Compton scattering on the proton and deuteron in chiral effective field theory

In this talk I will discuss recent efforts I have been involved in to describe Compton scattering in one- and two-nucleon systems using chiral perturbation theory ($\chi$PT). I will begin by summarizing the status of $\gamma$p scattering in $\chi$PT. For this reaction we fit the two undetermined parameters in the $O(Q^4)$ $\gamma$p amplitude of McGovern~[1] to experimental data in the region $\omega,\sqrt{|t|} \leq 180$ MeV, obtaining a $\chi^2/{\rm d.o.f.}$ of 133/113~[2]. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: $\alpha_p=(12.1 \pm 1.1~({\rm stat.}))_{-0.5}^{+0.5}~({\rm theory})$ and $\beta_p=(3.4 \pm 1.1~({\rm stat.}))_{-0.1}^{+0.1}~({\rm theory})$, both in units of $10^{-4}~{\rm fm}^3$. I will then discuss how the $\chi$PT formalism can be extended to treat deuteron Compton scattering. In particular, $\chi$PT provides a systematic treatment of the large isoscalar exchange currents that occur in this process, and so it facilitates extractions of nucleon polarizabilities from $\gamma$d data which have a well-motivated theoretical error bar~[2]. \begin{thebibliography}{9} \bibitem{judith} J.A.~McGovern, Phys.\ Rev.\ C {\bf 63}, 064608 (2001). \bibitem{allofus} S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, and U. van Kolck, Phys. Lett. B {\bf 567}, 200 (2003); Nucl. Phys. A {\bf 747}, 311 (2005). \end{thebibliography}