In this research, we are going to study of QCD penguin structure and calculated the second order approximation. The amplitude of decays related to QCD penguin in quark model up to the first and second orders calculated. We calculated the amplitude of QCD penguin on lowest order of for first order of the decay processes and for second order of the decay processes . We calculated the decay rates of the first and second order of QCD penguin for various b quark decays. We consider that, the second order of QCD penguin of b quark decays is much smaller than the first order of them. In the other hand, we can ignore the second order of QCD penguin in the b quark decays. We deduced various two and three body decays of B meson decays from various decays of b quark model. We compared the branching ratios of various decays of B meson, theoretically and experimentally and saw that the second order of QCD penguin term in b quark decays is small.

Keywords: Keyword QCD Penguin, Quark Model, Quark, B Meson, Decay Rate, Branching Ratios

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