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Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events — arXiv:2609.24796

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.24796
License (as archived): CC0-1.0
Archived: 2026-10-09T23:41:40.745Z
SHA-256 of the archived text: 47cd471ba35233e4d363fc44bb46b1395822e262fac4791a9805c400013f2f54
Stable URL of this page: https://metraipolis.com/documento/dc_db271fc0edb6

How to cite

Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events — arXiv:2609.24796 — arXiv (en), https://arxiv.org/abs/2609.24796 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_db271fc0edb6 (Metraipolis archive dc_db271fc0edb6, sha256 47cd471ba35233e4d363fc44bb46b1395822e262fac4791a9805c400013f2f54)

BibTeX

@misc{dcdb271fc0edb6,
  title = {Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events — arXiv:2609.24796},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.24796},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_db271fc0edb6; sha256 47cd471ba35233e4d363fc44bb46b1395822e262fac4791a9805c400013f2f54},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.24796. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\chi^{2}$ contributions along constrained dimensions will be arbitrary, yielding unphysically inflated $\chi^{2}$ values in global goodness-of-fit tests. We present the range-projected $\chi^{2}$, a test statistic that restricts the goodness-of-fit test to the subspace carrying independent statistical information, yielding a $\chi^{2}$ with $N_\text{bins} - N_\text{null}$ degrees of freedom, where $N_\text{null}$ is the number of independent constraints. We show that this rank deficiency is a predictable consequence of the event-sharing structure, and that $N_\text{null}$ 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.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-22 in physics.data-an).
Categorie arXiv: High Energy Physics - Experiment (hep-ex) ; Data Analysis, Statistics and Probability (physics.data-an).
Pagina del lavoro: https://arxiv.org/abs/2609.24796 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:47:04.549Z dalla pagina https://arxiv.org/catchup/physics.data-an/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).