Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>ρ</mml:mi><mml:mi>η</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display=

We study the decay processes of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi><a:mo stretchy="false">→</a:mo><a:mi>ρ</a:mi><a:mi>η</a:mi></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>ρ</d:mi><d:msup><d:mi>η</d:mi><d:mo>′</d:mo></d:msup></d:math> in the perturbative quantum chromodynamics (QCD) approach with a few improvements incorporated in it, where the contributions with large momentum transfer are calculated perturbatively, and the contributions with lower energy scale are treated by introducing soft transition form factors. In addition, color-octet contributions are introduced which are essentially long-distance contributions. With reasonable input parameters selected, we find that the theoretical results of the branching ratios and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>C</f:mi><f:mi>P</f:mi></f:math> violations are all consistent with experimental data. We also predict some unmeasured quantities, which can be tested by experiment in the future.