Prog. Theor. Phys. Vol. 38 No. 1 (1967) pp. 190-201
Mixing Effect between Particles and Resonances
Department of Physics, Nagoya University, Nagoya
*Research Institute for Fundamental Physics, Kyoto University, Kyoto
(Received February 23, 1967)
The system of pion, nucleon, and (3-3) particle acting mutually through the Yukawa interaction is investigated by means of the static meson theory. It is assumed that these particles (including the (3-3) particle) can be treated as elementary ones although they are equally constructed from urbaryons. An integral equation for the scattering amplitude is solved in some reasonable approximation. Since the Yukawa interaction is strong enough to produce resonances between pion and nucleon, one may expect that two resonances (or bound states) exist in the (3-3) state of pion-nucleon scattering. In fact, the solution with two resonances is obtained in case the mixing energy is small. It is shown, however, that one of them disappears when the mixing energy increases.
DOI : 10.1143/PTP.38.190
F. Gürsey and L. A. Radicati, Phys. Rev. Lett. 13 (1964), 173[APS].
B. Sakita, Phys. Rev. 136 (1964), B1756[APS].
- Y. Ohnuki and A. Toyoda, Nuovo Cim. 36 (1965), 1405.
G. F. Chew, Phys. Rev. 94 (1954), 1748[APS];
ibid. 94 (1954), 1755[APS].
The numerical result is given in the articles, G. F. Chew, Phys. Rev. 95 (1954), 285[APS].
F. F. Salzman and J. N. Snyder, Phys. Rev. 95 (1954), 286[APS]. See also reference 6).
G. F. Chew and F. E. Low, Phys. Rev. 101 (1956), 213[APS].
The numerical solutions of the Chew-Low equation are discussed by G. Salzman and F. Salzman, Phys. Rev. 108 (1957), 1619[APS].
There are many works, for example, S. C. Frautschi and J. D. Walecka, Phys. Rev. 120 (1960), 1486[APS].
Extension to the SU(3) symmetric system was made by A. W. Martin and K. C. Wali, Phys. Rev. 130 (1963), 2455[APS].
See also G. F. Chew, M. L. Goldberger, F. E. Low and Y. Nambu, Phys. Rev. 106 (1957), 1337[APS].
J. L. Gammel, Phys. Rev. 95 (1954), 209[APS].
Citing Article(s) :
Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1347-1360
A Model of the Nucleon and the P11 Resonance as a Bound State of a Hidden Channel
Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1402-1404
On the πN Phase Shift in the P33 State
Kisei Kinoshita and Nobuyuki Murai
Progress of Theoretical Physics Vol. 42 No. 2 (1969) pp. 317-331
The F/D Ratios and Odd-Parity Baryon Resonances
Kunio Shiga and Masayuki Kaiba