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

[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)?

 

[mfb]

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.

 

[Garlic]

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.

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

 

[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.

 

[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^-.

 

[Vanadium 50]

because the charm quark's mass was predicted as such to avoid having flavor changing neutral currents beyond what was actually found experimentally

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.

 

[Anchovy]

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

 

[arivero]

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

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.

 

[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.

 

[arivero]

Are there no GUTs...

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.

 

[mfb]

@arivero: Please don't forget our rules about personal speculations.

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^-.

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.

 

[arivero]

@arivero: Please don't forget our rules about personal speculations

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.

 

[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

 

[Garlic]

"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

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

 

[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.)

 

[mfb]

(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.)

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.

 

[Garlic]

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.)

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, let's 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.

 

[mfb]

I fixed the title.

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)"

That's a specific model they exclude.

The hypothetical graviton is not part of the Standard Model.

 

[arivero]

Huge mass differences between different generations doesn't seem that abnormal, I think..

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.

 

[arivero]

about personal speculations.

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.

 

[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.

 

[mfb]

the neutrinos are very close to each other compared to the rest of particles

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.

 

[ChrisVer]

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.

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

 

[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.

 

[arivero]

There's no clue,

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.

 

[ohwilleke]

And if there is a 4th generation, how heavy would be the one after t?

A naive extension of Koide's rule for the relationship of the charged leptons, which also holds to within the range of experimental error for the relationship between the t, b and c masses would predict that a fourth generation charged lepton would have a mass of 43.7 GeV (which is experimentally excluded), that a fourth generation down type quark would have a mass of 3,563 GeV and that a fourth generation up type quark would have a mass of 83,750 GeV. As previously noted, no really plausible relationship produces a fourth generation neutrino of more than the 45 GeV experimental bound.

The Standard Model requires mathematically that each generation of fermions have one up type quark, one down type quark, one charged lepton and one neutrino, so the bound from the non-detection of a heavy fourth generation neutrino makes a fourth generation highly unlikely.

The Standard Model extended to four generations (SM4), would also have to have an enlarged CKM matrix. But, since the sum of the CKM matrix entries squared in every column and row is experimentally measured to be almost exactly one, there is little room for interactions with fourth generation particles.

There is also an issue involved in mean lifetimes. The mean lifetime of the top quark is only slightly longer than the mean lifetime of the W boson by which it decays, and there is a clear trend among the Standard Model particles that heavier particles of the same type have shorter mean lifetimes than lighter particles of the same type. A much heavier fourth generation quark ought to have a mean lifetime much less than the W boson by which the decay of that quark occurs, which could potentially be a limiting factor.

Another bit of suggestive evidence that there are no fourth generation quarks is that the sum of the squares of the fundamental particle masses in the Standard Model is almost precisely equal to the square of the Higgs vev (and indeed, the sum of the square of the masses of the fundamental fermions is equal to the sum of the square of the masses of the fundamental bosons within the margin of error of the current experimental values). If either of these relationships has an actual physical law for some unknown reason, then any new Standard Model particles even as heavy as a bottom quark are ruled out.

 

[Vanadium 50]

There is no (sequential) 4th generation. A 4th generation will increase the Higgs cross-section by almost an order of magnitude.

I very much doubt there is any more physics in the Koide formula than there is in the Titus-Bode formula.

 

[ChrisVer]

Is there any reason to bring forth a 4th generation rather than a single heavy fermion? as for example in some axion models?

 

[ohwilleke]

There is no (sequential) 4th generation. A 4th generation will increase the Higgs cross-section by almost an order of magnitude.

I very much doubt there is any more physics in the Koide formula than there is in the Titus-Bode formula.

The Koide formula for charged leptons is consistent with all available data, and the experimental values have gotten notably closer to its prediction than they were when it was proposed. There is almost surely some deeper reason for this. The extensions of Koide's formula beyond that domain are not nearly so solid, but come closer to quantifying the pattern that we do see than any other attempt, and so can inform our intuition and provide some sense of what a theoretically grounded formula relating these constants might look like.

 

[Vanadium 50]

Is there any reason to bring forth a 4th generation rather than a single heavy fermion?

Yes. If you want your theory to be anomaly free, the sum of all the charges needs to be zero. More precisely and technically, you need to have complete multiplets for all the gauge groups. That means you can add as many right-handed neutrinos as you like, although that's not terribly interesting.

There is almost surely some deeper reason for this.

You could have said the exact same thing about the Titus-Bode law in 1775.

 

[nikkkom]

You could have said the exact same thing about the Titus-Bode law in 1775.

Titius-Bode law's errors vary from 0% to more than 5% for different planets. Koide rule's is less than 0.01%, and well within one sigma of error bars.

Moreover, if Koide rule is spurious, then the next round of more precise mass measurements should be almost certain to move measured value away from 2/3. Would you bet on this happening? ;)

 

[Vanadium 50]

Koide rule's is less than 0.01%

Like the Earth's polar diameter being half a billion inches? Or that there are pi x 10^7 seconds in a year? Or that the sun and the moon have the same angular size, as viewed from Earth? Or pi = 256/30e?

Sometimes a coincidence is just a coincidence.

 

[arivero]

There is no (sequential) 4th generation. A 4th generation will increase the Higgs cross-section by almost an order of magnitude.

I like this point. Until the discovery of the Higgs, our main bound for new generations was the Z0 peak.

Also I supposse that CP violation phases should be problematic. Hey, we already have the theta-problem, do we?

Returning to the OP question, I wonder which is the argument to say that charm and strange are the second generation.

For instance, if we put charm in the third generation, then m_c < m_b and m_u<m_d, and the question is solved, no contradiction. Is there some problem with CKM phases or similar things?

PS: I like also the Bode-law comparison (but not the ones involving dimension-full arguments; that is other league) for the Koide-like textures. Titius Bode was matching 8 values, more or less the same. Still, Titious used more empirical input. PS2: I am not 100% sure if the point of tidal forces of sun and moon being equal is coincidence, but I at least it is occasionally discused in the literature.

 

[Vanadium 50]

Looking at the CKM matrix, one can pair up u and d, c and s, and t and b, under the argument that the physical d is mostly the weak isopartner of the u, the physical s is mostly the weak isopartner of the c, and the physical b is mostly the weak isopartner of the t. It would be pervice to pair them any other way.

There is not a shred of evidence that the e goes with (u,d), the mu goes with (c,s) or the tau goes with (t,b). They are usually placed in tables this way, but not for any reason other than mass.

 

[arivero]

pervice

Hmm you did me to look up the dictionary :-D

1. stubborn, obstinate

(dictionary favours "pervicacious", but I did not know this word either. #TIL, I would say)

 

[ohwilleke]

There is not a shred of evidence that the e goes with (u,d), the mu goes with (c,s) or the tau goes with (t,b). They are usually placed in tables this way, but not for any reason other than mass.

Mean life time hierarchy also favors the current alignment of u-d-e, c-s-mu, t-b-tau. Lepton flavor conservation favors the alignment of the respective neutrino types with their respective lepton types. No second or third generation fundamental particles, and no composite particles containing second or third generation fundamental particles are stable. It also makes sense that t is the 3rd rather than the 2nd generation because its extremely short lifetime makes it an outlier as the non-hadronizing quark which fit an extreme rather than intermediate generation.

 

[Vanadium 50]

Mean life time hierarchy also favors the current alignment of u-d-e, c-s-mu, t-b-tau.

That's the same as the mass hierarchy, since weak decays go as m^5.

 

[nikkkom]

Like the Earth's polar diameter being half a billion inches?

Error of more than 0.1%

Or that there are pi x 10^7 seconds in a year?

Error of more than 0.3%

Koide formila says that Q = 0.666666666..., measured value is 0.666659(10), the difference is 0.000007... which is slightly more than 0.001% (and importantly, the difference is smaller than measurement uncertainty)

Of course, it can be spurious. There is no way to prove that it is not.

 

[arivero]

slightly more than 0.001%

I think that he refers to the current context. The koide tuple for (s,u,d) with an up mass equal to zero fails a bit,
it is Q(95,0,4.8)=.70031 well far away from 0.666... The koide tuple for (c,s,u) does a bit better,
Q(1235,95,0)=.66003, so a error of 1%. EDIT: We travel better with the last pdg value for charm mass
Q(1275,95,0)=.66309, but still not as good as for leptons.

Of course if we do not need a mass exactly 0, we can invoke a waterfall to produce masses for the first generation: use c,s to solve for u, and then s,u to solve for d. I am not very easy about the last step (also (b,s,d) is a suitable tuple if you look at the S4 symmetry argument) but at least for the question in case in effectively predicts a very small u mass. Namely,

mc=1275
ms=95
((sqrt(mc)+sqrt(ms))*(2-sqrt(3)*sqrt(1+2*sqrt(mc*ms)/(sqrt(mc)+sqrt(ms))^2)))^2
.01478

To be, the result, exactly zero, the proportion mc::ms should be 13.92, while experimentally it is 13.42 or 11.73 depending of how you measure it. In any case too low.