Measurement of the Generalized Polarizabilities of the Proton in Virtual Compton Scattering at $Q^2=0.92$ and $1.76{\mathrm{G}\mathrm{e}\mathrm{V}}^2$

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions $P_{LL}-P_{TT}/ϵ$ and $P_{LT}$, and the electric and magnetic generalized polarizabilities (GPs) ${\alpha }_E(Q^2)$ and ${\beta }_M(Q^2)$ at momentum transfer $Q^2=0.92$ and $1.76{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The electric GP shows a strong falloff with $Q^2$, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low $Q^2$, compensated at higher $Q^2$ by a paramagnetic contribution from $\pi N$ intermediate states.

Figure 1

A graphical representation of the LEX fit (straight line) for data sets I-a and II. Circles correspond to out-of-plane data, and the inner plot is a zoom on the lepton plane data (triangles). ${\Psi }_0$, $v_1$, and $v_2$ are defined in the text.

Figure 2

Compilation of the data on electric (a) and magnetic (b) GPs. Data points are from Ref. [2] (△), the LEX analysis of MAMI [7] (◇), and the present LEX (○) and DR (●) analyses of JLab. Some JLab points are shifted in abscissa for better visibility. The inner error bar is statistical; the outer one is the total error (statistical plus systematic). The curves show calculations in the DR model (see text).