content_image/371407.jpg content_image/371406.jpg content_image/371405.jpg content_image/371403.jpg content_image/371404.jpg content_image/371402.jpg content_image/371401.jpg
φ$_{ϵ}$ < π/ 4 results in a suppression effect in ϵ$_{k}$ relative to the approximate formula with ζ = 0 and φ$_{ϵ}$ = π/ 4. In order to include these corrections we have used the parametrization 

<img src='content_image/371407.jpg'>

where ¯ κ$_{ϵ}$ = 0 . 94 ± 0 . 02 and consequently κ$_{ϵ}$ = 0 . 92 ± 0 . 02, ¯ κ$_{ϵ}$ parameterizing the effect of ζ ̸ = 0 [61]. 

After some calculations it can be shown that [56] 

where λ$_{i}$ = λ ∗ $_{is}$λ$_{id}$ and x$_{q}$ = ( m 2 $_{q}$/M 2 $_{W}$) for all quarks q . 

Inserting (35) and (34) in (31) one finds 

where f$_{K}$ = 160 MeV. The value for B$_{K}$ has been taken from Ref. [62], in a recent analysis [63, 64] the error has been reduced to < ∼ 4%, however, in our analysis we use the more conservative value mentioned in Table. III from [62]. 

The effective Hamiltonian for K + → π $^{+}$ν ¯ ν can be written as 

First term is the contribution from the charm sector. The function X ( x ) is relevant for the top part, 

<img src='content_image/371406.jpg'>

<img src='content_image/371405.jpg'>

<img src='content_image/371403.jpg'>

<img src='content_image/371404.jpg'>

<img src='content_image/371402.jpg'>

where x$_{q}$ = ( m 2 $_{q}$/M 2 $_{W}$) for all quarks q . Here X$_{0}$ ( x ) is the leading contribution given by 

<img src='content_image/371401.jpg'>

