Model Independent Extractions of |V_{ub}| from Inclusive B Decays

We discuss the possibility of extracting |V_{ub}| from various spectra of inclusive B decays, without large systematic errors which usually arise from having to model the Fermi motion of the heavy quark. This strategy can be applied to the electron energy spectrum, as well as the hadronic mass spectrum. Modulo violation of local hadron-parton duality, the theoretical error in the extraction is estimated to be less than 10%.Comment: 3 pages. talk given at DPF 2000, Columbus, OH, August 11, 200

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for $S$-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.Comment: 5 page