Determination of |v Ub |

The element V ub of the CKM mixing matrix is the smallest of the quark couplings and is crucial in understanding CP violation in the B system. In this review, we discuss the present status of the determination of its magnitude, which involves a significant effort both experimentally and theoretically. Decisive progress has been achieved in recent years, thanks in part to the large data sets that have become available at the B factories. Based on these data we propose an average |V ub | value of (3.67 ± 0.47) × 10 −3 , which has an uncertainty of 13 %. With the experimental and theoretical progress expected in the next few years a determination to an accuracy of 10 %, or better, seems feasible. The precise determination of the magnitude of V ub with a robust, well-understood uncertainty remains one of the key goals of the heavy flavor physics programs, both experimentally and theoretically. Because |V ub |, 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 (see the minireviews on the CKM matrix 1 and on CP –violation 2 for details). Investigation of these issues require measurements that are precise and that have well–understood uncertainties. The charmless semi-leptonic (s.l.) decay channel b → uℓ¯ ν provides the cleanest path for the determination of |V ub |. 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 |V cb | (see the |V cb | minireview 3). The extraction of |V ub | and the interplay between experimental measurements and their theoretical interpretation are further complicated by the large background from b → cℓ¯ ν 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.