$K_L\to {\pi }^0\nu \bar{\nu }$ Beyond the Standard Model

Abstract

We analyze the decay $K_L\to {\pi }^0\nu \bar{\nu }$ in a model independent way. If lepton flavor is conserved the final state is (to a good approximation) purely CP even. In that case this decay mode goes mainly through CP violating interference between mixing and decay. Consequently, a theoretically clean relation between the measured rate and electroweak parameters holds in any given model. Specifically, $\Gamma (K_L\to {\pi }^0\nu \bar{\nu })/\Gamma (K^{+}\to {\pi }^{+}\nu \bar{\nu })={\sin }^2\theta$ (up to known isospin corrections), where $\theta$ is the relative CP violating phase between the $K-\bar{K}$ mixing amplitude and the $s\to d\nu \bar{\nu }$ decay amplitude. The experimental bound on $BR(K^{+}\to {\pi }^{+}\nu \bar{\nu })$ provides a model independent upper bound: $BR(K_L\to {\pi }^0\nu \bar{\nu })<1.1\times 10^{-8}$. In models with lepton flavor violation, the final state is not necessarily a CP eigenstate. Then CP conserving contributions can dominate the decay rate.

Comments: 12 pages, revtex, no figures