# The main arguments for Higgs

1. Aug 27, 2011

### exponent137

What were so strong arguments, that they go to such measurement?

Why it is wrong to say simply, that Higgs does not exist? Why it is necessary?

Last edited: Aug 27, 2011
2. Aug 27, 2011

### Staff: Mentor

3. Aug 28, 2011

### exponent137

In the standard model, at temperatures high enough so that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature, the symmetry is spontaneously broken, and the W and Z bosons acquire masses.

Why at high temperatures all elementary particles are massless? More precisely asked, why W+- and Z particles are massles? If we assume that they are not, where is contradiction?

I know that at low energies we have fine structure constant 1/137, if we are enough close to electron fsc is enlarged and enlarged and at 1/128 we have weak force and W+- and Z particles cause it. (not precisely written)
When electron and neutrino interact, Their immediate particle is W or Z boson. Masses of W and Z bosons are large. So this more rarely happens at low energies. Why then still it is necessary that W and Z at high energies does not have mass?

"The fact that the W and Z bosons have mass while photons are massless was a major obstacle in developing electroweak theory. These particles are accurately described by an SU(2) gauge theory, but the bosons in a gauge theory must be massless."
Why the bosons in a gauge theory must be massless?

Last edited: Aug 28, 2011
4. Aug 28, 2011

### Bill_K

Two reasons. A mass term like m2 WμWμ is not gauge invariant, so cannot be added to the Lagrangian. Secondly, a vector boson having mass is not quantum mechanically consistent. To avoid violating the basic principle of unitarity you must include precisely those terms that the Higgs contributes.

5. Aug 30, 2011

### Lapidus

Can anybody tell me or give me a link to what alternatives theoreticians have thought up if Higgs is not found?

thanks!

6. Aug 31, 2011

### Staff: Mentor

See post #2 in this thread.

7. Sep 8, 2011

### mike372

I would highly recommend Matt Strassler's Higgs FAQ to answer some of this:

http://profmattstrassler.com/articles-and-posts/the-higgs-particle/360-2/

Note he talks about the Higgs field. This is THE important thing that is being looked for at the LHC. We know (without doubt) there must be some field that breaks the electro-weak symmetry and this is really what is being looked for at LHC and will almost certainly be found. Matt Strassler calls this field the Higgs field.

Now in the most simple version of things, part of the Higgs field is the Higgs Boson, which, if it exists will hopefully be discovered this year. However the Higgs boson itself does not have to exist but some field (call it the Higgs field if you like) does have to exist to break the EW symmetry.

The arguments why the Higgs filed needs to exist are quite technical but I think the link above does a good job of seperating out the often consused notions of the field that breaks EW symmetry and a particular particle called the Higgs Boson.

8. Sep 9, 2011

### edpell

Frank Wilczek in his book "The Lightness of Being" seems to calculate the masses of the particles without using Higgs. Or more exactly he seems to get 95% of the mass. So is the Higss needed just for the 5%?

9. Sep 10, 2011

Staff Emeritus
See post #2. <sigh>

10. Jul 5, 2012

### exponent137

As I understand, this is mentioned for W+- and Z and possibly for gluons. Thus this is mentioned for quarks and thus for fermions and bosons.

But why Higgs boson creates the electron mass?

Last edited: Jul 5, 2012
11. Jul 5, 2012

### lpetrich

The Higgs particle interacts with the elementary fermions, like the electron, with a Yukawa interaction:
$y \bar{\psi}\psi\phi$
From left to right, the Yukawa-interaction strength, the conjugate of the fermion field, the fermion field, and the Higgs field. I'm simplifying it a bit, but this should give the essential idea.

Let's rearrange it a bit:
$(y\phi ) \bar{\psi}\psi$
If the Higgs field is constant and nonzero, then the term in ()'s acts like a mass. So the Higgs particle makes other particles massive by always being present.

12. Jul 6, 2012

### exponent137

http://physicsworld.com/cws/article/news/2012/jul/05/its-a-boson-but-what-sort
it is also written:
CERN physicist Gian Giudice. He says: “the Higgs mechanism accounts for about 1 per cent of the mass of ordinary matter, and for only 0.2 per cent of the mass of the universe. This is not nearly enough to justify the claim of explaining the origin of mass.”

Is this true?

13. Jul 6, 2012

### JPBenowitz

Only about 5% of the mass in protons and neutrons is to due to the Higg's Mechanism while the other 95% is gluon kinetic energy. Then there is dark matter which accounts for I think 84% of the matter in the universe. Whether or not DM interacts with the Higg's Field isn't known, so no the Higg's doesn't explain the origin of mass.

14. Jul 6, 2012

### lpetrich

All that Gian Giudice is pointing out is that most of the mass of familiar, baryonic matter is indeed produced by a mechanism other than the Higgs mechanism or something similar. It's a result of color confinement - QCD-colored particles cannot get more than about 10-15 m from each other, because of their interaction strength becoming superstrong. That means that the quark and gluon wavefunctions in a hadron can have at most that size, thus bumping up their kinetic energy. Protons' and neutrons' masses are thus about 98% QCD-induced effects, 1% electromagnetic interactions, and 1% quark masses, mostly up and down.

That does not diminish the value of the discovery of the Higgs particle or at least a Higgs-like particle, because the masses of the quarks, leptons, W, and Z must still be accounted for. There is no way to make them without breaking the electroweak symmetries, and that's what the Higgs mechanism was proposed for doing.

15. Jul 6, 2012

### lpetrich

More like 1% quark masses (Higgs mechanism), 1% electromagnetic, and 98% color-confinement effects: kinetic energies of the quarks and gluons.

The Lambda-CDM "Standard Model" of cosmology has these mass fractions for the present time:
Baryonic matter: 5%
Dark matter: 23%
Dark energy: 72%

The nature of dark matter and dark energy are obscure, though they cannot be Standard-Model particles.

16. Jul 7, 2012

### exponent137

Is this sure? Why not to built all matter?

The question appears a lot of times, what gives mass to Higgs boson?

17. Jul 7, 2012

### lpetrich

exponent137, consider what would happen if a putative dark-matter particle has QCD or electromagnetic interactions.

Short-short summary: it would act just like baryonic matter, the familiar kind, and it would produce various anomalies that we don't observe. See if you can try to work out some of them. Imagine some particle between 10 GeV and 10 TeV, say, 100 GeV or 1 TeV, with electric charge +1 or -1, or QCD multiplicity 3 (quarklike; electric charge -1/3+n), 3* (antiquarklike; electric charge +1/3+n), or 8 (gluonlike; electric charge n).

Seems like a good exercise for students in a particle-physics or astrophysics course.

So the only Standard-Model that has the right interactions for a dark-matter particle are neutrinos. But there's a problem: neutrinos' masses are too small, <~ 0.1 eV. They aren't massive enough to become "cold dark matter", the most common kind.

That's why dark-matter elementary particles cannot be Standard-Model particles.

In the Standard Model, the Higgs particle is self-interacting, and its self-interactions generate its mass.

For field strength f, its potential looks like V(f) = (1/2)*V2*f2 + (1/2)*V4*f4
The second term is a self-interaction term.

Find its minimum. That requires solving dV(f)/df = 0, giving f*(V2 + V4*f2) = 0

Consider each solution's stability. Find d2V/df2 = V2 + 3*V4*f2.
If > 0, then it's stable; if < 0, then it's unstable; if = 0, then it's borderline.

Solutions.

f = 0. Second derivative = V2

If V2 < 0, then there's another solution:

f = sqrt(- V2/V4)

The f = 0 solution is unstable, but this solution has second derivative -2V2 > 0, meaning that it's stable. A Higgs particle will have V2 < 0, making this solution stable, complete with nonzero f.

That's what's behind the analogy of a marble in a bowl with a central hump.

18. Jul 7, 2012

### lpetrich

I'll now illustrate how the Higgs particle makes mass with a toy model: electromagnetism with a complex charged scalar, a Higgs-like field.

Its Lagrangian:
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 ((\partial_\mu - iqA_\mu)\Phi)((\partial^\mu + iqA^\mu)\Phi^*) + \frac12 V(|\Phi|^2)$
Electromagnetic kinetic-energy, scalar kinetic-energy with electromagnetic interaction, scalar potential terms.

Let $\Phi = \phi e^{i\theta}$
where both quantities on the right are real. The Lagrangian becomes
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 \partial_\mu\phi \partial^\mu\phi + \frac12 (\partial_\mu\theta - qA_\mu)(\partial^\mu\theta - qA^\mu)\phi^2 + \frac12 V(\phi^2)$
The $\phi$ is a neutral scalar field, and the $\theta$ is the Goldstone mode. Do a gauge transformation on the electromagnetic field:
$A_\mu \to A_\mu + \frac{1}{q}\partial_\mu\theta$

The Lagrangian becomes
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 \partial_\mu\phi \partial^\mu\phi + \frac12 (q\phi)^2 A_\mu A^\mu + \frac12 V(\phi^2)$
The third term has the form of a mass term, with a mass
$m = q\phi$

The Lagrangian has become a Lagrangian for a neutral scalar field and a massive photon, with the Goldstone mode disappearing into the latter.

I hope that I got that right.

19. Jul 7, 2012

### exponent137

1. But the root of arising of masses is in quantum gravity (QG). It also defines natural units of mass, Planck's mass. So, how Higgs boson can be linked with QG? OK, it is known, supersymmetry, and additional dimensions. Can it go simpler, without this?

2. As visible in
http://physicsworld.com/cws/article/news/2012/jul/05/its-a-boson-but-what-sort
there are some different probabilites for decay channels, as predicted. How this can influence on properties of Higgs, such as that it is a creator of masses?
Ok, one argument is that Higgs boson was found where it was expected...

Last edited: Jul 8, 2012
20. Jul 14, 2012

### exponent137

I do not see, how Higgs mechanism is in agreement with GR. GR says that elementary particles build space-time. Thus, if all matter is removed from our universe, nothing remains, neither universe.

But, in Higgs mechanism space-time help to interact among particles and Higgs boson.

The only possible explanation, which I see, is that principles of GR are valid only in macroword?