3.3. Evidence from mass renormalisation

Another test comes from a combination of the masses of the W and the Z, together with the Weinberg mixing angle between the electromagnetic and the weak interactions. In the first approximation, these quantities are related by the equation:

(13)

When radiative corrections are taken into account however, this expression is no more exact because of the renormalisation it imposes on the masses of these particles. The most important corrections come from the inclusions of closed loops of fermions, especially those which are widely split in masses (as the b and the t quark whose mass difference is several tens of GeV).

The experimental ratio of the L.H.S. over the R.H.S. of eq. (13) differs from one by less than five percent. This is enough to exclude new families with quark mass splitting of the same order. Inspection of the data on table 1 shows that the quark mass splitting increases as we move from left to right. We can exclude the presence of new families in which this trend would continue. This confirms the previously quoted value of g^*.