W e determine the mass width o f the meson by applying the S-matrix formalism t o the reaction e+ei n+n-in the timelike region. W e obtain M p = (757.5 f 1.5) MeV and rp = (142.5 * 3.5) MeV, which are significantly smaller than the values quoted by the Particle Data Group. These values are almost independent o f the specific form used t o model the background. PACS number(s): 14.40.Cs, 11.55.Bq. 13.40.Gp, 13.65.-ti

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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)

Using the pole approach we determine the mass and width of the f 0 (980), in particular we analyze the possibility that two nearby poles are associated to it. We restrict our analysis to a neighborhood of the resonance, using ππ data for the phase shift and inelasticity, and the invariant mass spectrum of the J/ψ → φππ, φKK decays. The formalism we use is based on unitarity and a generalized version of the Breit-Wigner parameterization. We find that a single pole describes the f 0 (980), the precise position depending upon the ππ data used (see Eq. (19) of the main text). As a byproduct, values for the g f 0 ππ and g f 0 KK coupling constants are obtained.

We determine the mass and width of the ∆ ++ (∆ 0 ) resonance from data on π + p (π − p) scattering both, in the pole of the S-matrix and conventionalBreit-Wigner approaches to the scattering amplitude. We provide a simple formula that relates the two definitions for the parameters of the ∆. Isospin