LU TP 98-26, hep-ph/9811472
November 1998
The $\Delta I=1/2$ Rule in the Chiral Limit
Johan Bijnens, Joaquim Prades
Abstract:
We discuss the matching between long-distance and short-distance at
next-to-leading in $1/N_c$ and show how the scheme-dependence from the
two-loop renormalization group running can be treated. We then use this
method to study the three $O(p^2)$ terms contributing to non-leptonic kaon
decays, namely the usual octet and 27-plet derivative terms as well as the
weak mass term using the Extended Nambu--Jona-Lasinio model as the low energy
approximation. We also discuss subtleties in the momentum routing in the
low energy theory and a problem in separating factorizable and non-factorizable
contributions from the $Q_6$ operator in the chiral limit. We update our
earlier results on the $B_K$ parameter as well.
published in JHEP 01(1999)023