Testing Lepton Flavour Universality with (Semi)-Leptonic $D_{(s)}$ Decays

TL;DR

This paper performs a model-independent analysis of potential new physics effects in (semi)-leptonic $D_{(s)}$ decays, constraining operators and CKM elements, and predicting possible enhancements in rare leptonic decay modes.

Contribution

It introduces a comprehensive framework to analyze new physics contributions in charm meson decays and provides constraints consistent with the Standard Model.

Findings

Current data align with the Standard Model within uncertainties.

Constraints on new physics operators are derived from $D_{(s)}$ decay data.

Predictions suggest possible large enhancements in rare leptonic decay modes.

Abstract

Data in $B$-meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of $D_{(s)}$ mesons which originate from $c \to d \bar{\ell} \nu_{\ell}$ and $c \to s \bar{\ell} \nu_{\ell}$ charge-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements $|V_{cd}|$ and $|V_{cs}|$ of the Cabibbo--Kobayashi--Maskawa matrix and extract them from the $D_{(s)}$ decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic $D_{(s)}^+ \to e^+ \nu_e$ modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.