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Register a new userNew Insight in the $Q^2$-Dependence of Proton Generalized Polarizabilities
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J. Beriv{c}iv{c}
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Virtual Compton scattering on the proton has been investigated at three yet unexplored values of the four-momentum transfer $Q^2$: 0.10, 0.20 and 0.45 GeV$^2$, at the Mainz Microtron. Fits performed using either the low-energy theorem or dispersion relations allowed the extraction of the structure functions $P_{LL} -P_{TT} / epsilon$ and $P_{LT}$, as well as the electric and magnetic generalized polarizabilities $alpha_{E1}(Q^2)$ and $beta_{M1}(Q^2)$. These new results show a smooth and rapid fall-off of $alpha_{E1}(Q^2)$, in contrast to previous measurements at $Q^2$ = 0.33 GeV$^2$, and provide for the first time a precise mapping of $beta_{M1}(Q^2)$ in the low-$Q^2$ region.
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Background: Generalized polarizabilities (GPs) are important observables to describe the nucleon structure, and measurements of these observables are still scarce. Purpose: This paper presents details of a virtual Compton scattering (VCS) experiment, performed at the A1 setup at the Mainz Microtron by studying the $e p to e p gamma$ reaction. The article focuses on selected aspects of the analysis. Method: The experiment extracted the $P_{LL} -P_{TT} / epsilon$ and $P_{LT}$ structure functions, as well as the electric and magnetic GPs of the proton, at three new values of the four-momentum transfer squared $Q^2$: 0.10, 0.20 and 0.45 GeV$^2$. Results: We emphasize the importance of the calibration of experimental parameters. The behavior of the measured $e p to e p gamma$ cross section is presented and compared to the theory. A detailed investigation of the polarizability fits reveals part of their complexity, in connection with the higher-order terms of the low-energy expansion. Conclusions: The presented aspects are elements which contribute to minimize the systematic uncertainties and improve the precision of the physics results.
Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P_LL-P_TT/epsilon and P_LT, and the electric and magnetic generalized polarizabilities (GPs) alpha_E(Q^2) and beta_M(Q^2) at values of the four-momentum transfer squared Q^2= 0.92 and 1.76 GeV^2. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q^2-range, and point to their non-trivial behavior.
The generalized Baldin sum rule at finite four-momentum transfer Q^2 is evaluated utilizing a structure function parameterization fit to recent experimental data. The most recent measurements on F_1 from Hall C at Jlab, as well as the F_2 structure function data from Hall B at Jlab and SLAC, were used in constructing our parameterization. We find that at Q^2 below 1 GeV^2 the dominant contribution to the electric and magnetic polarizabilities of the nucleon comes from the resonance region.
The mean square polarizability radii of the proton have been measured for the first time in a virtual Compton scattering experiment performed at the MIT-Bates out-of-plane scattering facility. Response functions and polarizabilities obtained from a dispersion analysis of the data at Q2=0.06 GeV2/c2 are in agreement with O(p3) heavy baryon chiral perturbation theory. The data support the dominance of mesonic effects in the polarizabilities, and the increase of beta with increasing Q2 is evidence for the cancellation of long-range diamagnetism by short-range paramagnetism from the pion cloud.
The generalized forward spin polarizabilities $gamma_0$ and $delta_{LT}$ of the neutron have been extracted for the first time in a $Q^2$ range from 0.1 to 0.9 GeV$^2$. Since $gamma_0$ is sensitive to nucleon resonances and $delta_{LT}$ is insensitive to the $Delta$ resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on $delta_{LT}$ show significant disagreement with Chiral Perturbation Theory calculations, while the data for $gamma_0$ at low $Q^2$ are in good agreement with a next-to-lead order Relativistic Baryon Chiral Perturbation theory calculation. The data show good agreement with the phenomenological MAID model.
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