4 A$_{NN}$ A$_{N}$ Λ A$_{N}$ Σ A$_{N}$ Ξ A ΛΛ A ΛΣ A ΛΞ A ΣΣ A ΣΞ A ΞΞ Λ σ -108.28 -108.28 -108.28 -79.04 -68.21 -135.34 -135.34 -53.05 -108.28 -57.39 263.04 4/3 x A ′ NN A ′ N Σ ( A ) A ′ N Σ ( R ) A ′ N Ξ A ′ ΣΣ A ′ ΣΞ A ′ ΞΞ 0 -12.29 -12.29 -28.65 -8.98 -6.02 -12.29 -6.52 -1 -103.45 -103.45 -241.04 -75.52 -50.69 -103.45 -54.83 B$_{NN}$ B$_{N}$ Λ B$_{N}$ Σ ( A ) B$_{N}$ Σ ( R ) B$_{N}$ Ξ B ΛΛ B ΛΣ B ΛΞ B ΣΣ B ΣΞ B ΞΞ 106.35 106.35 106.35 247.80 77.64 67.00 132.94 132.94 52.11 106.35 56.37 C$_{τ}$$_{N}$$_{,τ}$$_{N}$ C$_{τ}$$_{N}$$_{,}$$_{−}$$_{τ}$$_{N}$ C$_{τ}$$_{N}$$_{,τ}$$_{Σ}$ C$_{τ}$$_{N}$$_{,}$$_{−}$$_{τ}$$_{Σ}$ C$_{τ}$$_{N}$$_{,τ}$$_{Ξ}$ C$_{τ}$$_{N}$$_{,}$$_{−}$$_{τ}$$_{Ξ}$ C$_{τ}$$_{Σ}$$_{,τ}$$_{Σ}$ C$_{τ}$$_{Σ}$$_{,}$$_{−}$$_{τ}$$_{Σ}$ C$_{τ}$$_{Σ}$$_{,τ}$$_{Ξ}$ C$_{τ}$$_{Σ}$$_{,}$$_{−}$$_{τ}$$_{Ξ}$ C$_{τ}$$_{Ξ}$$_{,τ}$$_{Ξ}$ C$_{τ}$$_{Ξ}$$_{,}$$_{−}$$_{τ}$$_{Ξ}$ -11.70 -103.40 -11.70 -103.40 -8.54 -75.48 -5.73 -50.67 -11.70 -103.40 -6.20 -54.80 C$_{N}$ Λ C$_{N}$ Σ 0 C ΛΛ C ΛΣ C ΛΞ C Σ 0 Σ C Σ 0 Ξ -57.55 -57.55 -36.26 -71.94 -71.94 -28.20 -57.55 TABLE I: Parameters for the MDI-Hyp-A and MDI-Hyp-R interactions with x = 0 and x = − 1. All except σ are in units of MeV. A ′ N Σ ( A ) and B$_{N}$ Σ ( A ) are for the MDI-Hyp-A interaction, and A ′ N Σ ( R ) and B$_{N}$ Σ ( R ) are for the MDI-Hyp-R interaction. Other parameters are the same for both interactions. at high momenta. Also, the density dependence of the high-momentum behavior of the mean-field potential is poorly known. Since the maximum Fermi momenta of nucleons and hyperons reached in hybrid stars are not very high, the incorrect nucleon potential and the un- certainty of hyperon potentials at high momenta given by the extended MDI interaction are thus not expected to affect significantly the properties of cold hypernuclear matter considered in the present study. It is known that both proton and neutron single- particle potentials in asymmetric nuclear matter of un- equal proton and neutron densities are approximately lin- ear in the isospin asymmetry δ of the matter. Whether this is also the case for hyperons is not clear in the litera- ture. For the extended MDI interaction introduced in the present study, such a linear dependence in isospin asym- momentum of nucleons. For nucleons, the single-particle potential from the MDI interaction is consistent with the Schr¨ o dinger equivalent potential obtained by Hama et al. from the nucleon-nucleus scattering data [64, 65] up to the nucleon momentum of 500 MeV. For hyperons, the momentum dependence of their single-particle potentials from the extended MDI interaction is similar to that ob- tained from the G-matrix calculations based on the free Nijmegen NY interaction [37]. Both show an increase with increasing momentum and are similar at low mo- menta as both are constrained by available experimen- tal data. They are, however, slightly different at high momenta. The momentum dependence of NY and Y Y interactions thus remains an open question, especially FIG. 3: (Color online) Symmetry potentials of nucleon, Σ and Ξ in asymmetric nuclear matter at saturation density ρ = ρ 0 . Σ( A ) and Σ( R ) are for the MDI-Hyp-A and MDI- Hyp-R interactions, respectively. FIG. 2: (Color online) Single-particle potentials in symmetric nuclear matter at saturation density ρ 0 as functions of particle momentum. The Schr¨ o dinger equivalent potential obtained by Hama et al. [64, 65] from the nucleon-nucleus scattering data is shown by stars for comparison. Σ(A) and Σ(R) are for the MDI-Hyp-A and MDI-Hyp-R interactions, respectively. 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