Study of lepton flavor universality and angular distributions in $D\to K^*_{J} (\to K\pi)\ell\nu_{\ell}$

TL;DR

This paper analyzes the decay processes of D mesons into various K* resonances and leptons, deriving angular distributions and decay ratios to enhance understanding of meson properties and lepton universality within the Standard Model.

Contribution

The study introduces a detailed helicity amplitude analysis of D meson decays involving multiple K* resonances, providing new calculations of decay widths and branching ratios with form factors from the quark model.

Findings

Branching ratio ratios for muon vs electron channels are close to unity for K*(892)

Significant differences in ratios for higher K* states, e.g., 0.714 for K*(1410)

Results aid future studies of charm quark transitions and meson properties.

Abstract

The decay of the D meson into multibody final states is a complex process that provides valuable insights into the fundamental interactions within the Standard Model of particle physics. This study focuses on the decay cascade $D^{+}\to K^{*}_{J} \ell^{+}\nu \to K^{\pm}\pi^{\mp} \ell^{+}\nu$ where the $K^*_J$ resonance encompasses the $K^*(892),K^{*}(1410),K^{*}_0(1430)$ states. We employ the helicity amplitude technique to derive the angular distributions for the decay chain, enabling the extraction of one-dimensional and two-dimensional distributions. Utilizing form factors for the $D\to K^*$ transition derived from the quark model, we calculate the differential and integrated partial decay widths, explicitly considering the electron and muon masses. Decay branching fractions are calculated, the ratios of the branching fractions are found to be $\frac{\mathcal{B}r(D^{+}\to K^{*}(892)(\to K ^{-}\pi^{+}) \, \mu^{+}\nu_{\mu})}{\mathcal{B}r(D^{+}\to K^{*}(892)(\to K ^{-}\pi^{+}) \, e^{+}\nu_{e})} = 0.975$, $\frac{\mathcal{B}r(D^{+}\to K^{*}(1410)(\to K ^{-}\pi^{+}) \, \mu^{+}\nu_{\mu})}{\mathcal{B}r(D^{+}\to K^{*}(1410)(\to K ^{-}\pi^{+}) \, e^{+}\nu_{e})} = 0.714$ and $\frac{\mathcal{B}r(D^{+}\to K^{*}_{0}(1430)(\to K ^{+}\pi^{-}) \, \mu^{+}\nu_{\mu})}{\mathcal{B}r(D^{+}\to K^{*}_{0}(1430)(\to K ^{+}\pi^{-}) \, e^{+}\nu_{e})} = 0.774$. Results in this work will serve a calibration for the study of $c \to s $ in $D$ meson decays in future and provide useful information towards the understanding of the properties of the $K^{*}$ meson, as well as $K \pi$ system.