Revisiting $B_s \to PP$ and $PV$ Decays with Contributions from $φ_{B2}$ with perturbativen QCD approach

TL;DR

The paper investigates $B_s \to PP$ and $PV$ decays within perturbative QCD, incorporating the subleading $B_s$ meson wave function component $φ_{B2}$ and higher-order final-state distribution amplitudes. By fitting the shape parameter $ω_{B_s}$ to PDG and LHCb data via a minimum $χ^2$ method, it demonstrates that including $φ_{B2}$ substantially influences branching ratios and CP asymmetries, and can improve agreement with measurements for several channels. Higher-order terms in final-state DAs yield smaller but non-negligible improvements, underscoring the need for refined nonperturbative inputs in pQCD calculations. The results emphasize the critical interplay between wave function modeling and higher-order contributions, with future experimental data providing stringent tests of these refinements.

Abstract

The $B_s \to PP$ and $PV$ decay modes are revisited at leading order within the perturbative QCD approach, incorporating the $B_s$ mesonic wave function (WF) $φ_{B2}$. Here, $P$ represents the pseudoscalar mesons $π$ and $K$, while $V$ denotes the ground-state vector mesons. The investigation incorporates two key refinements: the contribution of the sub-leading twist WF $φ_{B2}$ of the $B_s$ meson and the effects of higher-order terms in the distribution amplitudes (DAs) of the final-state mesons. Employing the minimum $χ^2$ method, we optimize the shape parameter $ω_{B_s}$ of the $B_s$ meson WF and systematically calculate the branching ratios and $CP$ violation parameters for these decay modes. Our results demonstrate that the inclusion of $φ_{B2}$ significantly impacts both the branching ratios and $CP$ asymmetries, offer an improved agreement with existing experimental data for specific channels. This underscores the necessity of accounting for $φ_{B2}$ in theoretical studies of $B_s$ weak decays. While the higher-order corrections in the final-state meson DAs yield comparatively smaller effects, they still enhance the theoretical predictions. These findings highlight the importance of refining both wave function modeling and higher-order contributions in pQCD calculations. Future high-precision experimental measurements will further test these predictions, while continued theoretical efforts are essential to explore additional interaction mechanisms and systematic uncertainties. The interplay between experimental advancements and theoretical improvements remains critical for a deeper understanding of $B_s$ meson decay dynamics.

Figures (7)

• Figure 1: A LO diagram for the $\bar{B}_s(p_{B_s})\to M_2(p_2)M_3(p_3)$ decay.
• Figure 2: The shapes of the $B_s$ DAs (${\phi}_{B}^{+}$ and ${\phi}_{B}^{-}$) as a function of the longitudinal momentum fraction $x$ (horizontal axis)
• Figure 3: Shape lines of the final meson DAs, with (solid lines) and without (dotted lines) higher-order Gegenbauer polynomials, as a function of the longitudinal momentum fraction $x$.
• Figure 4: Feynman diagrams contributing to the $\bar{B}^0_s \to M_1 M_2$ decay processes. Dots denote interaction vertices, while the dashed circles represent quark-level scattering amplitudes. Diagrams are categorized as follows: (a) and (b) factorizable emission diagrams; (c) and (d) nonfactorizable emission diagrams; (e) and (f) factorizable annihilation diagrams; (g) and (h) nonfactorizable annihilation diagrams.
• Figure 5: $\chi^2$ distribution as a function of the $B_s$-meson shape parameter $\omega_{B_s}$ for the $\bar{B}^0_s \to PP$ decay analysis. The global fit incorporates experimental constraints from $B_s \to PP$ measurements by PDG and LHCb. Red data points (marked by arrows) indicate the $\chi^2$ minima, corresponding to the optimized $\omega_{B_s}$ values.