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


Department of Physics,Semnan University


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 coecients 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 coecients, 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.