Which particles does the Higgs Field give mass to?

1,924

Solution 1

The Higgs field $\phi$ undergoes spontaneous symmetry breaking$^\dagger$ (from a complex doublet to a real scalar field, whose quantum is the Higgs boson) in a process named the Higgs mechanism. $^\dagger$: well it's a local/gauge symmetry, not global, so it's not "real" SSB, hence the different name "Higgs mechanism".

This has two consequences:

  • the gauge bosons $W^\pm$ and $Z^0$ acquire a mass term, which they couldn’t have had a priori without breaking gauge invariance. The mass depends on the VEV (vacuum expectation value) of the Higgs field, but it doesn’t arise from a direct interaction term (see below) between the Higgs field and the gauge bosons. This new mass mode is the “would-be” Goldstone boson associated with the breaking of the Higgs field symmetry. (By “no direct interaction term” I mean that the term containing a product between the gauge boson and the Higgs field is hidden in the gauge covariant derivate $D^\mu$.)

  • the fundamental fermions (quarks, leptons, but not neutrinos) also acquire a mass term. This arises from a direct interaction term between the fermionic field $\psi$ and the Higgs field, called the Yukawa Lagrangian sector. This looks like $ \mathcal{L}_Y \propto \Gamma \bar L \phi R, $ where $\Gamma$ is the Yukawa coupling to the specific fermionic field $\psi$, and $L$ and $R$ are the left- and right- handed components of $\psi$. Neutrinos have no right-handed partner so they cannot gain mass through a Yukawa coupling.

So the Higgs field is responsible for the masses of all the elementary particles (including the Higgs boson) short of neutrinos.

Solution 2

In the Standard Model, the Higgs field also gives mass to the six quarks (up, down, strange, charm, top, bottom) and the three charged leptons (electron, muon, tau) through Yukawa couplings. Some related mechanism may give neutrinos a small mass. (They’re massless in the Standard Model, but we know this is wrong.) Finally, one can argue that the Higgs field gives the Higgs boson its mass.

In short, every elementary particle except neutrinos gets its mass from the Higgs field. We’re not sure yet how neutrinos get theirs.

Solution 3

The Higgs field is coupled to the fermions (quarks and charged leptons) in the standard model via Yukawa couplings. As a result of the Higgs mechanism, the Higgs field then gives mass to these fermions, in addition to the weak bosons.

Solution 4

enter image description here

The Higgs Field gives mass to :-

  1. Everything marked in purple i.e. the quarks and anti-quarks
  2. Everything marked in green i.e. leptons and anti-leptons, which includes electrons, positrons, tau-particles, neutrinos etc.
  3. The yellow marked particle i.e. Higgs Boson, an excitation of the Higgs Field
  4. The orange-red marked particles, except for 2 (photon [$\gamma$] and gluon [$g$])

Solution 5

The Higgs field gives mass to all fermions and three weak gauge bosons (and itself) in the Standard Model. The masses of the fermions are proportional to their Yukawa couplings.

The Yukawa couplings of the neutrinos were long neglected due to their small size, and sometimes assumed to be zero. Although the evidence is consistent with nonzero neutrino Yukawa couplings, there are Standard-Model extensions where fermions also have Majorana masses. Such masses for the neutrinos have not yet been ruled out by experiment, which means we cannot be certain the neutrino Yukawa couplings are nonzero.

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sakurashinken
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sakurashinken

Updated on August 09, 2020

Comments

  • sakurashinken
    sakurashinken about 3 years

    I have found contradictory information about this. Does the Higgs field give mass only to the $W^+$, $W^-$, and $Z^0$ bosons or does it give mass to other particles as well?

    • Ross Presser
      Ross Presser over 3 years
      And now there is contradictory information here on this answer, with at least two answerers disagreeing with the accepted answer as regards neutrinos.
    • Ross Presser
      Ross Presser over 3 years
      The disagreement could probably have been reduced if your question title said according to the Standard Model, which particles...
    • sakurashinken
      sakurashinken over 3 years
      Would you say this is professional disagreement on forefront research or a breakdown in consistency in the science?
    • G. Smith
      G. Smith over 3 years
      Don’t assume that people who write answers on this site are necessarily professional physicists. Sometimes profiles will have this information. Neutrinos are a current research topic, and there are a variety of ideas about how to extend the Standard Model to explain their oscillations. I don’t think there is any breakdown in the consistency of the science.
  • G. Smith
    G. Smith over 3 years
    Can you support your claim that the Higgs definitely gives neutrinos mass?
  • sakurashinken
    sakurashinken over 3 years
    It seems from the other answers that its not proven but likely.
  • G. Smith
    G. Smith over 3 years
    Well, I changed my answer because we really don’t know. And Yukawa couplings would need right-handed neutrinos, as SuperCiocia mentioned.
  • benrg
    benrg over 3 years
    "Neutrinos have no right-handed partner so they cannot gain mass through a Yukawa coupling" is an oddly dated thing to say. They most likely do have a right-handed partner and a Higgs coupling just like all the other fermions. We shouldn't be asserting that they don't.
  • SuperCiocia
    SuperCiocia over 3 years
    Within the current formulation of the Standard Model?
  • benrg
    benrg over 3 years
    Almost certainly the neutrinos couple to the Higgs just like the other fermions. There's no reason they wouldn't. If there's a Majorana coupling, it's between the sterile neutrinos and antineutrinos, and they still have to couple to the weak charged neutrinos somehow.
  • benrg
    benrg over 3 years
    I think the current formulation of the standard model has right handed neutrinos and a Majorana term (whose coefficient may be zero). I don't think the standard model of twenty years ago should still be called standard when no one believes in it any more.
  • my2cts
    my2cts over 3 years
    @benrg "oddly dated" Did I miss something, was the right-handed neutrino found? A reference would help.
  • Ross Presser
    Ross Presser over 3 years
    @benrg "Standard Model" is its name, not its job description. Until a revision is generally accepted by the scientific community, it stays the same -- no neutrino masses. Yes, this contradicts observation. Yes, it means the Standard Model is somehow wrong. No, it doesn't mean the Standard Model suddenly changes its features in an inconsistent way.
  • benrg
    benrg over 3 years
    @my2cts If experimental detection of all of the particles was a prerequisite to being called "standard", then it never would have been called "standard".
  • benrg
    benrg over 3 years
    @RossPresser Where does that idea come from? When the model was consistent with all data and was literally the standard model of particle physics, I doubt anybody planned that it would keep that name forever even after contradictory data came along. When they found accelerating Hubble expansion, they modified the standard cosmological model in the simplest way that fit. It may turn out to be wrong. It's the standard model, not the correct model.
  • SuperCiocia
    SuperCiocia over 3 years
    You’re right. It may turn out to be wrong. Right-handed neutrino may turn out to be a thing. For now, they’re not.
  • benrg
    benrg over 3 years
    @SuperCiocia What you take as the standard model in your answer is definitely wrong. The simplest extension that allows neutrino mass, which everyone in practice now takes as the standard against which other proposed models of neutrino mass are judged no matter what you call it, may or may not be wrong.
  • Kai
    Kai over 3 years
    Does this mean that the fermions enter the theory initially as massless particles?
  • SuperCiocia
    SuperCiocia over 3 years
    You're right. It may or or may not be wrong.
  • G. Smith
    G. Smith over 3 years
    @Kai Yes, that’s right.
  • Joshua
    Joshua over 3 years
    @SuperCiocia: Observing a right-handed neutrino reaction became theoretically possible as soon as they were found to have mass due to relativistic effects. (There exists a frame in which any given neutrino is right-handed...)
  • Kai
    Kai over 3 years
    @G.Smith why is that? I understand why the gauge bosons have to be massless but why do we need the fermions to also obtain their masses from the Higgs mechanism/Yukawa coupling?
  • my2cts
    my2cts over 3 years
    @benrg You seem so certain of the sterile neutrino, but for now it is a hypothesis outside the standard model.
  • G. Smith
    G. Smith over 3 years
    @Kai The Wikipedia link explains that “mass terms preclude chiral gauge invariance”.
  • Kai
    Kai over 3 years
    @G.Smith right but I still don't get why, I always learned that gauge field cannot have mass terms because they are not gauge invariant ( i.e. $m^2 A^\mu A_\mu$). But I've never heard that massive matter fields preclude gauge invariance... But perhaps I need to understand the operative word "chiral" in the context of gauge invariance.
  • G. Smith
    G. Smith over 3 years
    @Kai This is probably elementary, but I don’t have a good explanation. I’m better at GR than I am at QFT, especially when chiral fermions are involved. Hopefully someone will explain it to both of us.
  • Sebastiano
    Sebastiano about 3 years
    I not forgot your explanation of the Lagrangian equation in chat :-)