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.

Review of review of 2012

Andrew Oh-Willeke has posted "A Review of Fundamental Physics in 2012 ".

Clearly the discovery of "boson X(126)" is the big event, the major payoff so far from the LHC. We agree on that.

The failure of anything else to show up so far - not just supersymmetry - is also significant, for its impact on the hierarchy problem. The mainstream discussion continues to be framed as a choice between "naturalness" - unknown particles like super-partners or top-partners make the Higgs mass more natural than it seems - and "finetuning" - e.g. there are anthropic reasons for having a Higgs mass in this range. The third way due to Shaposhnikov and Wetterich - the Higgs mass comes from special boundary condition to the RG flow at high energies - is long overdue for attention.

Technicolor in a narrow sense may be "dead", but the idea of a composite Higgs is still very alive.

"Dark Energy Is Still A Solved Problem" says Andrew - it's just a cosmological constant. Maybe that's what it is, maybe it isn't, but even if it is, we still wouldn't know why it has that magnitude or what it is that cancels out the enormous vacuum energy implied by standard QFT. Since he likes "physics numerology", he should look at some of the numerology that has been proposed regarding the size of the dark energy, e.g. by Riofrio, Chernin, and Padmanabhan.

Andrew is one of the handful of people aware of the generalizations of Koide's formula being pursued by Brannen, Rivero, and others in recent years, so this part of his review you definitely won't find elsewhere. I would quibble with one detail: he mentions Sumino and Goffinet as providing ideas about how to explain the exactness of the Koide relation for the pole masses of the charged leptons, when such relations should instead connect the running masses at high energies. But really it's only Sumino who has proposed a mechanism to cancel the deviations that should be produced by RG flow. Goffinet notices the problem, and his work is of interest for other reasons (e.g. the attempt to relate mixing matrices to the formula), but he doesn't have an answer, unlike Sumino.

As for quantum gravity, I remain pro-string and anti-loop, where "string" means, not just geometric phases of superstring theory, but also a variety of string-like possibilities. I consider the key "stringlike" properties to be (1) the existence of holographic dual descriptions of ordinary space-time physics (2) the possession of very special relations among amplitudes for quantum processes, like those discovered in the twistor revival.

There's a lot more in his review, especially on dark matter. Thanks to Andrew for posting it!