New Insight in the $Q^2$ Dependence of Proton Generalized Polarizabilities

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 $0.45{\mathrm{GeV}}^2$, 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 falloff of ${\alpha }_{E1}(Q^2)$, in contrast to previous measurements at $Q^2=0.33{\mathrm{GeV}}^2$, and provide for the first time a precise mapping of ${\beta }_{M1}(Q^2)$ in the low-$Q^2$ region.

Figure 1

The electric and magnetic GPs of the proton. Filled circles and squares at $Q^2=0.10$, 0.20 and $0.45{\mathrm{GeV}}^2$ are from this experiment. Open circles and squares are from previous experiments at MIT-Bates [10], MAMI [4, 6], and JLab [12]. Open and filled circles correspond to DR analyses; open and filled squares correspond to LEX analyses. The triangle point in ${\alpha }_{E1}(Q^2)$ is from the recent experiment of Ref. [8] and the RCS point (diamond) is from Ref. [25]. The dashed curve is obtained using the DR model [15] with dipole mass parameters ${\mathrm{\Lambda }}_{\alpha }={\mathrm{\Lambda }}_{\beta }=0.7\mathrm{GeV}$. The dotted curve with its error band (shaded area) is from covariant $\mathrm{B}\chi \mathrm{PT}$ [26]. Some data points are slightly shifted in abscissa for visibility. The inner and outer error bars are statistical and total, respectively.