Particle Masses: A solution of the wave-equation.

 
   

5.1

   

5.2

For , equation 5.1 simplifies to

 

5.3

solving for gives

 

5.4

where , G is the curvature scalar.

 

A spherically symmetric solution for is

 

5.5

Using the new De-Broglie relation,

 

5.6

for the integral in equation 5.4 is

 

 

which simplifies to

 

 

The wavefunction peaks when

 

 

Solving for r gives

 

 

Using 5.6, and it can be shown that the wavefunction peaks at an Energy E given by

 

5.7

   

For n>0, , E reduces to

 

 
   

For n=2, E(2)=172.6GeV which is near the mass of the Top Quark.

 
   

From the Lagrangian the energy of a boson is

 

 

The Curvature Scalar is determined by the potentials and omega.

 

Where f=3-6, it can be shown that for spherically symmetric potentials, and neglecting ‘magnetic’ potentials, the above curvature scalar is determined by the potentials

 

 

Which in terms of the coupling constants are

 
   

 
   

The energy of a boson for simplifies to

 

 
   

where

 

 
   

Using , solving for E gives

 
   

 
   

The coupling constants at Z energy are

 

 

And for , the rest energy of the Z is 93.4GeV

 

This compares with a measured value of 91.18GeV. This difference is due to another interaction with coupling strength , this gives a rest energy for the Z of 91.18Gev.

 

The carrier of this new interaction if uncoupled from the electroweak interation has a rest energy of approximately 420.3GeV and is possibly a dark energy boson.