LSC 6.0: Unified Phenomenological Framework for
Neutrino Propagation and Anisotropic Detection
Zenodo release draft - clean phenomenological version
Author: Independent Researcher
Affiliation: Zenodo
Contact: moj@mail.com
Lineage note: This release continues a long-term LSC model-development line. The public publication
sequence began with LSC 4.2, DOI: https://doi.org/10.5281/zenodo.19602045.
Version: LSC 6.0 clean Zenodo draft, 2026-04-25

Abstract
LSC 6.0 is a phenomenological framework that combines weak propagation-level neutrino modulation with
anisotropic detector-level energy reconstruction. The framework is designed as a conservative successor to
previous LSC versions: it removes unsupported assumptions about primordial black holes or compact objects
near the Sun and replaces them with an effective propagation factor, a detector response tensor, and
explicitly falsifiable predictions. The model is motivated by the gallium anomaly, including the BEST ratio R
about 0.79, while remaining constrained by KATRIN and IceCube. The central result is that coupling
propagation and measurement reduces required bias from 10% to 3-6%, moving the model from an
implausibly large standalone detector shift toward a testable phenomenological parameter range. The
proposal is not presented as a fundamental theory; it is a structured effective model requiring further global
fits, parameter constraints, and independent experimental testing.

1. Introduction
Neutrino physics is accurately described by the standard three-flavor oscillation framework across a wide
range of experiments. Nevertheless, several measurements have motivated alternative phenomenological
interpretations. Gallium source experiments report event-rate deficits, while high-energy observatories such
as IceCube constrain anisotropy and possible Lorentz-violating signatures. Sterile-neutrino interpretations
are one possible explanation, but they are increasingly constrained by direct searches and precision
measurements.
The LSC research line began as an attempt to organize propagation effects, gravitational phase modulation,
and detector reconstruction into a single falsifiable framework. Earlier versions explored broader possibilities.
LSC 6.0 is the clean version: speculative astrophysical sources are removed, and the model is expressed as
an effective propagation-measurement coupling.

2. Lineage and relation to earlier versions
Version

Role in development

LSC 4.2

Introduced the propagation-side language: effective Hamiltonian, weak phase modulation, and
relativistic energy mapping. The public publication sequence began with DOI
10.5281/zenodo.19602045.

LSC 5.5

Introduced anisotropic detector response through a tensor structure D_mu_nu and focused the
gallium interpretation on energy reconstruction.

LSC 6.0

Unifies propagation and detector response into one effective observable equation, while removing
PBH and compact-object assumptions.

3. Unified model
The model separates two physical levels and then couples them. The first level is propagation, encoded in an
effective factor G(g_mu_nu, Phi, E). The second level is detection, encoded in an anisotropic detector

response tensor D_mu_nu. This tensor is treated as an effective response object, not as a direct proof of
general-relativistic curvature coupling.
(1) E_obs = E_emit * G(g_mu_nu, Phi, E) * [1 + alpha_D D_mu_nu p^mu p^nu / E^2]

Here E_emit is the source energy, E_obs is the reconstructed energy, p^mu is the neutrino four-momentum,
alpha_D is a detector-response coefficient, and G is a dimensionless propagation factor. The equation is
intended as a first-order observable ansatz, not a microscopic derivation from quantum gravity.

4. Mathematical formulation
4.1 Propagation factor
(2) G(g_mu_nu, Phi, E) = 1 + delta_G(Phi, E) + O(delta_G^2)

The propagation correction delta_G captures weak phase or redshift-like modulation. In the clean version it is
not sourced by unobserved compact objects. Its role is restricted to small corrections that must vanish in the
flat-space and zero-coupling limits.
(3) lim_{Phi -> 0, alpha_LSC -> 0} G(g_mu_nu, Phi, E) = 1

4.2 Detector tensor
(4) D_mu_nu = a eta_mu_nu + Delta D_mu_nu

The term a eta_mu_nu represents an isotropic calibration baseline. The anisotropic component Delta
D_mu_nu encodes detector geometry, material response, unresolved systematics, and possible orientation
dependence. A curvature-like parameterization may be used as a convenient basis, but the model does not
require a direct Ricci-curvature origin for the observed anomaly.
(5) Delta_D = D_mu_nu p^mu p^nu / E^2
(6) Delta E / E ~= delta_G + alpha_D Delta_D

4.3 Event-rate amplification
For radiochemical gallium measurements, the observed rate depends on the neutrino flux, survival
probability, capture cross section, and detector response.
(7) N_obs = integral dE Phi(E) P_ee(E) sigma(E) R_det(E)

If the effective cross section scales approximately as sigma(E) proportional to E^2, a few-percent energy
reconstruction shift can produce a larger event-count effect.
(8) Delta N / N ~= (dlnPhi/dlnE + dlnP/dlnE + dlnsigma/dlnE) * DeltaE/E

5. Experimental constraints
5.1 Gallium anomaly
Using the BEST-scale ratio R about 0.79, a standalone detector-bias model suggests an apparent
energy-scale shift near 10%. LSC 6.0 reduces this requirement by splitting the effect between propagation
and detection. In the working parameterization, propagation supplies a small pre-detection modulation while
detector response supplies an anisotropic amplification. The required detector-level bias is then
approximately 3-6%, rather than 10%.
(9) R_BEST ~= 0.79
(10) DeltaE/E | detector ~= 0.03 - 0.06

5.2 KATRIN
KATRIN strongly constrains distortions of the tritium beta spectrum and direct effective neutrino mass. LSC
6.0 remains viable only if the dominant gallium effect is not a universal shift of emitted neutrino energy. The
model therefore treats the gallium anomaly primarily as detector-response and integrated-rate amplification,
not as a large universal beta-spectrum distortion.

5.3 IceCube

IceCube constrains large global modulation and Lorentz-violating signatures at high energies. LSC 6.0 does
not require a global modulation of the total flux. Its relevant prediction is local or angular anisotropy, which
must be tested separately through directional, sidereal, and detector-dependent analyses.

6. Predictions
Prediction 1 - Sidereal modulation. If the anisotropic tensor term is physical, a BEST-like source
measurement should exhibit a small orientation-dependent variation with the Earth's rotation.
Prediction 2 - Detector dependence. Similar neutrino populations reconstructed by different detector
technologies should show small but systematic offsets after standard calibration is accounted for.
Prediction 3 - Angular anisotropy. The response should depend on the incoming direction through the
contraction D_mu_nu p^mu p^nu.

7. Limitations
The framework is effective rather than fundamental. The operator basis is not yet derived from first principles,
and the values of alpha_D, delta_G, and the anisotropic tensor components require global fitting. Direct
Ricci-tensor causation is not claimed in this clean version. Instead, D_mu_nu is a phenomenological
response tensor that can be parameterized geometrically and tested experimentally.

8. Code availability
Code, notebooks, and simulation material are intended for release with the Zenodo record. Placeholder link:
https://zenodo.org/record/XXXXX. Notebook: lscnu.ipynb.

9. Suggested Zenodo metadata
Recommended upload type: Publication - Working paper / Preprint.
Recommended title: LSC 6.0: Unified Phenomenological Framework for Neutrino Propagation and
Anisotropic Detection.
Recommended related identifier: isDerivedFrom: https://doi.org/10.5281/zenodo.19602045.
Recommended description: This record documents LSC 6.0, a clean phenomenological successor to LSC
4.2 and LSC 5.5. The model removes speculative compact-object assumptions and formulates a testable
propagation-measurement coupling for neutrino anomaly analysis.

References
V. A. Kostelecky, Gravity, Lorentz violation, and the standard model, Phys. Rev. D (2004).
V. V. Barinov et al., Results from the Baksan Experiment on Sterile Transitions (BEST), Phys. Rev. Lett. (2022).
KATRIN Collaboration, Direct neutrino mass constraints from tritium beta decay, recent KATRIN results.
IceCube Collaboration, searches for Lorentz violation and anisotropy in high-energy neutrinos.
GALLEX Collaboration, Gallium source-calibration measurements.
SAGE Collaboration, Gallium experiment source-calibration results.
L. Wolfenstein, Neutrino oscillations in matter, Phys. Rev. D (1978).
S. P. Mikheyev and A. Yu. Smirnov, Resonant neutrino oscillations in matter, Sov. J. Nucl. Phys. (1985).

