Abstract
Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. Here we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0 GeV2. This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections.
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Data availability
Experimental data that support the findings of this study will be posted on the CLAS database (https://clasweb.jlab.org/physicsdb/) or are available from the corresponding author upon request.
Code availability
The computer codes that support the plots within this paper and the findings of this study are available from X.Z. upon request.
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Acknowledgements
All authors are members of The Jefferson Lab CLAS Collaboration. We thank the personnel of Jefferson Lab for their efforts that resulted in the successful completion of the experiment. We thank Kovacs for her contribution to the early analysis of the data. We are grateful to U.-G. Meißner and V. Pascalutsa for useful discussions on the theoretical χEFT calculations. This work was supported by the US Department of Energy (DOE), the US National Science Foundation, the US Jeffress Memorial Trust, the UK Science and Technology Facilities Council (STFC), the Italian Istituto Nazionale di Fisica Nucleare, the French Institut National de Physique Nucléaire et de Physique des Particules, the French Centre National de la Recherche Scientifique and the National Research Foundation of Korea. This material is based on work supported by the US Department of Energy, Office of Science, Office of Nuclear Physics under contract no. DE-AC05-06OR23177.
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The members of the Jefferson Lab CLAS Collaboration constructed and operated the experimental equipment used in this experiment. A large number of collaboration members participated in the data collection. The following authors provided various contributions to the experiment design and commissioning, data processing, data analysis and Monte Carlo simulations: M. Battaglieri, R. De Vita, V. A. Drozdov, L. El Fassi, H. Kang, E. Long, M. Osipenko, S. K. Phillips and K. Slifer. The authors who performed the final data analysis and Monte Carlo simulations were A. Deur, S. E. Kuhn, M. Ripani, J. Zhang and X. Zheng. The manuscript was reviewed by the entire CLAS Collaboration before publication, and all authors approved the final version of the manuscript.
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Supplementary Information
Two tables providing all the data shown in the manuscript. One figure displaying the full dataset for \({{{{g}}}^{p}_{1}}({{{Q}}}^{2},{{W}}).\)
Supplementary Data 1
Results for \({{\varGamma }^{p}_{1}},{{{{I}}}^{p}_{{\rm{TT}}}}\) and \({{\gamma }^{p}_{{\rm{0}}}}\), for the measured and the full ranges, along with their statistical and systematic uncertainties.
Supplementary Data 2
Results for \({{{{g}}}^{p}_{{\rm{1}}}}\) and \({{{{A}}}^{p}_{{\rm{1}}}}{{{{F}}}^{p}_{{\rm{1}}}}\) along with their statistical and systematic uncertainties.
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Zheng, X., Deur, A., Kang, H. et al. Measurement of the proton spin structure at long distances. Nat. Phys. 17, 736–741 (2021). https://doi.org/10.1038/s41567-021-01198-z
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DOI: https://doi.org/10.1038/s41567-021-01198-z