Eective Hamiltonian and Eective Penguin Model on b Quark Decays

Abstract. In this research, we investigated b quark decays by two dierent approaches; rstly,
according to the structure of penguin decays, and secondly, based on an eective 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 coecients of the eective Hamiltonian. We obtained
the decay rates of the tree and penguin and magnetic dipole terms all together to compare them with
the eective Hamiltonian current-current and penguin operators. We described the eective 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 eective penguin model, the simple coecients, d1;


; d6;8, are
dened according to the gluon penguin structure and used in the eective 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 Eective Hamiltonian (EH) and
Eective Penguin Model (EPM). Decay rates and branching ratios are very similar in all models, but in
the Eective Hamiltonian Magnetic Dipole, the total decay rate is about 10% larger than the simple tree or
Eective 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.