On theφ→K0K¯0γdecay

Abstract

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)

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