Spin of the proton in chiral effective field theory

Proton spin is investigated in chiral effective field theory through an examination of the singlet axial charge, a0, and the two non-singlet axial charges, a3 and a8. Finite-range regularization is considered as it provides an effective model for estimating the role of disconnected sea-quark loop contributions to baryon observables. Baryon octet and decuplet intermediate states are included to enrich the spin and flavour structure of the nucleon, redistributing spin under the constraints of chiral symmetry. In this context, the proton spin puzzle is well understood with the calculation describing all three of the axial charges reasonably well. The strange quark contribution to the proton spin is negative with magnitude 0.01. With appropriate Q 2 evolution, we find the singlet axial charge at the experimental scale to be ˆ0 = 0.31 +0.04 0.05, consistent with the range of current experimental values. In 1988 the European Muon Collaboration (EMC) published their polarized deep inelastic measurement of the proton’s spin dependent structure function g1. Their result suggested that the quark spins summed over the up, down and strange quark flavors contribute only a small fraction of the proton’s spin [1]. The EMC data shocked the particle physics community, because it was thought to be contradictory to the apparently successful, naive quark model descriptions of proton structure where the constituent quarks carry the total proton spin. It inspired a vigorous global program of experimental and theoretical developments to understand the internal spin structure of the proton extending for nearly three decades. For reviews of the spin structure of the proton, see for example Refs. [2–10]. The experimental efforts at CERN [11–14], DESY [15], JLab [16], RHIC [17, 18] and SLAC [19] have been impressive. A summary of the status and recent experimental results on the spin structure of the nucleon can be found in Ref. [2]. Unlike the early EMC result which suggested that the quark spin contribution, �, might be consistent with zero (14 ± 9 ± 21% [1]), today the experimental measurements indicate the nucleon’s flavorsinglet axial charge measured in polarized deep inelastic scattering is 0.35 ± 0.03(stat.) ± 0.05(syst.) at Q 2 = 3 GeV 2 . This tends to about one-third of the total spin 0.33 ± 0.03(stat.) ± 0.05(syst.) as Q 2 → ∞ [14, 15, 20]. The matrix elements of the non-singlet axial current J kµ and the singlet axial currentJ5µ are defined as follows