## The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis

## Abstract

We consider the Hamiltonian for neutrino oscillations in matter in the case of arbitrary potentials including off-diagonal complex terms. We derive the expressions for the corresponding Hamiltonian in the basis of the instantaneous eigenstates in matter, in terms of quantities one can derive from the flavor-basis Hamiltonian and its derivative, for an arbitrary number of neutrino flavors. We make our expressions explicit for the two-neutrino flavor case and apply our results to the neutrino propagation in core-collapse supernovae where the Hamiltonian includes both coupling to matter and to neutrinos. We show that the neutrino flavor evolution depends on the mixing matrix derivatives involving not only the derivative of the matter mixing angles but also of the phases. In particular, we point out the important role of the phase derivatives, that appear due to the neutrino-neutrino interaction, and show how it can cause an oscillating degeneracy between the diagonal elements of the Hamiltonian in the basis of the eigenstates in matter. Lastly, our results also reveal that the end of the synchronization regime is due to a rapid increase of the phase derivative and identify the condition to be fulfilled for the onset of bipolar oscillations involving both the off-diagonal neutrino-neutrinomore »

- Authors:

- CNRS/IN2P3 and Univ. of Paris-XI (France)
- North Carolina State Univ., Raleigh, NC (United States)

- Publication Date:

- Research Org.:
- North Carolina State Univ., Raleigh, NC (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1327858

- Grant/Contract Number:
- SC0006417

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Physics. G, Nuclear and Particle Physics

- Additional Journal Information:
- Journal Volume: 39; Journal Issue: 3; Journal ID: ISSN 0954-3899

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; neutrino; flavor transformation

### Citation Formats

```
Galais, Sebastien, Kneller, James, and Volpe, Cristina. The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis. United States: N. p., 2012.
Web. doi:10.1088/0954-3899/39/3/035201.
```

```
Galais, Sebastien, Kneller, James, & Volpe, Cristina. The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis. United States. doi:10.1088/0954-3899/39/3/035201.
```

```
Galais, Sebastien, Kneller, James, and Volpe, Cristina. Thu .
"The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis". United States. doi:10.1088/0954-3899/39/3/035201. https://www.osti.gov/servlets/purl/1327858.
```

```
@article{osti_1327858,
```

title = {The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis},

author = {Galais, Sebastien and Kneller, James and Volpe, Cristina},

abstractNote = {We consider the Hamiltonian for neutrino oscillations in matter in the case of arbitrary potentials including off-diagonal complex terms. We derive the expressions for the corresponding Hamiltonian in the basis of the instantaneous eigenstates in matter, in terms of quantities one can derive from the flavor-basis Hamiltonian and its derivative, for an arbitrary number of neutrino flavors. We make our expressions explicit for the two-neutrino flavor case and apply our results to the neutrino propagation in core-collapse supernovae where the Hamiltonian includes both coupling to matter and to neutrinos. We show that the neutrino flavor evolution depends on the mixing matrix derivatives involving not only the derivative of the matter mixing angles but also of the phases. In particular, we point out the important role of the phase derivatives, that appear due to the neutrino-neutrino interaction, and show how it can cause an oscillating degeneracy between the diagonal elements of the Hamiltonian in the basis of the eigenstates in matter. Lastly, our results also reveal that the end of the synchronization regime is due to a rapid increase of the phase derivative and identify the condition to be fulfilled for the onset of bipolar oscillations involving both the off-diagonal neutrino-neutrino interaction contributions and the vacuum terms.},

doi = {10.1088/0954-3899/39/3/035201},

journal = {Journal of Physics. G, Nuclear and Particle Physics},

number = 3,

volume = 39,

place = {United States},

year = {2012},

month = {1}

}

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