Anatomy of the amplitudes for the rare CP-conserving $K^\pm\to\pi^\pm\ell^+\ell^-$ and $K_S\to\pi^0\ell^+\ell^-$ decays

by Marc Knecht (CPT, Marseille, France)

Monday 19 Nov 2018, 16:00 → 17:30 Europe/Rome

Aula Rasetti (Dip. di Fisica - Edifcio G. Marconi)

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.