The Newtonian Gravitational Constant in Fermi Theory with Weak Radiative Corrections

The Newtonian gravitational constant G is still not known to high levels of accuracy after approximately two hundred years of experimental work. This presents a problem since G is one of the most fundamental constants in physics. We will attempt to advance the study of G by establishing a new method that relates it to the Fermi coupling constant. This will be done via a formulaic representation of G depending only on muonic and tauonic parameters, respectively. The first formula relates G with the muon Compton wavelength, mass and mean lifetime as well as the running value of the fine structure constant on the muonic scale. The second formula uses parameters of tau leptons. Using the mean lifetime of muons we rewrite the formula and establish the aforementioned relation between G and the Fermi coupling constant after which we proceed to account for the weak corrections on the muon mean lifetime. The results obtain by the two formulas for muons and tau leptons, respectively, are 98.11% and 99.9% in agreement with the value of G provided by NIST. It is concluded that there is a possibility for the “running” of G thus requiring the calculation of an effective value.