Abstract
In the four-Fermi interaction the neutrino interacts with the electron via the V-A current of the form
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We show later that lepton number cannot be gauged due to the presence of anomaly.
When we allow complex f e , we usually write the coupling that appears in (2.53) as the complex conjugate (math); see (2.74).
Gell-Mann and Levy (1958) [67] introduced this mixing angle to keep universality of the weak interaction and showed that it describes K decays. Cabibbo (1963) [126] then carried out a more extensive analysis, showing that this mixing describes well the weak interaction phenomenology of K mesons and hyperons. The mixing matrix in an orthogonal matrix form (the GIM form) was first introduced by Katayama et al. (1962) [121] and Maki, Nakagawa, and Sakata (1962) [122], and later by GIM.
In QED it is sufficient if the conservation of the vector current is sustained, and this is realised by Pauli-Villars regularisation. So, if the axial-vector current is introduced as an external current, its conservation is broken by anomaly. This leads to a physical effect such as π0 ’ 2γ.
The most accurate values from the three methods are 137.03599958(52) from the electron anomalous magnetic moment, 137.0360030(27) from quantum Hall, and 137.0360084(33) from ac Josephson. The values from quantum Hall and ac Josephson differ from that from electron anomalous magnetic moment by 1 and 2 σ, respectively.
The numbers in this table are obtained by interpolating the values given in [293] with respect to the Higgs mass.
The values in this table differ from those we derived in the text by no more than 0.001.
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© 2003 Springer-Verlag Berlin Heidelberg
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Fukugita, M., Yanagida, T. (2003). Standard Theory of Electroweak Interactions. In: Physics of Neutrinos. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05119-1_2
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DOI: https://doi.org/10.1007/978-3-662-05119-1_2
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