Practical problems in testing radiative corrections

As we have already seen for the leptonic sector and, as we shall see later for the hadronic sector, the SM in lowest order provides a wonderfully successful description of a huge range of experimental phenomena. But to test the theory more profoimdly requires the comparison of precise higher order calculations with precise experimental data. In the on shell renormalization scheme, all calculations are expressed in terms of the parameters Mz and The former is known to great accuracy and we would clearly like to have an equally precise value for the latter. Unfortunately, this is precluded by the limited precision in our measurements of Mw-Thus, taking e.g. the UA2 value (Table 5.1) Mw = (80.2 1.5) GeV/c and (Table 8.3) Mz = (91.177 0.006) GeV/c, we obtain the rather imprecise estimate Sw = 0.226 0.029. 

It therefore seems advisable for the present to adopt a procedure similar to the one used in comparing the SM with experiment in lowest order (as was done even before the discovery of the W and Z°). Thus we fit as many higher order calculations, containing the now unknown parameter s, to experiment and examine the compatibifity of the various determinations. This programme is complicated by the fact that the higher order formulae involve the unknown top and Higgs masses as is explained in Section 7.8. 

Given that the top mass is not expected to be exceedingly large, i.e. one expects = (130 40) GeV/c (see Section 8.6), we shall base the following discussion on eqn (7.6.2). 

Since the calculated value of Ar reflects the fundamental structure of the SM it is important to ask to what accuracy it can be deduced experimentally from a knowledge of Mw and Mz- 

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