Consistent Analysis of the Spin Content of the Nucleon

The recent measurements of lepton nucleon scattering with polarised neutron and deuteron targets are analysed together with the previous polarised proton data in a mutually consistent way. The detailed x-dependence of the polarisation asymmetry in the valence region is shown to be in agreement with historical predictions based on quark models. The Bjorken sum rule is shown to be confirmed at the 1σ level and estimates of the spin content of the nucleon ∆q are extracted. While the average value of ∆q from the three experiments comes out to be 0.41 ± 0.05 (to be compared with the naive quark model theoretical expectation of 0.58) this experimental average value is more than one standard deviation from the value obtained from any individual experiment. This inconsistency can be overcome by allowing arbitrary higher twist contributions but the resulting precision is poor, ∆q = 0.38 ± 0.48. Introduction The recent measurements of the polarised nucleon structure functions g1 for the deuteron[1] and the neutron[2] have re-kindled the debate over the spin content of the nucleon which began with the measurement of g1 for the proton[3] five years ago. The value of Ip = ∫ gΦp1(x)dx extracted in ref[3] was consistent with a tiny fraction of the proton’s spin being carried by the constituent quarks and this fuelled enormous speculation over our understanding of the nucleon in the quark model framework. Reviews of the various interpretations of this result and of the competing descriptions of the proton’s spin structure can be found in ref [4]. In order to draw conclusions from the three experiments it is important to compare them consistently, in particular at the same QΦ2 and with the same ancillary inputs (e.g. the unpolarised F1(x,QΦ2) used in constructing the polarised structure function g1(x,QΦ2) from the measured asymmetry A1(x)). It is the purpose of the present paper to do this. A central plank in our analys is will be the asymmetry A1(x) and we begin with a comment on this measured quantity. A significant feature of the data is that the x-dependences of the polari sation asymmetry in the valence region, A1(x > 0.2), confirm the quark model predictions[5][6] for proton, neutron (see fig.1) and deuteron systems. This suggests to us that there is an immediate message from these data: The polarisation of the valence quarks is canonical and this should be taken into account in any attempt to interpret the data. The A(x) has tended to be ignored in the literature while most of the attention, and associated controversy, has arisen from the value of the integrated structure function g1(x) and its interpretation. Much of our paper will address the implications of the new data for this question. One obvious intention of a simultaneous analysis of g1Φp, gΦn1 and gΦd1 is to compare the experimental estimate of Ip−n with Bjorken’s fundamental sum rule[7]