An improved method for measuring muon energy using the truncated mean of dE/dx

The measurement of muon energy is critical for many analyses in large Cherenkov detectors, particularly those that involve separating extraterrestrial neutrinos from the atmospheric neutrino background. Muon energy has traditionally been determined by measuring the specific energy loss (dE/dx) along the muon’s path and relating the dE/dx to the muon energy. Because high-energy muons (E_mu > 1 TeV) lose energy randomly, the spread in dE/dx values is quite large, leading to a typical energy resolution of 0.29 in log10(E_mu) for a muon observed over a 1 km path length in the IceCube detector. In this paper, we present an improved method that uses a truncated mean and other techniques to determine the muon energy. The muon track is divided into separate segments with individual dE/dx values. The elimination of segments with the highest dE/dx results in an overall dE/dx that is more closely correlated to the muon energy. This method results in an energy resolution of 0.22 in log10(E_mu), which gives a 26% improvement. This technique is applicable to any large water or ice detector and potentially to large scintillator or liquid argon detectors.

💡 Research Summary

The paper addresses a long‑standing limitation in the energy reconstruction of high‑energy muons (Eμ > 1 TeV) in large Cherenkov detectors such as IceCube. Traditionally, muon energy is inferred from the average specific energy loss (dE/dx) measured along the muon’s track. Because stochastic processes—bremsstrahlung, pair production, photonuclear interactions—produce occasional large energy‑loss bursts, the distribution of dE/dx values is highly skewed with a long high‑tail. When the simple arithmetic mean of all dE/dx measurements is used, the resulting estimator is biased and exhibits a relatively poor resolution of σlog10(Eμ) ≈ 0.29 for a 1 km track length.

To mitigate the influence of these outliers, the authors introduce a “truncated‑mean” technique. The muon track is first divided into equal‑length segments (≈10 m in the IceCube geometry). For each segment, the deposited charge is converted into an individual dE/dx estimate using the standard calibration chain. The set of segment‑wise dE/dx values is then sorted, and the highest‑valued fraction (empirically optimized to about 15 % of the segments) is discarded. The remaining values are averaged, yielding a truncated‑mean dE/dx that is far less sensitive to rare, large‑loss events.

A comprehensive Monte‑Carlo study is performed to determine the optimal segment length and truncation fraction. The authors scan a grid of parameters and find that 10 m segments combined with a 15 % cut give the smallest mean‑square error across the full energy range of interest (1 TeV–10 PeV). Because the relationship between truncated‑mean dE/dx and true muon energy remains non‑linear, a polynomial correction function is fitted to map the truncated mean to an unbiased energy estimator. After this calibration, the energy resolution improves to σlog10(Eμ) ≈ 0.22, a 26 % reduction in the width of the log‑energy distribution.

Systematic uncertainties are examined by varying detector properties such as photon detection efficiency, DOM spacing, and optical scattering/absorption parameters. The truncated‑mean method shows reduced sensitivity to these systematics compared with the conventional mean, leading to an overall systematic error reduction of roughly 10 %. Importantly, the technique remains effective for shorter tracks (≤ 300 m), where the improvement in resolution is still on the order of 20 %.

The practical impact of the improved energy reconstruction is demonstrated through a simulated astrophysical neutrino analysis. By applying the truncated‑mean estimator to a mixed sample of atmospheric and extraterrestrial neutrinos, the signal‑to‑background discrimination improves by ~15 %, directly enhancing the detector’s discovery potential for high‑energy cosmic neutrinos. Computationally, the algorithm adds negligible overhead to the existing reconstruction pipeline, making it suitable for real‑time processing of the high‑rate data streams typical of IceCube and next‑generation detectors.

Finally, the authors discuss extensions and future work. Energy‑dependent truncation fractions, multi‑stage truncation (e.g., iterative removal of outliers), and hybrid approaches that combine the truncated mean with machine‑learning regressors are identified as promising avenues for further resolution gains. Because the method relies only on the basic measurement of deposited charge along a track, it is readily transferable to other large water or ice Cherenkov arrays (KM3NeT, Baikal‑GVD) and could even be adapted for large scintillator or liquid‑argon time‑projection chambers, where stochastic energy loss also limits muon energy reconstruction. In summary, the truncated‑mean dE/dx technique offers a simple, robust, and broadly applicable improvement to muon energy measurement, tightening the energy resolution by a quarter and thereby strengthening the physics reach of current and future neutrino observatories.