Once-subtracted dispersion relations, current algebra, and k-l-3 form-factors
19684 pages
Published in:
- Phys.Rev. 174 (1968) 2033-2036
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Abstract: (APS)
Kl3 decay is treated using once-subtracted dispersion relations, current algebra, and partial conservation of axial-vector current. The dispersion integrals are evaluated by saturating them with the vector K* and and scalar κ intermediate states. The subtraction point is chosen so that the subtraction constants may correspond to the soft-pion result. It is shown that if f+(t) obeys once-subtracted dispersion relations and f−(t) an unsubtracted one (scheme I), and if fKfπ≃1.16−1.28, then f+(0) cannot be close to 1 unless a κ meson exists. In this case it is also shown that both λ+ and λ− are small, while ξ=f−(0)f+(0) is small and negative. We also consider the possibility of having once-subtracted dispersion relations for both f+(t) and f−(t) (scheme II). It is found that the results of schemes I and II are the same if either (a) there exists a κ meson with mass around 1 BeV and f+(0)≃1, or (b) no κ meson exists, but f+(0)≃fKfπ. If, on the other hand, no κ meson exists, and if f+(0)≃1, while fKfπ≃1.28, then one is able to get λ− an order of magnitude bigger than λ+ in scheme II. Thus there is a possibility for large λ− only in scheme II. Furthermore, in scheme I, using partial conservation of vector current for the strangeness-changing vector current, we obtain (fKfπ)f+−1(0)≃mκ2(mκ2−mK2). For (fKfπ)f+−1(0)≃1.28, we predict mκ≃1.06 BeV.- weak interaction: cabibbo angle
- cabibbo angle: weak interaction
- dispersion relation
- current algebra
- kaon: leptonic decay
- leptonic decay: kaon
- kaon: form factor
- form factor: kaon
- PCAC model
- model: pole dominance
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