### Abstract:

The New Physics, the Physics beyond the Standard Model, shows that New Physics which affects B decays with any topological amplitude can be absorbed by redefinitions of the SM amplitudes. This thesis studies the B → K∗ρ modes that are analogous of the much studied B → Kπ modes with B decaying to two vector mesons instead of pseudoscalar mesons using topoloigal amplitudes in Quark diagram approach. It is shown that how B → K∗ρ modes could be used to obtain many more observables than those for B → Kπ modes, even though the quark level subprocesses of both modes are exactly the same since there are three helicities for each of the modes of the amplitudes for B → K∗ρ. Hence, the number of amplitudes for the B → K∗ρ modes is three times that for the B → Kπ modes, i.e., there are 36 theoretical parameters. The four B → K∗ρ decay modes can experimentally yield at most 35 observables. Therefore, all the theoretical parameters can be determined in terms of the observables and γ without any model-dependent assumption. If γ is measured from somewhere else, then one has full information about topological amplitudes in terms of experimental observables. Hence the SM could be tested and NP effects could be probed as well. It is demonstrated that how B → K∗ρ can also be used to verify if there exist any relations between theoretical parameters, such as the hierarchy relations between the topological amplitudes and possible relations between the strong phases. Conversely, if there exist reliable theoretical estimates of amplitudes and strong phases, the presence of New physics could be probed. It is shown
that if the tree and color-suppressed tree are related to the electroweak penguins and color-suppressed electroweak penguins, it is not only possible to verify the validity of such relations but also to have a clean measurement of New Physics parameters.
In conclusion, a few aspects of B physics were studied and we emphasize on two main points:“B → Kπ puzzle” and “the signal of new physics”.