In this dissertation the matrix element (ME) for the weak decay of the B-meson into J/psi-particle and a kaon is analysed from the first principles using the method of effective field theory based on exploiting the decay kinematics. Namely, the large masses of the b- and c- quarks, the large energy of the s-quark in the rest frame of the B-meson makes it reasonable to use HQET, NRQCD, and SCET to express the ME of the decay in terms of the MEs of these theories. The covariant version of NRQCD necessary to describe the J/psi in the B-meson rest frame is proposed in the dissertation. The tree-level expression for the decay Lagrangian in the effective theory is derived to all orders in strong coupling. The Wilson coefficients for the decay Lagrangian at the leading logarithmic approximation and their initial values at mu=mb are calculated. It is shown that the singlet piece of the decay Lagrangian factorizes into the product of two currents at the leading order in power expansion in the effective theory but the octet piece doesn't. It is shown that the contribution due to the non-factorizable octet piece is of the same order of magnitude as the singlet contribution at mu=m and it is argued that the octet contribution although suppressed by one power of strong coupling compared to the singlet contribution cannot be ignored

Evidence for the existence of exotic, pentaquark baryons was first found in the invariant mass spectrum of a baryon-meson pair, with the baryon in the octet of flavor SU(3). Exotic pentaquarks may also decay into members of the spin-3/2 baryon decuplet. We calculate relations between decay rates of the exotic pentaquark into a baryon decuplet and an octet of pseudoscalar mesons based on SU(3) flavor symmetry, including the leading flavor symmetry breaking term. We consider all possible representations for an exotic pentaquark, namely, that it belongs to either a \bar{10}, 27, or 35 representation of flavor SU(3). In addition, we use the approximate SU(6) spin-flavor symmetry of baryons to derive relations between the reduced matrix elements of our calculation and those of an existing analogous calculation for decays into the baryon octet. By comparing several decay rates of exotics into both octet and decuplet baryons, our results could be used to elucidate the SU(3) nature of pentaquarks.