Complex K^-n scattering lengths and current algebra

Abstract

We calculate the real and imaginary parts of the s-wave K^- N scattering length in the I=0 channel, starting from the predictions of soft-meson current algebra. The multichannel ND^-1 formalism is used to unitarize the amplitudes obtained from current algebra. We isolate dynamical off-mass-shell corrections in certain residues for one-pole approximations to the numerator functions. These residues, for which we make assumptions of smooth extrapolation, are obtained by comparing the unitarized amplitudes with the results of current algebra. The coupling of the K^- N to the πΣ channel, which has a lower threshold, generates the imaginary part of the scattering length with the correct sign and reverses the (incorrect) sign of the real part. The magnitudes of the real and imaginary parts agree well with the results of recent experiments and are consistent with the existence of the Y₀^∗(1405) virtual bound state below the K^- N threshold.