Why three generations of particles

[LongOne]

Hi,
I'm curious as to what the most prevalent theories are as to why there are three generations of particles. I've roamed around the Internet but haven't found anything that speculates on this.

If you can point me to an article or document, that would be great!

Thanks.

[humanino]

Hi
If you can point me to an article or document, that would be great!Generally speaking, I think string theory aims at providing a rational explanations behind this number of generation. It is not easy though. Specific models have been published :

Number of Generations in Free Fermionic String Models (http://arxiv.org/abs/hep-th/9502153)
Local models of Gauge Mediated Supersymmetry Breaking in String Theory (http://arxiv.org/abs/hep-th/0605166)
The Standard Model in String Theory from D-branes (http://adsabs.harvard.edu/abs/2007NuPhS.171..119U)
but as for "why ?" those should be singled out is not yet answered.

The TASI 2004 Lectures on the Phenomenology of Extra Dimensions (http://arxiv.org/abs/hep-ph/0605325) give a fairly general presentation.

By the same token, non-commutative geometry (http://arxiv.org/abs/0706.3688) also takes this number 3 as an input.

Finally, let me cite this Schematic model of generations (http://arxiv.org/abs/hep-ph/0605089)

It might as well be that the question is no more relevant than "why 9 planets around the Sun ?" (yes, nowadays we would ask 8, but we don't ask the question anymore anyway :rolleyes:)

If I understand correctly, the number of generation is also constrained by anomaly cancellation in the standard model :
Number of Fermion Generations Derived from Anomaly Cancellation (http://arxiv.org/abs/hep-ph/0102010)

[alphanzo]

Hi,
I'm curious as to what the most prevalent theories are as to why there are three generations of particles. I've roamed around the Internet but haven't found anything that speculates on this.

If you can point me to an article or document, that would be great!

Thanks.

No one can say at the moment why there Must be three, but there is good evidence that there are no more than three within the framework of basic QFT. For instance, the width of the Z boson measurement is sensitive to the number of generations, and experiments agree with only three generations (a fourth generation would increase the width more than is observed--see Peskin and Schroeder's "Intro to QFT"). I hope I'm not mistaken because I don't have the book in front of me, but it seems that three generations were also necessary to eliminate gauge anomalies (if the anomalies didn't cancel QFT would be nonsense).

[Vanadium 50]

For instance, the width of the Z boson measurement is sensitive to the number of generations, and experiments agree with only three generations (a fourth generation would increase the width more than is observed--see Peskin and Schroeder's "Intro to QFT").

Strictly speaking, the Z boson width is sensitive to the number of light neutrinos. A 4th generation with a neutrino weighing more than 45 GeV is a logical possibility. (There are other difficulties, but this particular one can be evaded)

I hope I'm not mistaken because I don't have the book in front of me, but it seems that three generations were also necessary to eliminate gauge anomalies (if the anomalies didn't cancel QFT would be nonsense).

I assume you are talking about triangle anomalies? They cancel generation-by-generation.

[alphanzo]

Bah, of course. I remembered the number three and that it all seemed miraculous somehow. Yes, the quarks cancel the lepton anomalies. I should really start looking these things up before I type. I thought that the 45 GeV neutrino had been ruled out...

[LongOne]

Hi
Generally speaking, I think string theory aims at providing a rational explanations behind this number of generation. It is not easy though. Specific models have been published :

Number of Generations in Free Fermionic String Models (http://arxiv.org/abs/hep-th/9502153)
Local models of Gauge Mediated Supersymmetry Breaking in String Theory (http://arxiv.org/abs/hep-th/0605166)
The Standard Model in String Theory from D-branes (http://adsabs.harvard.edu/abs/2007NuPhS.171..119U)
but as for "why ?" those should be singled out is not yet answered.

The TASI 2004 Lectures on the Phenomenology of Extra Dimensions (http://arxiv.org/abs/hep-ph/0605325) give a fairly general presentation.

By the same token, non-commutative geometry (http://arxiv.org/abs/0706.3688) also takes this number 3 as an input.

Finally, let me cite this Schematic model of generations (http://arxiv.org/abs/hep-ph/0605089)

It might as well be that the question is no more relevant than "why 9 planets around the Sun ?" (yes, nowadays we would ask 8, but we don't ask the question anymore anyway :rolleyes:)

If I understand correctly, the number of generation is also constrained by anomaly cancellation in the standard model :
Number of Fermion Generations Derived from Anomaly Cancellation (http://arxiv.org/abs/hep-ph/0102010)


Thanks very much.

[arivero]

If CP where a need of Nature, then you could argue for three generations in order to have CP, could you?

Also, 3 generations are needed in my model of sBootstrap, which could vindicate superstring theory while killing it :-D

[wlln]

There are no reasons that why only three-generation fernions exit. But if more element feimions exist, they will lead to inconsistency with the konwn experimental results and severe ultra-divergence.

[Vanadium 50]

There are no reasons that why only three-generation fernions exit. But if more element feimions exist, they will lead to inconsistency with the konwn experimental results and severe ultra-divergence.

Not true. A heavy and almost degenerate 4th generation is compatible with the existing data. Granted, the fit is better with 3 generations than 4, but 4 can be made to work.

[wlln]

Not true. A heavy and almost degenerate 4th generation is compatible with the existing data. Granted, the fit is better with 3 generations than 4, but 4 can be made to work.

But if there was the fourth elment fermion, the SM could avoid the pertubative anomoly?

[Vanadium 50]

Which anomaly? Triangle anomalies cancel generation-by-generation.

[arivero]

Which anomaly? Triangle anomalies cancel generation-by-generation.

He refers to the previously mentioned paper of Poppitz and Dobrevscu.

[Vanadium 50]

He refers to the previously mentioned paper of Poppitz and Dobrevscu.

But that is a Beyond the Standard Model paper. Specifically, it relies on universal extra dimensions.

[humanino]

But that is a Beyond the Standard Model paper. Specifically, it relies on universal extra dimensions.I don't think any 4D SM anomaly cancellation can constrain the number of generations.

[BDOA]

Three generations fits nicely into Exception group 8, one of string theories fav groups, and
the group that Lisi Garret use for his ToE, <A HREF="http://www.physicsforums.com/showthread.php?t=196498">ESToE</A>.
Basicly E8 breaks to three copies of E6 and anti-E6, three generations of particles and
anti-particles, With the E6 ajoint group, left over to form the forces acting
equally on each generation.

E8 (248) -> 8? + E6_a (78) + 3E6 (3*27) + 3 anti-E6 (3*27)

So if E8 is the GUT group, generations pops out quite simply. Of course then you have
to fit the standard model into E6, which does go, but has room for 12 particles left over.

[arivero]

But that is a Beyond the Standard Model paper. Specifically, it relies on universal extra dimensions.

Right. He did not read beyond the abstract, it seems...

Really, I think the only 4D argument in the arena is CP violation.

But again, the mass of the top... it should be a clue. Damn, it is! it implies that all there are not "top-antiany" mesons, that the "bottomium" is the end of the ladder, and that then the number of mesons and diquarks classified under SU(3)xU(1) coincides again with the number of leptons and quarks.

I keep telling that it seems a clue, but nobody appreciates it :mad: You need exactly three generations if you want to get this coincidence. A remarkable detail... which does not get a footnote anywhere. And it has been behind our noses for more than ten years now.