First Measurement of $π^+$-Ar and $p$-Ar Total Inelastic Cross Sections in the Sub-GeV Energy Regime with ProtoDUNE-SP Data

TL;DR

Using ProtoDUNE-SP 1 GeV/$c$ beam data, the paper reports the first total inelastic cross sections for $π^+$–Ar in the kinetic-energy range $[500,900]$ MeV and for $p$–Ar in $[10,450]$ MeV, providing new hadron-argon data for DUNE. The analysis applies a modified energy-slicing method that defines $E_{\rm ini}$ and $E_{\rm end}$ from the beam energy, energy losses, and deposited energy, to extract σ(E) for each energy slice. After background subtraction and MC reweighting, a multi-dimensional unfolding based on the D'Agostini method implemented in RooUnfold corrects for detector effects, with optimal iterations $n=47$ for π^+$ and $n=16$ for protons. The measured cross sections agree with Geant4 10.6 Bertini predictions and with the empirical $\sigma \propto A^{2/3}$ scaling, providing the first modern argon cross-section dataset for sub-GeV hadron-argon interactions and supporting neutrino-argon interaction modeling for DUNE; additional measurements and ProtoDUNE-HD data will extend these results.

Abstract

The ProtoDUNE-SP detector, a kiloton-scale prototype for the Deep Underground Neutrino Experiment (DUNE), is the largest liquid argon time projection chamber built to date. Operated at CERN from 2018 to 2020, it collected both cosmic-ray data and a beam consisting of positively-charged particles with discrete momentum settings across a range of 0.3 GeV/$c$ to 7 GeV/$c$. In this letter, we report the total inelastic cross section measurements for $π^+$-Ar and $p$-Ar interactions using selected $π^+$ and proton samples from the 1 GeV/$c$ beam data. These results provide the first measurement of the total inelastic cross sections for $π^+$-Ar in the 500-900 MeV kinetic energy range and for $p$-Ar below 450 MeV, both of which are directly relevant to the DUNE energy range. The measured cross sections are consistent with predictions and provide a dataset that was previously unavailable for argon targets. These measurements are essential for constraining neutrino-argon interaction models, which are crucial for the precision physics goals of the upcoming DUNE experiment.

Figures (7)

• Figure 1: A top-down view illustrating the slicing method, which shows a portion of the ProtoDUNE-SP detector on the beam side within the range of the first APA.
• Figure 2: Reconstructed track length distributions after full selection for the (a) pion and (b) proton analyses. Error bars on data points are statistical-only. The stacked histograms show different event categories from the MC, with the total weighted counts normalized to match the data. The numbers in the legend indicate the weighted counts for each component. The bottom panel in each subplot displays the ratio of data to MC in each bin. MC reweighting, as described in the main text, is applied.
• Figure 3: The measured (a) $\pi^+$--Ar and (b) $p$--Ar cross sections. In each sub-figure, the red solid curve indicates the cross section model used in simulation, with the shaded band indicating the fluctuation considered in the systematic uncertainty for the cross section model. Other models are also shown. The correlation matrices with all uncertainties applied are provided as part of the Supplemental Material.
• Figure 4: The cross section measurements on various targets with (a) $\pi^+$ and (b) proton. Our argon results are shown as black points. In the inner panel in each sub-figure, an empirical curve $\sigma=k\cdot A^{2/3}$ is fitted to the datasets averaged in the kinetic energy ranges [500, 900] MeV for $\pi^+$ and [100, 400] MeV for protons.
• Figure 5: The energy histograms related to the cross section calculation ($N_{\rm ini}$, $N_{\rm end}$, $N_{\rm int}$, and $N_{\rm inc}$) before (red) and after (blue) unfolding for the (a) pion and (b) proton analyses. The error bars are statistical-only. MC is normalized to the data sample size before unfolding.