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As your QFT theory text should tell you, for an action invariant under G, addition of a Higgs potential only invariant under its subgroup H will spontaneously break the generators in G/H. You ought to do due diligence and study and understand and reproduce all examples of elementary classics such as Ling-Fong Li, PhysRev D9 (1974) 1723. There are, of ...

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The amplitude for low-energy muon scattering mediated by $Z$ bosons is given the the muon's "weak charge," in the same way that the amplitude for scattering mediated by photons is given by the electric charge. In units where the weak charge of the neutrino is 1, the weak charge of the charged leptons is suppressed; I think at first order it's ...

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You have no way to know if the virtual particle is a gamma or a Z. Actually, it does not really make sense, since no measurement can tell you what has been exchanged. You always have to envisage all the possibilities resulting from the perturbative series used to describe the theory. It's a bit as asking in the double slits young experiment, which slit has ...

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The early Universe is largely in a state of thermal equilibrium, after inflation the Universe has a large temperature allowing for all degrees of freedom to obtain equilibrium. This can be seen from the Boltzmann equation, which describes how the number density changes in the expanding Universe. Equilibrium is obtained by a particle species if $\Gamma \gg ... 1 When energy in a given reaction is much larger than the masses of all leptons, these masses can be neglected. For example if you consider$W\$ bosons decays, then $$M_W \gg m_\tau.$$ Tau is the heaviest among the charged leptons, so if you can neglect mass of the tau, you also can neglect masses of other leptons. But now you neglected the only quantity that ...

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