## Friday, January 22, 2016

### Susy II

In some ways, the MSSM seems promising as a framework for tHWZ numerology. The reason may be seen at the end of section 3.4 in Stephen Martin's primer: susy determines the couplings of the scalar potential, in terms of coupling constants elsewhere in the theory. If I am interpreting that passage correctly, the quadratic coupling will be set by the top yukawa, and the quartic by the gauge couplings.

However, the MSSM has a lot of annoying particles like gauginos and sfermions which get in the way. Here last decade's ideas about split susy are useful. In particular, in section 2.3.3 of "Predictive Landscapes..." we read about a framework midway between split and supersplit susy, in which only the Higgsino is light. That sounds worth exploring.

## Monday, January 18, 2016

### H, Z, susy

I finally noticed that the Higgs mass parameter μ, 89 GeV, is very close to the Z boson rest mass, 91 GeV (and the width of the Z is a few GeV).

In the standard model, these quantities should be independent. But in the MSSM, the Z boson is the upper bound on the tree-level mass of the Higgs.

I am too tired to develop an interpretation. But tomorrow is another day.

## Thursday, January 14, 2016

### t, H, W, Z in 2016

Recently I have been puzzling again, over the Dharwadker-Khachatryan sum rule

mH = mW + 1/2 mZ

The problem being that it works quite well; but theory tends to favor relations among the squares of these masses (e.g. the "Veltman condition").

The primary purpose of this post is just to observe that you can get such a relation by squaring both sides of the D-K equation.

You do also get a term mW mZ. Perhaps it could result from a geometric mean, as in Torrente-Lujan.

Another simple thing that I want to observe, is that you might obtain something like D-K, by taking the square root of a Veltman-like sum rule. In other words, it could be approximately true, not by chance and not because it is directly implied by a fundamental theory, but as an algebraic side-effect of the truly fundamental relationship.

(The same applies to the Lopez-Castro - Pestieau - Garces-Doz sum rule, previously discussed here, which does involve masses squared, and therefore even more closely resembles Veltman's condition.)

P.S. Dharwadker also has a numerology for the ratio baryonic matter : dark matter : dark energy, which he deduces to be 1:5:18.