Does the Higgs Field Consist of Higgs Bosons?

[PainterGuy]

Hi,

I'd request you to keep it simple so it's accessible by a layman.

Question 1:
Is Higgs field made up of Higgs bosons? Higgs field has a positive value everywhere. Other fields such as electron field, hover around zero though virtual particles come into existence and decay almost instantly. Only when enough energy is added to the electron field, a real electron comes into being. In my opinion, saying that electron field is made of electrons is not correct; electron field can give rise to electrons when it is excited with enough energy. So, is Higgs field really made up of Higgs bosons?

I also read that Higgs field is a scalar field and the way to detect it was to add enough energy to create a Higgs boson which in turn verifies the existence of Higgs field since every field has an associated particle with it.

Question 2:
Also many a time it is said that Higgs field is responsible for the mass of particles. In my opinion a little correct pop-sci version would be that Higgs field is only responsible for giving mass to the elementary particles such as as electrons and quarks, and their mass slowed them down to form protons, neutrons and finally atoms. On the other hand, protons, neutrons, and atoms get only a fraction of their mass from their intrinsic mass which is a result of Higgs field, and a bigger chunk of their mass results from trapped energy. For example, each proton is made up of three quarks which possesses lots of potential energy and kinetic energy, and energy is also mass.

Thanks for the help and your time, in advance!

Helpful links:
1: /watch?v=kixAljyfdqU (add www.youtube.com in front)
2: /watch?v=Ztc6QPNUqls (add www.youtube.com in front)
3: /watch?v=2kUFs6_DBrM (add www.youtube.com in front)
4: https://www.fnal.gov/pub/science/inquiring/questions/higgs_boson.html

 

[PeterDonis]

Is Higgs field made up of Higgs bosons?

No. It's the other way around. The Higgs field is the general thing that is always present. Higgs bosons are particular manifestations of the Higgs field that show up in particular scenarios, like running a high energy experiment at the LHC that collides the right kinds of particles in the right way.

Higgs field has a positive value everywhere.

More precisely, it has a positive vacuum expectation value. That does not mean it must have a positive value everywhere. It just means that, roughly speaking, its average value over the entire universe (most of which is vacuum or close to it) is positive rather than zero.

In my opinion, saying that electron field is made of electrons is not correct

That is correct; what I said above about the Higgs field being the general thing and the Higgs boson being a particular manifestation applies to all fields/particles, including the electron field/electrons.

Higgs field is a scalar field

Yes. That means that Higgs bosons, when we detect them, have zero spin (like, for example, pions). It also has more esoteric consequences that are probably beyond the scope of this discussion.

the way to detect it was to add enough energy to create a Higgs boson which in turn verifies the existence of Higgs field since every field has an associated particle with it

Yes, that's basically what I described above and what happens in the relevant LHC experiments.

Higgs field is only responsible for giving mass to the elementary particles such as as electrons and quarks

Actually, the simple Higgs mechanism, which says that the positive vacuum expectation value of the Higgs field, which arises from electroweak symmetry breaking, leads to positive masses for particles, only works for the electroweak gauge bosons--the W+, W-, and Z particles. It doesn't work for the fermions. There are various proposals for how to extend the mechanism to account for fermion masses, but I don't think any of them have been solidly established at this point.

protons, neutrons, and atoms get only a fraction of their mass from their intrinsic mass

More precisely, from the rest masses of their constituents (quarks in the case of protons and neutrons, nuclei and electrons in the case of atoms). This is true, but the fraction is much, much larger for atoms (atomic binding energies are a tiny fraction of a percent at best of the total mass of the atom). For protons and neutrons the fraction is indeed fairly small, about ten percent IIRC.

(For atomic nuclei, binding energy is roughly 10 percent at most of the total rest mass of the nucleus. So that is a somewhat intermediate case.)

a bigger chunk of their mass results from trapped energy. For example, each proton is made up of three quarks which possesses lots of potential energy and kinetic energy, and energy is also mass.

Yes, this is my understanding of how physicists currently account for the full rest masses of protons and neutrons (and other strongly interacting particles).

 

[PainterGuy]

Thanks a lot for the help!

Do you mean to say that what I had said "is correct"? I'd said that electron field was not made up of electrons.

 

[Orodruin]

Thanks a lot for the help!

View attachment 300871

Do you mean to say that what I had said "is correct"? I'd said that electron field was not made up of electrons.

Yes. Saying that the electric field is made of electrons would be like saying that the ocean is made of waves.

 

[PeterDonis]

Do you mean to say that what I had said "is correct"? I'd said that electron field was not made up of electrons.

Yes, that is what I meant: your statement that the electron field is not made up of electrons was correct, just as the Higgs field is not made up of Higgs bosons. (And as I said, the same goes for all other quantum fields and their associated particles.)

 

[PeterDonis]

@PainterGuy, btw, you don't need to post images of other people's posts. Just use the PF quote feature.

 

[vanhees71]

Actually, the simple Higgs mechanism, which says that the positive vacuum expectation value of the Higgs field, which arises from electroweak symmetry breaking, leads to positive masses for particles, only works for the electroweak gauge bosons--the W+, W-, and Z particles. It doesn't work for the fermions. There are various proposals for how to extend the mechanism to account for fermion masses, but I don't think any of them have been solidly established at this point.

I don't understand this statement. In the Standard Model the masses of the fundamental particles (the quarks and leptons) are also due to the vacuum-expecation value of the Higgs boson via the corresponding couplings between the Higgs field and the corresponding fermion fields describing quarks and leptons. That must be so, because otherwise you'd violate electroweak gauge invariance since the gauge symmetry based on the group $\mathrm{SU}(2)_{\text{L}} \times \mathrm{U}(1)_{\text{Y}}$ is a local chiral symmetry. The Higgs mechanism at the same time inevitably leads to massive gauge bosons without violating the underlying gauge symmetry either, which was the main motivation to introduce the Higgs field in the early 1960ies, because it was known that if the weak interaction is described via gauge bosons these should be massive.

More precisely, from the rest masses of their constituents (quarks in the case of protons and neutrons, nuclei and electrons in the case of atoms). This is true, but the fraction is much, much larger for atoms (atomic binding energies are a tiny fraction of a percent at best of the total mass of the atom). For protons and neutrons the fraction is indeed fairly small, about ten percent IIRC.

The "light hadrons" with up and down constituent quarks (among them protons and neutrons) get the least part of their mass not from the Higgs mechanism but is dynamically generated by the strong interaction. Although it's not completely understood, everything hints at the trace anomaly of QCD as the main mechanism leading to almost all of the mass of these light hadrons. The spontaneous breaking of the approximate (global!) chiral symmetry of the light-flavor sector of QCD (the socalled "$\sigma$ term") provides only the splitting between the parity partners of hadrons (like between the proton and $\mathrm{N}^*(1535)$ or the $\rho$ and $\mathrm{a}_1$ mesons, etc.).

One empirical hint comes from relativistic heavy-ion collisions, where the thermal-dilepton production is described by models, where the masses of the light vector mesons stay more or less where they are in the vacuum and only the corresponding axial-vector partners' masses go down (in contradistinction to the "dropping-mass scenario" a la Brown and Rho).

(For atomic nuclei, binding energy is roughly 10 percent at most of the total rest mass of the nucleus. So that is a somewhat intermediate case.)

Indeed, but here you can really describe the "bound state" (atomic nuclei) as being a bound state of "fundamental constituents" (the nucleons, i.e., protons and neutrons).

In the case of the hadrons as "bound states" of quarks and gluons this naive picture of "constituents" is not applicable anymore.

Today the only way to assess the hadron spectrum from first-principle QCD is the use of lattice-QCD calculations, and indeed there's a tremendous progress here: Indeed one can describe with an accuracy of a few percent the mass spectrum of the known hadrons (plus of some hadrons that haven't been observed yet).

An intuitive picture from "first principles" is still lacking, because it's indeed a problem which is not describable in any way by perturbation theory. One intuitive picture are the socalled "bag models", where the hadrons are understood as "bags" in the non-perturbative QCD vacuum containing and "confining" constituent quarks, which are quasi particles of some 100 MeV mass (in contradistinction to the "current quark masses" in the QCD Lagrangian) with their mass and thus the mass of the hadrons being dynamically generated in this way.

However, the naive picture of the hadrons being bound states of constituent quarks (3 quarks for baryons, a quark and an antiquark for mesons) is also not entirely right. From deep-inelastic scattering one can figure out the socalled parton-distribution functions, and this reveals that besides the "point like" partons a la Feynman there's also a cloud of sea quarks and antiquarks as well as gluons "inside" these hadrons. The question, how the "bulk properties" like mass and spin are "distributed" over these "constituents" is also under investigation and not so easy to define.

Yes, this is my understanding of how physicists currently account for the full rest masses of protons and neutrons (and other strongly interacting particles).

 

[PeterDonis]

I don't understand this statement.

My understanding may be incorrect. If you have good references they would be helpful.

 

[vanhees71]

My favorite as an introduction to the Standard Model is

O. Nachtmann, Elementary Particle Physics - Concepts and
Phenomenology, Springer-Verlag, Berlin, Heidelberg, New
York, London, Paris, Tokyo (1990).

Of course it doesn't contain the more recent developments (particularly neutrino masses and mixing), but it gives a very good introduction with a minimum of QFT needed to understand why the Standard Model looks the way it looks.

As I said in the Standard Model all fundamental masses are due to the Higgs mechanism: The W- and Z masses are generated by the Higgs mechanism. The upshot is: You start with a model for massless free quarks and leptons having the chiral flavor symmetry $\mathrm{SU}(2)_{\text{L}} \times \mathrm{U}(1)_{\text{Y}}$, which is spontaneously broken to $\mathrm{U}(1)_{\text{em}}$ via some scalar flavor multiplet (the minimal version is to introduce just a Higgs doublet). Then you make this symmetry local in the usual way by introducing gauge-boson fields and employ minimal coupling. In this process the Goldstone modes of the spontaneously broken global symmetries can be "gauged away" such that these field-degrees of freedom provide the additional third longitudinal polarization state of the then massive three gauge bosons, which then can be interpreted as the W- and Z-bosons. One of the four gauge fields stays massless and can be interpreted as the photon. There are no more massless Goldstone modes left as physical degrees of freedom, indicating the fact that a local symmetry cannot be spontaneously broken. In the case of the "minimal Higgs model" you are left with one physical massive scalar field, the Higgs field with the non-vanishing vacuum expectation value and with its excitations describing corresponding massive particles, the famous Higgs boson.

BTW this pattern has been found by Andersen in the context of superconductivity, and Higgs et al took this result up and used it in elementary-particle physics: starting with the electron-phonon model you get spontaneous symmetry breaking for an attractive effective interaction between the electrons, leading to BCS theory. Then introducing electromagnetism by gauging the usual global $\text{U}(1)$ symmetry the Goldstone modes are absorbed and the photons get massive (describing the Meissner effect of superconductors).

To make the model renormalizable you must also provide Yukawa couplings of the quarks and leptons to the Higgs field. The vacuum expectation value of the Higgs field then also leads to masses for the quarks and leptons (the neutrinos however stay massless in this model). The crucial point is that in this way you get the masses for the W- and Z-Bosons as well as the quarks and leptons without violating the chiral gauge symmetry, which is crucial of course. Another important finding is that with the phenomenologically motivated charge pattern for the quarks (including 3 additional color-degrees of freedom for each quark flavor) there's also no anomalous breaking of the gauge symmetry.