DETERMINATION OF jV ub j

The precise determination of the magnitude of jV ub j with a robust, well-understood uncertainty remains one of the key goals of the heavy avor physics programs, both experimentally and theoretically. Because jV ub j, the smallest element in the CKM mixing matrix, provides a bound on the upper vertex of one of the triangles representing the unitarity property of the CKM matrix, it plays a crucial role in the examination of the unitarity constraints and the fundamental questions on which the constraints can bear 1{2]. Investigation of these issues requires measurements that are precise and that have well-understood uncertainties. Since the initial observation of the b ! u transition by CLEO 3] and ARGUS 4] over a decade ago, we have made great strides both in deening and performing new measurements, and in evaluating the related uncertainties in the extraction of jV ub j. The charmless semi-leptonic (S.L.) decay channel b ! u` provides the cleanest path for the determination of jV ub j. However , the theory for the heavy-to-light b ! u transition cannot be as well-constrained as that for the heavy-to-heavy b ! c transition used in the determination of jV cb j 5]. The extraction of jV ub j and the interplay between experimental measurements and their theoretical interpretation are further complicated by the large background from b ! c` decay, which has a rate about 60 times higher than that for charmless S.L. decay. Measurements based both on exclusive decay channels and on inclusive techniques have been, and are being, pursued. We will review the current determinations of jV ub j by CLEO and the LEP experiments within this overall context, and outline the potential for precise determinations of jV ub j at the B factories. Exclusive determinations: Reconstruction of exclusive b ! u` channels provides powerful kinematic constraints for suppression of the b ! c` background. For this suppression to be eeective, an estimate of the four momenta of the undetected CITATION: K. Hagiwara et al.