Penguin decays in b quark

In this research, we are going to study the QCD penguin structure and calculate the second order approximation. The amplitude of decays related to QCD penguin in the quark model up to the first and second orders were calculated. We calculated the amplitude of QCD penguin on lowest order of αs for the first order of the decay processes b→qkg→qkqiqj and for the second order of the decay processes b→qkqiqj→ qkqiqjg→ qkqiqj(qoqp). 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 to be much smaller than the first order. We calculated the branching ratios of b quark- b antiquark decays and assuming that we can ignore the second order of QCD penguin.