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

[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.