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98

The Higgs field (note it is the field that is important here, not the Higgs boson itself, which is just a ripple in the Higgs field) gives particles mass in the same sense that the strong force gives the proton mass (context: $99\%$ of the mass of the proton comes not from the mass of its constituent quarks, but from the fact that roughly speaking the quarks ...


33

You probably know that the mass of the Higgs boson is around $125$ GeV, which means the energy it takes to create a Higgs boson is around $125$ GeV and therefore that the temperature at which significant numbers of Higgs bosons will be created will be given by $kT = 125$ GeV. One GeV is $1.602 \times 10^{-10}$J, so the corresponding temperature is around ...


20

Massless photon Photons interact with the "Higgs doublet" but they don't interact with the "ordinary" component of the Higgs field whose excitations are the Higgs bosons. The reason is that the Higgs vacuum expectation value is only nonzero for the component of the Higgs field whose total electric charge, $Q=Y+T_3$ where $Y$ is the hypercharge and $T_3$ is ...


20

The show you watched seems to get two concepts mixed up: Supersymmetry and Dark Matter. The existence of Dark Matter is strongly hinted at by comsological and astrophysical considerations. It is the easiest explanation for several observations we make in the universe. Supersymmetry on the other hand provides a candidate particle. The lightest ...


15

Most of the popular science TV programmes and magazine articles give entirely the wrong idea about how the Higgs mechanism works. They tend to give the impression that there is a single Higgs boson that (a) causes particles masses and (b) will be found around 125GeV by the LHC. The mass is generated by the Higgs field. See the Wikipedia article on the Higgs ...


15

Short answer: do not take it literally, without further context. In order to understand the Higgs boson's role in the Standard model, it is necessary to take a closer look at the framework in which we describe elementary particles: quantum field theory. In this approach, particles are described as excitations of fields that spans all spacetime. The ground ...


15

The proposal in that article is that the Higgs boson is ~70GeV and stable. Since the article was written, it has been discovered that the Higgs boson is ~126GeV and decays. The hypothesis has been disproven.


11

The analysis of the phase structure of gauge theories is a whole field. Some major breakthroughs were the t'Hooft anomaly matching conditions, the Banks-Zaks theories, Seiberg duality, and Seiberg Witten theory. There is a lot of controversy here, because we don't have experiment or simulation data for most of the space, and there is much more unknown than ...


10

"Binding a massless particle into a small space" is a good phrase for a popular discussion, but it is not the only way to picture the Higgs mechanism. Another perspective comes from the fact that every particle inside some interaction field behaves exactly like its energy or momentum has changed. This concept is called canonical momentum, in contrast to the ...


9

Just conserve angular momentum. If I have two photons on a collision course, their spin can either be aligned or anti-aligned, since photons must have spins lying on the same plane as their motion by virtue of their masslessness. Then, you can either add one to one to get two, or you can subtract one from one to get zero. If you have a decay to two ...


8

The difficulty with Higgs boson is it's high mass, so in order to create it, you need lots of energy (125GeV, using $E=mc^2$). What is important to give particles mass is s the Higgs field, not the Higgs boson (which is an excitation of the field). The problem is that you have mixed the concept of real particles and "virtual" or "force carrier" ...


8

Yes there are "virtual" Higgs bosons. A virtual particle isn't really a particle but a ripple / disturbance in a field. So a virtual electron is a ripple in the electron field. A virtual higgs is a ripple in the higgs field. Virtual particles are just a convenient conceptual model for describing field disturbances in terms of particles. Matt Strassler ...


8

I) At the perturbative/diagrammatic level of photon self-energy/vacuum-polarization $\Pi^{\mu\nu}$ , the photon masslessness is protected by the Ward identity, which in turn is a consequence of - you guessed it - gauge invariance. For the explanation in the setting of QED, see e.g. Ref. 1. Fig. 1: A one-loop contribution to the photon ...


8

I don't think you understand QFT. To be fair, I'm no expert myself, but I can certainly point out where you're going wrong here. A particle does not enter the Higgs field. However, the particle field that gets mass from the Higgs field does interact with the Higgs field. What this means is that in the Lagrangian of your model, there exists a term that will ...


8

Does a particle enter/interact with the Higgs Field when created, or at some other time? After reading your question a couple of times as well as your comments, it occurs to me that you're picturing something like this: a massless particle is created, interacts once with the Higgs field to acquire a permanent classical like mass which it then ...


7

Notwithstanding the previous answers, bear in mind that the Higgs boson fields is pervasive throughout the whole universe, according to the Standard Model of particle physics. The interaction between the Higgs field and the matter fermion fields (quarks, electron, muon, etc) provides the fermions with mass. This means that there are virtual Higgs bosons ...


7

Linear terms can be thought as source terms. They are important to define the effective potential (which is the Legendre transform of the (log of) the partition function with respect to the source). I'm not sure why one would say that one can forget about them, since, for instance, they imply a non zero value of $\langle \phi\rangle$ even in the symmetric ...


7

The electron-positron pair can produce directly a Higgs boson, but this process is very suppressed, because the coupling between the leptons and the Higgs is proportional to the tiny mass $m_e$: $$g_{\rm Hee}=-i\frac{ m_e}{v},$$ where $v\approx 246 \,\rm{GeV}.$ On the other hand, the process $e^+ e^-\to H Z$ is more likely to happen, because the coupling ...


7

In few words: All the data gathered on particle physics can be beautifully classified in what is called the Standard Model. It is based on group symmetries in the behavior of particles, three groups two of them special unitary groups and one a simple unitary group. SU(3) x SU(2) x U(1) strong weak electromagnetic each group representing ...


7

Courtesy of the question Bound State of Only Massless Particles? Follows a Time-Like Trajectory? the answer to your question is no. If you take the example of a glueball formed from two gluons, although the gluons are massless the glueball has a rest mass. In his answer to the above question Ben Crowell argues that the glueball must move on a timelike ...


7

does this mean there is some kind of self-interaction Yes, the Higgs field is self-interacting and, to the extent I understand it, it is this self-interaction and particularly, its form, that allows the Higgs field to "condense" by giving the lowest energy states of the field a non-zero expectation value. But the Higgs fields have electroweak charge. ...


7

It's certainly possible for a particle's mass to come partially from kinetic energy of massless particles; for example, about half of a proton's mass is the kinetic energy of its gluons. But the kind of mass that fundamental particles have, the kind that comes from the Higgs mechanism, doesn't appear to be of that kind. Maybe someday we will discover that it ...


6

Higgs mechanism is not the universal mass-responsible detail, but the ultimate. Other mechanisms could give you large quantities of mass - and in fact they do - but there is still some part which they are unable to explain. And that's why the Higgs mechanism is needed. Numbers for you: For the atom of hydrogen: Total mass - about 1 GeV Electromagnetic ...


6

That really depends on what you call necessary. If you completely forget all about $SU(2)_L$ (say, in an alternate universe with no Weak Interactions). Then mass terms in the Lagrangian for quarks and leptons are not forbidden by any symmetry and you would not need the Higgs field to generate the mass of the quarks or of the electron. Now, in OUR ...


6

It is important to distinguish between the Higgs boson and the Higgs field. The Higgs field is present in all of space and it has a nonzero value everywhere, because that's the lowest-energy configuration, whereas the Higgs boson is an excitation of this field which takes quite a bit of energy to get going. I'm definitely no expert, but here goes a very ...


6

Gauge Bosons Mass terms for any gauge bosons are forbidden since they are not invariant under gauge transformations. Suppose you have some symmetry $ SU(N ) $ with generators $ T ^a $. To be a symmetry there must be a set of gauge bosons which I denote $B _ \mu ^a $. The mass terms for these bosons are \begin{equation} - m ^2 B _ \mu ^a B ^{a, \mu} ...


6

This question is similar to "where is the electromagnetic field?" And the answer is: the electromagnetic field is everywhere; it exists at every point in space-time, but it simply happens that its average value is zero (or close to zero) at points far away from charges, currents, and waves. The Higgs field, like the electromagnetic field, is a quantum ...


6

Dark Matter candidates have to interact very weakly with the particles of the Standard Model in order to have a relic density compatible with the one measured by the Plank satellite. The Higgs boson cannot be Dark Matter, because the decay rate for a process like $H\to f\bar{f}$ is very high for a mass around $m_H=126 ~\rm{GeV}$. However, there are still ...


6

The advantage of unitary gauge is that it completely removes unphysical fields, while adding additional degrees of freedom to the gauge bosons, which consequently become massive. This gauge works well for tree-level calculations, but complications arise when considering loops: The propagators of gauge fields and ghosts (which are needed to impose the ...


6

The photon implements the electromagnetic force - it interacts with charged particles. Because the Higgs boson is neutral, it cannot (directly) interact with the photon. Another reason why the Higgs boson and the photon cannot (directly) interact is that interactions with the Higgs boson result in mass (after electroweak symmetry breaking). The photon is ...



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