We show that the current-algebra-PCAC (partial conservation of axial-vector current) procedure applied consistently to each final-state pion predicts seven K+2a and K -3 a decay amplitudes that very accurately reproduce the experimental results.PACS numbeds): 13.25. +m, 11.30.Rd, 11.40.Ha
I. INTRODUCI'IONIn this paper (I), we use chiral-symmetry (CS) and partially conserved axial-vector current (PCAC) techniques[I], extended via "PCAC consistency ," to calculate the seven charge modes of K + 2 n , 3 n weak decays. In the following paper (II), we will apply similar PCAC consistency methods to 16 two-and three-body charmedmeson weak decay modes. Previously, we briefly sketched the phenomenological application of these current-algebra-PCAC ideas not only to the kaon sector, but also to the charmed-meson and baryon sector [2], for two-body nonleptonic weak decays. Here we go into considerably more detail concerning PCAC consistency and also extend the analysis of kaon two-body decays to three-body decays.We will use the CS-PCAC reduction in Sec. I1 to relate the K +aa amplitudes to one-body K +a reduced matrix elements, which can be calculated from meson or quark loop graphs. We also include the small effects of final-state interactions in our analysis. In Sec. I11 the analogous CS-PCAC reduction will be employed to connect the K-3a amplitudes to the K + 2 a transitions that were determined in Sec. 11. The result of this study is that the PCAC consistency predictions for the seven K + 2~, 3 a decay amplitudes are consistently in good agreement with the data. We summarize our results in Sec. IV and verify PCAC consistency for K!, in the Appendix.Many of the first attempts at explaining the K +2n, 3 a decays, using PCAC and current-algebra ideas, utilized energy-dependent parametrizations of the amplitudes [3]. By constraining the parameters through PCAC, various ratios of physical observables were predicted. A slightly different approach was used in Ref.[4] to reduce the number of parameters in Ref. [3]. In these studies tadpole graphs were employed to systematically account for the rapid variation of momenta in K + 2 n , 3 a decays. There were still unknown parameters in the latter approach, but these were further reduced by overall momentum conservation [1,5]. Still, these rapidly varying pole schemes for two-body decays are difficult to generalize to three-body decays.In order to avoid such pole complications, in this paper we use PCAC consistency to circumvent the rapidly varying pole terms altogether. We will predict all seven K + 2a, 3 a decay amplitudes, including appropriate A1 =+,+ parts, with no free parameters and without explicit calculation of the pole terms.T o begin, we write the decay amplitude in the form M =Mp +M, where M p is the rapidly varying pole contribution and M is the background term that varies slowly with momentum. The amplitude M is found by letting one of the pions go soft, which results in the amplitude having the on-shell form M =Mcc+Mp-Mp(0) .
( l a )The charge commutator amplitude Mc...