Analysis of K− absorption in deuterium

Abstract

We have examined theoretically the capture of K− at rest by deuterium, principally in terms of final state YN interactions. In particular we calculated total rates, the momentum spectra associated with the production of Σ−+n+π+ and Λ0+p+π−, and the corresponding angular correlation. (The latter are not found to be useful except perhaps as a check). On the basis of total rates it is known that capture from theP Bohr orbit through thes wave KN channel probably dominates. This assignment is reinforced by the spectrum of the low momentum Λ peak (Λ’s converted from Σ’s). A definitive check can be made when a somewhat better converted Λ spectrum is measured, since one should observe a double peak (with a cusp at the maximum pion momentum associated with production) if this assignment is correct. Analysis of the high pion momentum Λ peak (directly produced Λ’s), using this assignment reveals that the spectrum is insensitive to the YN interaction and yet does not seem to agree with the data. This spectrum shape (and that for Σ−nπ+) depends significantly on the KN → Yπ absorption process off the energy shell, which in turn depends on the KN scattering lengths. Preliminary comparison of data and theory indicates a large negative real part for the isotopic spin one KN scattering length. Finally, from the relative rate for conversion of Σ’s into Λ’s, we deduce a minimum value for the imaginary part of the isotopic spin 1/2p wave σN scattering length. The result, larger than the pion Compton wavelength, indicates a very strong potential in the ΣN channel and/or coupling ΣN and ΛN channels, a potential much stronger than indicated by the universal pion baryon interaction. Capture from theS Bohr orbit is also extensively discussed. In this case, the spectra associated with Σ− and direct Λ production are sensitive to the final YN interaceion.