The J-PARC E05 collaboration measured the inclusive 12C(K−,p){}^{12}\mathrm{C}(K^{-},p) missing-mass spectrum at 1.8 GeV/cc and found that, while the region −300<BK<40-300 < B_K < 40 MeV is best described by a shallow Kˉ\bar{K}-nucleus optical potential (V0,W0)≈(−80,−40)(V_0, W_0) \approx (-80, -40) MeV, the spectrum contains a statistically significant event excess around BK∼100B_K \sim 100 MeV, fitted by a Breit-Wigner form with binding energy 90 MeV and width 100 MeV, for which the authors proposed - but could not establish - a deeply bound state of a hyperon-resonance-nucleus (Y∗Y^{*}-nucleus) system. The microscopic origin of the excess (genuine Y∗Y^{*}- or kaonic-nuclear binding versus unmodelled quasi-free or two-step reaction mechanisms) remains undetermined; the decisive exclusive decay-particle spectroscopy is under way in the successor J-PARC E42 experiment, whose first exclusive measurement (2026) directly determined a much stronger absorptive potential W0=−100W_0 = -100 MeV, evidencing dominant multi-nucleon absorption whose microscopic decomposition is itself open. The problem - identify the origin of the deeply bound excess and establish the in-medium Kˉ\bar{K}-nucleus interaction it implies - remains open; exclusive decay-particle spectroscopy, multi-nucleon absorption dynamics, AA-dependence systematics, and microscopic Y∗Y^{*}-doorway theory are discussed in the source and successor program as routes toward its resolution.

Background

The antikaon-nucleon (KˉN\bar{K}N) interaction is unusually strong and attractive in the isospin-0 channel; below threshold this attraction appears as the Λ(1405)\Lambda(1405) hyperon resonance, which in coupled-channel chiral-unitary descriptions (effective low-energy field theories in which the coupled meson-baryon channels are resummed to exact unitarity) is a superposition of a quasi-bound KˉN\bar{K}N component and a πΣ\pi\Sigma (pion plus Sigma-hyperon) component [Jido et al. 2003]. Akaishi and Yamazaki argued that this attraction should act as a deeply attractive center inside nuclei and produce "kaonic nuclei" - nuclear systems in which a K−K^- is bound by of order 100 MeV, far deeper than any ordinary nuclear state [Akaishi and Yamazaki 2002]. Whether such deep binding survives in the nuclear medium has been debated for two decades. The cleanest empirical handle, kaonic-atom X-ray spectroscopy (X-ray transitions of exotic atoms in which a stopped K−K^- has replaced an orbital electron), probes only the dilute nuclear surface and admits both "shallow" (V0∼−50V_0 \sim -50 to −80-80 MeV) and "deep" (V0∼−150V_0 \sim -150 to −200-200 MeV) choices of the phenomenological Kˉ\bar{K}-nucleus optical potential, a complex depth multiplying the nuclear density distribution whose real part V0V_0 gives the dispersive attraction and imaginary part W0W_0 the absorption of the K−K^- at the nuclear center.

In-flight (K−,p)(K^{-},p) missing-mass spectroscopy was developed to probe the nuclear interior. A 1.8 GeV/cc K−K^- beam scatters quasi-freely off a bound proton ("quasi-free elastic scattering", QFES); the forward-going proton is detected, and the missing mass - expressed as a kaon binding energy BKB_K measured from the K−K^- plus residual-nucleus threshold - maps the spectrum of the Kˉ\bar{K}-nucleus system, including its quasi-free continuum and any bound structures. Theoretical templates are computed with the Green's function method, which treats the bound-state and quasi-free continuum regions of the spectrum in one distorted-wave framework [Yamagata, Nagahiro and Hirenzaki 2006]. An earlier measurement of the same reaction at the KEK 12-GeV proton synchrotron (KEK-PS, experiment E548) reported indications of a deep potential but suffered from a coincidence bias that prevented comparison with inclusive calculations.

The J-PARC E05 experiment then measured the inclusive 12C(K−,p){}^{12}\mathrm{C}(K^{-},p) missing-mass spectrum at 1.8 GeV/cc [Ichikawa et al. 2020]. The spectrum in −300<BK<40-300 < B_K < 40 MeV is best reproduced with (V0,W0)=(−80,−40)(V_0, W_0) = (-80, -40) MeV, favoring a shallow potential. On top of this description, a significant event excess appears near BK∼100B_K \sim 100 MeV, in a region where the mesonic decay K−NN→πΣNK^- NN \to \pi\Sigma N is energetically closed, so that non-mesonic decays (K−NN→ΛNK^- NN \to \Lambda N and ΣN\Sigma N) dominate. The excess is well fitted by a Breit-Wigner form (the standard resonance line shape) with BK=90B_K = 90 MeV and width ≈100\approx 100 MeV, and could be explained neither by the explored optical potentials nor by the tested background channels. The authors' suggested interpretation is a deeply bound state of a Y∗Y^{*}-nucleus system, where Y∗Y^{*} denotes an excited hyperon - dominantly the Λ(1405)\Lambda(1405) - produced as a "doorway" in the reaction and then moving in the mean field of the residual nucleus; distinguishing this from a conventional kaonic-nucleus (bound K−K^-) assignment or from unmodelled reaction mechanisms requires detecting the decay products, which the inclusive measurement could not do.

Independent evidence that some Kˉ\bar{K}-induced binding exists comes from J-PARC E15, which observed a K−ppK^{-}pp-type bound state with B≈42B \approx 42 MeV and Γ≈100\Gamma \approx 100 MeV in the 3He(K−,Λp)n{}^{3}\mathrm{He}(K^{-},\Lambda p)n reaction [Yamaga et al. 2020]. The successor J-PARC E42 experiment re-measures 12C(K−,p){}^{12}\mathrm{C}(K^{-},p) at the same kinematics with decay-particle tracking (a time projection chamber with GEM (gas electron multiplier) readout, HypTPC, inside the Superconducting Hyperon Spectrometer) precisely to perform the exclusive spectroscopy that E05 lacked [Oura et al. 2025]. Its first exclusive result, the K−K^--escape cross-section measurement, finds V0=−72V_0 = -72 MeV (consistent with E05's real part) but W0=−100W_0 = -100 MeV - absorption far exceeding the W0∼−40W_0 \sim -40 MeV predicted by models including only one-nucleon absorption (K−N→YπK^- N \to Y\pi), indicating sizable multi-nucleon absorption [Oura et al. 2026]. Kaonic-atom analyses continue to refine the surface-constrained optical potential and its isospin dependence [Yamagata-Sekihara et al. 2025]. What no measurement or calculation has yet established is the origin of the deeply bound excess itself.

Problem Statement

Determine the microscopic origin of the deeply bound event excess observed near BK∼90B_K \sim 90-100100 MeV in the inclusive 12C(K−,p){}^{12}\mathrm{C}(K^{-},p) missing-mass spectrum, and thereby establish the in-medium Kˉ\bar{K}-nucleus interaction in a medium-heavy nucleus. These two goals constitute a single scientific objective - identifying the state or reaction mechanism that produces the excess and the dynamics that shape the Kˉ\bar{K} optical potential. The single resolution target - whose attainment thereby establishes the in-medium Kˉ\bar{K}-nucleus interaction it implies - is (i) a decision on the nature of the excess: a genuine deeply bound Y∗Y^{*}-nucleus state (a Λ(1405)\Lambda(1405)-doorway bound in the residual nucleus), a kaonic-nuclear state, or unmodelled quasi-free or two-step reaction mechanisms. The source paper and the successor E42 program discuss the following items as routes and prospects toward that decision, not as components every resolution must itself deliver: (ii) exclusive spectroscopy of the excess region through coincidence detection of decay particles, separating mesonic (πΣ\pi\Sigma, πΛ\pi\Lambda) from non-mesonic (ΛN\Lambda N, ΣN\Sigma N) channels and measuring the branching fractions of the candidate structure, which is what discriminates kaonic-nucleus from Y∗Y^{*}-nucleus assignments (the planned E42/HypTPC measurement); (iii) a quantitative, dynamics-based account of multi-nucleon absorption and dispersion in the Kˉ\bar{K}-nucleus potential - now known empirically to be strong (∣W0∣≈100|W_0| \approx 100 MeV at the nuclear center from the E42 escape measurement) but microscopically undecomposed - including its energy dependence; (iv) the target-mass (AA) dependence of the KˉA\bar{K}A interaction and of any Y∗Y^{*}-nucleus signal, via corresponding spectroscopy on additional nuclei (flagged in the source as interesting future work); (v) a theoretical framework that explicitly incorporates Y∗Y^{*}-doorway production and Y∗Y^{*}-nucleus binding, beyond an effective single-particle Kˉ\bar{K} optical potential, confronted with the exclusive data (conjectured in the source as a direction toward deriving the deep real potential). Any resolution must be consistent with the full set of existing constraints: the inclusive E05/E42 spectra and their fitted optical-potential parameters, the measured K−K^--escape cross section, and kaonic-atom data.

References

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