1,7,8].
However, their existence has not been conclusively established to date.
The simplest kaonic nucleus is theoretically considered to be the so-called K − pp state [2]; more generally, it is expressed as [K ⊗ {N N } I=1,S=0 ] I=1/2 with J π =0 − . Intensive theoretical works based on a few-body calculation have been performed for the K − pp system, all of which predicted the existence of bound states [2,9,10,11,12,13,14,15]. However, the predicted binding energies (B.E.) and widths (Γ) are widely spread from 9-95 MeV and 34-110 MeV, respectively, primarily depending on theKN interaction models.
On the experimental side, the FINUDA collaboration at DAΦNE investigated the stopped K − reaction on 6 Li, 7 Li, and 12 C, and observed a bump structure in the invariantmass spectrum of back-to-back Λp pairs [16]. They determined the B.E. and Γ to be 115 +6 −5 (stat ) +3 −4 (syst ) MeV and 67 +14 −11 (stat ) +2 −3 (syst ) MeV, respectively. The DISTO collaboration at SATURNE analyzed their dataset of the exclusive pp → ΛpK + channel and observed a bump structure in the K + missing-mass and the pΛ invariant-mass spectra at T p =2.85 GeV [17], with a large cross section comparable to Λ(1405) production, as predicted [18]. The B.E. and Γ were determined to be 103±3(stat)±5(syst) MeV and 118±8(stat)±10(syst) MeV, respectively. They argued for an important role of Λ(1405) as a doorway particle to form the K − pp state, which is also consistent with the absence of the peak structure at T p =2.5 GeV [18,19]. In addition to the above, a less significant signal was reported in the stopped-p reaction [20] and no peak was observed in the γ-induced reaction [21].
Since the K − pp is a basic ingredient for kaonic nuclear bound states, it is important to investigate it with different methods. We chose to further investigate these results using the in-flight kaon-induced reaction on 3 He at θ lab n = 0 • : which is one of the simplest reactions to produce the K − pp bound state. The kaon beam momentum was selected to be 1 GeV/c, based the K − beam yield and the elementary K − N reaction rate [22]. In this reaction, the momentum transfer is relatively small (0.2-0.4 GeV/c), and the forward-going neutron has a momentum of 1.2-1.4 GeV/c, depending on the binding energy. One of the advantages of the in-flight reaction is that most of the neutrons coming from the hyperon decays and ground-state hyperon production via the non-mesonic two-nucleon absorption processes, K − N N → Y N , are kinematically separated from the K − pp signal in the (K − , n) missing-mass spectrum.
There are two calculations of the forward neutron spectrum in this reaction. Koike and Harada predicted a large cross section for the K − pp bound state, as much as 2-3 mb/sr, at θ lab n = 0 • using phenomenologicalKN potentials [23]. In their calculation, a distinct peak structure appears when the potential reproduces the experimentally reported binding energies and natural widths. Another theoretical spectrum was calculated by Yamagata-Sekihara et al. based on a potential derived in the framework of a chiralunitary model [24]. They predicted a loosely-bound state with a few hundreds µb/sr cross section.  [26]. The apparatus consists of a beam line spectrometer, a cylindrical detector system (CDS) that surrounds the liquid 3 He target system to detect the decay particles from the target region, a beam sweeping magnet, and a neutron time-of-flight counter located ∼15 m downstream from the target position.
In this Letter, the results of the first measurement of the 3 He(K − , n) reaction at 1 GeV/c in the J-PARC E15 experiment are reported. The present results were obtained based on a data set taken in May, 2013 with 5.3 × 10 9 incident kaons on a helium-3 target.

Experiment and analysis
The J-PARC E15 experiment was performed at the K1.8BR beam line of the J-PARC hadron experimental facility [25]. The experimental apparatus is schematically shown in Fig. 1 and is briefly discussed below. More detailed description can be found elsewhere [26].
A K − beam, purified with an electrostatic separator, was identified with an aerogel Cherenkov counter and was confirmed by an off-line time-of-flight analysis. The beam momentum was analyzed with a beam-line spectrometer consisting of two sets of drift chambers installed across a dipole magnet. The momentum resolution was evaluated to be (2.0 ± 0.5) × 10 −3 with an absolute precision of 2 MeV/c at 1 GeV/c. A typical K − yield was 1.5 × 10 5 per spill 3 with a K − /π − ratio of 0.45. To eliminate background caused by pile-up beam particles, we requested only one track to exist in each beam-line chamber.
A cylindrical target cell 137 mm long and 68 mm in diameter was filled with liquid helium-3, and placed at the final focus point of the beam line. The density of the target was 0.081 g/cm 3 at a temperature of 1.4 K.
The momentum of the forward neutron was measured by the time-of-flight method with a neutron counter (NC) placed at a distance of ∼15 m from the target. The NC, segmented into 16-column (horizontal) × 7-layer (depth) units with a total volume of 3.2 m (horizontal) × 1.5 m (height) × 0.35 m (depth), had a coverage of ∼22.1 msr solid angle. Most of the charged particles, including beam particles, were swept out from the NC acceptance with a beam sweeping magnet. Furthermore, two types of scintillation counter arrays were installed to veto charged particles downstream of the target system and upstream of the NC.
To determine the flight length of a forward-going particle, the reaction vertex was reconstructed by a cylindrical detector system (CDS) surrounding the target. Charged particles emitted in the reaction were tracked with a 15layer cylindrical drift chamber (CDC) in a 0.7 T solenoidal field. A beam-line drift chamber just upstream of the target was utilized, together with the CDC tracks, to reconstruct the reaction vertex. The vertex resolutions were evaluated to be ∼1 and ∼7 mm in the perpendicular and parallel directions to the beam, respectively. The helium-3 fiducial volume was defined as 60 mm in diameter and 100 mm in length to cut the events where beam kaons interact with the target cell. A cylindrical detector hodoscope (CDH) was used as a trigger counter with a polar-angle acceptance from 54 to 126 degrees. The timing of the CDH provided particle identification together with the track momentum analyzed by the CDC. The CDS momentum acceptance is limited by the material budget from the target to the CDH: typically 80, 180, and 260 MeV/c for pions, kaons, and protons, respectively. Figure 2 shows a 1/β spectrum of forward neutral particles detected by the NC, and the measured energy deposited versus 1/β. The γ-ray peak position provided a reference to adjust timing offsets and time-walk effects of each NC segment. The time-of-flight resolution for the forward neutral particles was obtained from the width of the γ-ray peak to be 150 ps (σ). Another peak at around 1/β = 1.3 is a quasi-free peak attributed to the quasi-elastic scattering (K − "n" → K − n: double quotation marks indicate a quasi-free nucleon in 3 He) and the charge-exchange reaction (K − "p" → K 0 s n). Here the neutron timing was determined by the time-wise first-hit segment with an energy deposited larger than a threshold determined off-line. The threshold was optimized to be 8 MeVee (MeV electron equivalent) in terms of a signalto-background ratio at the quasi-free peak. The accidental background can be evaluated from the yield in the unphysical region, the 1/β range from 0.6 to 0.9, as the dotted line in Fig. 2 indicates. The signal-to-background ratio at the quasi-free peak was ∼100. The detection efficiency for a neutron was evaluated to be 0.23 ± 0.04 using ∼1.1 GeV/c neutrons by an exclusive analysis of the 3 He(K − , nK 0 s )d reaction. We assumed the neutron detection efficiency has no momentum dependence around 1 GeV/c since np and nC reaction cross sections are known to be flat in this region [27].  Figure 3 shows the 3 He(K − , n)X missing-mass distribution obtained based on a semi-inclusive condition by requiring at least one charged track in the CDS. The most prominent structure in the spectrum is a peak at around 2.4 GeV/c 2 . It corresponds to the quasi-free peak also seen in the 1/β spectrum. The inset of Fig. 3 demonstrates one of the source processes contributing to the quasi-free peak, K − "p" → K 0 s n, by reconstructing the K 0 s → π + π − decay with the CDS. The K 0 s -tagged spectrum also indicates that the peak broadening due to Fermi motion has little influence on the tail structure in the bound region. A continuum above the quasi-free peak is mainly attributed to hyperon production and subsequent decay into neutrons.

Semi-inclusive neutron spectrum
The missing-mass resolution, also shown in Fig. 3, is mainly due to the neutron time-of-flight resolution. A resolution of 10 MeV/c 2 (σ) was achieved around the region of interest. The precision of the absolute missing-mass scale was evaluated to be 3 MeV/c 2 from the peak positions of the missing-deuteron in the 3 He(K − , nK 0 s )d reaction and the Σ ± reconstructed by a neutron in the NC and a charged pion in the CDS. The widths of these peaks, including the quasi-free peak, were well reproduced by the resolution and Fermi motion in 3 He [28]. The spectrum was normalized as, where N n is the number of observed neutrons in the missing-mass interval ∆M , and Ω N C is the acceptance of the NC. The effective integrated luminosity, L, was evaluated to be 547 µb −1 by considering the beam analysis efficiency and the fiducial volume selection. The overall efficiency, ǫ, was evaluated using the experimental data to be 0.16, including the neutron detection efficiency, reaction losses between the target and the NC, the vertex reconstruction efficiency, the neutron over-killing ratio by the two veto counter arrays, the DAQ live rate, and the trigger efficiency. A CDS is the CDS tagging acceptance -namely the probability of having at least one charged particle within the CDS acceptance when a neutron is detected by the NC. There is a rather large uncertainty about A CDS since it depends on the angular distribution and the cross section of each reaction, which are not well-known for the K − + 3 He reaction. Therefore, we presented the spectrum without correcting A CDS . The systematic error of the normalization was evaluated as ± 17%, which was dominated by the uncertainty of the neutron detection efficiency.

Background evaluation in the K − pp bound-region
For further discussion on the structure in the K − pp bound region, background contributions were investigated. Here, four kinds of background sources are considered as follows.
Accidental background (BG accidental ). The purely accidental background, which is uncorrelated with the triggered beam, and is random in time, can be evaluated using the 1/β spectrum as shown in Fig. 2. This background component accounts for about half the observed yield in the unphysical region which is below the ΛN mass threshold in the neutron missing-mass.
Neutral particles other than neutrons (BG neutral ). The other source of the background in the unphysical region is the tail component of the γ-ray peak. It mainly comes from π 0 produced via hyperon-andK-decays. In addition, long-lived K 0 L also makes a NC signal through the K 0 N reaction and decay at the NC, which appears in the missing-mass below the K − pp threshold. Those contributions were evaluated by a Monte Carlo simulation based on the GEANT4 toolkit [29] with known elementary processes [30]. They can explain the remaining yield in the unphysical region when the absolute yield is normalized to the γ-ray peak. The overall uncertainty of those yields was estimated to be 20% from the relative uncertainty of the elementary cross sections.
Fast neutrons from Σ ± decays (BG Σ-decay ). Among the elementary reactions, only forward-going hyperons produced via the K − "N " → Y π reactions are kinematically allowed to produce fast neutrons which contribute to the K − pp bound region in the 3 He(K − , n)X missing-mass spectrum. For the K − "N " → Σ ± π reactions, most of these events have a CDS track of the charged pion coming from the Σ ± decay. Hence, their contribution was evaluated by reconstructing Σ ± from their decay particles n and π ± detected with the NC and the CDS, respectively. However, when only the pion associated with the primary reaction is detected with the CDS, the Σ ± cannot be reconstructed. Such a contribution was estimated by the Monte-Carlo simulation to be ∼10% of the K − "N " → Σ ± π reactions around the K − pp threshold, and to increase up to 50% at around 2.25 GeV/c 2 . This estimation involves a rather large uncertainty below 2.3 GeV/c 2 since the Fermi-motion effects have major influences near the reaction threshold. The contributions from the K − "N " → Λπ and K − "N " → Σ 0 π reactions were found to be negligible by the Monte-Carlo simulation.
Contamination from the target cell (BG cell ). In addition to the finite spatial resolution of the CDS, displaced decay vertices of hyperons andKs could worsen the vertex reconstruction. Therefore, reactions which occur on the target cell and other materials around the target can survive even after the fiducial volume selection in the analysis. Those contaminations were evaluated by using the empty-target data. Figure 4 summarizes the backgrounds in the K − pp bound region. In the figure, only Σ ± reconstructed events are plotted as the BG Σ-decay , namely, the minimum but definite background contribution from the Σ ± decays. In the missing-mass region below 2.29 GeV/c 2 , the observed events are explained by the background within their uncertainties discussed above. On the other hand, the yield of the tail-like component above 2.29 GeV/c 2 cannot be totally reproduced. Such sub-threshold structure would be attributed to the imaginary part of the attractiveKN interaction, in general. Especially in the (K − , n) reaction at 1 GeV/c, primary neutrons from the hyperon resonance production via the non-mesonic two-nucleon absorption processes (K − N N → Y * n) could make localized structures just below the K − pp binding threshold, kinematically. However, further information from the exclusive analysis is needed to discuss the origin of the subthreshold tail structures since the reconstruction of all the final-state particles is essential to identify these contributions. Hereafter, we focus on the deep-binding region only, where experimental observation were reported of a bump structure by different reactions. The upper limits of the formation cross section for a K − pp state were determined in the mass region from just above the Λp mass threshold (2.06 GeV/c 2 ) to 2.29 GeV/c 2 .

Upper limits for the production cross section of a deeply bound state
The intrinsic shape of the K − pp bound state is assumed to be a Breit-Wigner function. In the semi-inclusive spectrum, it would be distorted by the CDS tagging acceptance A CDS and then folded with the detector resolution σ MM as follows: where dσ/dΩ(θ lab = 0), M X and Γ are the formation cross section, mass and the natural width of the K − pp state, respectively, and C is a normalization factor. To evaluate A CDS , we need to assume the decay property of K − pp.
Here we assumed the branching ratio of K − pp → Λp to be 100% and the decay distribution to be uniform. It should be noted that A CDS for K − pp → (πΣ) 0 p decay is about half of that for K − pp → Λp at just above the π + Σ + p mass threshold (∼2.27 GeV/c 2 ). To evaluate a probability distribution as a function of the cross section dσ/dΩ, a likelihood function was calculated for each M X and Γ combination. In the calculation, the backgrounds shown in Fig. 4 were taken into account and a Poisson distribution for the contents of each bin was used. In this way, an upper limit at 95% confidence level was obtained by integrating the probability distribution convoluted with the systematic error coming from the normalization factor. The upper limits of the K − pp bound state, evaluated assuming the natural widths of 20, 60, and 100 MeV, are shown in Fig. 5 as a function of the 3 He(K − , n)X missing-mass. For a comparison, the cross sections of K − "n" → K − n and K − "p" → K 0 n reactions at p K − = 1 GeV/c and θ lab n = 0 • were evaluated with the present data set to be ∼6 and ∼11 mb/sr, respectively. Here, we used the angular distributions given in Ref. [31] and [32] to evaluate the detector acceptance. A realistic Fermi momentum distribution was also considered. The results show the upper limits obtained correspond to 0.5-5% and 0.3-3% cross sections of the quasi-free K − elastic and charge-exchange reactions, respectively. Our results also show disagreement with the theoretical calculation by Koike and Harada for the deep-binding K − pp case, such as the FINUDA and DISTO measurements, where they predicted a one-orderof-magnitude larger cross section than the upper limits obtained.

Conclusion
A search for the K − pp bound state was performed via the 3 He(K − , n) reaction at θ lab n = 0 • at a kaon momentum of 1 GeV/c. In the semi-inclusive analysis, no significant peak structure was found in the K − pp bound region, where the FINUDA and DISTO collaborations reported a bump structure in different production reactions. Mass-dependent upper limits of the production cross section were evaluated at 95% confidence level in the missingmass range from 2.06 to 2.29 GeV/c 2 for a K − pp → Λp isotropic decay. They were determined to be 30-180, 70-250, and 100-270 µb/sr, for natural widths of 20, 60, and 100 MeV, respectively. These values correspond to 0.5-5% and 0.3-3% cross sections of the quasi-free K − elastic and charge-exchange reactions, respectively.