# Top coupling = 1 + corrections

1. Mar 8, 2008

2. Mar 8, 2008

### kdv

Interesting. It seems like a more fundamental theory should make it natural for that coupling to be exactly one. Any idea what SUSY says (if anything)?
Do you have a reference for the values of the other Yukawa couplings?

3. Mar 8, 2008

### arivero

kdv, yukawa couplings are essentially mass divided between higgs vacuum.

As for susy+gut, the standard prediction is that the top coupling has sort of almost fixed point in the infrared when the higgs happens, and then it is natural for it to be "about unity". This is, anything between 10 and 0.1

A fundamental theory explaining it to be unity at the TeV scale is against the GUT "almost planck scale" ideology; this ideology predicates that the mass puzzle is solved at Planck scale, and that masses run down via renormalization group down to our GeV-TeV scales.

4. Mar 8, 2008

### kdv

Yes, of course. Sorry for the dumb question. So the Yukaway coupling of the muon is simply $$m_\mu/ m_{top}$$ times smaller.
[qupte]
As for susy+gut, the standard prediction is that the top coupling has sort of almost fixed point in the infrared when the higgs happens, and then it is natural for it to be "about unity". This is, anything between 10 and 0.1
[/quote]
Interesting. This is in the MSSM? What about the other Yukawa couplings? Do they have he same fate?
I know. I guess I was thinking about "solutions" to the hierarchy problem (brane worlds let's say) and I was thinking that if there was a model which not only predicted that the mass of the top must be much smaller than the Planck mass but in addition must be equal to one (in some appropriate units set by the weak scale), it would be interesting.

Thanks for your input!

5. Mar 10, 2008

### Barmecides

Hello,

I knew top-higgs yukawa coupling was ~ m_top/vev with Vev ~ 246 GeV.
So how do you come to this 0.9914 value ?

Thanks.

6. Mar 10, 2008

### Vanadium 50

Staff Emeritus
sqrt(2)/2 * vev

7. Mar 10, 2008

### arivero

Yep, and besides, it is the normalization advocated in some old books (Sakurai? Aitchison?)

8. Mar 10, 2008

### arivero

No; what happens is that the huge difference between the top and the rest makes it relevant in the running of the higgs coupling. The effect was noticed in the early eighties by Ibañez et al, as well as other groups. Its range of application is wider than the MSSM.

9. Mar 10, 2008

### Barmecides

Thanks,

so m_top ~ vev/sqrt(2) ...
But why this normalization is advocated ? Naturalness argument ?

10. Mar 10, 2008

### arivero

It seems that the sqrt(2) is an historical artifact from old fermi theory.

11. Mar 11, 2008

### arivero

Let me stress: the fact of the top quark mass being so hugely different of the rest of the quarks is very important.

The partisans of GUT have disminished this point because it involves a fancy manipulation (kind of adhoc) in the GUT scale, to get mass of bottom hugely separated of mass of top, and then propagate back to ElectroWeak scale.

Later, the partisans of SUSY GUT got hang on the details of this renormalization group scaling, noticing that it forces (or depends of) a relationship between top and higgs field mass values, "of order unity".

But the fact of being so near of unity seems to imply that the main phenomena happens at EW scale, not at GUT scale.

On the other hand, the other five quarks are almost massless respect to the EW scale. To me this is very important because the combinations of these five quarks have exactly the same counting of degrees of freedom that the full standard model itself, and including some chiral implications. It is a unique situation (once you have fixed the gauge groups): the thing I called "sBootstrap".

12. Mar 11, 2008

### Barmecides

Hello arivero,

I'm not theorist so I have only basic comments/questions.

Why so "hugely" different ? m_top/m_charm is same order as m_charm/m_up. So if you wonder why m_top/m_charm is large, you should wonder the same about m_charm/m_up.

I would rather turn the sentence the other way around. We have measured m_top. So the questions is why the hypothetical vev/sqrt(2) (we have not proved Higgs mechanism yet) is so close from m_top ?

13. Mar 11, 2008

### kdv

14. Mar 11, 2008

### arivero

Well I am not sure if I am a theorist anymore.

• The mass quotient should be considered against the v.e.v. So m_top/vev is near unity while for all the other is 1/100 or smaller.
• The top is isolated even from its SU(2) partner, the bottom
• More amusingly, and perhaps unrelated, all the other three mass sectors are hallmarked by a charged lepton. No leptons live in the top rangue.

I agree with this. Why is the vev inferred from Fermi constant so near of m_top?

15. Mar 11, 2008

### arivero

There is another fact on the top mass respective to the other five: it is too high for the quark to form mesons. Or, even the strong force is weak for it: The top quark disintegrates before of being able to bind with any other quark.

Thus, only the other five quarks can do mesons.

How many different? Try yourself. You will get six mesons of charge +1, six mesons of charge -1 and 13 neutral mesons (and surely some argument wipes one of them, in the same way that there are only 8 gluons instead 9).

How many degrees of freedom have the leptons in the standard model?. Well, six of charge +1, six of charge -1, 12 neutral.

Amusing.

Now try to use the five quarks to build different diquarks. Be surprised.

Last edited: Mar 11, 2008
16. Mar 12, 2008

### arivero

Did you try? Yes, they also coincide

But way, there are also three extra +4/3 diquarks, and its antidiquarks. It was a bug, but now I am thinking it is a feature. Having only three degrees of freedom (for each colour, as always), the only three generation arrangement we can do with them is to put into chiral fermions, each one with two components, particle and antiparticle, ¡of different charge!. This beast can not happen in an well-behaving world, and then a mechanism to bar it must exist. And if it is a mechanism based in chirality, we could get an understanding of the chiral aspects of the standard model.

17. Jul 31, 2008

### arivero

Note today the reported value for 2008 summer global fit, 172.4 +-1.2 GeV, thus using GF=
1.166367(5) 10^-5 GeV^-2

$$0.9902 \pm 0.0073$$

as we said elsewhere, it can not go better. Consider e.g. that an electromagnetic correction should contribute some fraction o(1/137). But in the spirit of other threads here, it could be remarked that the yukawa coupling of the tau particle is 0.01020. Also, the total sum $(\sum y_f^2)^\frac 12$ keeps still under unity, about .9906, but any model using this sum should also account for colour multiplicity, most probably.

18. Jul 31, 2008

### Haelfix

I think its a little early for numerology, given the rather large uncertainties in those plots. They still have a lot of data to go through. Moreover, we'll know for sure in about ~ a year.

Still its encouraging, b/c its amongst the first (but not the first) indirect evidence for SuSy and departures from the standard model. Several of us are rather happy, b/c new physics gives us job security for at least a little while =)

19. Aug 3, 2008

### blechman

Let me chime in a with few thoughts, for whatever they're worth.

First of all, just so that everyone's on the same page: it is important to remember that the fermion masses, unlike the Higgs mass, are "technically natural" - that means that when their value is set by whatever mechanism sets them, they will not get pushed around much by the quantum corrections. This means that there is no "hierarchy problem" in the Yukawa sector - whatever the Yukawa couplings are, that's just what they are. You don't have to "fine-tune" anything.

Many of my colleagues have denied that the "flavor puzzle" is a real puzzle for this reason! I personally think that the flavor hierarchy is more interesting than that, but I feel that someone should mention that there are lots of very smart people who do not consider the large top quark a problem at all. After all: the Yukawa couplings EXPLICITLY break the flavor symmetry of the standard model. With this symmetry gone, what right do we have to expect there to be any pattern among the masses? That plus the fact that the disparate masses are stable to radiative corrections takes the wind out of the problem in many people's minds.

This game of playing with parameters can take us to many strange places. For example, if you are worried about the top Yukawa, why aren't you also worried about QCD? Why is the strong coupling so much less than electromagnetism? After all, why couldn't $\Lambda_{\rm QCD}$ be only a tiny fraction of an eV? In such a case, you would still have asymptotic freedom, but the coupling would be MUCH less at room temperature - you would have free quarks, pions would be more analogous to hydrogen, etc. The fact that this is not the way nature works, and that $\Lambda_{\rm QCD}$ is more like 200 MeV so that the QCD coupling is large, is not considered a "problem" among particle physicists. It's just the way nature decided to be.

There are some people who play the game of trying to get the SM parameters to work out. For example, you might have a brane world where there are a bunch of branes that intersect at just the right angles to give the strings just the right tensions to reproduce the masses of the fermions, etc. Maybe there is a "landscape" of possible worlds... Personally, I don't put much stake in this approach, but that's just me.

Furthermore, if you feel that there is something to the flavor puzzle, may I suggest that you actually have it backwords: that is, the top quark is the ONLY quark that has the EXPECTED Yukawa - all the other fermions are screwy!! Why? Because the only scale in the problem is the Higgs vev, and therefore by dimensional analysis, we expect all the fermion masses should be that order. The fact that the electron is 10^6 times less than v suggests that there must be some new physics that introduces a bunch of small numbers that we don't know about. In fact, only the top quark has the "correct" mass.

Finally: a word of phenomenology. Everyone is in agreement that whether or not there is anything fundamentally special about the top quark, due to its large Yukawa coupling it will be the most sensitive probe of the physics of electroweak symmetry breaking. This is not (necessarely) because the top is special in the "eyes of God", but simply because the cross sections involving the top quark coupling to EWSB physics are larger than other probes. That is why, in my mind, people are so universally interested in the top.

Anyway, here are some of my thoughts on the flavor puzzle. I hope people find them enlightening.

20. Aug 3, 2008

### arivero

I agree that people should also worry about QCD and electroweak I hope they will. As for the topic, I liked your argument (boldfaced):

A goal is this posting is to hear about other developments explaining this fact: the existence of an approximate SU(5) flavour symmetry (and an approximate subgroup SU(3) for u,d,s) even if the natural mass scale is the one of the top quark. Furthermore, there are other puzzles, as you told in the passing, about QCD: why should the lightest QCD state (the pion) be closer to one of the lepton mass scales? Interesting puzzles, which probably are not worked in the literature vbecause of the faith on GUT.

For the first question, the difference of mass between udscb and t, you know I have a particular answer: that the flavour SU(5) representations 24 and 15 + 15, respectively from $5 \otimes \bar 5$ and $(\bar 5 \otimes \bar 5) \oplus (5 \otimes 5)$, do recursively provide again the full three-generations standard model, and then there is some kind of self-consistency: The 24 provides the leptons, while a subset 12 + 12 provides the three generations for a given colour of quarks. If I have not moved the model into the conference circuit is because I do not know how to extract technically the 12 out of 15; I guess than chirality, and thus weak SU(2), has a role here, but my math is too poor. So I keep very interesting on hearing of any other theories where the difference between the top mass and the other quark masses has a role to play.

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