In this thesis, flavor changing neutral current (FCNC) processes in semileptonic B decays, including the heavy-to-light transitions B ? a 1 ? + ? ? , B ? K 1 ? + ? ? and B ? K? + ? ? , are discussed in the context of the standard model (SM). The theoretical description of the semileptonic decays is relatively simple and provides much information about the strong forces that bind the quarks and gluons into hadrons. The FCNC semileptonic decays can be performed via the electroweak box and penguin diagrams which are sensitive to new physics (NP) contributions. To make predictions for the branching ratio value, dilepton invariant mass spectrum, forward-backward asymmetry and double lepton polarization, that provide us a lot of useful information, investigation of transition form factors is needed. In particle physics, reliable calculations of heavy-to-light transition form factors of semileptonic B decays are very important since they are also used to determine the amplitude of non-leptonic B decays, evaluate the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements as well as to test various properties of the SM. We calculate the form factors of the aforementioned exclusive decays in the frame work of two approaches; 1) the light-cone sum rules (LCSR) 227 that is one of the most effective tools used to determine non–perturbative parameters of hadronic states, and 2) correspondence between string states in anti-de Sitter (AdS) space and quantum chromo dynamics (QCD) in physical space-time (AdS/QCD). The application of conformal methods to QCD can be motivated from the experimental evidence, and theoretical discussions that the QCD coupling ? s ( Q 2) has an infrared fixed point at low Q 2. In this region, the AdS/QCD approach has been successful in obtaining general properties of phenomenological QCD such as hadronic spectra, decay constants, and wave functions. By evaluating the transition form factors with the help of the twist-2, ? 3, and ? 4 distribution amplitudes (DAs) of the K pseudoscalar meson in the AdS/QCD correspondence approach, we extracted the differential branching ratio for the B ? K? + ? ? decay on q 2. The differential branching ratio, forward-backward, and isospin asymmetries for B ? K? + ? ? transition have been measured at the BABAR, Belle, CDF and LHCb collaborations. A comparison with the experimental values show that our predictions with the AdS/QCD correspondence are better than those via the LCSR and lattice QCD methods.
