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

Eleftheria Solomonidi, Luiz Vale Silva

Abstract

We revisit the Standard Model description of the recently measured rare decays $D^0\toπ^+π^-\ell^+\ell^-$. 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 $D^0\to π^- a_1^+(1260)(\toπ^+ρ^0(\to\ell^+\ell^-))$, 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.

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

Abstract

We revisit the Standard Model description of the recently measured rare decays . 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 , 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.

Paper Structure

This paper contains 9 sections, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Special features of cascade contributions
  3. Fitting to LHCb data and predictions
  4. Conclusions
  5. Implementation of the cascade contribution
  6. Further details about the fit to LHCb data
  7. Alternative solution
  8. Comparison to non-leptonic decays
  9. Comparison of $a_1$ parameters to other processes

Figures (3)

  • Figure 1: Cascade topology contributing to charm-meson $D^0$ decay: an intermediate $a_1^+$ decays strongly to $\rho^0 \pi^+$, with subsequent $\rho^0 \to \mu^+ \mu^-$ electromagnetic decay. The pair of filled squares corresponds to the effective four-quark weak interaction.
  • Figure 2: Fit to the differential branching ratio as a function of the invariant mass of the pion pair, compared to LHCb binned data. The best fit curve, together with the main individual contributions, are displayed. The solid blue line represents the full contribution, while solid magenta, red and orange represent the individual $\rho^0/\omega \to \pi^+ \pi^-$, $\sigma \to \pi^+ \pi^-$ and cascade contributions, respectively. Dot-dashed curves represent interference terms with the cascade contribution.
  • Figure 3: Similar to Figure \ref{['fig:p2_distribution']}, where now the invariant mass of the muon pair is considered. The dot-dashed curves represent the (absolute values of the) interference terms of the $\sigma$ with the cascade contributions, while the dashed curve represents the (absolute value of the) interference of the $\rho^0 \rho^0$ and $\rho^0 \phi$ contributions.