The decays K→ππν ν ¯ ¯ ¯ within the standard model
Abstract
We study the reactions
K→ππν
ν
¯
¯
¯
within the minimal standard model. We use isospin symmetry to relate the matrix elements to the form factors measured in
K
ℓ4
. We argue that these modes are short distance dominated and can be used for precise determinations of the CKM parameters
ρ
and
η
. Depending on the value of the CKM angles we find branching ratios in the following ranges:
B(
K
L
→
π
+
π
−
ν
ν
¯
¯
¯
)=[2−5]×
10
−13
;
B(
K
L
→
π
0
π
0
ν
ν
¯
¯
¯
)=[1−3]×
10
−13
;
B(
K
+
→
π
+
π
0
ν
ν
¯
¯
¯
)=[1−2]×
10
−14
. We also discuss a possible
CP
-odd observable.