Studies of Three-Body Decay of B to J/ψηK and B(Bs) to ηcπK*

We investigate the B0→J/ψηK0 and B+→J/ψηK+ decay by using the Dalitz plot analysis. As we know there are tree, penguin, emission, and emission-annihilation diagrams for these decay modes in the factorization approach. The transition matrix element is factorized into a B→ηK form factor multiplied by J/ψ decay constant and also a B→K form factor multiplied by J/ψη decay constant. According to QCD factorization approach and using the Dalitz plot analysis, we calculate the branching ratios of the B0→J/ψηK0 and B+→J/ψηK+ three-body decay in view of the η-η' mixing and obtain the value of the (9.22-1.47+2.67)×10-5, while the experimental results of them are (8±4)×10-5 and (10.8±3.3)×10-5, respectively. In this research we also analyze the B(Bs)→ηcπK* decay which is similar to the previous decay, but there is no experimental data for the last decay. Since for calculations of the B(Bs)→ηcπK* decay we use assumptions of the B→J/ψηK decay, we hope that if this decay will be measured by the LHCb in the future, the experimental results will be in agreement with our calculations