Recently I have been puzzling again, over the

Dharwadker-Khachatryan sum rule
m

_{H} = m

_{W} + 1/2 m

_{Z}
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 m

_{W} m

_{Z}. 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.