Semileptonic neutral currents decays of $Ξ_b$ with dileptons or dineutrinos in the final state

TL;DR

This work systematically analyzes semileptonic FCNC decays of the $\Xi_b$ baryon in $b\to s(d)$ transitions, including dilepton and dineutrino final states, using perturbative QCD to compute ten baryonic form factors and a $z$-expansion to cover the full $q^2$ range. The authors formulate the angular distribution in terms of ten transversity amplitudes, derive a suite of observables including $F_L$, forward-backward asymmetries, and LFU ratios, and quantify how these observables depend on Wilson coefficients and form factors, with particular attention to lepton-mass effects and long-distance resonance contributions. Numerical results predict branching fractions around $\mathcal{O}(10^{-6})$ for $\Xi_b\to\Xi\ell^+\ell^-$ and $\mathcal{O}(10^{-8})$ for $\Xi_b\to(\Sigma,\Lambda)\ell^+\ell^-$, while dineutrino channels approach $\mathcal{O}(10^{-5})$ when summing over flavors; the ratio $|V_{td}/V_{ts}|$ can be independently extracted from baryonic decays, offering a valuable cross-check of flavor anomalies observed in mesons. The study highlights angular observables that are relatively form-factor independent and thus powerful probes of new physics, and it provides detailed predictions for future experimental tests at LHCb and future facilities.

Abstract

We perform a detailed analysis of semileptonic $Ξ_b$ decays mediated by flavor-changing neutral currents ($b\to s$ and $b\to d$) with dilepton or dineutrino final states within the perturbative QCD framework. All independent form factors including vector, axial-vector, tensor, and pseudotensor currents are calculated and are used to analyze the decay branching fractions and angular distributions. Our numerical results for the branching fractions of $Ξ_b\to Ξ\ell^+\ell^-$ decays suggest they are within measurable reach for the LHCb experiment in the near future. Furthermore, we show that a measurement of the ratio $\mathcal{B}(Ξ_b^-\to Σ^- μ^+μ^-) / \mathcal{B}(Ξ_b^-\to Ξ^- μ^+μ^-)$ will allow for an independent determination of $|V_{td}/V_{ts}|$. For the case of unpolarized $Ξ_b$ baryons, we derive several angular observables, which can provide new and complementary constraints on Wilson coefficients in semileptonic FCNC transitions compared to those from mesonic decays. Finally, we present a combined analysis of dilepton and dineutrino channels, comparing various observables in detail. Our results offer further insights into the long-standing anomalies observed in $B$ meson decays.

Figures (8)

• Figure 1: The $q^2$ distributions of the Weinberg form factors (left) and helicity form factors (right) with Gegenbauer model of baryonic LCDAs. Upper, middle, and lower panels correspond to $\Xi_b$ to $\Xi$, $\Sigma$, and $\Lambda$ transitions, respectively. Here, the uncertainties in these curves are not shown for clarity.
• Figure 2: The theoretical uncertainties in the PQCD predictions for the form factor $f_1(q^2)$ of $\Xi_b\to\Xi$ (left), $\Xi_b\to\Sigma$ (middle), and $\Xi_b\to\Lambda$ (right) transitions. The solid red lines show the $q^2$ shape at central values of model parameters. The dotted green curves show the effect of the variation of $A=0.5\pm0.2$ from the $\Xi_b$ baryon LCDAs. The dashed blue, cyan, yellow, and purple curves show the variation of the parameters $f_{\mathcal{B}_f}$, $\lambda_1$, $\lambda_2$, and $\lambda_3$ of daughter baryon LCDAs, respectively. The dot-dashed violet curves show the scale $t$ variation between $0.8t$ and $1.2t$.
• Figure 3: Differential branching ratios of the semileptonic $\Xi^-_b\to\Xi^- \ell^+\ell^-$ (left), $\Xi^-_b\to\Sigma^- \ell^+\ell^-$ (middle), and $\Xi^0_b\to\Lambda \ell^+\ell^-$ (right) decays in the full $q^2$ kinematic region. The gray bands account for uncertainties induced by the scale $t$. The solid lines in the center of the band refer to the PQCD results with default parameters.
• Figure 4: $q^2$ dependence of the differential branching ratios with and without including the long-distance contributions, labeled by "LD" and "NLD", respectively.
• Figure 5: LFU ratios as a function of $q^2$, where the red and blue bands denote $\mathcal{R}_\mu$ and $\mathcal{R}_\tau$, respectively.