## Simple and compact expressions for neutrino oscillation probabilities in matter

## Abstract

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm ^{2} scales. Unlike previous works, use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using this perturbation theory we derive extremely compact expressions for the neutrino oscillations probabilities in matter. We find, for example, that the ν _{e} disappearance probability at this order is of a simple two flavor form with an appropriately identified mixing angle and Δm ^{2}. Furthermore, despite exceptional simplicity in their forms they accommodate all order effects θ _{13} and the matter potential.

- Authors:

- Univ. de Sao Paulo, Sao Paulo (Brazil)
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- 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:
- 1212719

- Report Number(s):
- FERMILAB-PUB-15-196-T

Journal ID: ISSN 1029-8479; arXiv eprint number arXiv:1505.01826

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 180; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Minakata, Hisakazu, and Parke, Stephen J. Simple and compact expressions for neutrino oscillation probabilities in matter. United States: N. p., 2016.
Web. doi:10.1007/JHEP01(2016)180.
```

```
Minakata, Hisakazu, & Parke, Stephen J. Simple and compact expressions for neutrino oscillation probabilities in matter. United States. doi:10.1007/JHEP01(2016)180.
```

```
Minakata, Hisakazu, and Parke, Stephen J. Fri .
"Simple and compact expressions for neutrino oscillation probabilities in matter". United States. doi:10.1007/JHEP01(2016)180. https://www.osti.gov/servlets/purl/1212719.
```

```
@article{osti_1212719,
```

title = {Simple and compact expressions for neutrino oscillation probabilities in matter},

author = {Minakata, Hisakazu and Parke, Stephen J.},

abstractNote = {We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm2 scales. Unlike previous works, use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using this perturbation theory we derive extremely compact expressions for the neutrino oscillations probabilities in matter. We find, for example, that the νe disappearance probability at this order is of a simple two flavor form with an appropriately identified mixing angle and Δm2. Furthermore, despite exceptional simplicity in their forms they accommodate all order effects θ13 and the matter potential.},

doi = {10.1007/JHEP01(2016)180},

journal = {Journal of High Energy Physics (Online)},

number = 180,

volume = 2016,

place = {United States},

year = {2016},

month = {1}

}

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Cited by: 7 works

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