New Physics Effects and Hadronic Form Factor Uncertainties in B -> K^* l^+ l^-

It is well known that New Physics can contribute to weak decays of heavy mesons via virtual processes during its decays. The discovery of New Physics, using such decays is made difficult due to intractable strong interaction effects needed to describe it. Modes such as B -> K^* l^+ l^- offer an advantage as they provide a multitude of observables via angular analysis. We show how the multitude of "related observables" obtained from B -> K^* l^+ l^-, can provide many new "clean tests" of the Standard Model. The hallmark of these tests is that several of them are independent of the unknown universal form factors in heavy quark effective theory. We derive a relation between observables that is free of form factors and Wilson coefficients, the violation of which will be an unambiguous signal of New Physics. We also derive relations between observables and form factors that are independent of Wilson coefficients and enable verification of hadronic estimates. We show how form factor ratios can be measured directly from helicity fraction with out any assumptions what so ever. We find that the allowed parameter space for observables is very tightly constrained in Standard Model, thereby providing clean signals of New Physics. We examine both the large-recoil and low-recoil regions of the K^* meson and point out special features and derive relations between observables valid in the two limits. In the large-recoil regions several of the relations are unaffected by corrections to all orders in \alpha_s. We present yet another new relation involving only observables that would verify the validity of the relations between form-factors assumed in the low-recoil region. The several relations and constraints derived will provide unambiguous signals of New Physics if it contributes to these decays.