# S2: Accomplishments of the second funding period

• Scalar Polarizabilities of the Proton via RCS
We have taken beam asymmetry data below pion threshold for the very first time and the results have recently been published (Ref. 6). However, more data are necessary to improve the precision on $$\alpha_{E1}$$ and $$\beta_{M1}$$ to the required level, and we have three weeks of beamtime in Nov-Dec 2017 with the upgraded tagger focal plane, allowing for significantly increased counting rates.
The theory group has provided a new partial-wave analysis of Compton scattering observables, providing a model-independent extraction of proton polarizabilities (Refs. 12, 19).
• Spin Polarizabilities of the Proton via RCS
Data have been taken on all three polarization observables in the delta region: $$\Sigma_{2x}, \Sigma_3$$, and $$\Sigma_{2z}$$. The analyses for all three are complete, the paper on $$\Sigma_{2x}$$ has been published (Ref. 1), the manuscript on the $$\Sigma_3$$ asymmetry is almost complete (Ref. 14) and will be submitted to Phys. Lett. B next month, and we are working on the paper for the final asymmetry, $$\Sigma_{2z}$$ (Ref. 16). Moreover, we are in the process of conducting a global fit on all three observables to extract the proton spin polarizabilities. We are planning on taking more data on $$\Sigma_{2x}$$ observable in both the delta region with the butanol frozen-spin target and between pion threshold and the delta region with the new active polarized target.
On the theory side, we have performed an empirical evaluation of the spin-dependent forward Compton scattering (Ref. 3). The impact of spin polarizabilities on the hyperfine splitting in hydrogen and muonic hydrogen is studied in Refs. 10, 13. A combined theory-experiment review of this subject has appeared in Ref. 2.
• Generalized Polarizabilities of the Proton via VCS
A new experiment has been performed at MAMI in order to measure the electric and magnetic generalized polarizabilities of the proton, $$\alpha_{E1}(Q^2)$$ and $$\beta_{M1}(Q^2)$$, at three yet unexplored values of the four-momentum transfer: $$Q^2 =$$0.1, 0.2, and 0.45 $$GeV^2$$. The experiment used the A1 setup and the data taking covered the years 2011 to 2015. Three PhD students analyzed the data, each one at a different $$Q^2$$, and obtained preliminary results which are described in their PhD theses (defended in 2015 and 2016, under the supervision of H. Fonvieille from Clermont-Fd University and S. Sirca from Ljubljana University). These preliminary results were presented at the Mainz LEPP Workshop in 2016. They provide important insight in the $$Q^2$$-dependence of the structure functions $$P_{LL}-P_{TT} / \epsilon$$ and $$P_{LT}$$ and the generalized polarizabilities $$\alpha_{E1}(Q^2)$$ and $$\beta_{M1}(Q^2)$$. Namely, these new measurements connect rather smoothly to the existing ones, except at $$Q^2=$$0.33 GeV2 which is the region of the first pioneering VCS experiment. This calls for an understanding, possibly in terms of the methodology used in the LEX fit of polarizabilities. The analysis of the new MAMI experiment is now in its final stage and aims at reducing the systematic errors. The final results are to be published in 2018. On the theory side, a new calculation in chiral perturbation theory has been published (Ref. 7).
• Polarizability sum rule across real and virtual Compton scattering processes
We have verified the new sum rules relating polarizabilities extracted in different processes (Ref. 8). The sum rules involve the low-energy electromagnetic properties of the nucleon that are accessed in different experiments: the Pauli radius of the target (e.g., nucleon), one of its four lowest-order spin polarizabilities, and the slopes of two of its four lowest-order generalized polarizabilities. The present empirical and phenomenological information on these quantities for the proton was shown to obey the sum rules given the large experimental uncertainties. A paper of the spin-independent analog of sum rules considered in Ref. 8 will soon be submitted (Ref. 22).
• Compton scattering off deuteron in chiral effective-field theory and muonic deuterium
The work towards a consistent and systematic evaluation of the muonic-deuterium Lamb shift is currently underway (Refs. 5, 9), with first results on deuteron polarizabilities being prepared for publication (Ref. 21).