Does Higgs Theory Explain the Precision of the Koide Formula for Lepton Masses?

[roberto85]

I was wondering if Higgs theory offers an explanation for why the Koide formula gives such precise masses for the leptons? I would assume that any theory of mass would be able to predict the masses of particles, especially for ones where precise relations have been found between them like the leptons.

 

[humanino]

The standard Higgs model does not explain the numerical values of the masses themselves. They are "accidental" just as say the radius of planetary orbits for Newtonian gravitation. In fact, there is a long history of trying to explain numerical accidents, and it is rather brave to engage in a new chapter. For one thing, geometrical interpretations are never unique.

 

[arivero]

Some models with three higgses, developed ad hoc, are able to reproduce the formula. But no the standard higgs.

Let me note that Koide equation is not one, but two coincidences: that it predicts the mass of the tau beyond 99.99 percent of accuracy, and that the basic mass scale seems to be 313 MeV, a quantity amazingly near of the mass of a constituient quark. given that this quantity comes from QCD, one could speculate that the explanation of Koide formula at the end could be not from higgs, but from colour condensates in some exotic way.

In some sense, Koide-Brannen-... (where "..." is whoever who wrote the 313 MeV explicitly in the set of formulae) also tells us that leptons and quarks have, in the deep, the same mass.

 

[humanino]

one could speculate that the explanation of Koide formula at the end could be not from higgs, but from colour condensates in some exotic way.

Like Gribov's proposal maybe ?
Bound states of massless fermions as a source for new physics

 

[arivero]

Like Gribov's proposal maybe ?
Bound states of massless fermions as a source for new physics

Hmm, in an alternate life, in a different Everett's path, I was in Peñiscola in 1997 just in time to hear Gribov's last talk (http://www.slac.stanford.edu/spires/find/hep/www?eprint=hep-ph/9708424 ) and other adventures. To my regret, in this worldline I preferred to stay in Zaragoza or elsewhere, and I have not read these works. Thanks for the reference, it seems that it could fit, or at least give some inspiration.

(EDIT: Actually, hep-ph/9708424 lecture was cancelled, Gribov fell ill the day before, a friend of me drove him to the nearest hospital. No opportunity to discuss bound states anyway)

 

[yoron]

'energy' is mass?
Is that it?

 

[arivero]

Hmm, in the last paper, Gribov seems more optimistic about point-like condensates:

"The analysis leads to the following conclusion. The conditions for axial current conservation of flavour non-singlet currents (in the limit of zero bare quark
masses) require that eight Goldstone bosons (the pseudo-scalar octet) have to be
regarded as elementary objects with couplings defined by Ward identities"

 

[arivero]

I like more and more the connection to Gribov theory. Actually two quantities from Koide are very similar to QCD quantities: 313 MeV is very near the constituient quark mass, and 105 MeV (the muon mass) is very near the pion mass. And then we have that if instead the octet of SU(3) flavour we take the 24 of SU(5) flavour, the number of charged scalars are exactly the number of superpartners of the leptons in Koide equation.

I wonder if there is a way (isospin/flavour symmetry restoration? massless limit? Susy breaking?) of getting the 140 MeV of the pion down by a 25%, to 105 MeV, without moving the 313 of the quark constituent mass.

 

[mitchell porter]

I was wondering if Higgs theory offers an explanation for why the Koide formula gives such precise masses for the leptons? I would assume that any theory of mass would be able to predict the masses of particles, especially for ones where precise relations have been found between them like the leptons.

As humanino said, the Higgs mechanism gives rise to mass but does not explain the values of the masses. The mass is the result of two parameters, the vacuum expectation value (VEV) of the Higgs field, and the strength of the coupling between the particle and the Higgs field. For a model with a single Higgs field, the Higgs VEV experienced by all particles is the same, but the coupling is different.

In order to make Higgs models more predictive, one may suppose that there are several Higgs multiplets, with various symmetry properties, etc. Koide's own recent yukawaon models are a relatively complex and sophisticated elaboration of this theme. Until this year, such model-building was guided by positive facts about particle masses and other properties, and by negative facts about the failure of a Higgs to show up anywhere, directly or indirectly. The recently announced observations from the LHC may be the first direct data about the Higgs sector, in which case they provide a new kind of "positive fact" that model-builders will need to take into account.