Abstract
Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented.
Highlights
JHEP10(2016)039 ref. [5] for possible motivation, searches for hidden photons, K+ → μ + ν + A, see e.g. ref. [6] for recent results and ref. [7] for possible motivation
Decays K+ → μ+νμννand K+ → e+νeννare examined to the leading order in momenta in the framework of Chiral Perturbation Theory
Though the contribution of Kμ3ν is beyond the immediate registration, in many model of new physics we have no definite predictions for the signal strength
Summary
We are using the standard ChPT [1], which properly describes the dynamics of the octet of light pseudoscalar mesons forming the unitary matrix. Lμ and rμ are introduced as follows: rμ = vμ + aμ and lμ = vμ − aμ, where vμ, aμ are sums of the weak and the electromagnetic fields, interacting with vector and axial quark currents in SM. These interactions for the relevant set of three light quarks, q ≡ (u, d, s)T , which masses enter χ in (2.3), reads. In case of decay K+ → e+νeνμνμ diagram 6 has resonance divergence associated with muon producing on-shell We are dealing it by cutting out the phase space region, corresponding to |(p0 − p1)2 − m2μ| < (30 MeV)
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