Explanation of the seasonal variation of cosmic multiple muon events observed with the NOvA Near Detector

TL;DR

The paper addresses the seasonal variation of underground multiple-muon events and shows a robust anticorrelation with the effective atmospheric temperature $T_{eff}$ using 2018–2022 NOvA ND data. It combines a CORSIKA-based seasonal simulation with NOvA detector modeling to demonstrate that an altitude–geometry effect, not muon-decay or meson-interaction biases, drives the phase of the multiple-muon signal. The results reproduce the winter maximum for the NOvA/MINOS near detectors and resolve the long-standing discrepancy with single-muon seasonal behavior, establishing a general criterion where detector size and depth determine the observed phase. The work has implications for modeling cosmic-ray showers and backgrounds in underground experiments and provides a framework to predict seasonal phase shifts based on detector geometry and depth.

Abstract

The flux of cosmic ray muons at the Earth's surface exhibits seasonal variations due to changes in the temperature of the atmosphere affecting the production and decay of mesons in the upper atmosphere. Using 1473 live days of data collected by the NuMI Off-axis $ν_e$ Appearance (NOvA) Near Detector during 2018--2022, we studied the seasonal pattern in the multiple-muon event rate. The data confirm an anticorrelation between the multiple-muon event rate and effective atmospheric temperature, consistent across all the years of data. Previous analyses from MINOS and NOvA saw a similar anticorrelation but did not include an explanation. We find that this anticorrelation is driven by altitude--geometry effects as the average muon production height changes with the season. This has been studied with a CORSIKA cosmic ray simulation package by varying atmospheric parameters, and provides an explanation to a longstanding discrepancy between the seasonal phases of single and multiple-muon events.

Figures (11)

• Figure 1: Seasonal variation of multiple-muon rate for an infinite detector at the depth of the NOvA ND from CORSIKA initiated by primary proton cosmic rays. With detector size not included, the summer peak from atmospheric density effects on the muon rate is seen. The solid curve shows a cosine fit.
• Figure 2: Seasonal variation of multiple-muon rate for an 4m by 15.9m detector at the depth of the NOvA ND from CORSIKA initiated by the primary proton cosmic rays. The solid curve shows a cosine fit. With a detector size less than the average of the muon shower at this depth (105m), the summer peak has turned into a summer deficit because individual muons in the shower miss the detector, causing the event to not be classified as a multiple muon event. Error bars represent statistical uncertainties.
• Figure 3: Variation of average temperature with altitude and total weight function used to calculate effective temperature. This weight corresponds to the fraction of cosmic ray primaries left at a given height: for example, about half have already interacted at a height of 18km.
• Figure 4: Distribution of number of reconstructed muon tracks in an event (multiplicity) in the dataset (2018--2022) used for this analysis. The highest multiplicity observed is 10. Error bars represent statistical uncertainties.
• Figure 5: Distribution of the cosine of the angle between the track and the vertical upward direction (zenith angle). The ratio of data over the CORSIKA MC prediction is shown in the lower panel with statistical uncertainty.