S2: Accomplishments of the ﬁrst funding period

•  Scalar polarizabilities of the proton via RCS
We have taken beam-asymmetry data below pion threshold for the very ﬁrst time. Data analysis is almost complete (Ref. 22), but more data are necessary to improve the precision on $$\alpha_{E1}$$ and $$\beta_{M1}$$ to the required level. More data will be taken in early 2015. In a recent Phys. Rev. Letter (Ref. 4), the theory group has provided a model-indpendent framework for the extraction of polarizabilities from the Compton scattering beam-asymmetry. Impact of these polarizabilities in muonic hydrogen Lamb shift has been studied in Refs. 7, 12.
• 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 analysis for the ﬁrst of the three is complete and a paper has been submitted (Ref. 18). The data analysis for the second is nearing completion with the goal of submitting a manuscript in early 2015 (Ref. 21). Finally, we completed the data taking for the ﬁnal asymmetry this spring, and expect the data analysis to be completed in 2016. After results for all three asymmetries are ﬁnalized, we will conduct a global ﬁt to extract the proton spin polarizabilities. On the theory side, a comprehensive study of all these observables and polarizabilities is underway using the low-energy expansion (Refs. 16, 23) and chiral perturbation theory (Ref. 24). The journal of Prog. Part. Nucl. Phys. has commissioned a combined theory-experiment review of this subject, Ref. 25.
• Generalized polarizabilities of the proton via VCS
VCS data were taken at MAMI-A1 in 2011, 2012, and 2013 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: Q2 = 0.1, 0.2, and 0.5 GeV2. The data analysis is being performed mainly at Ljubljana and Clermont-Fd Universities (by three PhD students along with H. Fonvieille and S. Sirca). A ﬁrst-pass analysis of all settings is near completion, conﬁrming the good quality of the data and allowing preliminary ﬁts of the polarizabilities using the LEX or dispersion relation formalism. The ﬁnal results of the experiment are expected by the end of 2015.
• Polarizability sum rule across real and virtual Compton scattering processes
We have established a new sum rule that relates polarizabilities extracted in different processes, extending the celebrated Gerasimov-Drell-Hearn sum rule in photon virtuality (Ref. 19). It involves 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 rule given the large experimental uncertainties. The forthcoming Compton scattering experiments will deliver a substantially improved input of the quantities entering this sum rule.
• Resolution of the $$\sigma_{LT}$$ puzzle
In the course of the recent chiral perturbation theory evaluation of the moments of nucleon structure functions (Ref. 17), we have resolved the long-standing conﬂict between theory and experiment in the magnitude of the $$\sigma_{LT}$$ polarizability of the nucleon. More speciﬁcally, we obtain leading- and next-to-leading order free-parameter free results for the most prominent moments of the nucleon structure functions. They turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer (Q2 < 0.3 GeV2). The spin polarizability $$\sigma_{LT}$$ was thus far not reproducible in chiral perturbation theory for proton and neutron simultaneously. Our result for it is nonetheless in agreement with the empirical information. This problem, known as the "$$\sigma_{LT}$$ puzzle", is not seen in the present calculation.
• ECT* Trento Workshop on "Compton scattering off protons and light nuclei: pinning down the polarizabilities", July 29 – Aug 2, 2013
Organized by E. Downie, H. Fonvieille, B. Pasquini, and V. Pascalutsa, the workshop brought together more than 50 scientists actively working in this ﬁeld. One of the notable outcomes has been the theory letter of consensus and support of the ongoing experimental programs, Ref. 20.