E ective Hamiltonian and E ective Penguin Model on b Quark Decays

Abstract

Abstract. In this research, we investigated b quark decays by two di erent approaches; rstly, according to the structure of penguin decays, and secondly, based on an e ective Hamiltonian theory. Working with the standard model, the QCD penguin terms for various b and b decays are calculated. We also studied decay rates of the matter-antimatter of b quark decays. The gluonic penguin of b decays, b ! qkg ! qkqiqj , is studied through the Wilson coe cients of the e ective Hamiltonian. We obtained the decay rates of the tree and penguin and magnetic dipole terms all together to compare them with the e ective Hamiltonian current-current and penguin operators. We described the e ective Hamiltonian theory and applied it to the calculation of current-current (Q1;2), QCD penguin (Q3; ;6) and magnetic dipole (Q8) decay rates. Based on the e ective penguin model, the simple coe cients, d1; ; d6;8, are de ned according to the gluon penguin structure and used in the e ective Hamiltonian theory. In the other section of this research, the decay rates of processes like b ! cdc(b ! cdc), b ! csc(b ! csc), b ! udu(b ! udu) and b ! usu(b ! usu) are obtained based on the E ective Hamiltonian (EH) and E ective Penguin Model (EPM). Decay rates and branching ratios are very similar in all models, but in the E ective Hamiltonian Magnetic Dipole, the total decay rate is about 10% larger than the simple tree or E ective Hamiltonian. On the other hand, including the penguin induces matter-antimatter asymmetries. These are largest in the rate decays b ! udu, the decay rate of which is about 7% smaller than the decay rate b ! udu. Also, rate b ! suu is larger than rate b ! suu.