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 a study of which provides excellent probes for testing the Standard Model.

Figures (17)

• Figure 1: Feynman diagram for $\Xi_{cc}^{++} \rightarrow \Xi_{c}^{+} \bar{\ell}\nu_{\ell}$ decay
• Figure 2: Differential branching ratios $\mathcal{D}_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, and forward-backward asymmetry FBA$_k^{(m,n)}(q^2)$ as functions of $q^{2}$ for the SM unpolarized (black) and the longitudinally ($L$) polarized muon ($\ell$) cases. The $k=+$ longitudinally polarized state is in green and the $k=-$ one is in red. The dotted region represents uncertainty due to form factors.
• Figure 3: Differential branching ratios $\mathcal{D}_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, and forward–backward asymmetry FBA$_k^{(m,n)}(q^2)$ as functions of $q^{2}$ for the SM unpolarized (black) and the longitudinally ($L$) polarized daughter baryon $\Xi_c^+$ cases. Color coding is the same as in Fig. \ref{['longi_lepton']}.
• Figure 4: Differential branching ratios $\mathcal{D}_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, and forward–backward asymmetry FBA$_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, as functions of $q^{2}$ for the SM unpolarized (black) and the longitudinally ($L$) polarized parent baryon $\Xi_{cc}^{++}$ cases. Color coding is the same as in Fig. \ref{['longi_lepton']}.
• Figure 5: Differential branching ratios $\mathcal{D}_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, and forward–backward asymmetry FBA$_k^{(m,n)}(q^2)$, integrated over $\cos{\theta}$, as functions of $q^{2}$ for the SM unpolarized and the transversely ($T$) polarized muon $\ell$ cases. Color coding is the same as in Fig. \ref{['longi_lepton']}.