Unclear correlation structure among JLab-Fπ data points

Ascertain the correlation structure among the Jefferson Lab Fπ measurements of the spacelike electromagnetic pion form factor across q^2 = −2.45 GeV^2, q^2 = −1.6 GeV^2, and q^2 ∈ [−2.45, −0.6] GeV^2, to enable a correct multivariate likelihood treatment of these data.

Background

The analysis incorporates a single Jefferson Lab Fπ data point at q2 = −2.45 GeV2 due to its large leverage. Additional measurements at q2 = −1.6 GeV2 and across the interval [−2.45, −0.6] GeV2 exist.

However, the correlation structure among these data points is not specified, preventing a reliable multivariate Gaussian likelihood construction. Resolving the correlations would allow inclusion of the full dataset and potentially improve constraints on the form factor.

References

Other data points at q2 = -1.6\,GeV2 and in the interval q2 \in [-2.45, -0.6]\,GeV2 are also obtained; however, the correlation between the various data points is not clear to us.

— A Simple Parametrisation of the Pion Form Factor  (2410.13764 - Kirk et al., 2024) in Section 2 (Application to the Pion Form Factor), Likelihood description, JLab-Fπ item

This prescription does not give a unique answer. The reference $\chi2$ is not monotonic in $\ell$: correlations over roughly a bin width can accommodate structure in the residuals, whereas correlations over much larger scales cannot. The curve reaches a minimum near $\ell=0.12$ before rising steeply towards the fully correlated limit. It crosses unity twice for two reconstructions and once for the third. This criterion, therefore, cannot determine a single correlation length, nor would it establish the true covariance.

— Caught by its own light: Wimpzillas, the LHAASO knee and the diffuse $γ$-ray sky  (2609.17315 - Akl et al., 15 Sep 2026) in Appendix, Section 'The error model' (Appendix cov)