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

TL;DR

This paper investigates discrepancies between theoretical predictions and experimental data regarding the proton's spin structure and their impact on hyperfine splitting in muonic hydrogen, highlighting differences between B$ ext{ extchi}$PT and empirical evaluations.

Contribution

It compares covariant and heavy-baryon chiral perturbation theories in predicting spin polarizabilities and their effects on hydrogen hyperfine splitting, revealing notable discrepancies.

Findings

B$ ext{ extchi}$PT predicts smaller proton polarizability effects than empirical data.

Discrepancies affect the calculated Zemach radius of the proton.

Results are relevant for upcoming muonic hydrogen hyperfine splitting measurements.

Abstract

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 (B$\chi$PT), the manifestly-covariant counterpart of the heavy-baryon chiral perturbation theory (HB$\chi$PT). Whilst the two groups agree 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 $\delta_{LT}$. 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 B$\chi$PT 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.