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We calculate the different contributions to the decay $K_{L}\to \pi ^{0}\nu\bar{\nu}$ that arise if the neutrinos are massive. In spite of a chiralenhancement factor, we find that these contributions are negligibly small.Compared to the CP violating leading contributions, the CP conservingcontributions related to Dirac masses are suppressed by a factor of order $(m_Km_\nu/m_W^2)^2\lesssim10^{-12}$, and those related to Majorana masses aresuppressed by a factor of order $(\alpha_W m_K m_s^2m_\nu/m_W^4)^2\lesssim10^{-29}$. With lepton flavor mixing we find newcontributions with a single CP violating coupling leading to a final CP evenstate or with two CP violating couplings leading to a final CP odd state. Thesecontributions can be of the order of the Standard Model CP conservingcontributions to the flavor diagonal modes.Comment: 14 pages, LaTeX2e; minor corrections and additions, accepted for  publication in JHE

Implications of neutrino masses on the KL→π0νbar nu decay

Implications of neutrino masses on the K_L→π⁰νbar nu decay