Polarized scattering sum rule and the spin crisis

The EMC measurement of the asymmetry in polarized deep inelastic p scattering was discussed in Section 15.6 and the measured Ai x) shown in Fig. 15.12. We shall show now that this result has some rather unexpected implications which caused much excitement and led to interesting theoretical developments. 

If in (15.6.34) we neglect the term involving g2 x), since it is multiplied by a small coefficient, and if we feed in the very accurately measured Fi x) we can extract the scaling function gi x). The result is shown in Fig. 17.7 where also earlier SLAC data are included. 

From this one finds, from the EMC data, for the first moment, 

Then using the quark-parton model expression (16.8.21) for 5i(x), (17.1.18) implies 

In order to solve for the individual A/ we need one more relation. This can be obtained from a study of hyperon /3-decays, the data for which seem to be in good agreement with 5 7(3)ir invariance. If SU 3)f invariance holds, all decay amplitudes are expressed in the form [see (18.1.2) and (18.1.16)] 

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