Quasi-two-body decays in the perturbative QCD approach*

Abstract

In this work we study the quasi-two-body decays $B\to K^*\gamma\to K\pi\gamma$ in perturbative QCD(PQCD) approach. The two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $K\pi$ pair, which involve the time-like form factors and the Gegenbauer polynomials.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd. We calculate the CP averaged branching ratios for the $B_{(s)}\to K^*\gamma\to K\pi\gamma$ decays. Our results are in agreement with the new update data measured by Belle II, which suggests these quasi-two-body decays are more appropriate to be analyzed in three-body framework than in the two-body one. We also predict the direct CP-violation asymmetries for the considered decay modes and find that $A_{CP}(B_{u,d}\to K^*\gamma\to K\pi\gamma)$ is small and less than $1\%$ in magnitude, while $A_{CP}(B_{s}\to K^*\gamma\to K\pi\gamma)$ is larger and can arrive at a few percent. Our predictions can be tested by the future B meson experiments.

Resonance contributions from $χ_{c0}$ in the charmless three-body hadronic $B$ meson decays

“…The timelike form factor F χc0 (z, s) is parametrized with the RBW line shape [61] and can be expressed as follows [62][63][64],…”

Resonance contributions from χ c0 in charmless three-body hadronic B meson decays*

“…The timelike form factor is parameterized with the RBW line shape [61] and can be expressed as follows [62][63][64]:…”