LU TP 98-02, hep-ph/9801326
January 1998
Obtaining K --> PI PI from off-shell K --> PI Amplitudes
Johan Bijnens, Elisabetta Pallante, Joaquim Prades
Abstract:
We properly define off-shell $K\to\pi$ transition amplitudes and use them
to extract information for on-shell $K\to\pi\pi$ amplitudes within Chiral
Perturbation Theory. At order $p^2$ in the chiral expansion all three
parameters of weak interaction can be determined. At order $p^4$ we are able
to fix eleven additional constants out of thirteen contributing to off-shell
$K\to\pi$ transitions, which leaves four undetermined constants in the
on-shell $K\to\pi\pi$ amplitudes. All ${\cal O}(p^4)$ contributions have been
exactly derived with $m_\pi^2\ne 0$. We finally discuss the weak mass term
issue and find contributions to on-shell $\Delta S=\pm 1$ Kaon decays, in
particular to transitions like $K_L \to \gamma \gamma$, $K_L \to \mu^+\mu^-$
and $K_S \to \pi^0 \gamma \gamma$ at the lowest non-zero order.
to appear in Nuclear Physics B.