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CERN-THESIS-2012-153 26/07/2012 - CERN Document Server

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The CKM matrix is a 3 × 3 unitary matrix, V †<br />

CKM VCKM = 1, which can be parameterized by three mixing<br />

angles and a CP-violating phase. The unitarity of the CKM matrix imposes:<br />

∗<br />

i<br />

VijVik = δjk and ∗<br />

i<br />

VijVkj = δik<br />

(2.31)<br />

The current experimental values of the matrix elements are:<br />

⎛<br />

⎜<br />

⎝<br />

|Vud| |Vus| |Vub|<br />

|Vcd| |Vcs| |Vcb|<br />

|Vtd| |Vts| |Vtb|<br />

⎞<br />

⎛<br />

⎟<br />

⎠ =<br />

⎜<br />

⎝<br />

0.97427 ± 0.00015 0.22534 ± 0.00065 0.00351 +0.00015<br />

−0.00014<br />

0.22520 ± 0.00065 0.97344 ± 0.00016 0.0412 +0.0011<br />

−0.0005<br />

0.00867 +0.00029<br />

−0.00031<br />

0.0404 +0.0011<br />

−0.0005<br />

0.999146 +0.000021<br />

−0.000046<br />

⎞<br />

⎟<br />

⎠<br />

(2.32)<br />

The magnitudes of the CKM elements just quoted were extracted from Reference [20]. These are determined<br />

by a global fit that uses all available measurements and imposes the SM constraints (three generation<br />

unitarity).<br />

W- and Z-bosons Production and Decay Modes<br />

At pp colliders the electroweak gauge bosons are produced as single particles or in pairs through a parton-<br />

parton process, for example the Drell-Yan production of W- and Z-bosons, q¯q → Z and q¯q ′ → W. The<br />

Z-bosons decay into a pair of opposite charge fermions, that can either be two same-flavor leptons (e, µ, τ<br />

or ν) or two same-flavor quarks. The latter represents a hadronic final state, and it is the one with largest<br />

branching fraction (∼ 70%). The W-boson can decay to a lepton and a neutrino of the same generation, or<br />

two quarks of the first or second generation. In this case too, the hadronic final state carries most of the<br />

branching fraction (∼ 68%). Figure 2.2 shows the Feynman diagrams for the decays of these two bosons.<br />

(a) (b)<br />

Figure 2.2: Decay modes of the W- and Z-bosons. In the case of the W-boson, the lepton ℓ carry the same<br />

charge as the boson.<br />

13

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