The branching ratio of @-KOPoy is reexamined, considering the chain reactions @-+ K + K --fo(ao)+ y-KO+PO+ y.In a recent Letter, ' Nussinov and Truong have calculated the radiative decay $--+ K O + K O + y with K O K O in the S state. They find the branching ratio In this Rapid Communication, we present a critical review of their calculations. We have found analytical errors in Ref. 1. Furthermore, we will comment on the assumptions involved.Following Ref. 1, we use the model consisting of the following chain of decays: and is given by where where K ' are real or virtual. fo(976) is the scalar meson 1 -0 (Ref. 2) with momentum k. We observe that m], < 2mK < m,. The amplitude describing the decay $-K + K ---+ f o ( k ) + y can be written as Here g, and g stand for the $ K + Kand foK + Kcoupling constants, related to the widths by and ~( q ) and q(p) denote y and $ polarizations (momenta), respectively. a and b are defined as Then a -b = 2 p . q / m i + is proportional to the photon energy. I ( a , b ) has been computed in different contexts3 (4x -1 ) ' I 2 arcsin g ( x ) -' (4b) with Notice that Eq. (2) is in disagreement with Eq. (8) in the Erratum in Ref. 1, where Eq. (8) should be corrected as (in the first approximation where m, = m f o = 2 m~ 1. Our Eqs. (2)-(4) give an exact result. We have Using Eq. (2), we get ( 5 ) With m~,-976 MeV (Ref. 2) [i.e., x > i in Eqs. (4a)

It is shown that in the SU(2lL xU(1) model of electroweak interactions dimensional regularization guarantees the vanishing of the one-loop contributions to the neutrino charge for every dimension n and for every value of the gauge-fixing parameter 5 without the need for counterterms and without having to invoke Ward identities.There is no doubt that the charge of the neutrino in the standard electroweak model1 is a gauge-independent and vanishing quantity. To the best of our knowledge, however, it has not been shown how this actually happens at the one-loop level in the general linear R E gauge.2 The authors of Ref. 2 showed that the one-loop contributions to the neutrino charge vanish in the O(3) Georgi-Glashow3 electroweak model (which contains heavy fermions instead of neutral currents) provided one regularizes Feynman integrals in a gauge-invariant way even if the integrals are convergent. The calculations that exist in the literature for the one-loop contributions to the neutrino charge in the Glashow-Weinberg-Salam theory include (1) the work of Bardeen, Gastmans, and ~a u t r u p ,~ who adopt the unitary gauge from the beginning (inside the loop integrals) with the advantage that there are only proper-vertex contributions, (2) the work of Marciano and Sirlin,' who show explicitly using the 't Hooft-Feynman gauge how the y-Z selfenergy contributions cancel those which arise from the proper vertex, (3) the work of Sakakibara,6 who first defines renormalized coupling constants and renormalized self-energies in the 't Hooft-Feynman gauge and then proceeds to show that the proper-vertex contribution to the neutrino charge is cancelled by an appropriate counterterm, and (4) the work of Monyonko and ~e i d ,~ who show that in the nonlinear R, gauge (but not in the linear one) there is aWard identity which guarantees the vanishing of the neutrino charge. These authors also claim that in the linear R e gauge a Ward identity must be used to enforce exact cancellation of the neutrino charge.Here we show that, within the context of the SU(2)L x U(1) model, the one-loop contributions to the neutrino charge in the linear Rc gauge vanish for every value of n in the dimensional-regularization scheme without the need for counterterms and without having to invoke Ward identities.The one-loop contributions to the neutrino electric charge in the standard model can be divided into two classes, depending on whether they arise from (I) proper vertices [ Fig. 1 (a)-1 (f)] or (11) y -Z self-energy diagrams [Fig. 2(a)-2(g)l. In the nonlinear R S gauge the last contributions are absenL7 In the linear R gauge, class-I and class-I1 FIG. 1. Proper-vertex contributions to the neutrino form factor.FIG . 2. y -Z self-energy. c stands for the ghost particle, s for the s denotes the unphysical charged Higgs scalar.unphysical charged Higgs scalar, and f for a generic fermion. 1539-

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A comparison of the linear sigma model (LσM) and Chiral Perturbation Theory (ChPT) predictions for pion and kaon dynamics is presented. Lowest and next-to-leading order terms in the ChPT amplitudes are reproduced if one restricts to scalar resonance exchange. Some low energy constants of the order p 4 ChPT Lagrangian are fixed in terms of scalar meson masses. Present values of these low energy constants are compatible with the LσM dynamics. We conclude that more accurate values would be most useful either to falsify the LσM or to show its capability to shed some light on the controversial scalar physics.