Isgur-wise Function in Relativistic Quark Model

Hadronic matrix elements are expressed in the framework of BS formalism, and in the limit of heavy quark mass mQ → ∞, we find that all form factors in processes of B → D weak transition can be incorporated into a single universal Isgur-Wise (I −W ) function ξ(v · v′), which was first discovered by Isgur and Wise in heavy quark effective theory (HQET). By introducing a phenomenological interaction kernel, we solve the BS equation in leading order of 1/mQ, and calculate the numerical result for ξ(v · v′). We find that the slope of ξ(v · v′) at the zero recoil point v · v′ = 1 is larger for the process in which the involved light degree of freedom is s quark than the case of u, d quarks. Our results agree with others. In recent years a remarkable progress has been achieved in the physics of systems containing one heavy quark. HQET points out that in the limit of heavy quark mass mQ → ∞ a spin-heavy flavor symmetry [1] emerges and the weak decays of heavy hadrons can be described by a single form factor (the “I −W function”) ξ(v · v) [2] (where v and v are the four-velocities of heavy meson before (after) the transition). Since I−W function plays a center role in the weak decays of heavy hadrons, many authors try to study its analytical properties approximately by fitting with