New numerology for dark energy

At Physics Forums, a poster called "zeroace" has pointed out that, using the new values from the Planck satellite, the dark energy density is very close to 1 - 1/π.

The HWZ sum rule needs a Sumino mechanism

By "the HWZ sum rule", I mean the Dharwadker-Khachatryan formula that predicted the Higgs mass. (Perhaps we should call it the Dharwadker-Khachatryan sum rule.)

By a "Sumino mechanism", I mean something like Yukinari Sumino's mechanism which allows the Koide relation to be exact within experimental limits, despite the running of the masses.

This thought was prompted by Lykken's talk, mentioned in the previous post, in which a dark matter scalar controls the running of the Higgs mass. Perhaps some version of this model can also protect the DK formula from quantum corrections.

Scalar trinity

Michio Kaku is being criticized on a number of physics blogs for saying (on TV) that the "God particle" is the missing piece in the "Big Bang theory". While it would be apt for the particle dubbed God to be the first cause, there's no particular reason to think that the scalar responsible for inflation (the inflaton) is the same as the scalar responsible for mass (the Higgs boson).

Meanwhile, Joseph Lykken has described a model (see slide 26 forwards) in which the dark matter is yet another scalar - this possibility is sometimes called a "darkon" - which also ultimately serves to generate the Higgs mass in a finetuned way. So that would make three scalars doing fundamental things: the Higgs, the inflaton, and the darkon. Someone should tell the Pontifical Academy of Sciences about this.

t, b, tau

Of the three generational triples, t-b-tau works best (Andrew had to fudge the first generation a little, and the second is completely off); which shouldn't be a surprise, since t-b-c is already known to work well, and the masses of tau and charm are relatively close. It wouldn't surprise me if t-b-tau is already in the Koide-inspired literature (it is, incidentally, common to speak of t-b-tau mass unification in GUTs, but the idea there is that their masses are the same at the GUT scale).

Andrew's paradigm doesn't especially favor consideration of generational triples (with all the non-neutrino fermions of a generation) beyond the first generation. But a more conventional approach might hope to produce such triples through a type of "horizontal symmetry" (that skips the electrically neutral neutrinos). Indeed, one could reasonably also dub a generational triple a "horizontal triple", and a family triple could be a "vertical triple".

Andrew Oh-Willeke's paradigm

Andrew has a new post up describing his new way to think about Koide relations.

I'd say it's characterized by two ideas. First, the Higgs boson is somehow bundled with the W and Z bosons, and so mass generation is regarded as intimately linked with the weak force. Second, Koide relations arise from a sort of equilibrium of weak-force transitions between the fermions in question.

There's a lot to be said about the compatibility (or incompatibility) of these ideas with more commonplace theoretical notions, like seesaw or Froggatt-Nielsen, and with standard notions of the weak force, the Higgs mechanism, QFT, etc; and also much to be said regarding how these ideas could be given sufficient specificity to become the basis of a mathematical theory. Much to think about!

e, u, d

Andrew Oh-Willeke suggests a new Koide triple: electron, up, down.

I consider it rather unlikely (and it depends on the up mass being zero, an old idea which features in Rivero's Koide waterfall but which is out of fashion, presumably because it is empirically disfavored). But I'll say this for Andrew's triple, that it does have a little logic; those are all the first-generation fermions except for the electron-neutrino, and the neutrino masses differ from the others by orders of magnitude.

In the Koide lore of fringe physics, we have what I call "family triples" like the original electron/muon/tauon, and "sequential triples" like top/bottom/charm; I suppose this is a "generational triple".

Andrew now needs to look at the corresponding neutrinoless triples for the other two generations. If they work well, that's really interesting; if they don't, it doesn't necessarily kill the idea; there may just be other influences dominating the masses of the second and third generations, in that case.

Although I have much more confidence in the reality of the sequential triples appearing in Alejandro's waterfall for the quark masses, it may actually be easier to build models in which Andrew's generational triple is something real (i.e. has a cause, such as a new symmetry). The sequential triples alternate between up-type and down-type quarks in a way which makes them the most difficult to accommodate.

In general this also seems a positive development simply because it rounds out the picture, regarding possible generalizations of Koide's relation to all the fermions.