Probing invisible particles with charm

TL;DR

The paper develops a unified EFT and light-new-physics framework to study charm-hadron decays to invisible final states, covering dineutrinos, ALPs, and a light Z'. By combining SMEFT, νSMEFT, and WET with explicit operator bases and matching relations, it translates high-scale NP into charm observables and recasts existing experimental bounds to derive constraints on Wilson coefficients and model parameters. It shows that branching ratios can reach up to $10^{-3}$ for certain Z' scenarios and $10^{-4}$ for ALPs, with chirality-preserving operators being more constrained (down to a few $\times 10^{-5}$) by charged-lepton processes, while LNV and light-neutrino scenarios offer distinct, testable signatures across multiple charm modes. The work emphasizes missing-energy distributions and inter-mode correlations as discriminants between models, demonstrates the utility of data recasts to tighten ALP bounds, and outlines promising experimental paths at BESIII, Belle II, STCF, and future $Z$-factories to probe TeV-scale NP in the up-quark sector. It provides predictions and correlations that can guide searches and highlights the importance of improved hadronic form factors for sharpening null tests in charm invisibles.

Abstract

We point out opportunities to probe invisible particles, left- and right-handed neutrinos, axion-like particles (ALPs) and dark photons $(Z^\prime)$ with rare decays of charm hadrons. We employ and recast existing searches in $D \to (π, ω) X$, $D^ 0 \to X$ and $Λ_c \to p X$, where $X$ denotes one of the above invisible final states including dineutrinos. The branching ratios are clean null tests of the standard model, yet, are essentially unconstrained for some parameters of light new physics, limited only by weak lifetime constraints at the level of $\mathcal{O}(10^{-1})$. On the other hand, if models are probed, branching ratios still reach up to $10^{-3}$ ($Z^\prime$) and $10^{-4}$ (ALPs). Chirality-preserving operators from heavy new physics in the dimension six standard model effective theory (SMEFT) imply tighter upper limits, up to few $\times 10^{-5}$. Constraints on chirality-flipping heavy new physics, such as lepton number violation from dimension seven SMEFT, or with light sterile neutrinos, are weaker, with branching ratios up to few$\times 10^{-4}$. Sensitivities to different couplings arise with $Λ_c \to p X$ and $D \to ππX$ decays, in particular in relation with the other modes. Processes can be studied at running and future experiments with high charm luminosities, BESIII, Belle II, a super-tau-charm factory (STCF) and $Z$-factories, such as FCC-ee and CEPC.

Figures (13)

• Figure 1: The $\mathrm{d}\mathcal{B}(D^0 \to \pi^0 \nu \bar{\nu})/\mathrm{d}q^2$ distributions as functions of $q^2$. Solid curves $(SP+, LR+)$ are based on the form factors from Fermilab lattice FermilabLattice:2022gku. The main source of uncertainty stems from the form factors and is illustrated by the bands. Also shown (dashed curves) are form factors from the ETM collaboration Lubicz:2017syvLubicz:2018rfs, featuring larger uncertainties. The tensor form factor has only been provided by ETM, and is therefore shown by the solid (red) curve. For each of the solid curves a single $x_k$, $k\in\{SP+,LR+,T\}$ of Eq. \ref{['eq:variables']} is turned on such that $\mathcal{B}(D^0 \to \pi^0 \nu \bar{\nu} ) = 10^{-7}$. Identical values of $x_k$ have been used for the dashed and the solid curves. Distributions of $D^+ \to \pi^+ \nu\overline{\nu}$ are identical, see text for details.
• Figure 2: The $\mathrm{d}\mathcal{B}(D^0 \to \rho^0 \nu \bar{\nu})/\mathrm{d}q^2$ distributions as functions of $q^2$, see Fig. \ref{['fig:dBR_dq2_D_to_pinunubar']}. Central values are normalized to $\mathcal{B}(D^0 \to \rho^0 \nu \bar{\nu} ) = 10^{-7}$. Due to the proximity of masses and for similar form factors the distributions for $D^0 \to \omega \nu\overline{\nu}$ are similar. The distributions proportional to $x_{LR+}$ and $x_{SP-}$ overlap, see text.
• Figure 3: The $\mathrm{d}\mathcal{B}(\Lambda_c \to p \nu \bar{\nu})/\mathrm{d}q^2$ distributions as functions of $q^2$, see Fig. \ref{['fig:dBR_dq2_D_to_pinunubar']}. Central values are normalized to $\mathcal{B}(\Lambda_c \to p \nu \bar{\nu} ) = 10^{-7}$. The uncertainty includes statistical and systematic errors of the form factors given in Meinel:2017ggx.
• Figure 4: Branching ratio of $D^{0}\to \pi^0 a$ (lower band, blue) and $D^+\to \pi^+ a$ (upper band, orange) with the coupling $|k^V_{12}/f|^2$ factored out, depending on the ALP mass $m_a$. The difference between the charged and the neutral mode is lifetime and isospin factors. The main source of uncertainty stems from the $D\to \pi$ form factors. Solid (dashed) curves are using most recent (ETM) form factors, see Sec. \ref{['sec:D0toPi0nunubar']}.
• Figure 5: Branching ratio of $\Lambda_c \to pa$ against $m_a$ with only the axial coupling switched on (lower band, blue), and only the vector one turned on (upper band, orange). The couplings $|k^{V,A}_{12}/f|^2$ have been factored out, and the different sensitivity stems from different form factors, (\ref{['eq:aVand aA']}). The main source of uncertainty stems from the form factors, shown as bands.