New opportunities for rare charm from $Z\to c\bar{c}$ decays

TL;DR

This work investigates rare charm decays at a high-luminosity $Z$-pole collider (e.g., FCC-${}\text{ee}$ or CEPC) as probes of New Physics, focusing on $c\to u\nu\bar{\nu}$ and $c\to u\ell^+\ell^-$ transitions. It develops an EFT-based framework (SMEFT/WET) that links dineutrino and dilepton modes, derives the decay distributions for $D^0\to\pi^+\pi^-\nu\bar{\nu}$ using HH$\chi$PT form factors and a data-driven approach, and analyzes polarization-induced null tests in $\Lambda_c^+\to p\ell^+\ell^-$. The study highlights correlations between the two channels within SMEFT, provides upper limits on NP contributions, and demonstrates experimental sensitivity with the IDEA detector, projecting dineutrino reach down to $\mathcal{B}(D^0\to\pi^+\pi^-\nu\bar{\nu})\sim \text{a few}\times 10^{-7}$ and percent-level angular asymmetries in polarized $\Lambda_c^+$ decays. These results indicate that a Tera-Z program would significantly enhance NP searches in the up-type sector, complementing LHC flavor programs and enabling lepton-flavor structure discrimination. The analysis leverages resonance-rich and missing-energy final states, offering robust null tests and concrete SMEFT correlations across modes.

Abstract

We analyze the potential of rare charm decays as probes of new physics at a high-luminosity flavor facility operating at the $Z$ pole, such as the FCC-ee or CEPC. In particular, we identify clean null-test observables in $D^0 \to π^+ π^- ν\barν$ and in polarized $Λ_c^+ \to p \ell^+ \ell^-$ decays with $\ell=e, μ$. Complementarity with the LHC and HL-LHC flavor programs arises from the characteristic features of a Tera-$Z$ environment: the capability to study missing-energy modes and charm production with significant polarization. We improve the theoretical description of $D^0 \to π^+ π^- ν\barν$ decays and work out the phenomenology of polarization-induced null-test observables in $Λ_c^+ \to p \ell^+ \ell^-$ decays. In regions of dilepton mass near the $φ$ resonance, polarization asymmetries can reach $O(5 \%)$ for muons and $O(14 \%)$ for electrons times the $Λ_c^+$ polarization. We also point out synergies between the dineutrino and the dilepton modes using the SMEFT framework of heavy new physics. Using the IDEA detector concept at FCC-ee, we find in simulation studies that dineutrino branching fractions as low as $\sim 2 \times 10^{-7}$ can be probed, which reaches well into the parameter space of new physics, and also allows for discrimination of lepton flavor structures. Furthermore, the measurement of asymmetries in $Λ_c^+ \to p μ^+ μ^-$ at $O(1 \%)$ will be possible. Similar sensitivities are expected for dielectron final states, although robust predictions will require further dedicated studies.

Figures (8)

• Figure 1: Differential branching fraction of $D^0\to\pi^+\pi^-\nu\overline{\nu}$ decays for BSM benchmark $x_U^+=x_U^-=392$ (\ref{['eq:XU']}) against $q^2$ (right panel) and $p^2$ (left panel) for different hadronic models, HH$\chi$PT (red), HH$\chi$PT$_\text{res}$ (yellow) and data driven (green). For the HH$\chi$PT-based models the bands illustrate $50\%$ uncertainty in the branching fractions, while for the data driven one they give the $1 \sigma$ uncertainties resulting from the fit, which are below 10%.
• Figure 2: Breakdown of transversity contributions to the differential branching fraction of $D^0\to\pi^+\pi^-\nu\overline{\nu}$ decays as in Fig. \ref{['fig:dBR_dx2_dineutrino']} for central values showing the total, i.e., the sum (solid), longitudinal (dashed), parallel (dotted) and perpendicular (dash dotted) contributions.
• Figure 3: Correlation between $\mathcal{B}(D^0\to \pi^+\pi^-\nu\overline{\nu})$ and the angular observable $\langle A^e_{K_{24}}\rangle_{\text{low }\phi} \:/\: P_{焃_c}$ in $焃^+_c \to p e^+ e^-$ decays for fixed strong phases $(\delta_\rho = 0.0,\,\delta_{\omega-\rho}=6.0,\,\delta_{\phi-\rho}=5.7)$ and real Wilson coefficients within allowed constraints. We use non-zero $\mathcal{K}_R^U$ and $\mathcal{C}_R^U$ to highlight correlations via Eq. \ref{['eq:WET_correlations']}. The correlation is one-to-one for electron-specific (solid orange), LU (blue) and democratic (green) flavor scenarios, and gives a band for cLFC and general flavor structure with upper limits in dotted and dashed, respectively. The lower limit is the one of the electron-specific scenario. An electro-phob scenario is shown in red (horizontal line), and one which couples only to RH leptons in black (vertical line) to illustrate complementarity in NP reach.
• Figure 4: $\mathcal{B}(D^0\to \pi^+\pi^-\nu\overline{\nu})$ against $\langle A^\mu_{K_{24}}\rangle_{\text{low }\phi} \:/\: P_{焃_c}$ in $焃_c^+ \to p \mu^+ \mu^-$ decays, see Fig. \ref{['fig:correlations_A_K24ee_low_phi']}. Here the angular observable is maximized by the strong phases $\delta_\rho=5.6$, $\delta_{\omega-\rho}=2.5$ and $\delta_{\phi-\rho}=6.3$.
• Figure 5: Assumed separation power (in units of Gaussian standard deviations) between (left) pions and kaons and (right) kaons and protons using time-of-flight ($t_{\rm TOF}$), drift-chamber cluster-counting ($dN/dx$), and energy-loss ($dE/dx$) measurements within the IDEA detector concept.