Model-independent determination of proton polarizabilities from Compton scattering
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Abstract
The scalar and spin polarizabilities of the proton are fundamental quantities that characterize the ability of proton’s constituents to rearrange themselves in external electromagnetic fields. Their PDG values combine the Dispersion relation (DR) and the chiral perturbation theory (ChPT) results, whereas individually these theoretical approaches yield different values. In particular, ChPT and fixed-t DR (combined with Compton scattering data) give at present different values of the magnetic polarizability. Here we offer two model-independent approaches to extract the polarizabilities which are based on the low-energy and multipole expansions of Compton scattering observables. These approaches are complementary to the existing theoretical methods, and as such they give additional insight into the problem. What is more important, they offer an additional route to calculate observables that potentially can resolve the contro- versy over the values of the polarizabilities.
In the first part of this dissertation we derive the low-energy expansions of the helicity amplitudes and observables for the beam and spin-1/2 target polarizations. Here we identify and study three independent spin asymmetries which can be used to measure the proton polarizabilities. In particular, we show that the leading-order non-Born contribution to the beam asymmetry is given by the magnetic polarizability alone. Hence, this observable is a good candidate for a precision measurement of the magnetic dipole polarizability. To support this statement, we present preliminary results of a pilot measurement of the beam asymmetry below the pion production threshold. These results are obtained by the A2 collaboration at the Mainz Microtron. We provide a similar analysis for the target asymmetries, which, as we argue, give an access to the proton spin polarizabilities.
In the second part of this dissertation we obtain the multipole expansions of the helicity amplitudes and observables below the pion production threshold. To this end, we develop a fitting procedure which yields the scalar and spin polarizabilities from unpolarized Compton scattering data. We make several fits either using the full database or excluding a few inconsistent data points. We find that in the former case the fitted scalar polarizabilities coincide with the values in the DR framework, whereas in the latter case they are similar to the values computed using the baryon ChPT approach. This observation allows us to suggest that the difference between the baryon ChPT and DR values of the scalar polarizabilities is due to inconsistencies in the database used in the DR analysis. To resolve this inconsistency we propose to measure the unpolarized Compton scattering cross section at energy E= 110 MeV and backward angles. As far as the spin polarizabilities are concerned, the values we extract are consistent among the different fits, and are as well consistent with the values obtained in the baryon ChPT and DR analyses.
The presented multipole analysis of Compton scattering is the first of its kind. We believe that in the near future it will give us a unique opportunity to obtain accurate values of the polarizabilities in a model-independent way. The achievement of this goal will be facilitated by improvements of the existing data that are to come in the following years at experimental facilities around the globe, in particular, at the Mainz Microtron, and at the high-intensity electron facility MESA which currently is under construction in Mainz.