| Summary: | It is presently thought that the mass of all of the elementary particles is determined by the Higgs field. This scalar field couples directly into the trace of the energy momentum tensor of the elementary particles. The attraction between two or more masses arises from the exchange of gravitational quantum particles of spin 2, called gravitons. The gravitational field couples directly into the energy momentum tensor. Then there is a close connection between the Higgs field,
that originates the mass, and the gravitational field that dictates how the masses interact. Our purpose in this thesis is to discuss this close connection in terms of fundamental definitions of inertial and gravitational masses. On a practical level we explore two properties of mass from the viewpoint of coupling into the Higgs field: (i) The coupling of the both the Higgs and gravity to the energy-pressure tensor allows for the decay of the Higgs particle into two gravitons. We use
the self energy part of the Higgs propagator to calculate the electromagnetic, weak, fermionic and gravitational decay rate of the Higgs particle. We show that the former process appears to dominate the other decay modes. Since the gravitons are detectable with virtually zero probability, the number of Higgs particles with observable decay products will be much less than previously expected. (ii) Some new experimental results seem to indicate that the mass of the heavy elementary
particles like the $Z, W^{+},W^{-}$ and especially the top quark, depends on the particle environment in which these particles are produced. The presence of a Higgs field due to neighboring particles could be responsible for induced mass shifts. Further measurements of mass shift effects might give an indirect proof of the Higgs particle. Such can be in principle done by re-analyzing some of the production data e+e---> ZZ or W+W- already collected at the LEP experiment. About the
physical property of the top quark, it is too early to arrive at any conclusion. In the foreseeable future, there will be more extended top quark production statistics from the Tevatron accelerator so that the mass shift hypothesis can be experimentally probed.
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