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

TL;DR

This paper revisits $B_s o PP$ and $PV$ decays using perturbative QCD, emphasizing the impact of the sub-leading wave function component ${phi}_{B2}$ on decay predictions and aligning theory more closely with experimental data.

Contribution

It introduces the inclusion of the ${phi}_{B2}$ wave function component in pQCD calculations of $B_s$ decays, improving the accuracy of branching ratio and CP violation predictions.

Findings

Inclusion of ${phi}_{B2}$ significantly affects decay observables.

Theoretical predictions align better with experimental data after considering ${phi}_{B2}$.

Higher-order effects in meson DAs have smaller but notable impacts.

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) ${\phi}_{B2}$. Here, $P$ represents the pseudoscalar mesons ${\pi}$ and $K$, while $V$ denotes the ground-state vector mesons. The investigation incorporates two key refinements: the contribution of the sub-leading twist WF $\phi_{B2}$ 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 $\chi^2$ method, we optimize the shape parameter $\omega_{B_s}$ 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 $\phi_{B2}$ 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 $\phi_{B2}$ 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.