PoS - Proceedings of Science
Volume 449 - The European Physical Society Conference on High Energy Physics (EPS-HEP2023) - T08 Flavour Physics and CP Violation
$S$-wave contribution to rare $D^0 \to \pi^+ \pi^- \ell^+ \ell^-$ decays in the Standard Model and sensitivity to New Physics
L. Vale Silva*, S. Fajfer and E. Solomonidi
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Pre-published on: January 11, 2024
Published on: March 21, 2024
Physics of the up-type flavour offers unique possibilities of testing the Standard Model (SM) compared to the down-type flavour sector. Here, we discuss SM and New Physics (NP) contributions to the rare charm-meson decay $ D^0 \to \pi^+ \pi^- \ell^+ \ell^- $. In particular, we discuss the effect of including the lightest scalar-isoscalar resonance in the SM picture, namely, the $f_0 (500)$, which manifests in a big portion of the allowed phase space. Other than showing in the total branching ratio at an observable level, the $f_0 (500)$ resonance manifests as interference terms with the vector resonances, such as at high invariant mass of the leptonic pair in distinct angular observables. Recent data from LHCb optimize the sensitivity to $P$-wave contributions, that we analyse in view of the inclusion of vector resonances. We propose the measurement of alternative observables which are sensitive to the $S$-wave and are straightforward to implement experimentally. This leads to a new set of null observables, that vanish in the SM due to its gauge and flavour structures. Finally, we study observables that depend on the interference of the $S$-wave with generic NP contributions from semi-leptonic four-fermion operators.
DOI: https://doi.org/10.22323/1.449.0353
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