Cabibbo-suppressed charged-current semileptonic decays of $Ξ_b$ baryons

TL;DR

Problem: determine transition form factors and observables for Cabibbo-suppressed $\Xi_b \to (\Lambda,\Sigma)\ell\nu$ decays to constrain $|V_{ub}/V_{cb}|$ and test lepton-flavor universality. Approach: LO perturbative QCD calculations of six baryonic form factors using four LCDAs models, supplemented by a $z$-series extrapolation to cover the full $q^2$ range, with helicity amplitudes used to obtain differential rates and angular observables. Contributions: branching fractions are predicted at the $10^{-4}$–$10^{-5}$ level ($\Xi_b \to \Sigma\ell\nu$ vs $\Xi_b \to \Lambda\ell\nu$), LFU ratios are around 0.6, and lepton-mass effects significantly affect angular observables; a combined analysis of $b \to u$ and $b \to c$ transitions yields sub-percent precision for $R_\ell(\Sigma/\Xi_c)$ and $R_\ell(\Lambda/\Xi_c)$, enabling an independent extraction of $|V_{ub}/V_{cb}|$ with future data. Significance: provides theoretical input for CKM and LFU tests in baryonic decays, offering a complementary avenue to mesonic decays and guiding upcoming LHCb/Belle II measurements.

Abstract

We present the first perturbative QCD calculations of the $Ξ_b \to (Λ, Σ)$ transition form factors at leading order in $α_s$, which govern the Cabibbo-suppressed semileptonic decays $Ξ_b \to (Λ, Σ)\ell ν_\ell$ with $\ell = e, μ, τ$. Using these form factors, we evaluate differential and integrated branching fractions and angular observables within the helicity formalism. The branching ratios are predicted to be of order $10^{-4}$ for $Σ$ final states and $10^{-5}$ for $Λ$ final states, making them accessible to ongoing experiments such as LHCb. Ratios of decay rates between $τ$ and $e$ channels are also provided, offering new probes of lepton-flavor universality. Lepton-mass effects are found to significantly impact the integrated angular observables. Furthermore, a combined analysis of $b \to u$ and $b \to c$ transitions in $Ξ_b$ decays yields sub-percent precision for the ratios $\mathcal{R}_\ell(Σ/Ξ_c)$, enabling an independent determination of $|V_{ub}/V_{cb}|$ once the relevant decay-rate measurements become available.

Figures (5)

• Figure 1: Lowest-order diagrams for $\Xi_b\to \Sigma$ transition form factors. The symbol $\bullet$ denotes the electroweak vertex, from which the lepton pair emerges.
• Figure 2: The theoretical uncertainties in the S1 scheme for the form factor $f_1(q^2)$ of $\Xi_b\rightarrow\Sigma$ transition. The solid red line shows the $q^2$ shape at central values of model parameters. The dashed orange curves show the effect of the variation of $\omega_0=(0.4\pm0.1) \text{GeV}$ from the $\Xi_b$ baryon LCDAs. The dashed green, yellow, cyan, and purple curves show the variation of the parameters $f_{\Sigma}$, $\lambda_1$, $\lambda_2$, and $\lambda_3$ of $\Sigma$ baryon LCDAs, respectively. The dashed olive curves represent the scale $t$ variation between $0.8t$ and $1.2t$. The uncertainty arising from the standard errors of the $z$-series parameters is displayed by the dashed blue curves.
• Figure 3: $q^2$ dependencies of the form factors with four different models of $\Xi_b$ baryonic LCDAs. The solid (black), dashed (green), dotted (red), dot-dashed (magenta), double dot-dashed (blue), and the short dashed (orange) lines denote the $f_1$, $g_1$, $f_2$, $g_2$, $f_3$, and $g_3$, respectively. Upper and lower tows correspond to $\Xi_b^0\to \Sigma^+$ and $\Xi_b^-\to \Lambda$ transitions, respectively.
• Figure 4: The dependence of the observables on $q^2$ for $\Xi_b^0\to \Sigma^+ \ell \nu_\ell$ decays.
• Figure 5: Same as Fig. \ref{['fig:q2p']} but for $\Xi_b^-\to \Lambda \ell \nu_\ell$ decays.