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Two groups, ours (Mainz) and Bochum, have recently been re-evaluating thespin polarizabilities and spin structure functions at low $Q$, using the baryonchiral perturbation theory (B$\chi$PT), the manifestly-covariant counterpart ofthe heavy-baryon chiral perturbation theory (HB$\chi$PT). Whilst the two groupsagree that the B$\chi$PT framework works better than HB$\chi$PT in this sector,their quantitative results disagree in some of the quantities; most notably,the proton spin polarizabilities $\gamma_0$ and $\delta_{LT}$. Thesediscrepancies are especially intriguing in light of new experimental datacoming from the Jefferson Lab "Spin Physics Program". The preliminary data onthe proton are reported by Karl Slifer in a plenary session of this workshop.  Another theoretical discrepancy is emerging in the proton-polarizabilitycontribution to the hyperfine splitting (hfs) in hydrogen and muonic hydrogen.Our B$\chi$PT calculation shows a significantly smaller effect than thestate-of-the-art data-driven evaluations based on empirical spin structurefunctions. The smaller polarizability contribution leads to a smaller Zemachradius of the proton. This discrepancy could be relevant for the plannedfirst-ever measurement of the ground-state hfs in muonic hydrogen.

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