Determine a theoretically consistent tolerance prescription for nPDF uncertainties

Determine a generally accepted prescription for selecting the tolerance parameter in Hessian nuclear parton distribution function analyses, including how to account for dataset inconsistencies, underestimated experimental and theoretical uncertainties, and departures from the quadratic approximation.

Background

The nCTEQ26 uncertainties are obtained with a Hessian method and a tolerance of T=50, selected using a prescription based on Wilks’ theorem. Different tolerance prescriptions exist in global PDF analyses, and the appropriate choice depends on the dimensionality of the fit, dataset compatibility, uncertainty modeling, and the accuracy of the quadratic approximation.

Because these ingredients are not universally settled, the tolerance choice remains a methodological open problem affecting the reliability and interpretation of quoted nPDF uncertainty bands.

References

While a number of prescriptions for a determination of the tolerance has been proposed in the literature {Stump:2001gu,Martin:2009iq,Eskola:2009uj,Kovarik:2015cma,Eskola:2021nhw}, there is currently no consensus.

— nCTEQ26 nuclear parton distribution functions  (2610.13633 - Collaboration et al., 9 Oct 2026) in Appendix B, “Definition of the tolerance”