A comprehensive study of $B$, $B_s$ and $B_c$ meson semitauonic modes in potential quark model

TL;DR

This work addresses semitauonic decays of heavy-meson systems ($B$, $B_s$, $B_c$) as precise probes of SM flavor transitions. The authors apply the Relativistic Independent Quark Model with a confining harmonic potential and include one-gluon-exchange corrections plus center-of-mass adjustments to compute transition form factors across the full $q^2$ range, obtaining helicity amplitudes and differential rates for channels like $B \to D^{(*)}\tau\nu_\tau$, $B_s \to D_s^{(*)}\tau\nu_\tau$, and $B_c$ decays to charmonium and charm final states. They present branching fractions and angular observables using form factors $f_\pm(q^2)$, $V(q^2)$, $A_0(q^2)$, $A_+(q^2)$, and $A_-(q^2)$, finding overall SM-consistent results and good agreement with PQCD, LQCD, LCSR, and HQET within uncertainties, while highlighting channels with limited lattice data. The predictions serve as valuable SM input where lattice results are sparse and guide future experimental and lattice studies, providing benchmarks for SU(3) breaking and for the angular structure of semitauonic decays. This work underscores the continued relevance of potential-model frameworks in nonperturbative heavy-flavor phenomenology and the importance of cross-validation with lattice QCD and other nonperturbative methods.

Abstract

In this work, we derive the form factors and compute the branching fractions for the semitauonic decay modes, $B \to D^{(*)}\,τ\,ν_τ$, $B_s \to D_s^{(*)}\,τ\,ν_τ$, $B_c \to η_c\,(J/ψ)\,τ\,ν_τ$, and $B_c \to D^{(*)}\,τ\,ν_τ$ within the \emph{Relativistic Independent Quark (RIQ) Model}, emphasizing a quark potential model based analysis of these transitions. We outline the essential elements of the model, incorporating corrections from residual interactions and center-of-mass motion, and perform a comprehensive study of the form factors across the full physical kinematic range of $q^2$. The resulting predictions demonstrate consistency and good agreement with existing theoretical approaches and experimental measurements. Motivated by recent observations of polarization observables at LHCb and Belle, we further evaluate these quantities within our framework and find results compatible with Standard Model (SM) expectations. The predictions presented here serve as theoretical input in decay channels for which Lattice QCD results remain limited, offering guidance for future experimental and Lattice efforts. Thus, semileptonic $B$ decays continue to serve as precise and discerning probes of the fundamental mechanisms governing flavor transitions in the SM.

Figures (4)

• Figure 1: One gluon exchange contribution to the energy of $q\bar{q}$ configuration
• Figure 2: Leading order Feynman diagram for $B_q \rightarrow X_q\, \tau\nu_\tau$
• Figure 3: $q^2$ distribution spectra of the form factors for $B_s \to D_{s}^{(*)} \tau \nu_{\tau}$ and $B \to D^{(*)} \tau \nu_{\tau}$ transition
• Figure 4: $q^2$ distribution spectra of the angular observables in $B_c$ semitauonic decays