Abstract
Within the framework of perturbative QCD approach based on $k_T$ factorization, we studied 40 $B_c \to DS$ decay modes in the leading order and leading power, where "S" stands for the light scalar meson. Under two different scenarios (S1 and S2) for the description of scalar mesons, we explored the branching fractions and related CP asymmetries. As a heavy meson consisting of two heavy quarks with different flavor, the light-cone distribution amplitude of $B_c$ meson has not been well defined, so the $\delta$-function is adopted. The contributions of emission diagrams are suppressed by the vector decay constants and CKM elements, the contributions of annihilation are dominant. After the calculation, we found some branching fractions are in the range of $[10^{-5}, 10^{-4}]$, which could be measured in the current LHCb experiment, and other decays with smaller branching fractions will be tested at the high-energy colliders in future. Furthermore, some decay modes have large CP asymmetries, but they are unmeasurable currently due to the small branching fractions.
Highlights
The study of weak decays of the Bc meson are of interest, since it is the only heavy meson consisting of two heavy quarks with different flavors
The Collider Detector at Fermilab (CDF) Collaboration reported the discovery of the Bc ground state in ppcollisions [1], which was further confirmed by the CDF and D0 Collaborations [2] with more precise measurements
Within the perturbative QCD (PQCD) approach, we studied the branching fractions and CP asymmetries of 40 Bc → DS decays involving scalar mesons
Summary
The study of weak decays of the Bc meson are of interest, since it is the only heavy meson consisting of two heavy quarks with different flavors. Since it carries flavor explicitly and cannot annihilate into gluons, it is stable against the strong and electromagnetic annihilation processes and can only decay weakly, which provides a new window for studying the weak decay mechanism of heavy flavors. We have to stress that experimental data indicates that the light scalar mesons [such as f0ð980Þ and a0ð980Þ] are predominately four-quark states, in practice it is very hard for us to make quantitative predictions based on the four-quark picture because both the decay constants and the distribution amplitudes of S are beyond the conventional quark model.
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