We use the heavy quark effective theory to investigate the form factors that describe the semileptonic decays of a B meson into excited daughter mesons. For an excited daughter meson with charm, a single form factor is needed at leading order, while five form factors and two dimensionful constants are needed to order 1/m(sub)c in the heavy quark expansion. For non-charmed final states, a total of four form factors are needed at leading order. For the process B ->D^(*)Xlv, four form factors are also needed at leading order.

This thesis presents first measurements of moments of the hadronic nX2 distribution measured in inclusive semileptonic decays of B mesons to final states containing a charm quark, B 2!Xcl[nu]. The variable nX2 is a combination of the invariant mass of the charmed meson mX, its energy in the B-meson rest-frame EX;BRF, and a constant ~[Lambda] = 0.65 GeV, nX2 = mX2c4-2~[Lambda]EX, BRF + ~[Lambda]2. The moments nXk with k = 2,4,6 are measured as proposed by theory to constrain assumptions made in the theoretical description of inclusive observables in semileptonic B-meson decays. This description uses Heavy Quark Expansion (HQE), an effective QCD combined with an Operator Product Expansion. The measurement is based on a sample of 231.6 million e+e- 2 2!B$\bar{B}$ events recorded with the BABAR experiment at the PEP-II e+e--storage rings at SLAC. We reconstruct the semileptonic decay by identifying a charged lepton in events tagged by a fully reconstructed hadronic decay of the second B meson. Correction procedures are derived from Monte Carlo simulations to ensure an unbiased measurement of the moments of the nX2 distribution. All moments are measured requiring minimum lepton momenta between 0.8 GeV/c and 1.9 GeV/c in the rest frame of the B meson. Performing a simultaneous fit to the measured moments nXk up to order k = 6 combined with other measurements of moments of the lepton-energy spectrum in decays B 2!Xcl[nu] and moments of the photon-energy spectrum in decays B 2!Xs[gamma], we determine the quark-mixing parameter.

The book deals with an introductory idea of Leptonic and semileptonic decay of Heavy-Light mesons. It also highlight the application of a specific QCD potential model in this area of physics. Specifically, it also addresses the application of quantum mechanical perturbation method and explicitly the Dalagarno method of perturbation in this context. The necessity of modification of the model within the constraints of QCD and the model itself is explained and also improved accordingly. Out of the five chapters, the second and third chapters address the leptonic decay of B and D mesons whereas in the last two chapters, the study of semileptonic decay in terms of the universal form factor, Isgur-Wise function is well explained.