We theoretically investigate a possible existence of a p-wave HeΣ4 resonant state with Jπ=1−, T≃1/2 above the Σ threshold, using a coupled (3N–Λ)+(3N–Σ) model with a spreading potential. We calculate inclusive and Σ–Λ conversion π− spectra in a He4(K−,π−) reaction at 1.5 GeV/c, θlab=4–12° by the Green's function method in a distorted-wave impulse approximation. The pole position for the p-wave Σ resonant state in HeΣ4 is determined on the Riemann sheets in the complex E plane. The result shows that a peak of the HeΣ4 resonant state is clearly obtained in the conversion spectra above the Σ threshold, and that the angular distributions of these spectra enable extraction of the contribution of the resonant state from the π− spectra. Effects of the Σ-nucleus potential and the interference between Λ and Σ on the spectra are also discussed. Keywords: Hypernuclei, Resonant state, Sigma-nucleus potential
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