Explaining the Massive Vector Bosons' Masses

[khil_phys]

"Massive" bosons

I just read in Stephen Hawking's "A Brief History of Time" that particles of integer spin are the force-carrying ones, with no mass. Further on, he states that the massive vector bosons, namely W+, W- and Z⁰ are vector bosons with masses of around 100 GeV. He gives no explanation regard this phenomenon.
I looked up in Wikipedia and they say it has something to do with the Higgs mechanism. Can someone explain that to me?

 

[tom.stoer]

In gauge theories the symmetry of the theory is protected after quantization (gauge symmetry holds for the quantized theory); this guarantuess that the theory stays consistent, especially perturbatievely renormalizable. This is essentially the reasoning for all quantum field theories of the standard model of elementary particle physics.

Now we know that the weak force as a very short range which means that the gauge bosons mediating this force must be massive. But for massive gauge bosons all the nice features described above break down. So one needs a mechanism that the elementary gauge bosons can stay massles, but "behave as if they have a mass".

Assume you are a filmstar. You are slender and agile. Now unfortunately you are in a room which is crowded with fans, presse people and photographers. You are still slender but you will move as if would have a higher mass. That's what's happening in the Higgs mechanism. The crowd is replaced ba a so-called Higgs field (just another field with a particle, the Higgs-boson associated with it) which is always present, even in vacuum. Reducing it's field strength to zero would rise its energy which is quite unusual; usually lowering the field strength lowers the energy as well, but it can be modeled mathematically.

The interaction with this Higgs field generates masses for the gauge bosons w/o breaking gauge symmetry and spoiling renormalizibility of the theory.

But there is one problem: the Higgs boson hasn not been found so far. Both Tevatron and LHC experiments try to identify this last missing puzzle piece of the standard model.

For a more detailed description you may check the Wikipedia article http://en.wikipedia.org/wiki/Higgs_mechanism

 

[khil_phys]

So at least for the moment, the theory is quite meta-physical.

 

[tom.stoer]

So at least for the moment, the theory is quite meta-physical.

No, on the contrary; the theory is quite successful which means that there where numerous predictions over the decades which had been verified experimentally. It is possible to calculate the W- and Z-boson mass; these particles have been identified experimentally with correct mass and interaction strength. The Higgs is the only piece that is missing - but even for the Higgs there are indirect effects which allowed to restrict the allowed mass range.

But I agree, the standard model will be in trouble if the LHC does not find the Higgs.

 

[khil_phys]

This essentially means that the W and Z bosons of the weak interaction have been discovered, but the hypothetical Higgs boson hasn't been.

Do you mean to say that the Higgs mechanism is theoretically fool-proof, since we don't have any evidence supporting it's claim.

 

[tom.stoer]

This essentially means that the W and Z bosons of the weak interaction have been discovered, but the hypothetical Higgs boson hasn't been.

Exactly.

Do you mean to say that the Higgs mechanism is theoretically fool-proof, since we don't have any evidence supporting it's claim.

I am not sure what you mean by that.

The Higgs-mechanism is "borrowed" from condensed matter physics where similar effects are well-known and allow us to describe numerous physical effects. The main difference is that here the boson is an effective degree of freedom, not a fundamental particle. In the standard model the Higgs particle is fundamental.

Of course the Higgs mechanism and therefore the standard model (as of today) can be falsified by showing (experimentally) that the supposed particle does not exist. If this would be the case we would still believe that something like the Higgs does exist as an effective degree of freedom, as a low-energy approximation, ... simply becuse many of its predictions are still correct (especially W- and Z-boson masses). Therefore we would throw away everything bt try to find new a new model in which there is no fundamental Higgs but from which something like a Higgs can be derived in certain (not all!) approximations (well below the Higgs mass we may still be allowed to do caclulations based on the Higgs, but closed to the Higgs mass the theory is repülaced by something else)

 

[Nicodemus]

I think what he means is that even if there is no Higgs Boson of the type being searched for, the Higgs Mechanism would still have the potential to stand.

 

[tom.stoer]

OK, this is what I expect too; the electro-weak sector of the SM is too successful to be completey wrong.

 

[khil_phys]

I get it. The theory supports the existence of Higgs boson, although it hasn't been found yet.

 

[tom.stoer]

Yes.

What I wanted to say is that the Higgs effect is "there" (the gauge bosons are massive and theory and experiment agree very well at the currently accessable energies) but the Higgs particle (as a fundamental paricle) may not exist.

Particles manifest themselves as poles in certain functions. Let's look the function 1/(1-x) for small x. One can extract the behaviour ~1/(1-x) and therefore derive the pole at x=1. But perhaps we should deal with a different function f(x)/(1-x) where f is nearly constant for small x (and therefore does not change the 1/(1-x) behaviour) but has a zero (!) at x=1. So going to x~1 one finds that the pole fades away.

In that sense the Higgs particle could be a very good approximation for small energies (small compared to its "mass"), but going to the Higgs mass scale it may look different as it is replaced by something different

[The same happened to the pion: in nuclear physics and for small energies in nucleon-nucleon scattering an approximation with massless pions as elementary particles works rather well; but at higher energies the quark substructure of the pion becomes important; there are differences, e.g. it has nothing to do with the pion mass scale, but it may be somehow similar]