Four-Phase Structure of ρ Meson Coupled Skyrmions on S^3 : Particles and Fields

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Skyrmion configurations with the baryon number B=1, 2 and 3 of the π-p system, stabilized by fourth-order derivative terms, are studied in a curved space S^3 and in a flat space R^3. Adopting an axially symmetric ansatz, we obtain numerical soliton solutions. It confirms the existence of a four-phase structure of S^3 skyrmions coupled to the ρ meson. That is, there exist two types of solutions; parity conserving (PC) solutions and spontaneously parity violating (SPV) solutions. Furthermore, for both of the PC solutions and the SPV solutions there exist two phases respectively. One is a uniform phase which has a uniform or almost uniform distribution of energy and baryon number densities over the S^3. The other is a localized phase which has a well localized distribution of energy and baryon number densities. The transition from the localized phase to the uniform phase occurs at a critical radius L_<cr> of S^3. The L_<cr> for the PC solution decreases as the coupling constant e_A of the stabilizer term decreases, while the L_<cr> for SPV solution slightly increases as e_A decreases. The L_<cr> for the PC solution is larger than that for the SPV solution at any given value of e_A. For the usual physical coupling strength of the stabilizer terms, e.g., e_A≅6, the S^3 skyrmions are in the PC localized phase for the radius L>2.0 and are in the PC uniform phase for 2.0≥L≥0.9, but are in the SPV uniform phase for L<0.9.
理論物理学刊行会の論文
1991-03-25

Four-Phase Structure of ρ Meson Coupled Skyrmions on S^3 : Particles and Fields

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