# S2: Polarizabilities

### Goals

The project is devoted to the electromagnetic polarizabilities of nucleons and few-nucleon systems. Its purpose is to systematize and improve our knowledge of the nucleon and nuclear polarizabilities, and elucidate their role in precision atomic physics. The current level of precision in muonic-atom spectroscopy is in fact set by the uncertainty in polarizability contributions. On the experimental side, the project consists of two major components:

1. Compton scattering off the proton and light-nuclear targets, and
2. quasielastic electron scattering, with connection to polarizabilities via the sum rules of the Baldin and Gerasimov-Drell-Hearn variety.

On the theoretical side, the project is based on the frameworks of chiral perturbation theory and dispersion relations. They both are used to provide a systematic model-independent description of the above-mentioned two-photon processes, which allows one to evaluate the polarizability effects in observables. In the same framework we provide an evaluation of these effects in atomic systems, most notably the Lamb shift and hyperfine structure of light muonic atoms.

Current status of the proton electric vs. magnetic polarizability. The yellow band is the Baldin sum rule constraint, as evaluated in [10.1103/PhysRevD.92.074031]. PWA stands for the first partial-wave analysis of global Compton scattering database  [1712.05349]. PDG is the 2014 average of the Particle Data Group. BChPT is the NNLO chiral perturbation theory calculations [10.1140/epjc/s10052-009-1183-z10.1140/epjc/s10052-015-3791-0 HBChPT is the extraction from Compton scattering database using heavy-baryon chiral perturbation theory [10.1140/epja/i2013-13012-1] The rest are the results of individual Compton scattering experiments, click 10.1016/j.ppnp.2015.12.001 for a recent review.

In the second funding period we plan to advance the following areas of research:

• Magnetic polarizability of the proton from the beam asymmetry $$(\Sigma_3)$$ in Compton scattering $$\gamma p\to \gamma p$$ with an unpolarized hydrogen target [A2 Collaboration].
• Spin polarizabilities of the proton from the beam-target asymmetries $$(\Sigma_{2x}$$ and $$\Sigma_{2z})$$ in Compton scattering with a polarized hydrogen target [A2 Collaboration].
• Active target developments [A2 Collaboration].
• Neutron polarizabilities from Compton scattering and inclusive measurements on the deuteron and helium [A1 and A2 Collaborations].
• Precise measurements of the electrodisintegration of the deuteron at small momentum transfers [A1 Collaboration].
• Theoretical description of the timelike nucleon structure in the process of di-lepton photoproduction. Feasibility studies for di-lepton photoproduction experiments [A2 Collaboration].
• Feasibility studies for polarizability measurements at the upcoming MESA facility.
• Chiral effective-field theory for nucleon and light-nuclear polarizabilities. Calculations of the nucleon and nuclear polarizability effects in muonic atoms.