paper

Remarkable Relation from Minimal Imaginary Action Model

arXiv:1006.2455

Abstract

If it is to be true that the history of the universe should be adjusted to minimize the "imaginary part of action" [arXiv:0802.2991, arXiv:0711.3080, arXiv:0707.1919, arXiv:hep-ph/0612032, arXiv:hep-th/0509205, arXiv:hep-th/0701018], it would be "easiest" to have this "imaginary part of the action" to be rather independent of whether the neutrons are converted to electrons and protons (and neutrinos), and therefore of whether the contribution to the imaginary part of the Lagrangian were conserved under this conversion. Under the further assumption - which is reasonable - that the by far dominant term in the imaginary part of the Lagrangian density is the one corresponding to the Higgs mass square term in the Standard Model Lagrangian density mH**2 |phi(x)|**2 we derive a relation: (down mass square minus up mass square) = constituent quark mass times electron mass/"ln", where "ln" is defined by <1/gamma >= "ln"/ < gamma > and is of the order of 1 to 4, where gamma stands for relativity gamma of a valence quark inside a nucleon. This relation is very well satisfied with the phenomeno- logically estimated current algebra quark masses mu, md, and the constituent mass mconstituent for the light quarks, taken say to be one third of the nucleon mass. Our model has been criticised on the ground that it should have prevented cosmic rays with energies capable of producing Higgs particles, when hitting say the atmosphere. Indeed there is, however, a well known "knee" in the density curve as function of energy at an order of magnitude for the cosmic ray particle energy close to the effective threshold for Higgs production. A parameter giving the order of magnitude of number of Higgsses to be produced in order to get a significant effect is estimated to be about 300000.

This paper were at least somewhat inspired by the Spaatind conference January 2010 in as far as the material is near to the content of my talk there. This new version of the article has gotten stressed that genuine neotron life time has no significance, and the calculation of the "effective" Higgs threshold has been a bit expanded

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