I was watching a Leonard Susskind video, "Demystifying the Higgs.." https://www.youtube.com/watch?v=JqNg819PiZY

At some point he is discussing the Z-boson and what he terms the Zilch field. (weak iso-spin of the electron, or weak hypercharge?)
He seems to imply that the electron get's most of it's mass from this "Higgs-like" interaction with the Z-boson. Is this right? or am I just not understanding?

This question, seem to be what I'm asking.

Be gentle, I don't know much particle physics, (I audited the beginning of a Quantum Electro-dynamics course in grad. school. So I barely know iso-spin.)

(Note; there are a ton of other related questions. I'll try and post any that look relevant.)


1 Answer 1


The mechanism involves transferring components of the Higgs field to Longitudinal components of the $Z$ and $W^\pm$. This conserved degrees of freedom of the Higgs field by transferring them to the longitudinal component of these gauge particles.

A spin $1$ particle with mass has three possible projections of its spin $m~=~(-1,~0,~1)$. The $m~=~\pm 1$ correspond to the spin projected along the momentum in the left and right configurations. The spin $m~=~0$ case means the spin is in a frame where it has no projection along the momentum. This can only occur if it is possible to be in the rest frame of the particle. That means it must have a mass. This also means the gauge field has in addition to two longitudinal directions its field can be aligned, there is also a longitudinal component. .

A longitudinal wave is such that for sufficiently high energy its longitudinal component can at sufficiently high energy travel faster than light. This is why it was apparent that something was wrong with quantum field theories with massive gauge bosons. Engelbert and Higgs realized a way out of this problem by having the gauge bosons massless at sufficiently high energy, but where at lower energy they acquire mass with the Higgs field.

The Higgs field is a pair of doublet field $$ \phi^+~=~\left(\matrix{H^+\cr H^0}\right),~\phi^-~=~\left(\matrix{H^-\cr h^0}\right). $$ The covariant derivative of the Higgs field $\partial_\mu\phi^a~+~ig\epsilon^{abc}A^b_\mu\phi^c$ couples the Gauge bosons to the Higgs field. At low energy the gauge tensor leaves $\frac{1}{2}m^2A^2$ terms for a massive boson, and the $H^\pm,~H^0$ components or Goldstone bosons are absorbed. This in a nutshell is how the weak interaction becomes mediated by massive bosons, $Z^0$ for the neural weak current and $W^\pm$ for flavor changing charged current. The remaining $h^0$ is the Higgs particle detected in 2012.

For fermions things are more phenomenological. For the fermion $\psi$ there are proposed coupling terms with the Higgs field with Lagrangian terms $$ {\cal L}_y~=~g\bar\psi H\psi, $$ called Yukawa Lagrangians. These are nuanced in some ways. However, with lattice QCD it is thought something like this must give quarks mass so the mass of hadrons is not just due to QCD mass gap. Of course electrons and other leptons, including neutrinos, have mass. Yet given the tiny mass of neutrinos and the large mass of the top quark this has a huge range of coupling constants.

  • $\begingroup$ "Woosh", The sound of most of that going over my head. From your first sentence, I take your answer to my question to be a qualified yes. Is that correct? (I'm going to have to watch Susskind's video again.) $\endgroup$ May 22, 2017 at 20:00

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