https://github.com/ppanh-phy/nuoscprob_hamiltonian
https://github.com/ppanh-phy/nuoscprob_hamiltonian
computational-physics neutrino-physics python-3
Last synced: 7 days ago
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- Host: GitHub
- URL: https://github.com/ppanh-phy/nuoscprob_hamiltonian
- Owner: PPAnh-phy
- Created: 2025-11-13T10:45:57.000Z (7 months ago)
- Default Branch: main
- Last Pushed: 2025-11-13T14:45:20.000Z (7 months ago)
- Last Synced: 2025-11-13T16:32:29.432Z (7 months ago)
- Topics: computational-physics, neutrino-physics, python-3
- Language: Python
- Homepage:
- Size: 434 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# NuOscProb_Hamiltonian
For the purpose of serving ongoing and underdeveloped experiments such as JUNO, DUNE, Hyper-K, etc, which require an accurate and efficient computational tool for precise measurements, we examined the Hamiltonian approach to compute neutrino oscillation probability. our program vs analytical formulas and other approximate/exact packages. Both vacuum and matter effects are taken into account. This study benchmarks and optimises computational approaches for obtaining the eigenvalues of the Hamiltonians for a wide range of problems in medium- to long-baseline experiments. We also examined our program with other available packages. The results highlight the importance of precise treatment of the conversion parameters and trade-offs between precision and efficiency, providing practical guidelines for selecting computational strategies in neutrino oscillation simulations, and contributing to optimised analyses for current and future experiments.
### Requirements
The program is fully written in Python 3, using standard modules that are available on most Python installations.
- Python 3.8 or newer (tested with Python 3.11.4)
- Install dependencies:
```bash
pip install numpy scipy
## Structure
### Inside the Study packages file [7][8]:
* **PMNS**: define parameters (we used NuFit 6.0 best fit data), and compute the PMNS matrix.
* **hamiltonian_vs_packages**: compute neutrino oscillation probability and compare between packages (NuFAST and NuExact)
* **plot**: create plots of neutrino oscillation probability and differences between packages
* **running_time**: compute running time between packages
* **Myglobaldefs**: my modified parameters for more precise results of NuExact packages (modifications used for NuFAST are already included in the file 'hamiltonian_vs_packages')
---
### Notes on Neutrino Oscillations
* **Oscillation**: the process of changing flavour identity of neutrinos ($e, \mu, \tau$) after propagation through a distance and time. Detectors measure different mixing–mass states, indicating oscillation in the mass eigenstates.
* **Explanation**: caused by mass differences ($\Delta m^2 \neq 0 \ \Rightarrow\ m_i \neq m_j \\Rightarrow\ \text{neutrinos are massive}$
).
### Quantum Mechanics
* Start from the initial state $|\nu_\alpha\rangle \ \(\Psi(x, 0)\)$; $(\alpha = e, \mu, \tau)$ to the final state $|\nu_\beta\rangle \ \(\Psi(x, t)\)$; $(\beta = e, \mu, \tau)$.
* Apply time evolution: $\Psi(x, t) = \Psi(x, 0) \. e^{-i H t} $.
* Oscillation probability is given by overlap $\| \Psi(x, t) \|^2$.
* In matter: Neutrinos propagating in matter interact with electrons and nucleons.
* **CC interactions** ($\nu_e + e^- \to \nu_e + e^-$) affect only electron neutrinos.
* **NC interactions** ($\nu_i + n,p \to \nu_i + n,p$) affect all flavours equally and thus do not change oscillations.
**$\Rightarrow$ Matter effect**: adds an extra potential `V_CC` in the Hamiltonian, modifying oscillation behaviour (MSW effect).
---
## References
\[1] Mark Thomson, *Modern Particle Physics*
\[2] G. Fantini, A. Gallo Rosso, and F. Vissani, *The Formalism of Neutrino Oscillations: An Introduction*, \*\*arXiv:\*\*hep-ph/1802.05781v2 (2020)
\[3] Son Van Cao, *Study of Antineutrino Oscillation Using Accelerator and Atmospheric Data in MINOS*, DOI: 10.2172/1151746
\[4] Ivan Esteban, M. C. Gonzalez-Garcia, Michele Maltoni, Ivan Martinez-Soler, João Paulo Pinheiro, Thomas Schwetzh, *Updated global analysis of three-flavor
neutrino oscillations*, \*\*arXiv:\*\*hep-ph/2410.05380v2 (2024)
\[5] Peter J. Mohr, David B. Newell, Barry N. Taylor, and Eite Tiesinga, *CODATA Recommended Values of the Fundamental Physical Constants: 2022*, \*\*arXiv:\*\*hep-ph/2409.03787v2 (2024)
\[6] Ara Ioannisian and Stefan Pokorski, *Three Neutrino Oscillations in Matter*, \*\*arXiv:\*\*hep-ph/1801.10488v4 (2018)
\[7] Peter B. Denton and Stephen J. Parke, *Fast and Accurate Algorithm for Calculating Long-Baseline Neutrino Oscillation Probabilities with Matter Effects: NuFast*, \*\*arXiv:\*\*hep-ph/2405.02400v1 (2024)
\[8] Mauricio Bustamante, *NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities*, \*\*arXiv:\*\*hep-ph/1904.12391v2 (2019)
\[9] JUNO Collaboration, *JUNO Physics and Detector*, \*\*arXiv:\*\*hep-ph/2104.02562v2 (2021)
---