# Why is c quark heavier than s while u is lighter than d?

1. Sep 28, 2015

### Garlic

Why are charm quarks (+2/3e) heavier than strange quarks (-1/3 e) while up quarks (+2/3e) are lighter than down quarks (-1/3e)?

Last edited: Sep 28, 2015
2. Sep 28, 2015

### Staff: Mentor

No one knows. In the standard model, the quark masses are free parameters.

-1/3, not -1/2, but I guess that is a typo.

3. Sep 28, 2015

### Garlic

Oops, it is a typo. Thank you.
Ps: I hope it isn't bothering anyone that I am bombarding the forum with questions

4. Sep 28, 2015

### mathman

You are not bothering anyone. That is what the forums are for. Note that u and d have approximately the same mass, while the plus charge quark has much greater mass than the minus charge quark for each of the other two pairs.

5. Sep 28, 2015

### ChrisVer

one fun note, of course it's not a reason but ok:
because the charm quark's mass was predicted as such to avoid having flavor changing neutral currents beyond what was actually found experimentally, as for example in the $K^0 \rightarrow \mu^+ \mu^-$.

6. Sep 28, 2015

Staff Emeritus
No, that's not true. That's not what the paper said. The paper's mention of mass was only to explain why charm was undiscovered in 1970.

7. Sep 29, 2015

### Anchovy

Are there no GUTs where a reason for this emerges? Like the ratios of fermion masses that sometimes pop out?

8. Sep 30, 2015

### arivero

At most, traditional GUT obtains a relationship between mass of charged lepton and mass of the down-type quark, so that it is m=m/3, m=m, 3m=m, This is from Cecile Jarlskog and Giorgi.

9. Sep 30, 2015

### arivero

There was some expectative that the yukawa mass of the up quark were zero, and the observed mass were a effect via $$\Delta m_u = {m_s m_d \over \Lambda_\chi}$$
The same correction should apply to the other two quarks, cyclically, but it is negligible. I looked into this a couple years ago (when I accidentally predicted m=0 for some quark applying Koide numerology), and it seems that it is still a valid possibility depending on how do you interpret the results of lattice calculations. Still, it does not answer the question because the trick is the factor $m_s/\Lambda_\chi$; if only grants that a quark has a mass half of the other, not which is the smaller one.

Last edited: Sep 30, 2015
10. Sep 30, 2015

### arivero

Also some personal thought on this. You could also expect that the exotic yukawas $Y_t=1$,$Y_u=0$ happen due to the mechanism that breaks the GUT, and not in the GUT representations themselves. So perhaps at GUT level all quarks are massless, and then they get some simple yukawa/CKM matrix but the up and top are heavily corrected. Or perhaps it is a two-steps process, where first the top gets the "natural" yukawa value (so all the others should be protected by an unknown symmetry) and then this value forces masses to go between zero and 1. This second approach, still, does not explain why the candidate for zero mass is the "up" instead of the "down quark".

Even more speculatively, which could be the spectrum if we do not need to force up and top out of the system? I think that we could have three SU(4)xSU(2)xSU(2) multiplets $\nu_\tau, \tau, c,d$ with M= 1+sqrt(3)/2, $\nu_\mu, \mu, t,s$ with M= 1-sqrt(3)/2 and $\nu_e, e, u,b$ with M=0

or perhaps better (it exhibits a nice quark-hadron pairing)
$\nu_?, e, u,b$ with M=4
$\nu_?, \tau, c,d$ with M= 1+sqrt(3)/2
$\nu_?, \mu, t,s$ with M= 1-sqrt(3)/2

So that we have $m_c > m_s$ because they are actually in different multiplets, contrary to the traditional labeling (I find hard to have such mass difference only from electromagnetic differences) and we also have granted $m_b > m_c$. For all the others, a severe correction must happen to drive them to the current values. Forget about the masses if you wish, this is even more speculative. The mass values proportional to 0,2-sqrt(3),2+sqrt(3) were proposed by Harari, Haut and Weyers in an attempt to fix the Cabbibo angle to 15 degrees; they used them for u,d,s; so the extension to cover c,b, and eventually t is ad-hoc from myself in a wat that for a basic unit of 909 MeV you get realistic masses. Whatever, this correction happens, neutrinos get lost down the see saw, top becomes a topper, and we go to the broken spectrum:

$., \ \ ,t\ ,\$ with M=... well, huge.
$., \ \ , \ \ ,b$ with M=4
$\:\; ,\tau, c, \$ with M= 1+sqrt(3)/2 = 1.87
$\;\; , \mu,\ , s$ with M= 1-sqrt(3)/2 = 0.13
$., \ \ ,\ \ ,d$ with M= (1-sqrt(3)/2)^2/(1+sqrt(3)/2) =0.0096
$\;\; , e, u, \$ with M=0

The point that s,c,b get only a minor correction, or do not move at all, indicates that we should need a GUT where the charge of c and its multiplet partner d were exchanged respect to the other two families (u,b), (t,s). I have seen occasionally this kind of GUTs on susy-motivated generalisations of the Left-Right model, but they are not usual. Typically all the three generations are always the same for all the charges, new or known.

Last edited: Sep 30, 2015
11. Sep 30, 2015

### Staff: Mentor

The top mass had a reasonable prediction from precision measurements (early predictions were off, but shortly before the discovery they got better), but that is still a prediction based on experimental results related to the top.

12. Sep 30, 2015

### arivero

Indeed, so the lowercase. The rest of the comment is speculation as talk motivated by the question, I know this is a fuzzy line but chatting about the topic is the difference between a forum and a question and answer site. For the question on-topic, let me stress that:

- It is perfectly possible to consider strange, charm and bottom in different GUT multiplets, so that their difference of masses is automatic. This is in fact done in literature, and Harari et al do such trick, but no without criticism, because at the end it reduces to set up a very complicated Higgs mechanism and the question then is to explain why should it be needed.

- I think, but with less confidence, that is also possible to consider charm with a different set of GUT charges than up and top. But afaik it only happens in variants of L-R models coming from super-string theory and I am not sure of the interpretation.

13. Oct 5, 2015

### eltodesukane

"Why is c quark heavier than s while u is heavier than d?"
-- u is not heavier than d
mass u = 2.3 MeV/c^2
mass d = 4.8 MeV/c^2

14. Oct 5, 2015

### Garlic

Ugh. You are right, I corrected it. But other people got what I was meaning.

15. Oct 5, 2015

### eltodesukane

In any case, the mass pattern is puzzling, and it is begging for an explanation.
Just look at the huge mass jump from u to c to t.
And if there is a 4th generation, how heavy would be the one after t?
(I read somewhere that a 4th generation was not possible for some cosmological reason related to the Big Bang, but I wonder how definitive that conclusion is.)

16. Oct 5, 2015

### Staff: Mentor

Z decays: If there is a 4th generation, the neutrino would need a mass above 45 GeV, otherwise the Z would have more invisible decays. As the other neutrinos are lighter than ~0.1 eV, that would be a really huge mass jump.
Cosmology also gives a constraint, more than three light particles (not necessarily neutrinos) would lead to a different cosmic microwave background.
There is also something with anomaly cancellation but I don't know details.

17. Oct 5, 2015

### Garlic

My question was about +2/3 charged u being lighter than -1/3 charged d, while +2/3 charged c being heavier than -1/3 charged s. Huge mass differences between different generations doesn't seem that abnormal, I think.
If fourth generation quarks exist, I would say that they will have much more mass than top quark, lets say tens of tev range. In the wikipedia article, it says that fourth generation fermions and further are unlikely. It also says "According to the results of the statistical analysis by researchers from CERN, and Humboldt University of Berlin, the existence of further fermions can be excluded with a probability of 99.99999% (5.3 sigma)", as far as I've understood, it is probably referring about the fifth generation.
Note 1: Where did you find this standard model? It looks weird. Why is graviton excluded from the table?
Note 2: I couldn't correct the title, I don't have access to the editing options now, it's probably because it has been a I little while since this was posted. But it is unimportant, everyone understood my question right.

18. Oct 5, 2015

### Staff: Mentor

I fixed the title.
That's a specific model they exclude.

The hypothetical graviton is not part of the Standard Model.

19. Oct 6, 2015

### arivero

You are partly right. Looking at the whole thing, up and down look to be just in middle ground,

but this is because of the already very small mass of electron. Most of the game seems to happen near to the QCD scale, and in this sense top is abnormal. Which is funny, because really is the only normal ("natural") one, near of the Higgs mass and electroweak vacuum scale.

20. Oct 6, 2015

### arivero

On other hand, I really would like to hear your opinions -and the ideas of other physicists of the group- about this question. Not an answer, as we already agree there is none, but which is your hunch about this inversion: a still unseen quantum number? Some GUT thing? Pure randomness of yukawa couplings? Differente perturbative effects in the +1/2 or -1/2 sector of isospin? I find hard to believe that people has never stopped to think this kind of things, even if they are not its main field of research.

21. Oct 6, 2015

### ChrisVer

as I was told once, and I agree, the picture you posted becomes even worse if you also include neutrinos...(although neutrinos are a little different if they don't get their masses like the rest of particles).
the picture then becomes way more unclear, covers large orders of magnitudes (from meV to MeV ~1,000,000,000 , so 9 orders of magnitude larger axis from the left), the neutrinos are very close to each other compared to the rest of particles and in my opinion the overall pic looks uncorrelated. So I'd go with "pure randomness of yukawa couplings" for now. If there is some GUT which would actually bring the fermions all-together then probably you can get some relationship between their masses once the GUT is broken, I think.

22. Oct 6, 2015

### Staff: Mentor

We don't know. They could have a hierarchy similar to the quark masses.
The ratio between the heaviest and the intermediate neutrino mass eigenstate is at most ~6, but the lightest one does not have a lower limit.

23. Oct 7, 2015

### ChrisVer

to quarks the same ratio is ~42...to the leptons that is still around 20 too

24. Oct 7, 2015

### vanhees71

I think that's one of the big puzzles in physics. There's no clue, as far as I know, why the parameters in the standard model take the values they do. There are more then 20 free parameters in the standard model. As one of my professors said when I listened to his lectures on the standard model: "Each of this parameters, which have to be fit to observations, are a manifestation of our ignorance." As far as I know, we are as ignorant today as we were 20 years ago when I heard these lectures.

25. Oct 8, 2015

### arivero

And yet, one could expect at least to have a situation where some GUT models explain some parameters and other GUT models explain another set, leaving the judgement to further experiments. But the real situation is that it seems we are even unable to give to a question as the OP one an answer in terms of families of models explaining it.