Constituent pions

I have stumbled upon an idea regarding the structure of a "constituent quark": a bare quark plus three pions. Now to see if it makes sense and if it would explain anything.

Today's crackpot synthesis

1. If one assumes that QCD embeds in a GUT group, then one can show that the proton mass m_p is proportional to a power of the top mass, m_t^2/27.

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 m_p/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 m_p, 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 m_p ∝ m_t^2/27 is already true in the QCD-like theory on one side of the duality. The appearance of m_p 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".

hep-dada #2

Another transparently fake paper, posted to vixra. Maybe they are coming from David Simmons-Duffin, the inventor of snarxiv, or even from Andrew Bulhak, who wrote the original Postmodernism Generator. Anyway, it gets old fast.

hep-dada

This blog was originally inspired by the parodies of arxiv abstracts produced by snarxiv. snarxiv in turn reminded me of the Postmodernism Server, which generated whole essays written in bland postmodernese. Now the wheel has turned further and someone has posted to vixra a whole "paper", expanding on a snarxiv-like abstract.

Coincidentally, the Italian net.artist Roberta Betti recently took to tweeting out the text of imaginary papers in mathematics, complete with the typographic mangling produced e.g. by viewing Google's cached copy of such a document. Behold "Canonically Stochastic Fibonacci Spaces Over Matrices", "Existence In Real Logic", and "On the Integrability of Universally Parabolic Lines". Could Betti (aka Stalagmathron) be behind the new vixra paper by "Baruch Seiberg and Claude Witten"? Has someone written a script which generates full-length snarxiv papers? Will vixra now be spammed with cheap machine dada? Time will tell.

edit: @Stalagmathron has disappeared, but some of Betti's earlier work lives on at archive.org. 

Vik's relation

Over two years ago, a series of posts on tHWZ relations was launched here, starting with the observation that

<ϕ> ~ √2 m_t, m_t ~ √2 m_H

which I was prompted to record, when Andrew Oh-Willeke remarked that

<ϕ> ~ 2 m_H

(Where <ϕ>, also often written as v, is the Higgs field "vacuum expectation value".)

Recently a paper appeared on arxiv, noting that first relation, in the form

4 m_H² = 2 m_t² = v²

and Andrew commented that

"I think it is more likely that the observed relationship is really an approximation of the relationships

sum((Fi(^2)=v^2/2 and sum((Bj)^2)=v^2/2 for all fundamental fermion rest masses Fi and fundamental boson rest masses Bj"

which is an aspect of the LC&P sum rule, of which he also says that it is

"quite a bit more profound than the fact that the heaviest fermion by itself accounts for about half of the Higgs vev squared, or that the Higgs mass square accounts for about a quarter of the Higgs vev squared."

I agree that the LC&P sum rule looks to be the fundamental thing here. But there is an interesting final twist which he didn't note.

To recapitulate:

1. The sum of the squares of all the fundamental particle masses, is approximately the square of the Higgs VEV.

2. The contributions to this total from bosons and fermions are approximately equal. (Given the love of supersymmetry in the particle physics community, it really is remarkable that this isn't visibly being talked about.)

3. The top quark is responsible for the great majority of the fermion contribution, and thus about half of the total.

4. The Higgs boson is responsible for about half the bosonic contribution, and thus about a quarter of the total.

So where does the rest of the bosonic contribution come from? It comes from the W and Z bosons. So we have a fifth fact:

5. The W and Z bosons are responsible for the other half of the bosonic contribution, and thus for the remaining quarter of the total.

If we write this up as an equation, we get

m_H² ~ m_W² + m_Z² ~ 1/2 m_t²

The first part of this equation appeared as a blog comment by S. Vik, who is apparently a retired physicist from Wilfrid Laurier University in Canada. At the time I gave it a low probability of being meaningful, but I did record it. It would be ironic if it is yet another genuine clue to what lies beneath the standard model.

vixra watch

Many times on this blog I have cited papers from vixra, the alternative to arxiv. Today I just want to note two surprising new additions to the vixra user base, Simon Plouffe and Jacob Barnett. They both have biographies at Wikipedia: Plouffe is, I guess, a computational number theorist, and Barnett is a teenage theoretical physicist who has been in the media since he was 12 (he's 16 now).

Goldfain on LC&P

I record here the existence of two papers by Ervin Goldfain 1 2 claiming to derive the LC&P sum rule.

His concept seems to be that the effective dimension of space-time varies with energy scale, that the masses of SM particles define special scales, and that the LC&P formula follows from a "closure relation" that must connect these different scales.

Incidentally, he is not just talking about spaces with an integer number of dimensions, as in Kaluza-Klein theories or string theories, where e.g. the number of dimensions may increase from 4 to 10 or 11, at energies above the compactification scale. Instead he talks of there being 4+ε dimensions, reminiscent of dimensional regularization... but the modified concept of dimensionality that he really emphasizes is that of fractals.

Informally, one might say that Goldfain's concept is that space is crinkled or creased in a fractal way, so that e.g. the volume of space inside a cube doesn't simply vary as the third power of the side of the cube. Instead, the exponent describing the change in volume is non-integer, and also varies with the size of the cube (length of its side). If we take a cube and shrink it, we might find that as the side shrinks to one millimeter, volume is proportional to size^3.1, but by the time we have shrunk to one micrometer, volume is proportional to size^3.3. Apparently in the world of fractals, such behavior is called multifractal.

The references to millimeter and micrometer above are purely illustrative. Goldfain seems to believe that the first significant deviations from integer dimensionality (4 space-time dimensions) only begin to occur above the electroweak energy scale, which would correspond to distances less than 10^-18 meters.

Goldfain is an independent investigator who publishes at vixra and in various web "journals", but the concept of multifractal space-time isn't just some whimsy of his, it has seen some mathematical development. The real problem I am having with his work so far, is that I don't understand where the "closure relation" comes from - and that's the crucial step towards obtaining the LC&P formula. 

See for example equation 5 in paper "1". The "r"s are the different scales, and the "D" is a fractal dimension. The LC&P formula is a sum of squares, and so if scales were associated with masses, and if D was equal to 2, then we might be able to obtain it from equation 5. 

Goldfain has written other papers trying to obtain SM mass ratios from fractal dimensional flow. A skeptical reading might say that all we have here is a conceptual framework in which multiple length scales can assume a special significance, and since masses can be mapped to length scales in physics, this multiscale conceptual framework can be a playground for a physics numerologist trying to explain particle masses. 

I am skeptical, but dimensional flow is not a bad thing to think about. I will make a follow-up post if I have anything more concrete to add.