t, H, W, Z

Andrew Oh-Willeke mentions (in a blog post whose headline observation is the same as that made by  Dharwadker and Khachatryan) that the Higgs VEV is approximately twice the mass of the LHC's maybe-Higgs. This is one of a set of numerological connections between t, H, W and Z that have been on my list of items to ponder. Obviously I need to rush into print with those observations now, or else Andrew and others will get all the credit (when they figure it out for themselves)...

So, first item: top mass is approximately sqrt(2) times Higgs mass, Higgs VEV is approximately sqrt(2) times top mass. This is an extra twist on the basic observation that Higgs VEV is approximately two times Higgs mass.

Second item... This one isn't an observation so much as a conjunction of observations. I've already blogged Malcolm Mac Gregor's observation that m_top =approx m_W + m_Z. (He has a new paper today with lots of hadron numerology.) One then needs to consider this alongside the Dharwadker-Khachatryan observation (prediction, actually) that m_Higgs = m_W + 1/2 m_Z, and finally alongside the observation from the first item that m_top =approx sqrt(2) m_Higgs.

If you set the two expressions for m_top equal to each other, you get that m_W + m_Z "equals" sqrt(2) x (m_W + 1/2 m_Z), which would be true if m_W = 1/sqrt(2) m_Z, which isn't true. But maybe it's true "to zeroth order"? ... in the same unknown (and possibly nonexistent) theoretical framework where all these relationships aren't just coincidences.

Dark matter and powers of two

This post will mention my very own crackpot idea!

Right now we have some blog coverage (Reference Frame, Resonaances) of a paper claiming a signal of dark matter annihilation in the galactic center, producing gamma rays of about 130 GeV.

Now, a few years back there was a claim of "lepton jets" that might be produced by "three new states with energies 15 GeV, 7.3 GeV, and 3.6 GeV. The heavier states cascade decay to the lighter ones while the lightest one decays into a tau pair after 20 ps or so: so the 15 GeV particle should decay to 8 tau's! To say that the masses of some dark sector states should be fine-tuned to be 2m_tau, 4m_tau, and 8m_tau surely looks bizarre." (Quote from Lubos Motl.)

Now I notice that this new claim of 130 GeV, plus or minus a few GeV [*], is around 64m_tau. It's producing photons, not muons, but that just means there's a different decay channel available for this mass, right?

A more urgent theoretical question is whether we suppose that there is a sequence of states with mass 2x, 4x, 8x, 16x, 32x, 64x... m_tau, or whether we just jump straight from 2, 4, 8 to 64. Interestingly, the latter four numbers have a status as "Hermite constants" related to hyperspatial packing densities. Those are the Hermite constants for 3, 4, 5 and 7 dimensions. Hyperspace theorists, this is your chance!

[*] quite a few