Quasi-two-body decays B_c → K^* h → K πh in the perturbative QCD

2023/07/23 by Ziyu Zhang, Z. Zhang, Zhang, Zi-Yu +7
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2307.12351

openalex publication_date 2023/07/23 · openalex created_date 2023/07/26 · openalex updated_date 2026/07/28

Abstract

In this work we study the quasi-two-body decays B_c → K^* h → K πh (h = D, D_s, K, π, η, η') in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes (DAs) Φ^P-wave_Kπ are introduced to describe the final state interactions of the K πpair, which involve the time-like form factors F_Kπ(s) parameterized by the relativistic Breit-Wigner function and the Gegenbauer polynomials. We calculate the branching ratios for these quasi-two-body decays, from which one can obtain the branching raios for the corresponding two-body decays under the narrow width approximation relation. We find that B⁺_c→ K^*+D⁰ and B⁺_c→ K^*0D⁺ have the largest branching ratios, which can reach up to 10^-6, while the branching ratios for other two-body decays are very small and only about 10^-8∼10^-7. As we expected that the branching ratios of the pure annihilation decays are usually small, while in our considered such type of decays, the channel B_c⁺ → K^*0K⁺ has the largest branching ratio, which is near 10^-6. These results are consistent with the previously PQCD calculations obtained in the two-body framework, which can be tested by the future LHCb experiments. For the decays B_c⁺ → K^*+ D⁰→ K⁰π⁺D⁰ , B_c⁺ → K^*0D⁺→ K⁺π^-D⁺ and B_c⁺ → K^*0D_s⁺→ K^-π⁺D_s⁺, we calculate their direct CP violations and find that A_CP(B_c⁺ → K^*+D⁰→ K⁰π⁺D⁰)=(-14.6_-1.12^+9.19)% is the largest one, which is possible measured by the present LHCb experiments. For the pure annihilation type decays, there is no CP violations because only the tree operators are involved. Furthermore, we also give the differential distributions of the branching ratios and the direct CP violations for the decays B_c→ K^* D_(s)→ K πD_(s).

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