On the amplitudes for the CP-conserving K ± ( K S ) → π ± ( π 0 ) ℓ + ℓ − rare decay modes

D’Ambrosio, Giancarlo ( INFN — Sezione di Napoli, Via Cintia, I-80126, Napoli, Italy) ; Greynat, David (Grenoble, France) ; Knecht, Marc (Centre de Physique Théorique, CNRS/Aix-Marseille Univ./Univ. du Sud Toulon-Var (UMR 7332), CNRS-Luminy Case 907, F-13288, Marseille Cedex 9, France)

10 February 2019

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.

Published in: JHEP 1902 (2019) 049
Published by: Springer/SISSA
DOI: 10.1007/JHEP02(2019)049
arXiv: 1812.00735
License: CC-BY-4.0

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