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Prog. Theor. Phys. Vol. 38 No. 1 (1967) pp. 190-201

Mixing Effect between Particles and Resonances

Toshihide Maskawa, Hiroki Kondo and Ziro Maki^*

Department of Physics, Nagoya University, Nagoya
^*Research Institute for Fundamental Physics, Kyoto University, Kyoto

(Received February 23, 1967)

Abstract:

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.

URL : http://ptp.ipap.jp/link?PTP/38/190/
DOI : 10.1143/PTP.38.190

[ Full Text PDF : FREE ACCESS (677K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. F. Gürsey and L. A. Radicati, Phys. Rev. Lett. 13 (1964), 173[APS].
   B. Sakita, Phys. Rev. 136 (1964), B1756[APS].
2. Y. Ohnuki and A. Toyoda, Nuovo Cim. 36 (1965), 1405.
3. 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).
4. 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].
5. 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].
6. J. L. Gammel, Phys. Rev. 95 (1954), 209[APS].

Citing Article(s) :

1. 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

   Masayuki Uehara

2. 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

3. 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

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