Gluon and gluino penguin diagrams and the charmless decays of thebquark

Gluon mediated exclusive hadronic decays of $b$ quarks are studied within the standard model (SM) and the constrained minimally supersymmetric standard model (MSSM). For all allowed regions of the MSSM parameter space $(A,\tan \beta {,m}_0{,m}_{1/2})$ the penguin magnetic dipole form factor $F_2^R$ is dominant over the electric monopole and can be larger than the magnetic dipole form factor of the SM. However, overall the SM electric monopole decay amplitude $F_1^L$ dominates the decay rate. The MSSM penguin contributions to the free quark decay rate approach the 10% level for those regions of parameter space close to the highest allowed values of $\tan \beta$ $\left(\sim 55\right)$ for which the gluino is light ${(m}_{\tilde{g}}\approx 360\hspace{0.5em}\mathrm{GeV})$ and lies within the range of the six $\tilde{d}$ squark masses. In these regions the supersymmetric box amplitudes are negligible. The MSSM phases change very little over the allowed parameter space and can lead to significant interference with the SM amplitudes.