# Research Highlights Archive

## Origin of the Spin of the Proton

Prepared by A. W. Thomas, Jefferson Lab, for the DNP webpage

The proton is far from being an elementary Dirac particle. The quest to discover how its spin is distributed among the quarks and gluons of which it is composed is one of the most fascinating challenges in modern nuclear physics. In the simplest model, the proton spin arises from the spins of its three constituent quarks. More realistically, the quarks and the gluons that bind them carry both spin and orbital angular momentum.

It has now been 20 years since the European Muon Collaboration reported1 that almost none of the proton spin was due to the spin of the quarks (although with large uncertainties), in a dramatic challenge to existing models. As relativistic motion of quarks in the proton was expected to reduce the quark spin contribution to ~65%, this quickly led to speculation about a large contribution to the spin from polarized gluons, ΔG ~ 4, larger than the spin of the proton, with a corresponding largely canceling orbital angular momentum contribution.

Experimental work at CERN, DESY, JLab, SLAC and RHIC over the intervening period has given two improved constraints2. First, the fraction of the nucleon spin determined to come from the quark spins has increased to about 1/3. Second, the fraction of the nucleon spin coming from the polarized glue in the proton is significant, but not dominant as had been speculated. It is likely less than 10%, too small for the axial anomaly to account for the discrepancy between the expected and measured quark spin contribution.

While it is important to improve the experimental constraints on the quark and gluon spin contributions to the proton spin, the apparent absence of substantial polarized glue requires a new theoretical explanation of the missing spin, which was recently provided by Fred Myhrer and Anthony Thomas3. They established that the combination of relativistic quark motion, chiral symmetry and finally an exchange current correction associated with the spin dependent gluon exchange force, required in hadron spectroscopy, was able to account for the modern data. All of these contributions have the effect of converting quark spin to orbital angular momentum, as quantified in a recent Physical Review Letter4. There it was shown that around half of the spin of the proton is carried as orbital angular momentum by up and anti-up quarks.

Testing this fascinating explanation is clearly a high priority. The experimental tool of choice appears to be the exciting new observables known as Generalized Parton Distributions. However, as explained in4, what we see in such experiments at relatively high resolution (Q2 > 2 GeV2) will differ dramatically from what one might expect naively from a quark model. In fact, it is shown to be a model independent consequence of QCD evolution that Lu must switch from large and positive to negative as one moves from low to high resolution, while Ld grows more positive. Remarkably, after QCD evolution, the predictions of the Myhrer-Thomas model are consistent with the constraints on Ju and Jd extracted, within a particular model5, from recent measurements at Hermes6 and JLab 7. In the future, we can look forward to extensive investigations of the quark orbital angular momentum in the valence region, for which the 12 GeV Upgrade at JLab is uniquely suited.

This work was supported by DOE contract DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, operates JLab.

### References

1. J. Ashman et al., Phys. Lett. B 206, 364 (1988).
2. An example of a recent fit to the world data of the contributions to the nucleon spin is D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 101, 072001 (2008).
3. F. Myhrer and A. W. Thomas, Phys. Lett. B 663, 302 (2008).
4. A. W. Thomas, Phys. Rev. Lett. 101, 102003 (2008).
5. K. Goeke et al., Prog. Part. Nucl. Phys. 47, 401 (2001).
6. F. Ellinghaus et al., Eur. Phys. J. C 46 729 (2006); Z. Ye [Hermes Collaboration], Proc. of the Workshop on Exclusive Reactions at High Momentum Transfer (World Scientific, Singapore, 2008) p.21; arxiv:hep-ex/0606061.
7. M. Mazouz et al., Phys. Rev. Lett. 99 242501 (2007).

Figure 1: Evolution of the total angular momentum carried by up and down quarks (top and bottom curves, respectively) as well as the orbital angular momentum (up long-dash, down short-dash) - from Ref.4.

Figure 2: Comparison of the total orbital angular momentum of up and down quarks in the model of Myhrer and Thomas (black square) with the (model dependent) constraints derived from recent experiments at JLab and DESY - from Ref. 4.