Impact of the $a_1(1260) \pi$ cascade contribution on $D^0 \to \pi^+ \pi^- \ell^+ \ell^-$ decays

TL;DR

This paper analyzes the rare decay $D^0 o \pi^+\pi^-\ell^+\ell^-$ within the Standard Model, highlighting the significant impact of the cascade topology involving the $a_1(1260)$ resonance on decay rates and distributions, aligning predictions with experimental data.

Contribution

It introduces the first detailed consideration of the cascade topology involving $a_1(1260)$ in $D^0$ decays, improving theoretical predictions and agreement with experimental measurements.

Findings

Cascade topology significantly affects decay rates and distributions.

Standard Model predictions now align with LHCb data.

Hadronic parameters are consistent across different decay analyses.

Abstract

We revisit the Standard Model description of the recently measured rare decays $D^0\to\pi^+\pi^-\ell^+\ell^-$. Because of the effectiveness of the Glashow-Iliopoulos-Maiani mechanism in charm flavour-changing neutral currents, those decays are driven by non-local insertions of four-quark operators. Following previous work, we consider the mediation of resonances both for the dipion and dilepton pairs. For the first time, we incorporate the effect of the cascade-type topology $D^0\to \pi^- a_1^+(1260)(\to\pi^+\rho^0(\to\ell^+\ell^-))$, which manifests distinctly in the invariant-mass and angular distributions. We find that this partial amplitude comprises one of the largest contributions to the decay rate and obtain an unprecedented agreement of the Standard Model prediction with the available LHCb data. Finally, we compare to the available CLEO-c, LHCb, and BESIII amplitude analyses for the analogous four-body hadronic decays and find that similar values of the hadronic parameters of our model successfully describe the two classes of decays.