rpp2010-rev-vcb-vub - 1 DETERMINATION OF Vcb AND Vub...

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–1– DETERMINATION OF V cb AND V ub Updated March 2010 by R. Kowalewski (Univ. of Victoria, Canada) and T. Mannel (Univ. of Siegen, Germany) INTRODUCTION Precision determinations of | V ub | and | V cb | are central to testing the CKM sector of the Standard Model, and com- plement the measurements of CP asymmetries in B decays. The length of the side of the unitarity triangle opposite the well-measured angle β is proportional to the ratio | V ub | / | V cb | , making its determination a high priority of the heavy flavor physics program. The semileptonic transitions b ν ± and b ν ± pro- vide two avenues for determining these CKM matrix elements, namely through inclusive and exclusive Fnal states. The experi- mental and theoretical techniques underlying these two avenues are independent, providing a crucial cross-check on our under- standing. Recent measurements and calculations are reflected in the values quoted in this article, which is an update on the previous review [1]. The theory underlying the determination of | V qb | is mature, in particular for | V cb | . The theoretical approaches all use the fact that the mass m b of the b quark is large compared to the scale Λ QCD that determines low-energy hadronic physics. The basis for precise calculations is a systematic expansion in powers of Λ /m b ,wh e r 500 700 MeV is a hadronic scale of the order of Λ QCD , using e±ective-Feld-theory methods to separate non-perturbative from perturbative contributions. The expansion in Λ /m b and α s works well enough to enable a precision determination of | V cb | and | V ub | in semileptonic decays. The large data samples available at the B factories have opened up new possibilities experimentally. Analyses where one B meson from an Υ(4 S ) decay is fully reconstructed allow a recoiling semileptonic B decay to be studied with higher purity than was previously possible. Improved knowledge of CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34
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–2– B X c ± ν ± decays allows partial rates for B X u ± ν ± transi- tions to be measured in regions previously considered inacces- sible, increasing the acceptance for B X u ± ν ± transitions and reducing theoretical uncertainties. Experimental measurements of the exclusive B π± ν ± decay are quite precise. Further improvement in the theoretical calculation of the form factor normalization is needed to fully exploit these measurements. Throughout this review the numerical results quoted are based on the methods of the Heavy Flavor Averaging Group [2]. DETERMINATION OF | V cb | Summary: The determination of | V cb | from B D ± ν ± decays is currently at a relative precision of about 3%. The main limitation is the knowledge of the form factor near the maximum momentum transfer to the leptons. For the B ν ± channel experimental measurements have recently been substantially improved, allowing this channel to provide a meaningful cross- check on B D ± ν ± .
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rpp2010-rev-vcb-vub - 1 DETERMINATION OF Vcb AND Vub...

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