Nickolay S. Martynenko 1, 2, *, Grigory I. Rubtsov 2, Petr S. Satunin 2, 1, 3, Andrey K. Sharofeev 1, 2, Sergey V. Troitsky 2, 1
1 Lomonosov Moscow State University, 1-2 Leninskie Gory, Moscow 119991, Russia
2 Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow 117312, Russia
3 Branch of Lomonosov Moscow State University in Sarov, Parkovaya 2, Sarov 607328, Russia
* Corresponding author: martynenko@inr.ac.ru
Public NumPy data products for the study Constraining Lorentz invariance violation from the depth of air-shower maximum.
This repository provides processed simulation tables, forward-folded probability tables, and likelihood-scan outputs for a toy-model sensitivity study of subluminal photon-sector Lorentz invariance violation (LIV) using Pierre Auger fluorescence-detector reconstructed shower-maximum distributions.
Large files are stored with GitHub LFS under data/.
To work with the datasets, you will need:
- Git LFS — for downloading large NumPy files.
- Python 3 (recommended: 3.12.7) — for running the demo script.
- NumPy (recommended: 2.4.4) — for handling the structured data.
| File | Content |
|---|---|
data/dataset.npy |
Preprocessed CONEX shower table and Gaisser–Hillas fit results |
data/binned_probas.npz |
Forward-folded Auger-bin probabilities |
data/likelihood_ratio_test.npy |
Likelihood-ratio scan and mock calibration |
Load:
import numpy as np
dataset = np.load("data/dataset.npy").view(np.recarray)Schema:
dataset: (414720,)
event:
epsilon (414720,) true primary energy variable
Y (414720,) mass variable, ln(A)
eta (414720,) LIV-scale variable
zeta (414720,) combined energy–mass–LIV variable
profile:
depth (414720, 200) slant depth [g cm^-2]
e_dep (414720, 200) deposited energy [GeV g^-1 cm^2]
fit_inputs:
fluctuated_e_dep (414720, 200) fluctuated deposited energy [GeV g^-1 cm^2]
sqroot_var_e_dep (414720, 200) square root of profile-point variance [GeV g^-1 cm^2]
fit_outputs:
epsilon_cal (414720,) fitted calorimetric-energy variable
depth_max (414720,) fitted shower maximum [g cm^-2]
shape_r (414720,) fitted Gaisser–Hillas shape parameter R
shape_l (414720,) fitted Gaisser–Hillas shape parameter L [g cm^-2]
success (414720,) fit convergence flag
Load:
import numpy as np
binned = np.load("data/binned_probas.npz")Contents:
eta: (2002,)
tested LIV-scale grid
eta[-1] = +∞ is the Lorentz-invariant limit
Y: (4,)
fitted mass-group grid: H(1,1), He(4,2), N(14, 7), Fe(56,26)
depth_max_reco_bins: (100,)
left (100,) Xmax,reco bin left edges [g cm^-2]
right (100,) Xmax,reco bin right edges [g cm^-2]
epsilon_reco_bins: (20,)
left (20,) epsilon_reco bin left edges
right (20,) epsilon_reco bin right edges
slope (20,) local power-law slope inside the bin
counts: (20, 100)
Auger binned Xmax,reco counts
probas: (2002, 20, 4, 100)
val forward-folded bin probabilities
err.model model uncertainty
err.detector detector-response uncertainty
err.integration numerical-integration uncertainty
err.total total uncertainty
Load:
import numpy as np
scan = np.load("data/likelihood_ratio_test.npy").view(np.recarray)Schema:
scan: (201,)
eta: (201,)
tested LIV-scale grid
hat_F: (201, 20, 4)
fitted composition fractions
D_obs: (201,)
observed likelihood-ratio statistic
D_mock: (201, 10000)
mock-data-set statistic values
p_value:
val (201,) calibrated p-value
err (201,) estimated p-value uncertainty
reliable (201,) reliability flag (if `False`,
the p-value is saturated by the
finite mock sample: no mock data
set generated under the tested
LIV hypothesis produced a statistic
at least as large as the observed one)
The analysis tests subluminal photon-sector LIV through its effect on electromagnetic shower development. Suppressed Bethe–Heitler pair production modifies the longitudinal shower profile and the reconstructed-energy response. The reported result should be interpreted as a toy-model shower-maximum-based sensitivity estimate, not as a full detector-level experimental limit.
If you use these data products, cite:
@article{Martynenko2026LIVAugerFD,
title = {Constraining Lorentz invariance violation
from the depth of air-shower maximum},
author = {Martynenko, Nickolay S. and
Rubtsov, Grigory I. and
Satunin, Petr S. and
Sharofeev, Andrey K. and
Troitsky, Sergey V.},
year = {2026},
eprint = {2608.05106},
archivePrefix = {arXiv},
reportNumber = {INR-TH-2026-007},
note = {16 pages, 4 figures. Submitted to Physical Review D}
}
MIT License, see LICENSE