What is the global significance of a 5-sigma Higgs signal?

[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?

 

[jtbell]

The Higgs boson (or bosons; there might be more than one) is necessary in the oldest and most popular proposed mechanism for "giving" other fundamental particles their masses in the context of electroweak unification.

http://en.wikipedia.org/wiki/Higgs_mechanism

Other mechanisms have been proposed:

http://en.wikipedia.org/wiki/Higgsless_model

 

[exponent137]

The Higgs boson (or bosons; there might be more than one) is necessary in the oldest and most popular proposed mechanism for "giving" other fundamental particles their masses in the context of electroweak unification.

http://en.wikipedia.org/wiki/Higgs_mechanism

Other mechanisms have been proposed:

http://en.wikipedia.org/wiki/Higgsless_model

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?

 

[Bill_K]

Why the bosons in a gauge theory must be massless?

Two reasons. A mass term like m² W^μW_μ 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.

 

[Lapidus]

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

thanks!

 

[jtbell]

See post #2 in this thread.

 

[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.

 

[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%?

 

[Vanadium 50]

See post #2. <sigh>

 

[exponent137]

Two reasons. A mass term like m² W^μW_μ 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.

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?

 

[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.

 

[exponent137]

At comments of Higgs boson
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?

 

[JPBenowitz]

At comments of Higgs boson
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?

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.

 

[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.

 

[lpetrich]

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.

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.

 

[exponent137]

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

Is this sure? Why not to built all matter?

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

 

[lpetrich]

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

Is this sure? Why not to built all matter?

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.

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

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.

 

[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.

 

[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...

 

[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?

 

[Dead Boss]

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.

GR says nothing like that. Without particles the space-time would be flat (Minkowski) but it would still be there.

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

Nope. In Higgs mechanism Higgs field interacts with particles. Space-time acts the same as it does in all QFT - as background.

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

This may very well be true.

 

[exponent137]

Nope. In Higgs mechanism Higgs field interacts with particles. Space-time acts the same as it does in all QFT - as background.

Yes, but in GR there is no background, there is contradiction. If GR is macro effect, how then background exists in microworld?

 

[exponent137]

GR says nothing like that. Without particles the space-time would be flat (Minkowski) but it would still be there.

I do not agree with this.
Sean Carroll: http://arxiv.org/pdf/gr-qc/9712019.pdf page 138:

Let’s put some of these ideas into the context of general relativity. You will often hear it proclaimed that GR is a “diffeomorphism invariant” theory. What this means is that, if the universe is represented by a manifold M with metric gμν and matter fields ψ, and φ : M → M is a diffeomorphism, then the sets (M, gμν , ψ) and (M, φ∗gμν, φ∗ψ) represent the same physical situation. Since diffeomorphisms are just active coordinate transformations, this is
a highbrow way of saying that the theory is coordinate invariant. Although such a statement is true, it is a source of great misunderstanding, for the simple fact that it conveys very little
information. Any semi-respectable theory of physics is coordinate invariant, including those based on special relativity or Newtonian mechanics; GR is not unique in this regard. When people say that GR is diffeomorphism invariant, more likely than not they have one of two
(closely related) concepts in mind: the theory is free of “prior geometry”, and there is no preferred coordinate system for spacetime. The first of these stems from the fact that the
metric is a dynamical variable, and along with it the connection and volume element and so forth. Nothing is given to us ahead of time, unlike in classical mechanics or SR. As a consequence, there is no way to simplify life by sticking to a specific coordinate system
adapted to some absolute elements of the geometry. This state of affairs forces us to be very careful; it is possible that two purportedly distinct configurations (of matter and metric) in GR are actually “the same”, related by a diffeomorphism. In a path integral approach
to quantum gravity, where we would like to sum over all possible configurations, special care must be taken not to overcount by allowing physically indistinguishable configurations to contribute more than once. In SR or Newtonian mechanics, meanwhile, the existence
of a preferred set of coordinates saves us from such ambiguities. The fact that GR has no preferred coordinate system is often garbled into the statement that it is coordinate invariant (or “generally covariant”); both things are true, but one has more content than the other.

Remark: Minkowski space is preferred coordinate system.

 

[jtbell]

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?

Whoever answers this question convincingly will be a strong candidate for a Nobel Prize.

 

[exponent137]

Whoever answers this question convincingly will be a strong candidate for a Nobel Prize.

Yes, but above I gave question, how Higgs mechanism cannot be in contradiction with general relativity.

 

[Dead Boss]

I do not agree with this.
Sean Carroll: http://arxiv.org/pdf/gr-qc/9712019.pdf page 138:

Remark: Minkowski space is preferred coordinate system.

I agree that it was a bit too strong statement. What I meant is that space-time is meaningful concept on it's own. Vacuum solutions to EFEs are relevant and perfectly physical.

 

[exponent137]

When Higgs boson will be completely proved, thus this means that this will be the main proof that elementary particles are not black holes or that gravity does not make elementary particles?

What are EFEs?
If space-time is meaningful concept on it's own, this is against GR.

 

[Dead Boss]

What are EFEs?

Einstein's field equations.

 

[mfb]

When Higgs boson will be completely proved, thus this means that this will be the main proof that elementary particles are not black holes or that gravity does not make elementary particles?

No, as the Standard Model does not include gravity anyway. On the other hand, most concepts to unify gravity and the other interactions have supersymmetry as a feature, and this has multiple Higgs particles. If there is just one, it might become tricky for some SUSY models, at least for the minimal supersymmetric model (MSSM).

 

[exponent137]

No, as the Standard Model does not include gravity anyway. On the other hand, most concepts to unify gravity and the other interactions have supersymmetry as a feature, and this has multiple Higgs particles. If there is just one, it might become tricky for some SUSY models, at least for the minimal supersymmetric model (MSSM).

I ask because if Higgs mechanism creates masses of particles, gravitational self-interaction cannot make them? One or the other.

 

[exponent137]

An electron in a semi-conductor has changed mass. Is there any similarity between mass given by Higgs boson and this "semi-conductor" mechanism?

I forget also, what is the principle of electron mass change in semi-conductor?

 

[exponent137]

Now I found derivation of effective electron mass in semi conductor
http://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)
It is in the section "derivation".
Is any similar principle for Higgs boson?

 

[atyy]

Now I found derivation of effective electron mass in semi conductor
http://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)
It is in the section "derivation".
Is any similar principle for Higgs boson?

No, the analogue in condensed matter of the Higgs mechanism is the Meissner effect for superconductors. Actually, this was discovered by Anderson before Brout, Englert, Higgs, Guralnik, Hagen and Kibble did their famous work, and Higgs based his work on Anderson's. There's an explanation of the Anderson-Higgs mechanism here: http://arxiv.org/abs/cond-mat/0503400.

 

[exponent137]

I will read this. I will read also
http://en.wikipedia.org/wiki/Higgs_mechanism
But is it possible to explain much shorter?
Cooper's pairs expel magnetic field.
Higgs bosons expel what?...How Z and W get masses?
Maybe this step of explanation goes without wave functions?

 

[exponent137]

Measurement of Higgs boson was better than 5 sigma ob background, this means that probability for accident is 1/3500000. But, what is there a Gaussian curve, and what is its width. I saw same graphs, such as on
http://blog.vixra.org/2012/07/10/global-combination-gives-unofficial-discovery-with-2011-data/
but I do not understand what they mean?

 

[mfb]

You can plot a curve "likelihood versus signal strength" - that will give (approximately) a gaussian curve with the maximum at the observed signal strength and "zero signal" about 5 standard deviations away. The real analysis is a bit more complicated, but that is the basic idea.

 

[Vanadium 50]

Vixra is not an acceptable source here, so please be careful with it. I am letting it in here because it's being used as an example for a certain kind of plot, but normally it cannot be used.

 

[exponent137]

You can plot a curve "likelihood versus signal strength" - that will give (approximately) a gaussian curve with the maximum at the observed signal strength and "zero signal" about 5 standard deviations away. The real analysis is a bit more complicated, but that is the basic idea.

Yes, let us say simplified, that is that Higgs signal gives some gaussian curve with center close to 125 GeV and with width somewhere <1 GeV, thus 5 sigma < 5 GeV.
But, what is zero signal? Is it some grass everywhere on energy scale and this grass has some bumps?

I am not sure if we should look 5 sigma of those bumps, but Higgs signal should be out of those 5 sigma?

 

[exponent137]

You can plot a curve "likelihood versus signal strength" - that will give (approximately) a gaussian curve with the maximum at the observed signal strength and "zero signal" about 5 standard deviations away. The real analysis is a bit more complicated, but that is the basic idea.

On blog, Gibbs writes many reports from Higgs measurement and he does not write many speculations. viXra archive is not the same as his blog. Similar surnames similar topics :) .

 

[mfb]

Yes, let us say simplified, that is that Higgs signal gives some gaussian curve with center close to 125 GeV and with width somewhere <1 GeV, thus 5 sigma < 5 GeV.

No, that is a completely different thing.
The significance is related to the signal strength ("number of Higgs events in the peak") and its uncertainty. Assuming gaussian errors, this uncertainty would be about 20%. This is called "local significance", as it is the significance of the peak at that position.

Zero signal would be "background-only model fits perfectly". Of course, that will not happen due to statistical fluctuations, so you expect to see some 1-2 sigma deviations in many different spots. However, you do not expect to see a 5-sigma deviation. If you calculate the (small) probability to get a 5-sigma signal by random fluctuation, you can calculate a "global significance" of your 5-sigma result.


@post 39: I think you quoted the wrong post there