So, B-L is a U(1) generator extracted out of some unified theories of leptons and quarks and in such theories it is traceless, with B=1/3 and L=1, and the trace taken over a "four coloured" multiplet, namely a lepton and three colored quarks.(adsbygoogle = window.adsbygoogle || []).push({});

Now, I am amazed that there is another Matrix that happens to be traceless, and it is the product of B-L times Mass, when taken only with a single colour of light quarks, I mean we have

Tr (L x M )=sum of lepton masses = [itex] 1882.98 \pm 0.16 [/itex] MeV

Tr (B x M) = 1/3 sum of udscb masses= [itex]1852.37 \pm 13.13[/itex] MeV

Moreover, there is at least one lattice team out of the consensus for charm quark,

http://arxiv.org/abs/1311.2793 and with the quark values of this paper, we would have Tr(B x M) = 1882.23 It is also true that the same group has another paper with a slightly higher b mass, but with a compatible error anyway.

So it seems that discarding the top quark, the matrix (B - L) x M is compatible with tracelessness when looking only to one colour.

The question is, are there GUT theories using this product matrix? or topcolor or technicolor theories? Georgi-Jarlskog?

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# Has B-L some role in the mass matrix?

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