Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events
Abstract
When multiple differential cross-section measurements are extracted from a common event sample, the same events contribute simultaneously to multiple distributions. This event-sharing structure imposes exact linear constraints among the bin counts, reducing the effective dimensionality of the measurement below the total number of bins. Since the covariance matrix obeys these inter-distribution constraints, it contains a rank deficiency. While limited numerical precision may inadvertently restore invertibility, the χ2 contributions along constrained dimensions will be arbitrary, yielding unphysically inflated χ2 values in global goodness-of-fit tests. We present the range-projected χ2, a test statistic that restricts the goodness-of-fit test to the subspace carrying independent statistical information, yielding a χ2 with Nbins − Nnull degrees of freedom, where Nnull is the number of independent constraints. We show that this rank deficiency is a predictable consequence of the event-sharing structure, and that Nnull decomposes into a structural contribution determined a priori from the binning geometry and a kinematic contribution that depends on the phase-space occupancy. The method is validated with an analytical toy model and a simulated neutrino--argon cross-section measurement including unfolding and multi-source systematic uncertainties.
Related
- Cross Section Measurements and Searches for New Structures in e+e- Annihilations at BESIII
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- Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns
- Signal selection and model-independent extraction of pionless charged-current muon neutrino cross section using double-differential kinematic imbalance observables on carbon and oxygen with the T2K experiment
BibTeX
@misc{lopez2026goodnessoffit,
title = {{Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events}},
author = {Francisco Martinez Lopez and London Cooper-Troendle and Steven Gardiner and Patrick Green and Tanaz Mohayai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24796},
eprint = {2609.24796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24796},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events
AU - Francisco Martinez Lopez
AU - London Cooper-Troendle
AU - Steven Gardiner
AU - Patrick Green
AU - Tanaz Mohayai
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24796
UR - https://arxiv.org/abs/2609.24796
AB - When multiple differential cross-section measurements are extracted from a common event sample, the same events contribute simultaneously to multiple distributions. This event-sharing structure imposes exact linear constraints among the bin counts, reducing the effective dimensionality of the measurement below the total number of bins. Since the covariance matrix obeys these inter-distribution constraints, it contains a rank deficiency. While limited numerical precision may inadvertently restore invertibility, the χ^2 contributions along constrained dimensions will be arbitrary, yielding unphysically inflated χ^2 values in global goodness-of-fit tests. We present the range-projected χ^2, a test statistic that restricts the goodness-of-fit test to the subspace carrying independent statistical information, yielding a χ^2 with N_bins − N_null degrees of freedom, where N_null is the number of independent constraints. We show that this rank deficiency is a predictable consequence of the event-sharing structure, and that N_null decomposes into a structural contribution determined a priori from the binning geometry and a kinematic contribution that depends on the phase-space occupancy. The method is validated with an analytical toy model and a simulated neutrino--argon cross-section measurement including unfolding and multi-source systematic uncertainties.
ER -