Kπ phase shifts from K ℓ3 decay

Abstract

We discuss the S-and P-wave Kπ phase shifts which are connected to the K ℓ3 form factors by the dispersion relation approach. Also the K ∗ (890) resonance dominates the Kπ P-wave. We find that plausible phase shifts can be obtained only when | ξ o| < 0.5 and β ≈ 10 −2 (where ξ o and β are defined by f −( s)/ tf +( s) = ξ( s) = ξ o + βs/ m π 2). An S-wave Kπ interaction would be quite unusual if ξ( s) is negative and large (say ξ < −0.5). Existence of the K-meson seems to be improbable if ξ < −0.3. The case of the zeros of the form factors is also discused.