Progress of Theoretical Physics, Vol. 46, No. 5, November 1971 Nonleptonic Kaon Decays, Current Algebra and Generalized Veneziano Model Akio HOSOYA and Naoki TOKUDA Department of Physics, University of Tokyo, Tokyo (Received May 17, 1971) 1491 Nonleptonic kaon decays are investigated in a generalized Veneziano model. Decay am- plitudes, which are constructed under the conditions that they should contain no exotic res- onance and satisfy current-algebra relations, obey the I.Jll =1/2 rule automatically. Numerical results agree with experiment. § 1. Introduction Current algebraic approaches to nonleptonic kaon decays have been success- fully attained. Callan and Treiman first derived the so-called Callan-Treiman relations between and decay amplitudes by postulating commuta- tion relations between the axial-vector currents and the nonleptonic weak Hamil- tonian and using the partially conserved axial-vector current (PCAC) hypothesis. 1 ) Several authours examined the validity of these relations and argued the decay processes along these lines. 2 )-i) Hara and Nambu obtained further information by assuming that the K decay amplitudes are quadratic functions of meson four momenta. 5 ) On the other hand since the proposal of a Veneziano model it has been widely recognized that the dual property of the scattering amplitudes is important in describing the expected Regge behavior at high energy and poles corresponding to the observed resonances simultaneously. 6 ) It is found that the results at low energies are compatible with those from current algebra. 7 ),S) The principle of duality may be useful for the weak as well as for the strong processes of ele- mentary particles. Some attempts have been successfully made for semileptonic kaon decays. 9 )-l 2 ) Satisfactory results are not yet achieved for nonleptonic kaon decays, however. 13 )' 14 ) In this article we investigate nonleptonic kaon decays in a generalized Vene- ziano model_1 5 )-l 7 ) By introducing a spurion which is responsible for transitions due to the strangeness-changing weak nonleptonic interaction we express the K-----72n and K-----73n decay amplitudes in terms of the four- and five-point Vene- ziano functions, respectively. These dual amplitudes are constructed under the prescriptions that they should contain no exotic resonance, satisfy current-algebra relations and be expressed in terms of a finite number of beta functions. The last statement is not a physical but a mathematical postulate. The amplitudes Downloaded from https://academic.oup.com/ptp/article-abstract/46/5/1491/1862749 by guest on 06 June 2020