rpp2010-rev-vud-vus(1)

rpp2010-rev-vud-vus(1) - 1 Vud , Vus , THE CABIBBO ANGLE,...

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–1– V ud , V us , THE CABIBBO ANGLE, AND CKM UNITARITY Updated November 2009 by E. Blucher (Univ. of Chicago) and W.J. Marciano (BNL) The Cabibbo-Kobayashi-Maskawa (CKM) [1,2] three- generation quark mixing matrix written in terms of the Wolfen- stein parameters ( λ, A, ρ, η ) [3] nicely illustrates the orthonor- mality constraint of unitarity and central role played by λ . V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb = 1 λ 2 / 2 λA λ 3 ( ρ ) λ 1 λ 2 / 2 2 3 (1 ρ ) 2 1 + O ( λ 4 ) . (1) That cornerstone is a carryover from the two-generation Cabibbo angle, λ =s in( θ Cabibbo )= V us . Its value is a critical ingredient in determinations of the other parameters and in tests of CKM unitarity. Unfortunately, the precise value of λ has been somewhat controversial in the past, with kaon decays suggesting [4] λ ± 0 . 220, while hyperon decays [5] and indirect determinations via nuclear β -decays imply a somewhat larger λ ± 0 . 225 0 . 230. That discrepancy is often discussed in terms of a deviation from the unitarity requirement | V ud | 2 + | V us | 2 + | V ub | 2 =1 . (2) For many years, using a value of V us derived from K πeν ( K e 3 ) decays, that sum was consistently 2–2.5 sigma below unity, a potential signal [6] for new physics e±ects. Below, we discuss the current status of V ud , V us , and their associated unitarity test in Eq. (2). (Since | V ub | 2 ± 1 × 10 - 5 is negligibly small, it is ignored in this discussion.) V The value of V ud has been obtained from superallowed nuclear, neutron, and pion decays. Currently, the most precise determination of V ud comes from superallowed nuclear beta- decays [6] (0 + 0 + transitions). Measuring their half-lives, t , 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– and Q values which give the decay rate factor, f ,l ead stoa precise determination of V ud via the master formula [7–9] | V ud | 2 = 2984 . 48(5) sec ft (1 + RC) (3) where RC denotes the entire eFect of electroweak radiative corrections, nuclear structure, and isospin violating nuclear eFects. RC is nucleus-dependent, ranging from about +3 . 0% to +3 . 6% for the best measured superallowed decays. The most recent analysis of Hardy and Towner [10, 11] gives a weighted average (with errors combined in quadrature) of V ud =0 . 97425(22) (superallowed) , (4) which, assuming unitarity, corresponds to λ . 2255(10). The new average value of V ud is shifted upward compared to our 2007 value of 0.97418(27) primarily because of improvements in the experimental values and nuclear isospin breaking corrections employed. We note, however, that the possibility of additional nuclear coulombic corrections has been raised recently [12]. Combined measurements of the neutron lifetime, τ n ,and the ratio of axial-vector/vector couplings, g A G A /G V ,v i a neutron decay asymmetries can also be used to determine V ud : | V ud | 2 = 4908 . 7(1 . 9) sec τ n (1 + 3 g 2 A ) , (5) where the error stems from uncertainties in the electroweak radiative corrections [8] due to hadronic loop eFects. Those eFects have been recently updated and their error was reduced
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rpp2010-rev-vud-vus(1) - 1 Vud , Vus , THE CABIBBO ANGLE,...

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