# On the amplitudes for the CP-conserving K$K^\pm(K_S)\to\pi^\pm(\pi^0)\ell^+\ell^-$ rare decay modes

Abstract : The amplitudes for the rare decay modes K$^{±}$ → π$^{±}$ℓ$^{+}$ℓ$^{−}$ and K$_{S}$ → π$^{0}$ℓ$^{+}$ℓ$^{−}$ 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.
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https://hal.archives-ouvertes.fr/hal-01959945
Contributor : Inspire Hep <>
Submitted on : Wednesday, December 19, 2018 - 9:56:09 AM
Last modification on : Wednesday, April 17, 2019 - 1:20:28 PM

### Citation

Giancarlo d'Ambrosio, David Greynat, Marc Knecht. On the amplitudes for the CP-conserving K$K^\pm(K_S)\to\pi^\pm(\pi^0)\ell^+\ell^-$ rare decay modes. JHEP, 2019, 02, pp.049. ⟨10.1007/JHEP02(2019)049⟩. ⟨hal-01959945⟩

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