Higgs Mechanism, how does it work?


by friend
Tags: higgs, mechanism, work
friend
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#19
Sep2-13, 10:48 AM
P: 962
Is it true that interaction with the Higgs field causes the spin of the electron (and other massive particles, I assume) to oscillate? How does that work, I wonder?
RGevo
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#20
Sep2-13, 11:03 AM
P: 81
I am guessing what is being referred to is the higgs interactions with fermions. i.e.

y {f_{L}}^{\dagger} phi f_{R}

i.e. the sandwich of the higgs doublet phi with an SU(2) doublet of left handed fermions and right handed fermion singlet (y is the yukawa coupling). The interaction is between the left and right handed fields.. which is probably what is meant from the 'spin of the electron (and other massive particles, I assume) to oscillate?'

Perhaps someone else has a better explanation..
Bill_K
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#21
Sep3-13, 03:21 PM
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Quote Quote by friend View Post
Is it true that interaction with the Higgs field causes the spin of the electron (and other massive particles, I assume) to oscillate? How does that work, I wonder?
It's not the spin that's involved, it's a quantity called the chirality. The chirality operator is γ5, with eigenvalues 1 and projection operators (1 γ5). Given any fermion field ψ, we split it into right- and left-handed parts, ψR = (1 + γ5) ψ and ψL = (1 - γ5) ψ.

For a massless fermion, chirality is a good quantum number, but for a massive one it is not. In fact the mass term in the Hamiltonian can be written

mψψ = m(ψLψR + ψRψL)

showing that it couples ψL and ψR. Hence the energy eigenstates of the fermion do not have unique chirality.

Don't blame it on the Higgs! This holds equally true whether the mass crossterm is put in by hand, or generated by coupling to the Higgs field.


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