ar X iv : h ep - p h / 96 07 44 5 v 1 2 6 Ju l 1 99 6 JLAB – 96 – 17 July 1996
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چکیده
A calculation of the semi–leptonic decays of the kaon (K l3) is presented. The results are direct predictions of a covariant model of the pion and kaon introduced earlier by Ito, Buck, Gross. The weak form factors for K l3 are predicted with absolutely no parameter adjustments of the model. We obtained for the form factor parameters: f − (q 2 = m 2 l)/f + (q 2 = m 2 l) = −0.28 and λ + = 0.028, both within experimental error bars. Connections of this approach to heavy quark symmetry will also be discussed. A covariant model based on coupled Bethe–Salpeter and Schwinger–Dyson equations with an NJL–like interaction was successfully used earlier to describe electromagnetic properties of pions and kaons. Using this model, we analysed form factors of K l3 decays (describing the processes K → πlν). Assuming that only the vector weak current contributes to the decays, the matrix element may be written as J µ = G F sin θ C √ 2 [f + (t)(P K + P π) µ + f − (t)(P K − P π) µ ], where P K and P π are the four–momenta of the K and π mesons, G F is a Fermi coupling constant, θ C is a Cabibbo angle, and f + and f − are dimensionless form factors which can depend only on t = (P K − P π) 2. For the decay channel, the physical region is limited by the masses of the lepton, pion and kaon: m 2 l ≤ t ≤ (m K − m π) 2. In our model, the pion and the kaon both share the same light quark mass of 250 MeV. It is this mass, together with the corresponding mesonic vertex functions (wave functions) employed in the calculation of the elastic and transition form factors of the pion and kaon that is now employed in the
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تاریخ انتشار 1996