Is Nucleon Spin Structure Inconsistent with Constituent Quark Model?

Hadron structure studies might be traced back to Fermi-Yang [1] and Sakata models [2]. Gell-Mann [3] and Zweig [4] proposed the quark model of hadrons. Lepton-nucleon deep inelastic scattering (DIS) [5] verified the quark structure of hadrons. However the quark revealed in DIS is found to be different from the quark as a carrier of SU(3) symmetry in Gell-Mann-Zweig model. The former is almost a free particle, the later is strongly bounded. Even though this lead Feynman [6] to call the quark detected in DIS as parton, such qualitatively different behavior of quark didn’t hurt the hadron structure studies in both directions. On the contrary, phenomenological success of SU(6) quark model in explaining the hadron properties and the evidence obtained in DIS for the existence of quark inside hadrons worked together and motivated the development of a new strong interaction theory, the quantum chromodynamics (QCD) [7]. The asymptotic freedom and confinement properties of QCD fitted perfectly weak interaction parton picture revealed in DIS and the fact that no free quark was discovered in all intensive experimental searches. The weak interacting high energy process can be calculated and tested due to asymptotic freedom of QCD and gave strong support to this new strong interaction theory. However the hadron structure and low energy hadron interactions are hard to be calculated due to confinement. Lattice QCD is promising to find low energy solution but still suffers numerical uncertainty for the time being. Various QCD models developed under this condition. Different models emphasize different effective degree of freedom inspired by QCD properties [8]. Among them, constituent quark model is the most successful one in explaining hadron properties [9] and hadron interactions [10]; and gives the most popular intuitive picture of hadron internal structure. The most striking feature of constituent quark model is that it gives a very simple but quite successful explanation of the baryon spin and magnetic moment by means of effective constituent quark masses. Once again, one meets the qualitatively different behaviors of quark, i.e., the constituent quark mass needed in the hadron spectroscopy is much larger than the current quark mass revealed in high energy processes. This lead Weinberg to ask “why do quarks behave like bare Dirac particles” [11]; and the relation between constituent quark and current quark is a holy grail in hadron physics. In the (1s) pure valence nonrelativistic constituent quark model, the nucleon spin is solely carried by quark spin, the orbital angular momentum is zero because quarks are assumed to be in the lowest s-wave (1s) state. The nucleon magnetic moment is also solely contributed by quark spin magnetic moments. In 1988, EMC group [12] measured the polarization asymmetry of polarized μ-proton deep inelastic scattering and extracted the proton spin structure function which showed that quark spin contributes only a small amount of the proton spin. Constituent quark model has been challenged by this surprising result and lead to the proton spin crisis. Many models and mechanisms have been invoked to explain why quark spin contribution is suppressed and how to supply angular momentum to compensate the missing spin of nucleon [13]. After ten years intensive studies both experimentally and theoretically, the prevailing view point seems to be that the nucleon spin structure discovered in DIS is inconsistent with constituent quark model. Only a minority [14] keeps the view point that quark spin is primarily responsible for generating the nucleon spin because in the valence quark region the polarization asymmetry confirmed the constituent quark model prediction. The sea quark component neglected as an approximation in pure valence quark model plays a vital role in suppressing the quark spin contribution ∆q extracted from DIS. This report stands by the minority through both a qualitative QCD analysis and a quantitative model calculation. In section II, the difference between the quark spin sum ∆Σ of the constituent quark model and the ∆q measured in DIS is explained. In section III, the duality of nucleon spin structure is explained. In section IV, QCD relations of baryon spin, magnetic moment, and tensor charge are derived and discussed. A constituent quark model with valence-sea quark component mixing is shown to be able to reconcile the difference between the quark spin sum ∆Σ and ∆q and fit other baryon properties as well in section V. The discussions and conclusions are put in section VI.