**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*^{*}.