New approach to nonleptonic weak interactions. II. Application to strange- and charm-meson decays

Abstract

The constraints obtained in I for the asymptotic two-body meson matrix elements of the weak nonleptonic Hamiltonian are related to the physical K --tar and D--tKa decay amplitudes by using a soft-pion approximation in the infinite-momentum frame of the parent particle. In this new milder extrapolation, a part of the so-called surface terms survives in addition to the usual equal-timecommutator term and plays a significant role, especially for the D-Kr decays. However, to the approximation in which only the ground-state-meson contribution is kept in the surface terms, the + 1 / A I / = rule for the K-27 decays and the 6@ 6* rule [in exact SU(3) symmetry] for the D-KT decays are shown to hold exactly and the amplitudes predict a reasonable value for the ratio of the rates, r (~; + a +~-) / r (~O t~-p + ) .A semiquantitative scenario is also drawn, which suggests that the L = 1 meson contribution to the surface terms plays an important role for the violation of these selection rules and yields the right order of magnitude for the violation of the I AT 1 = rule in K -2 r decays. For the D-Ea decays it leads to a more significant violation of the 6@ 6* rule.

Charmed Scalar Resonances

“…The masses of the other members areestimated very crudelyas mD 2.22 GeV, mDs 2.42 GeV, mÊ 2.32 GeV, by using the above quarkcounting andtaking mF+ I 2.32 MeVasthe input data. Using the hardp ion techniquew ith the asymptotic SU f (4) symmetry [ 8,9],t aking [12,17] |β 0 | 2 = 1/12 describing the overlap of color and spin wavefunctions in theopen-charmmeson decays and Γ(δ s → ηπ) exp = 50 − 100 MeV [ 3] as the input data, and correcting the SU f (4) symmetrybreaking, we obtain [12,17] asufficiently narrowwidth, To see numerically the narrowwidth, we comparetheF + I → D + s π 0 decay withtheδ s → ηπ, where a 0 (980) has been assigned toδ s ∼ [ns][ns] I=1 .H owever,w es hould be careful when we compared ecays with different energy scales, in particular,t he decays of open-charm scalar mesons with those of the light scalar mesons.…”

“…To check if D 0 can be interpreted as thes calar D * 0 ∼{ cn }meson,w eh eres tudy two-body decays of D * 0 (and itss trange partner D * + s0 )b yu sing ah ardp ion (or kaon) techniquei nt he infinite momentum frame [8,9], which is an innovation of the old current algebra. (For the technical details in this article,s ee references quoted.)…”

Two-body decays of charm mesons and the role of exotic mesons

“…The amplitude for a three-pseudoscalar (PSImeson process, P , ( p )-P2( k) + P 3 ( q ) , can be approximated in the form [2,7,8] which is realized by using the partially-conserved axialvector current (PCAC) hypothesis and an extrapolation q+O in the light-cone frame [(LCF), i.e., p+ m 1. The above approximation can be considered as an innovation of the old soft-pion technique [9].…”

Ds+→π+η and π

“…Here Our crucial starting point is the following approximate the equal-time commutator (ETC) term and the surface term, which is expressed in terms of a sum of asymptotic pole amplitudes, have to be evaluated in the IMF, where the notation is given in Refs. [2] and [3]. The above can be considered as an innovation of the old soft pion technique [4].…”

“…We thus realize that the essential features of nonle~tonic weak decavs must be found in the dynamics which will show up among the asymptotic matrix elements of Hw appearing in Eqs. (2) and ( [3,9,10] is based on more intuitive quark-line arguments. We have also pointed out [8- On the same line as our previous papers mentioned above, we now investigate Cabibbo-angle-favored decays of charm mesons into two-body final states involving 7 or n'.…”