An improved perturbative QCD study of the decays $B_c^+ \to η_c L^+$

TL;DR

The paper addresses the decays $B_c^+ \to \eta_c L^+$ using the improved perturbative QCD framework at leading order in $\alpha_s$ to predict CP-averaged branching ratios and relative ratios for a wide set of light mesons $L$. It employs the $k_T$-dependent, Sudakov-suppressed factorization of the decay amplitude, with a convolution over $B_c$, $\eta_c$, and $L$ light-cone wave functions and the hard kernel, yielding explicit expressions for factorizable and nonfactorizable contributions. The authors also derive multibody branching fractions via $\eta_c$ decays under the narrow-width approximation, enabling connections to experimentally accessible final states. They report that factorizable-emission dominated modes give large BRs (e.g. $BR(\eta_c\pi^+)\sim\mathcal{O}(10^{-3})$) while certain suppressed channels exhibit strong $\Delta S$-dependent effects, with some ratios reaching $\mathcal{O}(10^2)$, providing rich tests for QCD dynamics in $B_c$ decays at the LHC. These predictions offer a concrete benchmark to test the reliability of iPQCD in heavy-maryon decays and to constrain the hadronic parameters of light mesons and $\eta_c$ through future LHC measurements.

Abstract

We perform an improved perturbative QCD study of the decays $B_c^+ \to η_c L^+$ ($L$ denotes the light ground state pseudoscalar, vector mesons and the corresponding $p$-wave scalar, axial-vector, and tensor ones) and predict their branching ratios (BRs) associated with relative ratios at leading order in the strong coupling $α_s$. Our results ${\rm BR}(B_c^+ \to η_c π^+) =(2.03^{+0.53}_{-0.41}) \times 10^{-3}$ and ${\rm BR}(B_c^+ \to η_c π^+)/{\rm BR}(B_c^+ \to J/ψπ^+) = 1.74^{+0.66}_{-0.50}$ are consistent with several available predictions in different approaches within uncertainties. Inputting the measured $η_c \to p\bar p$ and $η_c \to π^+π^- (π^+π^-, K^+ K^-, p\bar p)$ BRs with $p$ here being a proton, we derive the multibody $B_c^+ \to η_c (π, ρ)^+$ BRs through secondary decay chains via resonance $η_c$ under the narrow-width approximation, which might facilitate the (near) future tests of $B_c \to η_c$ decays. Under the $q\bar q$ assignment for light scalars, different to $B_c$ decaying into $J/ψ$ plus a scalar meson and other $B_c^+ \to η_c L^+$ modes, surprisingly small $ΔS =0$ BRs around ${\cal O}(10^{-7}-10^{-9})$ and highly large ratios near ${\cal O}(10^{2})$ between the $ΔS=1$ and $ΔS=0$ BRs are found in the $B_c$ decays to $η_c$ plus light scalars, with $S$ being strange number. Many large BRs and interesting ratios presented in this work could be tested by the Large Hadron Collider experiments, which would help us to examine the reliability of this improved perturbative QCD formalism for $B_c$-meson decays and further understand the QCD dynamics in the considered decay modes, as well as in the related hadrons.

Figures (1)

• Figure 1: (Color online) Leading order Feynman diagrams for the decays $B_c^+ \to \eta_c L^+$ in the iPQCD formalism.