M ar 2 00 6 An improved study to the s wave πK elastic scatterings and the kappa resonance

An improved study to the s wave πK elastic scatterings and the kappa resonance Abstract We point out that the dispersion relation for the left hand cut integral presented in one of our previous paper (Nucl. Phys. A733(2004)235) is actually free of subtraction constant, even for unequal mass elastic scatterings. A new fit to the LASS data is performed and we find a κ pole with M κ = 694 ± 53M eV , Γ κ = 606 ± 59M eV. The correct use of analyticity also put strong constraints on threshold parameters – which are found to be in good agreement with those obtained from chiral theories. We also studied the K * 0 (1430) and K * 0 (1950) resonances and pointed out that the LASS data do not require them to have the twin pole structure of a typical Breit–Wigner resonance. The debate on whether there exists a κ meson in the I,J=1/2,0 channel πK scatterings has a rather long history. [1, 2] In a previous paper [3] we studied the problem on the existence of the κ resonance and have concluded, based on the LASS phase shift data on πK scatterings, [4] that the κ resonance should exist if the scattering lengths are close to those predicted by χPT. [5] The conclusion is obtained using a new parametrization form for the elastic scattering amplitude respecting unitarity and analyticity. [3] It should be emphasized that one only needs to assume the validity of Mandelstam representation in order to establish the parametrization form (herewith called the PKU parametrization form). One of the most remarkable advantages of the parametrization form is that it keeps track of the contribution from the left hand cut which is of great help in stablizing the fit κ pole location, [6] and meanwhile, the pole location is not sensitive to the details of the input left hand cut (in Ref. [3] χPT estimates on the left hand cut was used) and hence the theoretical uncertainties are severely suppressed.