Obtaining K to pi pi from Off-Shell K to pi Amplitudes

Details Obtaining K to pi pi from Off-Shell K to pi Amplitudes Obtaining K to pi pi from Off-Shell K to pi Amplitudes

1998-01-16

arxiv.org/abs/hep-ph/9801326v1

Nucl.Phys. B521 (1998) 305-333

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 31 pages, 4 postscript figures, uses epsf.sty

Scientific paper

10.1016/S0550-3213(98)00202-8

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.

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