| | |
| | |
Stat |
Members: 3667 Articles: 2'599'751 Articles rated: 2609
15 February 2025 |
|
| | | |
|
Article overview
| |
|
An Improved Method of Estimating the Uncertainty of Air-Shower Size at Ultra-High Energies | Alan Coleman
; Pierre Billoir
; Oliver Deligny
; | Date: |
4 Jan 2023 | Abstract: | The collection of a statistically significant number detected of cosmic rays
with energy above $10^{17}$ to $10^{18}$ eV requires widely-spaced particle
detectors at the ground level to detect the extensive air showers induced in
the atmosphere. The air-shower sizes, proxies of the primary energies, are then
estimated by fitting the observed signals to a functional form for expectations
so as to interpolate the signal at a reference distance. The functional form
describes the rapid falloff of the expected signal with the distance from the
shower core, using typically two logarithmic slopes to account for the
short-range and long-range decreases of signals. The uncertainties associated
to the air-shower sizes are determined under the assumption of a quadratic
dependence of the log-likelihood on the fitted parameters around the minimum,
so that a meaningful variance-covariance matrix is provided. In this paper, we
show that for an event topology where one signal is much larger than the
others, the quadratic dependence of the fitted function around the minimum is a
poor approximation that leads to an inaccurate estimate of the uncertainties.
To restore a quadratic shape, we propose to use the polar coordinates around
the detector recording the largest signal, projected onto the plane of the
shower front, to define the likelihood function in terms of logarithmic polar
distances, polar angles and logarithmic shower sizes as free parameters. We
show that a meaningful variance-covariance matrix is then recovered in the new
coordinate system, as the dependence of the fitted function on the modified
parameters is properly approximated by a quadratic function. The use of the
uncertainties in the new coordinate system for subsequent high-level analyses
is illustrated. | Source: | arXiv, 2301.01558 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|