Nucleon Polarizabilities from Low-Energy Compton Scattering

S.R. Beane, M. Malheiro (Sao Paulo), J.A. McGovern (Manchester), D.R. Phillips 9Ohio U.), U. van Kolck (University of Arizona)

An effective field theory is used to give a model-independent description of Compton scattering at energies comparable to the pion mass [43]. The amplitudes for scattering on the proton and the deuteron, calculated to fourth order in small momenta in baryon $\chi$PT, contain four undetermined parameters that are in one-to-one correspondence with the nucleon polarizabilities. These polarizabilities are extracted from fits to data on elastic photon scattering on hydrogen and deuterium. For the proton we find: $\alpha_p = 12.1 +/- 1.1 +/-0.5$, $\beta_p = 3.4 +/- 1.1 +/- 0.1$, both in units of $10^{-4}fm^3$. For the isoscalar polarizabilities we obtain: $\alpha_N = 9.0+/- 1.5 +3.6/-0.8$, $\beta_N = 1.7 +/- 1.5 +1.4/-0.6$, in the same units. Our results are consistent, within error bars, with the recent extraction of $\alpha_N \pm \beta_N$ from the Lund data using the detailed model of Levchuk and L'vov [44,45]. (But see also the values found using the data of Refs. [46,47] and this model [47,45].). The EFT can be improved by the introduction of an explicit $\Delta$-isobar field, a complete treatment of the very-low-energy region, and a better understanding of the dependence of the results on the choice of deuteron wave function.