The effects of polarization on the observables in the decay $Ξ_{cc}^{++} \rightarrow Ξ_{c}^{+} \bar{\ell}ν_{\ell}$

Abstract

We investigate the effects of polarization on several physical observables in the semileptonic decay $Ξ_{cc}^{++} \rightarrow Ξ_c^{+} \bar{\ell}ν_{\ell}$. We analyze the polarization effects of the particles involved in the decay, namely $Ξ_{cc}^{++}$, $Ξ_c^{+}$, and the charged muon $\ell$. Using the form factors obtained from QCD sum rules, we compute the $q^{2}$-dependent observables including the differential branching ratio, forward-backward asymmetry, and polarization asymmetries for both longitudinal and transverse polarization states. We also define and examine several polarization ratios and discuss correlations among different observables. In addition, we evaluate the lepton flavor universality ratio defined as $\mathcal{R}_{Ξ_c^+}(μ/e) \equiv \mathcal{D}(Ξ_{cc}^{++}\to Ξ_c^+μ^+ν_μ)/\mathcal{D}(Ξ_{cc}^{++}\to Ξ_c^+e^+ν_e)$ and analyze its behavior over the available dynamical range. Our results show that these observables are quite sensitive to polarization effects, and can provide suitable probes for testing Standard Model predictions.