sci.physics.research

On Oct 2, 8:19 am, "ariv...@ " < ...@ > wrote:
I am not sure if adding some context to the question will motivate or
demotivate experts to answer.

Last week (27th Sept) T. A. Mir, aka taarik, did an observation
relating the masses of charges leptons with the mass of the neutral
pion. As you know, there is no theory to explain why the mass of the
muon is in the range of the pion mass, the later comes from QCD, the
former from electroweak symmetry breaking.

The observation was:
\sqrt {m_e} \sqrt {m_\tau - m_\mu} = MeV
m_\pi - m_\mu = MeV.

The conjecture of Taarik and his collaborator was that this quantity
is a fundamental quantity in the spectrum, very much as McGregor and
other proposals. But this is not the history here, or not exactly.

Looking for an explanation, I invoked my old quark/diquark
supersymmetry, which in the lepton sector translates to lepton/meson
susy: the five quarks of QCD build a 5x-5 representation which
decomposes in 24+1, and this 24 provides the charges and number of
degrees of freedom you need to three generations of electrons and
neutrinos.

In this setup, it was natural to think that the doublet of muon and
muonic neutrino is the partner of an octet similar to the flavour
octet. From taarik observation, it seems that this symmetry breaks due
to the presence of other two supermultiplets having not easy
accomodation (the electron has no mesons of nearby mass, and the tau
has a lot of them).

It is reasonable then to try the other two permutations of Taarik
formula. Due to the low mass of the electron, both permutations give
the same result, within a couple of MeVs:

\sqrt {m_\mu} \sqrt {m_\tau - m_e} \approx \sqrt {m_\tau} \sqrt {m_\mu
- m_e}
\approx \sqrt {m_\tau \pm m_e} \sqrt {m_\mu \pm m_e}
\approx \sqrt {m_\mu} \sqrt {m_\tau} = MeV

So? It is not inmmediately obvious, because of mixing eta-eta', but if
you extract the other octet member, eta8, via the formula of GellMan
and Okubo, you have m_{\eta_8}=sqrt((4*kaon^2-pion^2)/3)= MeV

and now the second surprise:
m_{\eta_8} - m_\pi = MeV

No bad for the numerologists!

> Can anybody hint to some review of supersymmetry including the GSW
> model, ie no quarks, only leptons under SU(2)xU(1). Or is there some
> fundamental obstruction (besides anomalies, in any case) to build it?
>
> A SU(2) model could be enough.
>
> What I am intrigued about is that in such models, the sfermions could
> be arranged to form a octet, and then I wonder if susy-SU(2) implies a
> SU(3) "flavour" in the sfermions.
>
> Such model could "scale up" to three generations, and then 24
> sfermions to be arranged into a SU(5) "flavour".
>
> Alejandro