Friday, July 31, 2015

Today's crackpot synthesis

1. If one assumes that QCD embeds in a GUT group, then one can show that the proton mass mp is proportional to a power of the top mass, mt2/27.

Today I realized that Brannen's reformulation of the Koide relation can be described as follows: the Brannen mass scale of e,mu,tau is mp/3, and the Brannen phase is 3 * 2/27.

2. If the quark families (b,s,d and u,c,t) are treated as Koide triples, their phases are also (arguably) multiples of 2/27.

There is also a "waterfall" of Koide triples, descending from the top, which alternate between the families. One of these triples - s,c,b - has a Brannen mass of mp, and a Brannen phase of 2/3.

3. In Rivero's sBootstrap, the leptons are superpartners of mesons made of the five light quark flavors, and the quarks themselves are superpartners of diquarks made of those five flavors.

I proposed to interpret this as similar to a Seiberg duality. The primordial theory is like six-flavor QCD with one heavy quark and five massless quarks, and N=1 supersymmetry. The other is the standard model, with the light quark masses, the leptons, and the electroweak sector all emerging from the duality.

The leptons would then be the mesinos of the primordial theory, and the phenomenological quarks would be a mixture of the primordial quarks and the diquarkinos.

4. This suggests a way of thinking about the numerology in 1 & 2.

The primordial fact would be that mp ∝ mt2/27 is already true in the QCD-like theory on one side of the duality. The appearance of mp and 2/27 in standard model numerology is then to be attributed to the duality. 1 comes from the "lepton-mesino duality", and everything in 2 from the "quark-diquarkino self-duality".


  1. Sounds interesting as is.... now does the crackpot determine the perception of the universe or the universe grounds the crackpot and his perception?

  2. Synthesis appreciated. I've seen these relationships suggested piecemeal, but this helps put it in context.

  3. Also s,c,b phase is three times the phase of leptons.

  4. Actually, the derivation of the exponent 2/27 depends on there being three quarks with masses above the QCD scale, so it should not appear in the dual theory as described (in which only the counterpart of the top quark has mass).