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5

It is not possible to fairly explain the origin of masses – and most other things – without "any mathematics" at all. Charged fermions get masses through their cubic "Yukawa" interactions with the Higgs $$L_{Yuk} = y\cdot h \psi_L \psi_R$$ When the Higgs field is $h=v$ in the vacuum, the simple part of this cubic term generates the quadratic term  m \...

1

To answer first to your last question, it is an experimental fact that only left-handed fermions are affected by weak interactions. The couplings of the fermions to the $W$ bosons is proportional to their weak isospin $T_3$. Therefore, right-handed fermions must have $T_3=0$. Left-handed fermions are observed to have the same isospin (charged currents ...

1

It seems like you're fixing the representation of $\mathrm{SU}(2)$ to be $T^i=\frac{1}{2}\sigma^{i}$ (i.e., the fundamental representation). This makes sense if you're talking about the Higgs mechanism. Now you want to find the generator $Y$ for the $\mathrm{U}(1)$ part of $\mathrm{SU}(2)\times\mathrm{U}(1)$. Let's call that generator $Y$. Now, any ...

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