# More generations of leptons and quarks

1. Jan 2, 2008

### Jim Kata

Does anyone believe that there are only three generations of leptons and quarks and that higher generations will not be found? I'm curious about people's opinions on this subject. If you believe that higher generations are going to be found why do you believe so, and if you don't believe that there are higher generations of leptons and quarks why do you believe that.

2. Jan 2, 2008

### mormonator_rm

I think they do not exist, but I stress the fact that I really do not know. But I am more inclined to think not. Several reasons come to mind: 1) Z decay width to leptons is divided equally between the three generations of leptons that we know to exist, 2) in Rishon theory the nine-Rishon (fourth-generation fermion) configuration will instantly fall apart into three first-generation fermions, and 3) experimental evidence upwards of 1 TeV shows no sign of and very little suggestion of a fourth-generation. Thus, the only model I see in which further generations seem suggestible explains why there are NOT any generations beyond the familiar three.

3. Jan 2, 2008

### will.c

As I understand it, evidence comes not only from Z-decay, but also from astronomical observations. If more lepton families exist, the energy balance in the universe after the big bang is different, such that the ratios of hydrogen to helium atoms formed as the universe cools no longer would agree with what we observe. In both cases though, this evidence can be circumvented if you posit that any other lepton families have heavy neutrinos.

4. Jan 3, 2008

### malawi_glenn

I also think that there is not more than 3generations, with same argument as the posters above. Altough I am open to the existence Supersymmetric particles, such as the neutralino etc. But I am not a particle physicsists, I am rather a Nuclear / Hadron guy.

Would be fun if blechman could share his though with us =)

5. Jan 3, 2008

### blechman

I also am of the opinion of three and only three, but would be happy to be proven wrong by my experimental colleagues. Everything everyone said up to this point I agree with (cosmology, Z width and EW precision, don't know about the Rishon stuff, but why not?!).

I did an experiment project as an undergrad years ago when the top quark was first discovered at Fermilab. I was trying to measure V_{tb} - one of the CKM matrix elements related to the top decay to W + b-quark. This number is indirectly predicted (from b-decays) to be VERY close to 1.0, but if it's sizably smaller than 1, it would suggest the presence of a fourth generation. According to the Particle Data Book, the current measurements for this quantity are |Vtb|>0.78 to 95% confidence. This is weaker than I would have guessed, but it's still a pretty tight fit.

There's another, more subtle reason to doubt a fourth generation. Presumably, such a set of particles would have to be heavier than the top quark. But the top quark is almost as heavy as a particle can be. It's Yukawa coupling (mass/higgs-vev) ~ 1. If this number gets too big, it means that there's strong coupling in the EW sector, and this would have violent effects on EW precision which we don't see. But in any event, the LHC will tell us something about these issues.

Also if you believe in Grand Unification, adding a fourth generation spoils that dream. I'm not necessarily saying that I believe in GUT's, but if you do, then you don't want to see a fourth generation.

Let me close with a plug for one of my colleagues: he is considering a scenario where there is NO higgs boson (avoiding some of the problems I mentioned in the last paragraph), while there is a fourth generation of particles WITH strong coupling. This is reminiscent of technicolor models (for which this guy is very famous for). I'm not saying I believe it, but it shows that people are seriously considering such situations. You can check out his paper at http://arxiv.org/abs/hep-ph/0702037 if you're interested.

In conclusion: I personally do not expect to see evidence of another SM-like generation of particles, but I would be very happy to be proved wrong. And while I think the majority of theoretical particle physicists would agree with me, there are some that are still hopeful. And, of course, the experimentalists are happy to look for ANY signal of new physics, so they're going for it!

6. Jan 3, 2008

### malawi_glenn

very interessting an illuminating as always :) thanx blechman for sharing!

7. Jan 12, 2008

### mormonator_rm

Its okay to be the nuclear/hadron guy. I am mostly just a hadron guy too, but out of necessity had to explore more fundamental stuff and am now in this arena for the first time. Its been tough, but I think I might be getting the hang of it... slowly...

8. Jan 12, 2008

### mormonator_rm

The Rishon stuff gets really complicated, but one would think a 9-rishon object would break into three 3-rishon objects in much the same way one thinks of a tetraquark easily disintegrating into two mesons. The 5-rishon and 7-rishon (2nd and 3rd generation) states could not fission in this same way.

For some reason I had thought |V_{tb}| to be much more conclusively closer to one than that. I'm a little surprised, I guess.

I will have to check out this paper. Thanks for the info, and thanks to malawi_glenn for asking.

9. Jan 12, 2008

### blechman

Yeah, I just don't know anything about "Rishon" theory, so I'm not able to make any intelligent deductions based on it.

There's a new measurement just out this week from D0 on improving this bound:
http://arxiv.org/abs/0801.1326
Might want to have a look. But you can see that the problem is that the error is of order 10%, and that brings the bound down quite a bit (remember: 95% c.l. is 2*sigma).

10. Jan 27, 2008

### Oxymuon

Which models/theories predict a 4th generation?

I know that technicolor models in which the technifermions transform under the 2-index symmetric representation generally include a fourth lepton generation because they suffer from the Witten anomaly. Does the MSSM predict a 4th lepton family? Any other models?

11. Jan 28, 2008

### blechman

MSSM does not suffer from any anomalies (once you include 2 higgs doublets) so there are no fourth-gen fermions there; although there's no reason to forbid it. I know of no other models that *require* a new generation of SM-like particles, although I don't know of anything forbidding it either, short of what I already said.

12. Jan 30, 2008

### jal

Quote http://arxiv.org/abs/hep-ph/0702037
Authors: B. Holdom

“A fourth family, and its implication that there is no light Higgs, no low-energy supersymmetry, and no evidence for any required fine-tuning, would shift the focus away from theories of much higher energy scales, and towards the dynamics of a theory of flavor.”
-----------
Question?
What would be the impact on renormalizing and the minimum length?
jal

13. Jan 31, 2008

### blechman

I don't think this has anything to say about renormalization/minimum length. All Bob is saying is that rather than looking for new physics above the weak scale, we should be looking for new flavor physics at or even below the weak scale. such a scenario would be counter to what the average particle physicist believes (and hence is worth considering! ).

There's still renormalization in this picture - beta functions and runnings, etc.

14. Feb 1, 2008

### Jim Kata

Yeah, without supersymmetry, it does seem a little weird to think that it is just a barren wasteland between 300 GeV and 10^15 GeV. Does anyone think that there could be more symmetry breaking in between these numbers. Something like big gauge group broken to
su(3)XG at 10^15 GeV then somewhere else down the line G is broken to su(2)Xu(1) and then at 300 GeV su(2)xu(1) is broken to $$u(1)_em$$

15. Feb 1, 2008

### Haelfix

Jim, i'd say most particle physicists would agree with that statement. The wasteland scenario is basically minimalist model building that has historically been pretty wrong.

Theres a ton of plausible phenomenology inbetween. For instance fifth force scenarios that are nice and confining and pretty self contained (so that it doesn't spoil too much beta function running). Alternatively extra dimension hierarchies and so forth. But I doubt we will see an extra generation.

16. Feb 3, 2008

Staff Emeritus
Actually, for the point of view of this discussion, the limit is too strong. This limit is obtained by comparing how often a top decays to W+b compared to W+[d,s or b]. Experimentally, there is no evidence that the top goes to anything but W+b, and then a limit is extracted.

However, this limit is calculated under the assumption of 3 generation unitarity. If there were four generations, all you could tell was that $V_{tb}$ was several times larger than $V_{ts}$ (the larger of the two). And that leaves plenty of room for a 4th generation.

In short, if you relax the assumption of 3 generations, you can no longer conclude there are 3 generations.

This doesn't bother me. There is no reason to conclude that the mechanism by which fermions get their mass is the same as the mechanism by which gauge bosons get their mass. It's maybe not as elegant, but that doesn't make it wrong.

Speaking of elegance, a sequential fourth generation falls pretty flat in that regard. We know:
1. There are 3 generations of light neutrinos. There are no undiscovered quarks or leptons with masses below about 45 GeV.
2. The W mass tells us that the largest difference between u-type and d-type quark masses is about 170 GeV.
3. Measurements of B, K and D mixing tells us that the mass ratio between the heaviest u-type and d-type quarks is around 35, albeit with fairly large uncertainties: perhaps half of that value.

This paints a 4th generation into a corner. Everything has to be heavy and degenerate in mass, otherwise we run into problems with 1 and 2. But then we run into problems with 3 - specifically, the slow rate of D mixing.

There are two ways out, neither pretty. One way has a very heavy 4th generation that couples exceedingly weakly to everything that we can see. Essentially, you posit a 4th generation with no observable consequences. The other is to tune the masses and CKM parameters so that the 4 generation theory has essentially the same predictions for what we have already measured as the old 3 generation theory.

17. Feb 5, 2008

### blechman

It's been a very long time since I looked at these things, but I thought D0/CDF were trying to avoid unitarity assumptions (thus allowing for a potential 4th gen) - I thought that was one of the reasons the bound was so low! The measurement you speak of studying t->bW branching fraction (called "Rtb") has a very strong constraint:

$$R_{tb}=\frac{|V_{tb}|^2}{|V_{td}|^2+|V_{ts}|^2+|V_{tb}|^2}=0.98$$

to 95% cl if I remember correctly (if I'm not remembering correctly, plz feel free to correct me! ). If you assume 3-generation unitarity, you would have $V_{tb}=\sqrt{R_{tb}}$, since the denominator would just be 1.

a fair point.

Last edited: Feb 5, 2008
18. Feb 5, 2008