Study of Form Factors and Observables in $B_c^- \rightarrow D_{s}^{*-}\ell^+\ell^-$ and $B_c^- \rightarrow D_{s}^{*-}ν\barν$ decays

TL;DR

This work provides a comprehensive SM study of the rare decays $B_c^{-}\to D_s^{(*)-}\ell^{+}\ell^{-}$ and $B_c^{-}\to D_s^{(*)-}\nu\bar{\nu}$ by combining perturbative QCD form factors with lattice inputs to fix meson LCDAs, then leverages heavy-quark spin symmetry to extend the $q^{2}$ dependence. The authors extract universal HQET functions $\Sigma_{1}$ and $\Sigma_{2}$ and implement a BGL $z$-expansion to obtain the full $q^{2}$-range behavior for $B_c\to D_s^{*}$ form factors, including thorough angular analyses of cascade decays and a suite of observables (branching fractions, CP asymmetries, forward-backward, polarization, and clean $P_i$ observables). They report precise SM predictions for branching fractions, LFU ratios, and zero-crossing points in angular observables, providing robust benchmarks for future LHCb measurements and potential New Physics investigations. The approach integrates lattice QCD inputs, HQET relations, and model-independent form-factor parameterizations to deliver a coherent, testable SM framework for heavy-heavy FCNC processes in the $B_c$ sector.

Abstract

We investigate the decays $B_c^- \rightarrow D_{s}^{(*)-}\ell^+\ell^-$ and $B_c^- \rightarrow D_{s}^{(*)-}ν\barν$ within the Standard Model (SM), employing perturbative QCD form factors that are sensitive to the wave functions of $B_c$ and $D_{s}^{(*)}$ mesons. We determine the shape parameters of these mesons and the $B_c \to D_s^{(*)}$ form factors at $q^2 = 0$ from available lattice QCD inputs for $B_s \to D_s^{(*)}$ and $B_c \to D_s$ transitions. To obtain the $q^2$ dependence of the $B_c \to D_s^*$ form factors, we employ heavy-quark spin symmetry and an appropriate parametrisation scheme over the allowed $q^2$ region. Based on these inputs, we present predictions for branching ratios and lepton-flavour-sensitive observables. Furthermore, we perform a detailed angular analysis of the cascade decay $B_c^- \to D_s^{*-}(\to D_s^- π^0)\,\ell^+\ell^-$, providing Standard Model predictions for several angular observables.

Figures (9)

• Figure 3: Kinematics of $B_{c}^{-}\rightarrow D_{s}^{*-}(\rightarrow D_{s}^{-}\pi^{0}) \ell^{+}\ell^{-}$ four body decay.
• Figure 4: Plots showing the $w$ distribution of $\Sigma_{1}(w)$ and $a_{0}\Sigma_{2}(w)$.
• Figure 5: Plots showing the $q^{2}$ distribution of $B_{c}\rightarrow D_{s}$ form factors $F_{+}$, $F_{0}$ and $F_{T}$. The red markers denote the synthetic data points generated using the BCL parameters supplied by HPQCD.
• Figure 6: $q^{2}$ distribution of $B_{c}\rightarrow D_{s}^{*}$ vector and axial-vector form factors. The blue curve denotes the distribution obtained using the extracted BGL coefficients, the red and black markers denote the form factor values obtained using the extracted soft functions and pQCD, respectively.
• Figure 7: $q^{2}$ distribution of $B_{c}\rightarrow D_{s}^{*}$ tensor form factors. The blue curve denotes the distribution obtained using the extracted BGL coefficients, the red and black markers denote the form factor values obtained using the extracted soft functions and pQCD, respectively.