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Production of the H dibaryon via the (K^-,K^+) reaction on a $^{12}$C target

We study the production of the stable six-quark $H$ dibaryon via the $(K^-,K^+)$ reaction on a $^{12}$C target within a covariant effective Lagrangian model. The calculations are performed within a factorization approximation, in which the full production amplitude is written as a product of the amplitudes for the $K^- + p \to K^+ + Ξ^-$ and $Ξ^- + p \to H$ processes. The $K^+Ξ^-$ production vertex is described by excitation, propagation and decay of $Λ$ and $Σ$ resonance states in the initial collision of a $K^-$ meson with a target proton in the incident channel. The parameters of the resonance vertices are taken to be the same as those determined previously by describing the available data on total and differential cross sections for the $p(K^-, K^+)Ξ^-$ reaction within a similar model. The $Ξ^- + p \to H$ fusion process is treated within a quark model where the $H$ dibaryon is considered as a stable particle. For the $K^+$ meson angle fixed at 0$^o$, the $H$ production cross-section is found to be about 2.9 $μb/sr$ for $H$ mass just below the $ΛΛ$ threshold at a $K^-$ beam momentum of 1.67 GeV/c. This is an order of magnitude larger than the value for this quantity reported earlier in calculations performed on a $^3$He target using a different model for the cascade hyperon production. We have also calculated the beam momentum dependence of the $H$ production cross section and the energy spectrum of the emitted $K^+$ meson.