# S2: Accomplishments of the second funding period

• Scalar Polarizabilities of the Proton via RCS
The pilot experiment performed in June 2013 and published in 2017 has allowed us to prove the feasibility of a high-precision measurement of the proton scalar polarizabilities $$\alpha_{E1}$$ and $$\beta_{M1}$$ (Ref. 9). Following the successful upgrade of the tagging system completed in 2017, necessary to improve both the statistics and the systematics of the measurement, a ten-day run in February and two three-week runs in March and July 2018 were done, using a linearly polarized photon beam and an unpolarized liquid hydrogen target. The data taking was successful and the analysis is ongoing, showing an improvement of about six times in statistics compared to the pilot experiment. The preliminary results on both beam asymmetry $$\Sigma_3$$ and unpolarized cross-section below the pion threshold are very promising and show a big improvement in statistics and quality (Ref. 19). The analysis is expected to be completed by the end of 2019. After results are finalized, we will perform a global fit of both $$\Sigma_3$$ and unpolarized cross sections to extract the proton scalar polarizabilities, $$\alpha_{E1}$$ and $$\beta_{M1}$$, with a heretofore unprecedented precision. The theory group has provided a new partial-wave analysis of Compton scattering observables, geared for a model-independent extraction of proton polarizabilities from experimental data (Refs. 14 and 24).
• Spin Polarizabilities of the Proton via RCS
Data have been taken on 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. 3), the manuscript on the $$\Sigma_3$$ asymmetry is almost complete (Refs. 20 and 25) and will be submitted to Phys. Lett. B in the next month, and we are working on the paper for the final asymmetry, $$\Sigma_{2z}$$ (Refs. 24 and 26). 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 the $$\Sigma_{2x}$$ 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 (Refs. 1, 2, and 4).
On the theory side, we have performed an empirical evaluation of the spin-dependent forward Compton scattering (Ref. 6). The impact of spin polarizabilities on the Lamb shift and hyperfine splitting in hydrogen and muonic hydrogen is studied in Refs. 17 and 25. A combined theory-experiment review of this subject has appeared in Ref. 5.
• 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: $$Q^2= 0.1,0.2,0.45$$\,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 that are described in their PhD theses (Refs. 21, 22, and 23). These 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 $$Q^2=0.33$$\,GeV$$^2$$, which is the region of the first pioneering VCS experiment. This calls for a further investigation, possibly in terms of the methodology used in the LEX fit of polarizabilities. The analysis is now in its final stage and aims at reducing the systematic errors. The final results are to be published at the beginning of 2019 (Ref. 29).
On the theory side, a new calculation in chiral perturbation theory has been published (Ref. 10).
• Polarizability sum rule across real and virtual Compton scattering processes
We have verified the new sum rules relating polarizabilities extracted in different processes (Refs. 11, 13). 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 pedagogical review of this subject has recently been published in Ref. 15.
• 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, with first results on deuteron polarizabilities being prepared for publication (Ref. 30).
• Development and operation of an active polarized proton target
In order to measure spin observables in Compton scattering or pion production at low energies, an active polarized target has been developed (see Refs. 1, 2, and 4). By detecting the recoiling proton in the target material itself, the kinetic energy threshold is significantly reduced compared to the standard frozen-spin target. In the beginning of the funding period the operation of optical detectors, especially of Silicon Photomultipliers (SiPMs), at liquid helium temperatures, 4 K, was a huge challenge. Within the PhD thesis of Maik Biroth the operation of SiPMs at 4 K was successfully demonstrated. This was possible due to the development of a differential SiPM amplifier that could be operated meters away from the photodetector outside of the cryostat. In a ten-day test run in June 2016, the first active polarized proton target was operated successfully inside of a $$^3$$He-$$^4$$He-dilution cryostat located at the centre of the Crystal Ball detector. Maximum proton polarizations between 45-50 % with relaxation times around 75 h at 45 mK were reached. The maximum detection efficiency for recoil protons integrated over all trajectories was estimated to be ($$55\pm1$$) %. The analysis is almost completed and a publication is expected in 2019.
• Development of an active high-pressure helium target
For experiments to measure the polarizabilities of the neutron, an active high-pressure target for $$^3$$He and $$^4$$He gas is being developed that fits inside of the Crystal Ball detector (Ref. 16). As part of the M.Sc.\ thesis project of Jan Hillebrand, a prototype with 144 silicon photomultipliers inside a 20-cm-long high-pressure container was constructed and tested at 10 bar using a radioactive source of 5.5-MeV $$\alpha$$-particles. Scintillation light in pure He falls mainly in the vacuum UV region, which is difficult to detect efficiently. Therefore the amplitude of the signal was measured with different admixtures of N$$_2$$ acting as a wavelength shifter. The results are very encouraging and the successful operation of such a target has been demonstrated. Based on these results the target design with improved front end electronics is being finalized.