Theoretical discrepancies in the nucleon spin structure and the hyperfine splitting of muonic hydrogen

Two groups, ours (Mainz) and Bochum, have recently been re-evaluating the spin polarizabilities and spin structure functions at low Q, using the baryon chiral perturbation theory (BχPT), the manifestly-covariant counterpart of the heavy-baryon chiral perturbation theory (HBχPT). Whilst the two groups agree that the BχPT framework works better than HBχPT in this sector, their quantitative results disagree in some of the quantities; most notably, the proton spin polarizabilities γ₀ and δLT. These discrepancies are especially intriguing in light of new experimental data coming from the Jefferson Lab ``Spin Physics Program''. The preliminary data on the proton are reported by Karl Slifer in a plenary session of this workshop. Another theoretical discrepancy is emerging in the proton-polarizability contribution to the hyperfine splitting (hfs) in hydrogen and muonic hydrogen. Our BχPT calculation shows a significantly smaller effect than the state-of-the-art data-driven evaluations based on empirical spin structure functions. The smaller polarizability contribution leads to a smaller Zemach radius of the proton. This discrepancy could be relevant for the planned first-ever measurement of the ground-state hfs in muonic hydrogen.