Quark mass dependence of H-dibaryon in $ΛΛ$ scattering

We study the quark mass dependence of the H-dibaryon in the strangeness $S=-2$ baryon-baryon scattering. A low-energy effective field theory is used to describe the coupled-channel scattering, in which the quark mass dependence is incorporated so as to reproduce the lattice QCD data by the HAL QCD collaboration in the SU(3) limit. We point out the existence of the Castillejo-Dalitz-Dyson (CDD) pole in the $ΛΛ$ scattering amplitude below the threshold in the SU(3) limit, which may cause the Ramsauer-Townsend effect near the $NΞ$ threshold at the physical point. The H-dibaryon is unbound at the physical point, and a resonance appears just below the $NΞ$ threshold. As a consequence of the coupled-channel dynamics, the pole associated with the resonance is not continuously connected to the bound state in the SU(3) limit. Through the extrapolation in quark masses, we show that the unitary limit of the $ΛΛ$ scattering is achieved between the physical point and the SU(3) limit. We discuss the possible realization of the "H-matter" in the unphysical quark mass region.

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