# Duality in Left-Right Symmetric Seesaw Mechanism

## Abstract

We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m{sub {nu}} and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution f-circumflex=m{sub {nu}}/v{sub L}-f, where v{sub L} is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2{sup n}. We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f.

- Authors:

- Physik Department T30, Technische Universitaet Muenchen, James-Franck Strasse, D-85748 Garching (Germany)
- (Russian Federation)
- Department of Physics, University of California, Riverside, California 92521 (United States)

- Publication Date:

- OSTI Identifier:
- 20778606

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevLett.96.061802; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DUALITY; EQUATIONS; EXPECTATION VALUE; HIGGS BOSONS; MASS; MATHEMATICAL SOLUTIONS; NEUTRINO OSCILLATION; NEUTRINOS; NONLINEAR PROBLEMS; TRIPLETS; YUKAWA POTENTIAL

### Citation Formats

```
Akhmedov, E.Kh., Kurchatov Institute, Moscow, and Frigerio, M.
```*Duality in Left-Right Symmetric Seesaw Mechanism*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVLETT.96.0.

```
Akhmedov, E.Kh., Kurchatov Institute, Moscow, & Frigerio, M.
```*Duality in Left-Right Symmetric Seesaw Mechanism*. United States. doi:10.1103/PHYSREVLETT.96.0.

```
Akhmedov, E.Kh., Kurchatov Institute, Moscow, and Frigerio, M. Fri .
"Duality in Left-Right Symmetric Seesaw Mechanism". United States.
doi:10.1103/PHYSREVLETT.96.0.
```

```
@article{osti_20778606,
```

title = {Duality in Left-Right Symmetric Seesaw Mechanism},

author = {Akhmedov, E.Kh. and Kurchatov Institute, Moscow and Frigerio, M.},

abstractNote = {We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m{sub {nu}} and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution f-circumflex=m{sub {nu}}/v{sub L}-f, where v{sub L} is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2{sup n}. We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f.},

doi = {10.1103/PHYSREVLETT.96.0},

journal = {Physical Review Letters},

number = 6,

volume = 96,

place = {United States},

year = {Fri Feb 17 00:00:00 EST 2006},

month = {Fri Feb 17 00:00:00 EST 2006}

}