p-Wave Interactions inτDecay

Abstract

We have calculated the effect of final-state $s$- and $p$-wave interactions on the spectra in $K\to 3\pi$ decay using the Faddeev formalism derived in an earlier paper. In our model, $p$ waves are not produced directly by the weak interaction but only by the recoupling of pion pairs in the multiple scattering series. For large $s$-wave scattering lengths ($\sim 1.0{m_{\pi }}^{-1\mathrm{}}$), the $p$ state has very little influence on the spectrum, and a fit to the experimental spectra requires ${a_2}^2>{a_0}^2$. However, for small $s$-wave scattering lengths ($\sim 0.2{m_{\pi }}^{-1\mathrm{}}$) the $p$ wave can become dominant, and fits to the data can be achieved with ${a_2}^2<{a_0}^2$. These $p$-wave-dominant solutions are cutoff-sensitive, so that there is no unique fit. The final-state interaction phase is also calculated.