Wiki Quote 1 - Higgs Mechanism?

[enotstrebor]

"The Higgs mechanism in the standard model successfully predicts the mass of the W±, and Z weak gauge bosons,"

How does the higgs mechanism predict the masses of the W & Z? The Higgs has no specific coupling value to any particle and it is the coupling value that gives the mass value Is this SM propaganda?

I am looking for a specific journal, book, web source that shows how the masses are prodicted, not conjecture.

 

[hamster143]

The correct statement would be that the Higgs mechanism correctly predicts the ratio of these masses. In the electroweak theory with the Higgs mechanism, the ratio of W and Z masses is related to a parameter of the theory (the electroweak mixing angle) which also emerges in a few other places, e.g. relative couplings of Z and photon to other particles. The precise form of the relationship is dependent on the way you do electroweak breaking, basic Higgs model is the simplest theory that is compatible with observations.

The Higgs has no specific coupling value to any particle

This is true for leptons and quarks, but the coupling of Higgs to electroweak gauge bosons is a different story.

 

[enotstrebor]

In the electroweak theory with the Higgs mechanism, the ratio of W and Z masses is related to a parameter of the theory (the electroweak mixing angle) ...

Actually, the correct statement would be that the electroweak theory says that the electroweak angle can be given via a relationship to the masses of the W and the Z particle given by 1-m_W^2/m_Z^2.

This has nothing to do with the Higgs mechanism, only the electroweak theory! This was developed independently and about 20-30 years before the Higgs mechanism.

The precise form of the relationship is dependent on the way you do electroweak breaking, basic Higgs model is the simplest theory that is compatible with observations.

Actually, the Higgs model is the only known present way to break symmetry in a gauge invariant way, but is not compatible with observations if one includes gravity. See
Introduction to the Standard Model and Electroweak Physics and search (find) on "gravity"


P.S.

By the way, did you know that the W Z mass ratio does not produce the same electroweak angle as either the measured charged particle weak angle nor the neutrino weak angle.

Thus there are three statistically different weak angles for which there is no SM reason, leading to a declaration of new physics rather than indicating a problem with the SM version of the electroweak theory.

 

[humanino]

By the way, did you know that the W Z mass ratio does not produce the same electroweak angle as either the measured charged particle weak angle nor the neutrino weak angle.

Maybe you will finish the chapter before lecturing us ? Quarks and leptons come in three generations, so they have more than one angle to mix. They have a 3x3 unitary matrix, so three angles and a phase.

 

[hamster143]

Actually, the correct statement would be that the electroweak theory says that the electroweak angle can be given via a relationship to the masses of the W and the Z particle given by 1-m_W^2/m_Z^2.

This has nothing to do with the Higgs mechanism, only the electroweak theory! This was developed independently and about 20-30 years before the Higgs mechanism.

This is incorrect. Gauge boson mass matrix depends on the specific method of symmetry breaking. There's nothing in electroweak theory itself to prescribe anything about W/Z mass ratio. And what's this 20-30 year thing? That would place the alleged development of that relationship in 1930's.

 

[enotstrebor]

Maybe you will finish the chapter before lecturing us ? Quarks and leptons come in three generations, so they have more than one angle to mix. They have a 3x3 unitary matrix, so three angles and a phase.

You are confusing the electroweak angle of the electroweak theory and quark (mixing) matrix of QCD.

These are two different things.

The electroweak angle (though sometimes referred to as a mixing angle) is actually a coupling constant (like the fine structure constant) and a coupling of two forces, as indicated by its use in the V-A theory.

So your reference to the quark mixing matrix is off topic and nothing to do with the origin of the electroweak angle via the Salam-Weinberg mass ratio and the fact that the prediction of the Z and W masses via the associated weak angle has nothing to do with the Higgs mechanism.

Thus the I still request any evidence that the Higgs mechanism predicts the masses of the Z and W !

humanino, so far on the Higgs wiki quotes your ZERO for TWO.

Would you like to make it ZERO for three?

 

[enotstrebor]

This is incorrect. Gauge boson mass matrix depends on the specific method of symmetry breaking. There's nothing in electroweak theory itself to prescribe anything about W/Z mass ratio. And what's this 20-30 year thing? That would place the alleged development of that relationship in 1930's.

My understanding was that the process of symmetry breaking mechanism was not specific and that the weak angle's association to the W/Z masses was independent of the specifics of the symmetry breaking mechanism (1967).

I had believed that the Higgs mechanism was developed (not as a conjecture but formalized) 20 or so years afterward, but your are right and I was wrong. As indicated in Salam's Nobel prize lecture (in 1979), he refers to the symmetry breaking mechanism as "what is now known as the Higgs mechanism".

So certainly these are not the 20 years apart (1967-1979), and I stand corrected.

You may be correct that the specifics of the symmetry breaking mechanism may be required before the W/Z mass ratio becomes the weak angle, but my gut says it should not (but not a valid argument).

I thank you for pointing me in the correct direction to determine the validity of the wiki statement.

If you (or any other reader) find specific authoritative historical information, journal or otherwise, please give the reference.

Thanks hamster143

 

[humanino]

The electroweak angle (though sometimes referred to as a mixing angle) is actually a coupling constant (like the fine structure constant) and a coupling of two forces, as indicated by its use in the V-A theory.

So I'm confused : maybe then you can point me out to which angle you are referring to in

By the way, did you know that the W Z mass ratio does not produce the same electroweak angle as either the measured charged particle weak angle nor the neutrino weak angle.

Thus there are three statistically different weak angles for which there is no SM reason, leading to a declaration of new physics rather than indicating a problem with the SM version of the electroweak theory.

I am unaware of another lepton mixing apart from the CKM matrix, encoding different basis for the mass and flavor states. Besides, there is only Weinberg angle

So please explain what you mean, if you are referring to another angle, please do not hesitate to quote an equation number in the RPP
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-standard-model.pdf
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-ckm-matrix.pdf

 

[humanino]

Besides, there is only Weinberg angle

In anticipation, I hope that you have a better argument than the NuTeV so-called "anomaly", because it is now largely accepted that the anomaly was not in the measurement but in the calculation, and the SM still stands firm.
NuTeV anomaly supports new effect in bound nucleons

the NuTeV data turn out to be in excellent agreement with the Standard Model.

 

[blechman]

Dates of relevance:

1961: Glashow's original suggestion that SU(2) x U(1) is the gauge group of the SM.

1964: 3 papers written independently by Higgs; Guralnik, Hagen, Kibble; Brout, Englert that proposed what is now called the "Higgs Mechanism", in particular explaining why a spontaneously broken gauge symmetry does not have massless scalars ("Nambu Goldstone Bosons") flying around.

1968: Weinberg and Salam independently propose a "Higgsed SU(2) x U(1)" gauge theory with Yukawa couplings to the matter fields that describes nature.

1979: Nobel Prize awarded to Glashow, Weinberg, Salam.

2008: Nobel Prize awarded to Nambu.
*********

There is a difference between "Higgs Mechanism", which pretty much all high energy physicists believe is responsible for what is going on at the weak scale, as well as explaining the Meisner effect in superconductivity (where it is called the "Anderson-Higgs Mechanism"), etc. and the "Higgs Boson" which is the *MINIMAL* model, proposed by Weinberg and Salam, for how the "Higgs Mechanism" is carried through; minimal in the sense that there is only one additional scalar field required.

There are MANY who believe that there is NO Higgs boson. I, personally, would love to believe that. Unfortunately for us, all of the precision EW observables, which depend on the existence of the details of the "Higgs sector" are in perfect agreement with the theory of a single scalar field with a mass of 115 GeV (for details, check out the RPP referenced above, for example). It is hard to ignore these facts.

But just because there is no "Higgs Boson" does not mean that there is no "Higgs mechanism" at work. This could be explained for example by theories such as "technicolor" or "composite Higgs theories" as well as some extra dimension theories where the role of the "Higgs boson" is played by something else. Again, this is not in line with EWP measurements, but there is a little wiggle room.

As to what the "Higgs Mechanism" explains: well, again, one can compute EWP observables and again, they agree with experiment. That includes things like the $\rho$ parameter mentioned above (ratio of the W,Z masses), and again, when you assume the "Higgs boson" exists and has its couplings the model demands, you can calculate these numbers and they agree perfectly with the data, as long as the mass is 115 GeV, up to error bars.

I don't think there is any more doubt left that a "Higgs mechanism" is at work in the electroweak theory, the REAL question is: what's up with that stupid "Higgs boson"?!

I hope that helps a little.

************
People: let's try to calm down a bit! There's no reason to be adversarial or nasty! This is a perfectly valid question and deserves a good answer. As to touchy, nasty words like "propaganda": Hey: I'm the first person to tell you to break away from the box! But this really is more than propaganda. EWP cannot be ignored!

Save words like "propaganda" for supersymmetry! (BTW: I'm a SUSY theorist, so I'm allowed to say things like that! )

 

[hamster143]

Unfortunately for us, all of the precision EW observables, which depend on the existence of the details of the "Higgs sector" are in perfect agreement with the theory of a single scalar field with a mass of 115 GeV (for details, check out the RPP referenced above, for example).

IIRC, the precision EW observable method can't distinguish between the Higgs around W/Z masses (80-90 GeV) and there being no Higgs at all, because corrections due to the Higgs are proportional to log of the ratio of Higgs mass to W/Z masses. And current error bars are wide enough to allow the possibility of no Higgs.

 

[enotstrebor]

Besides, there is only Weinberg angle

The SM view is that there is only one weak angle (I have never seen it called the Weinberg angle but I sure some has).

However experimentally this is not the case (For documentation, see references below).

The three values are the SM Salam-Weinberg W,Z mass squared ratio value .2227 [1], $$\sin^2 \theta_{\mathrm{W}} (M_{\mathrm{Z}})_{\overline{\mathrm{MS}}} = .2312$$ [2], and the neutrino value $$s^2_W = .2277$$ [1]. Given the quoted error, these three values are statistically different.

Even converting between formalism does not resolve the differences.

[1] Zeller, G. P. et al. (NuTeV Collaboration),
Precise Determination of Electroweak Parameters in
Neutrino-Nucleon Scattering, Phys. Rev. Lett. 88
091802 (2002)

[2] P. J. Mohr, B. N. Taylor, D. B. Newell, COData Recommended Values of the
Fundamental Physical Constants: 2006, Rev. Mod. Phys.
80, 633 (2008); Updated - Particle Data Group, Physical Constants,
http://pdg.lbl.gov/2009/constants/rpp2009-phys-constants.pdf
(2009)

If you know more recent neutrino results let me know.

 

[humanino]

If you know more recent neutrino results let me know.

I told you not to quote NuTeV to justify your claims and provided a reference for your reading.