Recent developments in rare kaon decays

We discuss issues in rare and radiative kaon decays. The interest is to extract useful short-distance information and uncover underlying dynamics. We emphasize channels where either we can understand non-perturbative aspects of QCD or there is a chance to test the Standard Model.Comment: Invited minireview for Modern Physics Letters A (MPLA), 15 pages, 9 figures, usepackages epsf,colo

Theory of rare kaon decays

We review some recent theoretical results on rare kaon decays. Particular attention is devoted to find Standard Model tests. This is theoretically easy in $K\to \pi \nu \bar{\nu}$, while a careful study of the long distance contributions is needed for $K_{L}\to \pi ^{0}e$, $K_{L}\to \mu \bar{\mu}$ and $K\to \pi \pi \gamma$Comment: 11 pages Latex file, no figures;Invited plenary talk at the 3rd International Conference on B Physics and CP Violation (BCONF99), Taipei, Taiwan, 3-7 Dec 199

Explaining h→μ±τ∓h\to\mu^\pm\tau^\mp, B→K∗μ+μ−B\to K^* \mu^+\mu^- and B→Kμ+μ−/B→Ke+e−B\to K \mu^+\mu^-/B\to K e^+e^- in a two-Higgs-doublet model with gauged Lμ−LτL_\mu-L_\tau

The LHC observed so far three deviations from the Standard Model (SM) predictions in flavour observables: LHCb reported anomalies in $B\to K^* \mu^+\mu^-$ and $R(K)=B\to K \mu^+\mu^-/B\to K e^+e^-$ while CMS found an excess in $h\to\mu\tau$. We show, for the first time, how these deviations from the SM can be explained within a single well-motivated model: a two-Higgs-doublet model with gauged $L_\mu-L_\tau$ symmetry. We find that, despite the constraints from $\tau\to\mu\mu\mu$ and $B_s$--$\overline{B}_s$ mixing, one can explain $h \to\mu\tau$, $B\to K^* \mu^+\mu^-$ and $R(K)$ simultaneously, obtaining interesting correlations among the observables.Comment: 6 pages, 2 figures, corrected formula for LFV tau decay with new HFAG limit. References added, accepted for publication in PR

On the amplitudes for the CP-conserving K±(KS)→π±(π0)ℓ+ℓ−K^\pm(K_S)\to\pi^\pm(\pi^0)\ell^+\ell^- rare decay modes

The amplitudes for the rare decay modes $K^\pm\to\pi^\pm\ell^+\ell^-$ and $K_S\to\pi^0\ell^+\ell^-$ are studied with the aim of obtaining predictions for them, such as to enable the possibility to search for violations of lepton-flavour universality in the kaon sector. The issue is first addressed from the perspective of the low-energy expansion, and a two-loop representation of the corresponding form factors is constructed, leaving as unknown quantities their values and slopes at vanishing momentum transfer. In a second step a phenomenological determination of the latter is proposed. It consists of the contribution of the resonant two-pion state in the $P$ wave, and of the leading short-distance contribution determined by the operator-product expansion. The interpolation between the two energy regimes is described by an infinite tower of zero-width resonances matching the QCD short-distance behaviour. Finally, perspectives for future improvements in the theoretical understanding of these amplitudes are discussed.Comment: 49 pages, 11 figures, matches the published versio