Dibaryon with S=-1 in the Bound Kaon Approach to the Skyrme Model T. NISHIKAWA (Tokyo Institute of Technology) Y. KONDO (Kokugakuin univ.) 2018/11/23 KEK研究会「 現代の原子核物理 」

Discovery (?) of strange multibaryons Strange tribaryon @KEK-PS T. Suzuki et al., 2004 stopped K- reaction in 4 He deeply bound ppnK- and pnnK- states Strange dibaryon @DAΦNE M. Agnello et al., 2005 strong Back-to-back correlation between Λ and p from K- absorption Evidence for ppK- bound state ? B.E.=115MeV, Γ=67MeV

Purpose of this work appropriate for the study of strange multibaryons To explore the possibility of deeply bound strange dibaryon in the bound kaon approach to the Skyrme model structure, mechanism responsible for the large B.E. (>100MeV) The bound kaon approach naturally incorporates KN interaction. well describes Λ(1405) as well as positive parity hyperons appropriate for the study of strange multibaryons

Skyrme model Nucleons = topological solitons of pion field Skyrme’s ansatz (“Hedgehog” ansatz): Mapping from S3(phys.) to S3(int.) F(r): profile function Winding number (conserved) = baryon number n (integer): “winding number”

Skyrme model Skyrme, 1961 　　 Nucleons as topological solitons of pion field t’Hooft, 1974 In NC →∞, QCD → weakly coupled meson theory. Witten, 1979 Baryons appear as solitons of pion field Adkins & Nappi, 1984 Collective coordinate quantization The model qualitatively (~30%) reproduces static properties of the nucleon

Bound kaon approach to the Skyrme model (Callan and Klevanov, 1985) Basic idea: SU(2) Skyrmion has fluctuating kaon field. The kaon field has bound states ! The lowest state: L=1 the next state: L=0 Wess-Zumino-Witten term split S=±1 states S=-1 states: bound states hyperons S=+1 states (ex. pentaquark): continuum

Spectrum of hyperons P-wave bound states : positive parity hyperons S-wave bound state: negative parity hyperons I=0 state: Λ(1405) M=1325 MeV (Rho, Riska and Scoccola, 1992) Λ(1116) Σ(1193) Ξ(1318) M(MeV) 1105 1203 1332 (mπ=0, fπ and e are fitted to MN and MΔ.) (Schat, Scoccola and Gobbi, 1995)

Our approach to strange dibaryon Place two rotating solitons Derive the equation of motion for the kaon under the diskyrmions y x z Skyrmion -R/2 R/2 kaon energy and wave function as functions of relative distance of the 2-skyrmions, R

Possible R-dependence of kaon energy EK If EK<mK in the intermediate region or EKmK in the short range, suggest NNK bound states R

Ansatz for chiral field Ansatz for U where U(1) and U(2): Skyrmions centered at z=R/2 and -R/2 UK: kaon field C: relative orientation of the 2-Skyrmions

Relative orientation of the 2-Skyrmions SS interaction strongly depends on the relative orientation, C. (Oka&Hosaka, 1992) Kaon-diskyrmion interaction may be so. We examine 2-cases. C=1 (“HH channel”) Unrotated hedgehogs C=iσ2 (“ATR channel”) One hedgehog is rotated by π around y-axis. For ATR channel, 2-Skyrmion system has the lowest energy configuration.

Derivation of kaon eq. of motion Substitute the ansatz into the Lagrangian and expand up to O(K2) terms Collective coordinate quantization Projection of the 2-skyrmions onto IJ=10 state

How to solve the eq. of motion First, solve the eq. of motion for R=0 Starting from the configuration for R=0, gradually increase R. ΔR 2ΔR R Numerical relaxation method (Veerbarschot, 1987)

Eq. of motion for K- (R=0) Eq. of motion The last term comes from Wess-Zumino-Witten term and play a role of potential. For small r, Lowest state: l=0 (cf. lowest state is l=1 for B=1)

Results of kaon energy (R=0) B=1 (Callan&Krevanof) B=2 (HH-channel) (ATR-channel) L=0 367MeV ≅0 188MeV L=1 153MeV 309MeV unbound (2-Skyrmions are projected onto IJ=10 state.)

Summary We have applied the bound kaon soliton model to study the strange dibaryon. The equation of motion for K- coupled with diskyrmions was derived. The interaction of K- with SS seems to strongly depend on the relative orientation of SS. When the 2-skyrmions overlap, the s-wave kaon is bound much deeper than that for baryon#=1.