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The easiest way to form $SU(2)$ singlets in the most general way is to use the techniques of Young Tableau. The method is discussed from a physicists perspective in many lecture notes online. One such example is given here. Using such method its easy to show that 2 lepton doublets make a singlet and a triplet under $SU(2)$, \begin{equation} 2 \otimes 2 = 3 ...


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CP-violation in standard model is due to CKM complex phase of the quarks sector. You can see the parametrization of CKM matrix, like Wolfenstein parametrization, and see that there is only a phase in CKM matrix, the work of Kobayashi-Maskawa is about to understand that you need three generation of quarks to have CP-violation. Now you can have a similar ...


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In the Standard Model, the lepton sector does not have CP violating couplings (at tree level). The quark sector however has CP-violating couplings (through the CKM matrix). The PMNS matrix (describing neutrino mixing), may have a complex phase (implying CP violation). Whether it has a nonzero phase or not remains to be tested experimentally. This is ...


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Notation $W^{-}, W^{+}$ may confuse in a sense that it may seem that here are two different particles which aren't connected by charge conjugation. But of course, $W^{+}$ is only $(W^{-})^{\dagger}$, so it is an antiparticle to $W^{-}$. So term $( W^{-} \cdot W^{+} )$ is simple $|W|^{2}$ (which is standard for the mass-term), and, of course, both of particle ...


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The electroweak Lagrangian contains terms which are not eigenstates of $P$, but (to good approximation) only terms which are eigenstates of $T$. Since $CPT$ is an exact symmetry, the electroweak Lagrangian must contain terms which are not eigenstates of $C$.


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Weak interactions include only the left neutrinos (and right antineutrinos). It means that all neutrino-interaction terms in the Lagrangian also consist only the left particles (and right antiparticles), because $\bar{\Psi}\gamma^{\mu}\Phi_{R, L} = \bar{\Psi}_{R, L}\gamma^{\mu}\Phi_{R, L}$. It means that the charged current terms $L_{\int}^{CC} = g ...



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