Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-11-25
JHEP 9901 (1999) 023
Physics
High Energy Physics
High Energy Physics - Phenomenology
33 pages, 6 figures, uses JHEP.cls, minor changes in presentation, misprints and numerical error corrected, accepted in JHEP
Scientific paper
10.1088/1126-6708/1999/01/023
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.
Bijnens Johan
Prades Joaquim
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