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PF Gold
P: 2,904
 Quote by mitchell porter In my opinion, this s-c-b relation is a big big clue about family symmetries.
Indeed. I have done a first surview of the early theories, who aimed to calculate the Cabibbo angle and occasionaly met some mass formula, such as the one from Harari et al. All of them proceed by putting a discrete symmetry but most of them do not use the standard model but the Left-Right symmetric model. They put the symmetry in the R part, then they break this SU(2)_R. It makes sense, as then a up quark is linked not only with a down_L but also with a bottom_R, and then the mass pattern needs some more levels to accommodate everything.

By the way, are we two the only persons reading the thread? It is good to exchange and archive ideas (I am finding now in PF some valuables from six years ago) but it should me nice if other readers have some input, or just a wave and a hello. In order to give other persons an entry point, let me coalesce all the bc -l code in a single cut-paste block:

pi=4*a(1)
me=0.510998910
mmu=105.6583668
mtau=((sqrt(me)+sqrt(mmu))*(2+sqrt(3)*sqrt(1+2*sqrt(me*mmu)/(sqrt(me)+sqrt(mmu))^2)))^2
m=(me+mmu+mtau)/6
cos=(sqrt(me/m)-1)/sqrt(2)
tan=sqrt(1-cos^2)/cos
delta=pi+a(tan)-2*pi/3
mc=3*m*(1+sqrt(2)*c(3*delta+4*pi/3))^2
ms=3*m*(1+sqrt(2)*c(3*delta+2*pi/3))^2
mb=3*m*(1+sqrt(2)*c(3*delta))^2
mtop=((sqrt(mc)+sqrt(mb))*(2+sqrt(3)*sqrt(1+2*sqrt(mc*mb)/(sqrt(mc)+sqrt(mb))^2)))^2
I'd be glad if someone uploads some equivalent maxima, macsima or symbolic algebra whatever code.

And of course, there is a pending puzzle: to explain the phase of the triplet charm-bottom-top