Revisiting $$B\rightarrow K^*\pi $$ and $$B\rightarrow K\rho $$ decays using the modified perturbative QCD approach

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Abstract We revisit $$B\rightarrow K^*\pi $$ B → K ∗ π and $$B\rightarrow K\rho $$ B → K ρ decay processes using the modified perturbative QCD approach, which is developed based on the perturbative QCD approach with a few improvements. A critical infrared cutoff scale $$\mu _c$$ μ c is introduced to separate hard and soft contributions in the decay process. Hard contributions with scale $$\mu $$ μ larger than $$\mu _c$$ μ c are calculated with perturbative QCD, and soft contributions with $$\mu <\mu _c$$ μ < μ c are described in terms of soft transition and production form factors. In addition, color-octet contributions are considered phenomenologically. The branching fractions and CP violations of $$B\rightarrow K^*\pi $$ B → K ∗ π , $$K\rho $$ K ρ decays are calculated. With appropriate parameter inputs, the theoretical results can be in good agreement with experimental data.