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The gauge symmetry group associated to the SM is $SU\left(3\right)_{c}\times SU\left(2\right)_{L}\times U_{Y}\left(1\right)$. Then we can not build the lagrangian of the SM with terms of the form $m\bar{\psi}\psi$ because they are not gauge invariant. A term of this kind mix the right and left handed parts, which transforms differently. In order to give mass ...

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In a few words, as Luke Pritchett writes, the Higgs mechanism provides us description of particles mass without breaking of the unitarity, i.e., breaking gauge symmetry explicitly. It is interesting fact that even if You start from electroweak theory in the broken phase and don't know about Higgs boson, $W/Z$-boson and existense of hidden gauge invariance (i....

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Because "spontaneous symmetry breaking" does not actually break any symmetries. This is a pretty important principle that is not always adequately taught. In spontaneous symmetry breaking the symmetry in question is always a full symmetry of the theory. The difference between a spontaneously broken symmetry and an unbroken symmetry is just in how the ...

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