K L → π 0 ν ν ¯ Beyond the Standard Model
Abstract
We analyze the decay
K
L
→
π
0
ν
ν
¯
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,
Γ(
K
L
→
π
0
ν
ν
¯
)/Γ(
K
+
→
π
+
ν
ν
¯
)=
sin
2
θ
(up to known isospin corrections), where
θ
is the relative CP violating phase between the
K−
K
¯
mixing amplitude and the
s→dν
ν
¯
decay amplitude. The experimental bound on
BR(
K
+
→
π
+
ν
ν
¯
)
provides a model independent upper bound:
BR(
K
L
→
π
0
ν
ν
¯
)<1.1×
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.