# Higgs boson's mechanism for giving mass?

What is the Higgs boson's mechanism for giving mass?

OK, so the Higgs boson interacts with particles to give them mass (as per the previous movie) but still, does anyone know the mechanism of interaction?

does anyone here know what the Higgs mechanism is?

cristo
Staff Emeritus
does anyone here know what the Higgs mechanism is?

Did you read the wikipedia page? Since you replied a minute after it was posted, I gather that you did not. If you did, what is there on that page that you do not understand?

bapowell
To clarify: it's the interaction with the Higgs field that gives gauge particles mass. The Higgs boson is the excitation of this field.

1 person
quite a bit actually. The wiki post and my post were only a coincidence. The math of the wiki post notwithstanding, it is really that simple?

"Don't shoot, it's only me," Bob hope 1990.

Last edited:
mfb
Mentor
"Simple"? It is simple if you make the model so simple that it is a very rough, and often misleading description of the actual physics.

is the Higgs field equivalent to space itself?

bapowell
is the Higgs field equivalent to space itself?
No. It's just like any other quantum field, except that there is a property of the Higgs field that is nonzero in space.

do the particles that are given mass by the Higgs field affect the Higgs field?

bapowell
Yes. For example, the mass of the Higgs particle depends on all the particles to which the Higgs couples. More generally, any property of the Higgs that gets renormalized depends on all such particles.

1 person
In general is the technique of renormalization required because of interactions?
I know the question is vague. That's because there's a lot i don't know.

bapowell
Actually the Higgs field in the vacuum should be so strong that according to Nobel laureate Veltman the universe would collapse to the size of a football.

http://lepfest.web.cern.ch/LEPFest/OfficialCeremony/Speeches/MartinusVeltman.html
That's the energy of the Higgs vacuum; I'm referring to the vacuum expectation value of the field. The latter is definitively nonzero, the former is unknown. I have no idea Veltman thinks there needs to be an energy associated with the Higgs field that would cause the universe to collapse.

That's the energy of the Higgs vacuum; I'm referring to the vacuum expectation value of the field. The latter is definitively nonzero, the former is unknown. I have no idea Veltman thinks there needs to be an energy associated with the Higgs field that would cause the universe to collapse.

Can you explain the difference?

That's the energy of the Higgs vacuum; I'm referring to the vacuum expectation value of the field. The latter is definitively nonzero, the former is unknown. I have no idea Veltman thinks there needs to be an energy associated with the Higgs field that would cause the universe to collapse.

On slide 17 of http://www.nikhef.nl/pub/theory/academiclectures/Higgs.pdf Veltman explains how he reaches this conclusion.

In general is the technique of renormalization required because of interactions?
I know the question is vague. That's because there's a lot i don't know.

That is correct.

bapowell
Can you explain the difference?
See the figure in this post: http://dorigo.wordpress.com/2007/11/10/the-goldstone-theorem-for-real-dummies/. The values +/- $\nu$ are the vacuum expectation values of the field for the corresponding vacuum. The Higgs starts in the middle, at the local maximum (the false vacuum), and rolls down to one of the minima (true vacua). The energy of the true vacua, $V(\pm \nu)$, is the vacuum energy of the Higgs. So the vacuum expectation value of the field and the vacuum energy are different things. It is generally assumed that $V(\nu)=0$, but this is really just put in by hand. If $V(\nu)<0$, then the universe should collapse if the Higgs field is dominating the energy density of the universe (this might be what Veltmann is talking about). Otherwise, if $V(\nu)>0$, the universe should inflate once the Higgs field dominates.

Here's how I like to explain it. The Higgs particle gets a nonzero field value from interacting with itself. That nonzero field value then makes it always there for particles that interact with it, and that's what gives those particles their masses.

bapowell
But you should distinguish between the Higgs field and the Higgs particle, which is the excitation of the field. Gauge bosons acquire mass through their coupling to the VEV, not through Yukawa-type couplings to the field directly.

Gauge particles don't just couple to the Higgs VEV, but to the entire Higgs field, as elementary fermions do.

bapowell
Of course, but the gauge boson mass terms arise specifically from the coupling with the VEV: $M \sim gv$, where $v$ is the VEV and $g$ the coupling.

The elementary-fermion mass terms also arise in that fashion.

Rather schematically,
$$L = |(g\cdot W)\cdot H|^2 + (y \cdot \psi_R \cdot H \cdot \psi_L) + \text{H.C.}$$
for the gauge particles and the elementary fermions.
$$H = v + \phi$$
Higgs particle -> VEV + excitations

So it works the same for both:
$$L = (m_W)^2 |W|^2 (1 + \phi/v)^2 + (m_f \cdot \psi_R \cdot \psi_L) (1 + \phi/v) + \text{H.C.}$$
where mW = g*v and mf = y*v.