We reexamine the theoretical estimates of the decay $K\to \pi H$ and the experimental constraints on the existence of a light Higgs boson from this process. We find that (i) pole diagrams generated from the Higgs-boson-gluon coupling via a loop of heavy quarks do contribute to $K\to \pi H$, (ii) there is an additional contribution to the $K\to \pi H$ amplitude coming from the effective $\mathrm{KHW}$ and $\pi \mathrm{HW}$ couplings, (iii) even if $B$, the unknown parameter in the chiral-Lagrangian description of $K-\pi H$ transitions, is nonzero and even if the real part of the $K\to \pi H$ amplitude is canceled accidentally, the imaginary contribution alone suffices to rule out a Higgs boson lighter than $2m_{\pi }$, and (iv) whether Higgs bosons in the mass range $2m_{\pi }<m_H<350\mathrm{}$ MeV are excluded by the imaginary part of the $K\to \pi H$ amplitude depends on the branching ratio or $H\to {\mu }^{+}{\mu }^{-}$ and the top-quark mass. Decay modes $K_L\to {\pi }^{+}{\pi }^{-}H$ and $K^{+}\to l^{+}\nu H$ are briefly discussed.

• Received 11 May 1989

DOI:https://doi.org/10.1103/PhysRevD.40.2980