Flavor in the Standard Model
The standard model of particle physics describes the fundamental particles and their interactions, the strong, weak and electromagnetic force, very successfully.
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Flavor in the Standard Model
2.1 The CKM Matrix The standard model of particle physics describes the fundamental particles and their interactions, the strong, weak and electromagnetic force, very successfully. An important quantum number in this model is the flavor of quarks, introduced by Gell-Mann in 1953 [1]. The three generations of quark flavor pairs are:
up d own
c harm s trange
t op b ottom
(2.1)
Each pair consists of an up-type quark with electric charge +2/3e and a down-type quark with charge −1/3e. The generations are distinguished by the different masses, increasing from the first to the third. In the standard model the flavor quantum number is conserved in strong and electromagnetic interactions. It can only be changed by charged current weak processes, described by the exchange of a W ± boson. The neutral current weak interaction (Z 0 boson exchange) is flavor-conserving. Therefore flavor changing neutral currents (FCNC) do not occur in the standard model at tree level. This makes FCNC processes a good candidate to search for deviations from the standard model because new particles or new interactions may introduce flavor changing tree level amplitudes, that are of comparable size or larger than the amplitude of the higher order standard model loop processes. The W boson couples to good approximation to the pairs of left handed quarks within one generation as shown in Eq. (2.1). The β decay of the neutron is one example for such a process. But as the decay K − → π 0 μ− v¯ μ demonstrates transitions between generations are possible, too, in this case from a s quark to a u quark. The coupling of the W boson to a us pair, however, is much smaller than to a ud pair. To describe this effect Cabibbo introduced a mixing angle θc [2] in order to preserve a common coupling parameter g that is multiplied by the factor cos θc for ud pairs and
T. Kuhr, Flavor Physics at the Tevatron, Springer Tracts in Modern Physics 249, DOI: 10.1007/978-3-642-10300-1_2, © Springer-Verlag Berlin Heidelberg 2013
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2 Flavor in the Standard Model
sin θc for us pairs. This leads to a 2 × 2 mixing matrix for the first two generations of quarks. This model describes the experimental results for processes involving the first two generations already quite well, but it turned out to be only an approximation of a more general theory. The decays B 0 → D − π + and B 0 → π + π − show that there are also transitions from the third to the second and first generation, respectively. The coupling of the W to a cb or ub pair, however, is even more suppressed than the us coupling. To describe the different coupling strengths across the three generations the 2×2 Cabibbo matrix is extended to a 3×3 matrix. The Cabibbo-Kobayashi-Maskawa matrix, or short CKM matrix, ⎛ ⎞ Vud Vus Vub (2.2) VCKM = ⎝ Vcd Vcs Vcb ⎠ Vtd Vts Vtb determines the coupling of W bosons to pairs of up- (u, c, t) and down-type quarks (d, s, b). The dynamics of the charged current interaction between left handed quarks can be expressed by the Lagrangian ⎛ ⎞
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