# Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter

## Abstract

We further develop a simple and compact technique for calculating the three flavor neutrino oscillation probabilities in uniform matter density. By performing additional rotations instead of implementing a perturbative expansion we significantly decrease the scale of the perturbing Hamiltonian and therefore improve the accuracy of zeroth order. We explore the relationship between implementing additional rotations and that of performing a perturbative expansion. Based on our analysis, independent of the size of the matter potential, we find that the first order perturbation expansion can be replaced by two additional rotations and a second order perturbative expansion can be replaced by one more rotation. Numerical tests have been applied and all the exceptional features of our analysis have been verified.

- Authors:

- Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Univ. of Chicago, IL (United States). Enrico Fermi Inst.

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1464312

- Alternate Identifier(s):
- OSTI ID: 1462107

- Report Number(s):
- arXiv:1806.01277; FERMILAB-PUB-18-213-T; IFT-UAM/CSIC-18-54; IFT-UAM-CSIC-18-54

Journal ID: ISSN 2470-0010; PRVDAQ; 1676422; TRN: US1902105

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Denton, Peter B., Parke, Stephen J., and Zhang, Xining. Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.033001.
```

```
Denton, Peter B., Parke, Stephen J., & Zhang, Xining. Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter. United States. doi:10.1103/PhysRevD.98.033001.
```

```
Denton, Peter B., Parke, Stephen J., and Zhang, Xining. Mon .
"Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter". United States. doi:10.1103/PhysRevD.98.033001.
```

```
@article{osti_1464312,
```

title = {Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter},

author = {Denton, Peter B. and Parke, Stephen J. and Zhang, Xining},

abstractNote = {We further develop a simple and compact technique for calculating the three flavor neutrino oscillation probabilities in uniform matter density. By performing additional rotations instead of implementing a perturbative expansion we significantly decrease the scale of the perturbing Hamiltonian and therefore improve the accuracy of zeroth order. We explore the relationship between implementing additional rotations and that of performing a perturbative expansion. Based on our analysis, independent of the size of the matter potential, we find that the first order perturbation expansion can be replaced by two additional rotations and a second order perturbative expansion can be replaced by one more rotation. Numerical tests have been applied and all the exceptional features of our analysis have been verified.},

doi = {10.1103/PhysRevD.98.033001},

journal = {Physical Review D},

number = 3,

volume = 98,

place = {United States},

year = {2018},

month = {8}

}

DOI: 10.1103/PhysRevD.98.033001

*Citation information provided by*

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Web of Science

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