Resonances in $D^0\to\pi^+\pi^-\ell^+\ell^-$ and sensitivity to New Physics

TL;DR

This paper investigates the rare decay $D^0 o extpi^+ extpi^- extell^+ extell^-$, focusing on resonance effects and potential signals of New Physics, with improved modeling of the scalar resonance $f_0(500)$ and proposals for new observables.

Contribution

It introduces an improved resonance model including $f_0(500)$ for the decay and proposes new observables to test the Standard Model and probe New Physics effects.

Findings

Resonance effects significantly influence decay observables.

Including $f_0(500)$ improves agreement with experimental data.

Proposed observables can serve as null tests for New Physics.

Abstract

The study of processes involving the weak decays of the charm quark offers unique possibilities to test the Standard Model from the up-type sector and to probe different New Physics scenarios. In here we focus on the rare decays $D^0\to\pi^+\pi^-\ell^+\ell^-$. The effectiveness of the Glashow-Iliopoulos-Maiani mechanism in charm results in a series of observables that serve as null tests of the Standard Model. Simultaneously, the dominant Standard Model contribution to such decays comes from long-distance dynamics. Following previous literature we describe this with the mediation of resonances. Motivated by recent experimental results on analogous semileptonic decays we investigate the effect of the $S$-wave of the pion pair by considering the scalar resonance $f_0(500)$. The experimental mass distributions and angular observables are described well with our model and there is a significant improvement on the agreement when accounting for $f_0(500)$, which amounts to around 20\% of the total branching ratio. Furthermore, we propose and estimate the size of a series of additional observables to be measured, which can help probe the $S$-wave and act as complementary null tests of the Standard Model.