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A standard phrase in popular discussions of the Higgs boson is that "it gives particles mass". To what extent is this a reasonable, pop-science, level of description of the Higgs boson and it's relationship to particles' masses?

Is this phrasing completely misleading? If not, what would be the next level down in detail to try to explain to someone?

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I'd say that yes, this is very misleading. The next step would be to explain the concept of fundamental fields and the way they give rise to particles. –  Danu Aug 18 at 13:29
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Essentially, the Higgs mechanism provides the "bare" mass for the elementary particles. As soon as these elementary particles are allowed to interact with other particles say, the corresponding interactions will modify the effective mass of these elementary particles. In addition, the mass of any bound state of elementary particles (like a proton for instance) contains the interaction part which can be completely dominant in some cases when compared to the sum of the masses of the elementary particles. –  gatsu Aug 18 at 14:12
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As almost always, "popular science" is a collection of mis-conceptions, that have almost nothing to do with reality. It is not obvious to me, that "the next level of explanation" is any more useful to anybody than this one. Sometimes one has to study the real thing to understand... the real thing. I am afraid that particle physics may be one of these cases. –  CuriousOne Aug 18 at 14:45
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... and what gives mass to the Higgs ...? –  bright magus Aug 21 at 13:27
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Yeah, I didn't even know it was Catholic. –  Hot Licks Aug 21 at 17:54

5 Answers 5

up vote 98 down vote accepted

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 have a large amount of kinetic energy but are bound by the strong force). If any force confines energy into a small amount of space, then that bound energy has a mass given by $E=mc^2$. This is what the Higgs field does: it binds a massless particle into a small space, and therefore by $E=mc^2$ (and the fact that the particle now has a frame of reference in which it is stationary) that particle has an effective rest mass.

To get an intuitive feeling for what's going on, as an exercise you can derive $E=mc^2$ by considering a photon confined by a mirror box. The photon is bouncing back and forth exerting pressure on the mirror, and if you try to push the box it will have inertia due to the photon exerting more pressure on the front of the mirror than the back. If you work it out you will find that the mirror box has an effective inertial mass of $m=E/c^2$. The Higgs field provides a force that acts like this mirror box, thereby "giving" mass to the particle inside it.

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Wow! This is also a great explanation of inertia, which has always been a mystery to me! –  Sam Washburn Aug 18 at 17:50
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good answer, but imo does not explain why the higgs field "confines energy in a small amount of space", it seems is used to get to $E=mc^2$ and then take it from there. Seems somewhat circular. –  Nikos M. Aug 18 at 18:07
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@Nikos M, one has to stop somewhere, but to answer your question: particles that get mass from the Higgs field do so because they have some nonzero coupling between them and the Higgs field. The Higgs field is a bosonic field, so a coupling between it and another field represents a force. The effect of this coupling (force) is that the Higgs causes the particle to flip helicity at a rate that is proportional to its mass (seen directly from the interaction term in the Lagrangian). Heuristically this flipping can be thought of as being like a photon being knocked back and forth... (continued) –  user1247 Aug 18 at 19:10
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@Nikos M, that's the whole point! The Higgs field takes a massless particle (like a photon), confines it, yielding a composite system with invariant mass. The example shows that photons can indeed "acquire mass" if you enclose them in a tiny mirror. –  user1247 Aug 18 at 19:19
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+1. The best 5 minute explanation of the Higgs field / boson I've seen since the boson's discovery. –  Señor O Aug 19 at 16:09

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 state of the field corresponds to vacuum, what we call particles corresponds to excitations of the latter. If you are familiar with quantum mechanics, think of a harmonic oscillator to understand the concept.

The point is now that the mass creation effect is due to the presence of the field, not the associated particle. The existence of the particle arises as a kind of consistency requirement, which was confirmed recently at the LHC.

In this sense, the answer to your question depends entirely on what you mean by "Higgs boson": having massive particles does not mean that there are bosons in the sense of particles constantly surrounding them. They are far too heavy for this to be a viable option, as 125 GeV is far beyond what one experiences in daily life (a proton comes at a rest mass of almost 1 GeV).

For a particle physicist, it is obvious that "boson" refers to a property of the field as a whole, and not the excitation of the latter. A layman, however, will associate it with a particle moving through space time. Hence, you should not take this phrase literally. I would refrain from using it freely without providing any additional explanation.

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+1, I am still thinking if there is a way to give a particle-like picture without invoking the field as some theorists tend to see the field strengths as "that sum of creation/annihilation operators". Since the constant value in space would correspond to the zeroth Fourier coefficient, I think you could still say the particle is attached to space by a certain "soup" of Higgs bosons with zero momentum. –  Void Aug 18 at 14:45

"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 usual (kinetic) momentum $m\vec{v}$. For example, in the magnetic field the canonical momentum is $\vec{P}=m\vec{v}+e\vec{A}$, and in the static electric field the canonical energy is $E=\tfrac{1}{2}mv^2+e\varphi$ (these formulas are non-relativistic). The latter is most simply understood, because we are used to call $e\varphi$ potential energy. A force acts on the particle when such additional term changes with spatial position.

Variations of this idea depend on the tensor type of the interaction field. The electromagnetic field is a vector field, and the Higgs field is a scalar field. (The other types of fields are also possible, for example, the gravitational field in GR is a tensor field of order 2.) That leads to an important fact: the energy and the momentum change by the same factor (in the relativistic sense), which is the same as the mass would change. $\vec{P}=m\gamma\vec{v}+\Delta m\,\gamma\vec{v}$ and $E=m\gamma c^2+\Delta m\,\gamma c^2$, $\Delta m=gh$ where $g$ is the coupling constant.

Thus, wherever some scalar interaction field gets a non-zero value, particles move like they have gained some mass. And the Higgs field does have a constant non-zero value all over the Universe, $h=h_0$. Thus, all particles have their Higgs masses, and they can have no explicit mass besides it, and the theory supposes so.

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A standard simple answer (for the standard Higgs boson field) is that a particle acquires mass by passing through this field, which changes the particle's inertia (thus appearing as acquiring mass which is a measure of inertia among others)

Of course the standard Higgs boson is still investigated (if it is the standard one and not some variation of other proposals) and this is not the only way one can reason or explain how it gives mass to other particles.

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You should take it completely literally. (Quibbles about the Higgs field vs the Higgs boson are misguided. Particles don't acquire masses until the point at which the Higgs boson appears, so attributing the particle masses to the Higgs boson is just as correct.)

However, there is a simple way to picture this. The concept of a Higgs boson is completely generic, although in particle physics, one is usually referring to the standard model Higgs. A "Higgs boson" appears when a system undergoes a phase transition that breaks some symmetry.

There are many examples from solid state physics where the same thing happens. In a superconductor, for instance, at the critical temperature, the cooper pairs become the "Higgs" bosons and the particle which acquires a mass is the photon. This is the famous BCS theory of superconductors. Compare with Ginzburg-Landau theory of phase transitions, in which one expands the potential in even powers of the field).

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Before the electroweak phase transition, particles were massless, but Higgs bosons existed nevertheless. So there was a point with Higgs bosons and without masses. Masses cannot be attributed to anything but non-sezo VEV. –  firtree Aug 20 at 13:44
    
By the way, thank you for the example with the superconducting phase transition. –  firtree Aug 20 at 13:47
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I do not think that the distinction between a field and its excitations is a quibble. A field is defined in all space time, a higgs boson is an excitation of the field, and in our reality it needs 125 GeV to manifest. The mass of the electron is ~o.5MeV, and it is due to the higgs field. "Particles don't acquire masses until the point at which the Higgs boson appears," is wrong. –  anna v Aug 20 at 13:57

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