Charmless $B_{c}$ $\to$ $PP$, $PV$ decays in the QCD factorization approach

TL;DR

This paper investigates charmless $B_c$ decays into light mesons using QCD factorization, comparing two schemes and different wave functions, revealing small predicted branching ratios and highlighting the need for future experimental tests at LHCb.

Contribution

It introduces a comparative analysis of $B_c$ decay predictions using two QCD factorization schemes and multiple wave functions, emphasizing the impact of infrared behavior on annihilation contributions.

Findings

Scheme I predicts very small branching ratios, unlikely to be measured.

Scheme II, incorporating a dynamical gluon mass, enhances annihilation contributions.

Predicted branching ratios remain smaller than those from perturbative QCD, indicating theoretical uncertainties.

Abstract

The charmless $B_{c}$ $\to$ $PP$, $PV$~(where $P$ and $V$ denote the light pseudoscalar and vector mesons, respectively) decays can occur only via the weak annihilation diagrams within the Standard Model and provide, therefore, an ideal place to probe the strength of annihilation contribution in hadronic $B_{u,d,s}$ decays. In this paper, we study these kinds of decays in the framework of QCD factorization, by adopting two different schemes: scheme I is similar to the method usually adopted in the QCD factorization approach, while scheme II is based on the infrared behavior of gluon propagator and running coupling. For comparison, in our calculation, we adopt three kinds of wave functions for $B_{c}$ meson. It is found that: (a) The predicted branching ratios in scheme I are, however, quite small and are almost impossible to be measured at the LHCb experiment. (b) In scheme II, by assigning a dynamical gluon mass to the gluon propagator, we can avoid enhancements of the contribution from soft endpoint region. The strength of annihilation contributions predicted in scheme II is enhanced compared to that obtained in scheme I. However, the predicted branching ratios are still smaller than the corresponding ones obtained in the perturbative QCD approach. The large discrepancies among these theoretical predictions indicate that more detailed studies of these decays are urgently needed and will be tested by the future measurements performed at the LHCb experiment.