Department of Physics, Tokyo University of Science, 2641,

Yamazaki, Noda, Chiba 278-8510, JAPAN

E-mail: sawado@ph.noda.tus.ac.jp, miss_nonno@mub.biglobe.ne.jp, oryu@ph.noda.tus.ac.jp

**Multi-soliton solutions in the chiral quark soliton
model**

**Abstract:**

We present recent results of higher baryon-number states based on quark dynamics. The chiral quark soliton model is the simple quark model that incorporates the basic features of QCD, e.g. the chiral symmetry and its breakdown or the appearance of the Goldstone bosons [1]. For B = 1 and 2, the model has spherically symmetric and axially symmetric solutions. From the study of the Skyrme model, it is expected that the minimal energy solutions with high winding numbers have some particular discrete symmetries. For example, B = 3 soliton has a tetrahedral symmetry T_{d}, B = 4 has a cubic O_{h}, B = 5 possesses the symmetry D_{2d} and B = 7 has a icosahedral symmetry Y_{h}, and so on. We shall impose the same symmetry on the chiral fields to our calculations of CQSM using rational map ansatz [2]. We obtain the stable solutions for B = 3 ~ 9,17. Particularly interesting property of the result is the degeneracy of the valence quark states [3, 4]. Such degeneracy play an important role for the stability of the solitons. It may be a hint for obtaining solutions with minimum energy. Also we confirm the shell structure for the quarks. The shells are comprised of the four-fold degenerate ground state and also higher levels with various degenerate patterns. These structure are realized by the interplay of two symmetries, SU(2)_{L}×SU(2)_{R} symmetry for the quarks and above discrete symmetries of the background fields. We discuss about this in detail.

**References:**

- D.I. Diakonov, V.Yu. Petrov, and P.V. Pobylitsa, Nucl. Phys. B306, 809 (1988).
- C.J. Houghton, N.S. Manton and P.M. Sutcliffe, Nucl. Phys. B510, 507 (1998).
- N. Sawado and N. Shiiki, Phys. Rev. D66, 011501 (2002); hep-ph/0204198.
- N. Sawado, N. Shiiki, S. Oryu, hep-ph/0211403.