Abstract
The visible world is founded on the proton, the only composite building block of matter that is stable in nature. Consequently, understanding the formation of matter relies on explaining the dynamics and the properties of the proton’s bound state. A fundamental property of the proton involves the response of the system to an external electromagnetic field. It is characterized by the electromagnetic polarizabilities1 that describe how easily the charge and magnetization distributions inside the system are distorted by the electromagnetic field. Moreover, the generalized polarizabilities2 map out the resulting deformation of the densities in a proton subject to an electromagnetic field. They disclose essential information about the underlying system dynamics and provide a key for decoding the proton structure in terms of the theory of the strong interaction that binds its elementary quark and gluon constituents. Of particular interest is a puzzle in the electric generalized polarizability of the proton that remains unresolved for two decades2. Here we report measurements of the proton’s electromagnetic generalized polarizabilities at low four-momentum transfer squared. We show evidence of an anomaly to the behaviour of the proton’s electric generalized polarizability that contradicts the predictions of nuclear theory and derive its signature in the spatial distribution of the induced polarization in the proton. The reported measurements suggest the presence of a new, not-yet-understood dynamical mechanism in the proton and present notable challenges to the nuclear theory.
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Data availability
The raw data from the experiment are archived in Jefferson Laboratory’s mass storage silo and at Temple University, Department of Physics. The filtered data are archived at Temple University. The data are available from the authors on request.
Code availability
The data analysis uses the standard C++ ROOT framework, which was developed at CERN and is freely available at https://root.cern.ch. The simulation of the experiment was generated with the Jefferson Lab simulation code SIMC. The DR fit was done using the DR code developed by B. Pasquini14,15,16. The computer codes used for the data analysis are available on request.
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Acknowledgements
WE would like to thank M. Vanderhaeghen, as this work greatly benefitted from his input and suggestions. This work has been supported by the US Department of Energy Office of Science, Office of Nuclear Physics under contract nos. DE-SC0016577 and DE-AC05-06OR23177.
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N.S. is the spokesperson of the experiment. He initiated, guided and supervised this effort. R.L worked on the data analysis and the extraction of the cross sections and generalized polarizabilities. H.A. worked on the data analysis and the extraction of the electric and magnetic polarizability radii. M.K.J. and M.P. co-supervised the data analysis efforts and worked on the simulation of the experiment. B.P. developed the DR code for VCS and produced the induced polarization density. The entire VCS collaboration participated in the data collection and online analysis of the experiment.
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Extended data figures and tables
Extended Data Fig. 1 Cross-section measurements of the VCS reaction for out-of-plane kinematics.
a, Cross-section measurements for out-of-plane kinematics at Q2 = 0.28 GeV2. Results are shown for different bins in the total centre-of-mass energy of the (γp) system, W. Top, middle and bottom panels correspond to ϕγ*γ = 140°, ϕγ*γ = 28° and ϕγ*γ = 38°, respectively. b, Measurements for out-of-plane kinematics at Q2 = 0.33 GeV2. Top and bottom panels correspond to ϕγ*γ = 150° and ϕγ*γ = 30°, respectively. c, Measurements for out-of-plane kinematics at Q2 = 0.40 GeV2. Top, middle and bottom panels correspond to ϕγ*γ = 152°, ϕγ*γ = 35° and ϕγ*γ = 50°, respectively. The solid curve shows the DR fit for the two scalar generalized polarizabilities. The dashed curve shows the Bethe–Heitler plus Born VCS (BH+Born) cross section. The error bars correspond to the total uncertainty, at the 1σ or 68% confidence level.
Extended Data Fig. 2 Q2 dependence of the electric generalized polarizability.
a, The empirical fits to the electric generalized polarizability: the yellow band corresponds to a dipole fit (\({\chi }_{\nu }^{2}=3.7\)) and the purple band corresponds to the dipole + Gaussian fit (\({\chi }_{\nu }^{2}=1.9\)). The world data values for the electric generalized polarizability (open symbols) from the experiments MIT-Bates, MAMI-I, MAMI-IV, MAMI-V, MAMI-VI and JLab-I are summarized in the review paper of ref. 2. b, The Q2 dependence of the electric generalized polarizability as derived from the experimental measurements using the GPR technique, a data-driven method that assumes no direct underlying functional form. The error bars and the uncertainty bands correspond to the total uncertainty, at the 1σ or 68% confidence level.
Extended Data Fig. 3 Electric polarizability radius fits.
Top, the mean square electric polarizability radius fits using combinations of different functional forms (exp, gaus, pol and dipole correspond to exponential, Gaussian, polynomial and dipole functions, respectively). The fits denoted with solid lines were performed over the full Q2 range of the world data. The three functional forms denoted with dashed lines were performed in the low-Q2 range, namely in Q2 = [0, 0.28] GeV2. Bottom, the extracted mean square electric polarizability radius from the individual fits. The error bars correspond to the total uncertainty, at the 1σ or 68% confidence level. The blue band marks the final value for the extracted \(\langle {r}_{{\alpha }_{{\rm{E}}}}^{2}\rangle =1.36\pm 0.29\,{{\rm{fm}}}^{2}\).
Extended Data Fig. 4 Electric polarizability radius.
The electric polarizability radius \({r}_{{\alpha }_{{\rm{E}}}}\equiv \sqrt{\langle {r}_{{\alpha }_{{\rm{E}}}}^{2}\rangle }\) derived from this work is compared with the previous extractions of this quantity (open red symbols). The theoretical predictions of the models discussed in the paper are also shown as red triangles. The recent measurements of the proton charge radius rE (blue symbols) are also shown. The error bars correspond to the total uncertainty,at the 1σ or 68% confidence level.
Extended Data Fig. 5 Magnetic polarizability radius fits.
Top, the mean square magnetic polarizability radius fits using combinations of different functional forms (exp, pol and dipole correspond to exponential, polynomial and dipole functions, respectively). Bottom, the extracted mean square magnetic polarizability radius from the individual fits. The error bars correspond to the total uncertainty, at the 1σ or 68% confidence level. The blue band marks the final value for the extracted \(\langle {r}_{{\beta }_{{\rm{M}}}}^{2}\rangle =0.63\pm 0.31\,{{\rm{fm}}}^{2}\).
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Li, R., Sparveris, N., Atac, H. et al. Measured proton electromagnetic structure deviates from theoretical predictions. Nature 611, 265–270 (2022). https://doi.org/10.1038/s41586-022-05248-1
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DOI: https://doi.org/10.1038/s41586-022-05248-1
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