The J-PARC E05 inclusive 12C(K−,p)^{12}\mathrm{C}(K^-, p) missing-mass measurement at 1.8 GeV/c established a shallow antikaon–nucleus optical potential near threshold, (V0,W0)≈(−80,−40)(V_0, W_0)\approx(-80,-40) MeV, and revealed an unexplained event excess roughly 100 MeV below the K−+11BK^-+{}^{11}\mathrm{B} threshold, fitted by a Breit–Wigner form with binding ≈90\approx 90 MeV and width ≈100\approx 100 MeV. It remains open whether this excess is a bound state of an excited hyperon Y∗Y^* (canonically the Λ(1405)\Lambda(1405), acting as a doorway) with the residual nucleus, or an artifact of reaction dynamics omitted from the theoretical templates — dispersive (real) contributions of two-nucleon and multinucleon Kˉ\bar K absorption, or other unmodeled final-state processes — or a combination. Subsequent work sharpens the context without answering the question: the 2026 exclusive K−K^--escape measurement by J-PARC E42 pins the absorptive strength to W0≈−100W_0\approx-100 MeV, far beyond one-nucleon absorption, yet explicitly leaves the microscopic mechanism unidentified. The problem is to determine the mechanism that generates the deep-binding excess, in a manner that quantitatively confronts the inclusive spectrum, the exclusive coincidence channels, and independent kaonic-atom constraints.

Background

An antikaon (K−K^-, the negatively charged strange meson; Kˉ\bar K denotes the antikaon generically) interacts with a nucleon with an exceptionally strong isospin-0 attraction. In chiral unitary models this attraction dynamically generates the Λ(1405)\Lambda(1405) resonance, understood not as a conventional three-quark baryon but as a quasi-bound KˉN\bar K N molecular state lying about 28 MeV below the K−pK^- p threshold, with a characteristic two-pole internal structure. The strength of this attraction led Akaishi and Yamazaki to predict deeply bound 'kaonic nuclear' systems in which a K−K^- is bound inside a nucleus by a potential far deeper than any ordinary hadron-nucleus potential; the lightest such system, K−ppK^- pp (a proton-proton pair bound to a K−K^-), was subsequently observed by the J-PARC E15 experiment in the 3He(K−,Λp)n{}^3\mathrm{He}(K^-, \Lambda p)n reaction, with a first report of binding 47±347\pm3 MeV and width 115±7115\pm7 MeV and final-statistics values B=42±3B=42\pm3 MeV, Γ=100±7\Gamma=100\pm7 MeV. Whether heavier kaonic nuclei exist, and how strongly an antikaon binds in nuclear matter more generally, remain contested.

The standard phenomenology encodes the Kˉ\bar K–nucleus interaction in an optical potential Uopt(r)=(V0+iW0) ρ(r)/ρ(0)U_\mathrm{opt}(r) = (V_0 + i W_0)\,\rho(r)/\rho(0), where ρ(r)\rho(r) is the nuclear density distribution: the real depth V0V_0 measures attraction and the imaginary strength W0W_0 measures absorption of the antikaon by the nucleus. Kaonic-atom X-ray spectroscopy (exotic atoms in which a K−K^- replaces an electron) constrains this potential only at the nuclear surface, and global analyses have long admitted two disjoint solution classes — 'shallow' (V0∼−80V_0\sim-80 to −50-50 MeV, chiral-unitary motivated) versus 'deep' (V0∼−200V_0\sim-200 to −150-150 MeV) — that fit the atomic data equally well; even after the sub-eV-precision kaonic-helium measurements of J-PARC E62 and updated global fits, this shallow-versus-deep ambiguity persists.

In-flight (K−,N)(K^-,N) reactions at beam momenta below 2 GeV/c probe the nuclear interior: in the quasi-free elastic scattering process, in which a K−K^- scatters elastically off a bound proton (K−p→K−pK^- p\to K^- p), the forward nucleon is detected, and the missing mass MXM_X of the residual system defines an antikaon binding energy BK=M(11B)+MK−MXB_K = M({}^{11}\mathrm{B}) + M_K - M_X. Theoretical templates for the resulting spectra are computed with a Green's-function method within a distorted-wave impulse approximation (a framework treating the outgoing wave's distortion and the nuclear continuum in one formalism), and multinucleon absorption processes such as K−NN→YNK^- NN \to Y N (where YY is a hyperon, i.e. a baryon carrying strangeness) enter these templates only through an absorptive imaginary term.

The J-PARC E05 experiment measured the inclusive 12C(K−,p)^{12}\mathrm{C}(K^-, p) spectrum at 1.8 GeV/c. Near threshold the spectrum favored a shallow potential (V0,W0)≈(−80,−40)(V_0, W_0)\approx(-80,-40) MeV. But a statistically significant event excess appeared in the deeply bound region around BK∼90B_K\sim 90–100 MeV, with a Breit–Wigner fit giving binding ≈90\approx 90 MeV and width ≈100\approx 100 MeV. A Kˉ\bar K bound by ~100 MeV in carbon is implausible under a shallow potential, so the favored interpretations were (a) a bound state of an excited hyperon Y∗Y^* — canonically the Λ(1405)\Lambda(1405), formed as a 'doorway' state that then binds to the residual nucleus — or (b)–(d) reaction-dynamics effects missing from the template set: the dispersive (real) parts of two-nucleon and multinucleon absorption, unmodeled final-state or correlated-emission processes, or a combination. The successor experiment J-PARC E42 repeated the measurement with a large-acceptance time-projection chamber (HypTPC) inside the Superconducting Hyperon Spectrometer, enabling exclusive coincidence channels; its first exclusive result (the K−K^--escape channel, 2026) directly fixed W0=−100−1+7 (stat.) −16+0 (syst.)W_0 = -100^{+7}_{-1}\,\mathrm{(stat.)}\,{}^{+0}_{-16}\,\mathrm{(syst.)} MeV — far stronger than the ∼−40\sim -40 MeV predicted from one-nucleon absorption alone — confirming that multinucleon absorption is large, while explicitly declining to identify the dominant mechanism. How the deep-binding excess arises is thereby still undecided.

Problem Statement

Determine the physical mechanism that generates the event excess observed in the deeply bound region (binding energy BK≈90B_K \approx 90–100 MeV below the K−+11BK^- + {}^{11}\mathrm{B} threshold) of the inclusive 12C(K−,p)^{12}\mathrm{C}(K^-, p) missing-mass spectrum measured at 1.8 GeV/c (J-PARC E05). Specifically, establish whether the excess arises from (a) a genuinely bound excited-hyperon–nucleus state formed via a Λ(1405)\Lambda(1405) doorway, (b) dispersive real-part contributions of multinucleon absorption that effectively deepen the potential, (c) yet-unmodeled final-state or correlated-emission processes, or (d) a combination, quantitatively accounting for the observed yield, line shape (≈90\approx 90 MeV binding, ≈100\approx 100 MeV width), and the established absorptive strength, in a manner consistent with the published inclusive spectrum, the exclusive K−K^--escape data (escape fraction ≈29%\approx 29\%, W0≈−100W_0 \approx -100 MeV) and other available coincidence channels, and independent kaonic-atom constraints. The required deliverable is the identification of the dominant mechanism, which the quantitative account of the yield, line shape, and absorptive strength and the consistency with the inclusive, exclusive, and kaonic-atom data must support; if the answer is (d), it must state which of (a)–(c) combine and their relative importance.

References

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