# Neutrino mass matrices with M{sub ee}=0

## Abstract

Motivated by the possibility that the amplitude for neutrinoless double beta decay may be much smaller than the planned sensitivity of future experiments, we study Ansaetze for the neutrino mass matrix with M{sub ee}=0. For the case in which CP is conserved, we consider two classes of real-valued mass matrices: ''Class I'' defined by |M{sub e{mu}|}=|M{sub e{tau}|}, and ''Class II'' defined by |M{sub {mu}{mu}|}=|M{sub {tau}{tau}|}. The important phenomenological distinction between the two is that Class I permits only small values of V{sub e3} up to {approx}0.03, while Class II admits large values of V{sub e3} up to its empirical upper limit of 0.22. Then we introduce CP-violating complex phases into the mass matrix. We show that it is possible to have tribimaximal mixing with M{sub ee}=0 and |M{sub {mu}{tau}|}=|M{sub {mu}{mu}|}=|M{sub {tau}{tau}|} if the Majorana phase angles are {+-}{pi}/4. Alternatively, for smaller values of |M{sub {mu}{tau}|}=|M{sub {mu}{mu}|}=|M{sub {tau}{tau}|} it is possible to obtain |V{sub e3}|{approx}0.2 and generate relatively large CP-violating amplitudes. To eliminate phase redundancy, we emphasize rephasing any mass matrix with M{sub ee}=0 into a standard form with two complex phases. The discussion alternates between analytical and numerical but remains purely phenomenological, without any attempt to derive mass matrices frommore »

- Authors:

- Department of Physics, University of California, Santa Barbara, California 93106 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 21607758

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.84.073012; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; CP INVARIANCE; DOUBLE BETA DECAY; MASS; NEUTRINOS; REDUNDANCY; SENSITIVITY; BETA DECAY; BETA-MINUS DECAY; DECAY; ELEMENTARY PARTICLES; FERMIONS; INVARIANCE PRINCIPLES; LEPTONS; MASSLESS PARTICLES; NUCLEAR DECAY

### Citation Formats

```
BenTov, Yoni, Zee, A., and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106.
```*Neutrino mass matrices with M{sub ee}=0*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.84.073012.

```
BenTov, Yoni, Zee, A., & Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106.
```*Neutrino mass matrices with M{sub ee}=0*. United States. doi:10.1103/PHYSREVD.84.073012.

```
BenTov, Yoni, Zee, A., and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106. Sat .
"Neutrino mass matrices with M{sub ee}=0". United States. doi:10.1103/PHYSREVD.84.073012.
```

```
@article{osti_21607758,
```

title = {Neutrino mass matrices with M{sub ee}=0},

author = {BenTov, Yoni and Zee, A. and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106},

abstractNote = {Motivated by the possibility that the amplitude for neutrinoless double beta decay may be much smaller than the planned sensitivity of future experiments, we study Ansaetze for the neutrino mass matrix with M{sub ee}=0. For the case in which CP is conserved, we consider two classes of real-valued mass matrices: ''Class I'' defined by |M{sub e{mu}|}=|M{sub e{tau}|}, and ''Class II'' defined by |M{sub {mu}{mu}|}=|M{sub {tau}{tau}|}. The important phenomenological distinction between the two is that Class I permits only small values of V{sub e3} up to {approx}0.03, while Class II admits large values of V{sub e3} up to its empirical upper limit of 0.22. Then we introduce CP-violating complex phases into the mass matrix. We show that it is possible to have tribimaximal mixing with M{sub ee}=0 and |M{sub {mu}{tau}|}=|M{sub {mu}{mu}|}=|M{sub {tau}{tau}|} if the Majorana phase angles are {+-}{pi}/4. Alternatively, for smaller values of |M{sub {mu}{tau}|}=|M{sub {mu}{mu}|}=|M{sub {tau}{tau}|} it is possible to obtain |V{sub e3}|{approx}0.2 and generate relatively large CP-violating amplitudes. To eliminate phase redundancy, we emphasize rephasing any mass matrix with M{sub ee}=0 into a standard form with two complex phases. The discussion alternates between analytical and numerical but remains purely phenomenological, without any attempt to derive mass matrices from a fundamental theory.},

doi = {10.1103/PHYSREVD.84.073012},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 7,

volume = 84,

place = {United States},

year = {2011},

month = {10}

}