### Abstract

We analyze zero energy solutions of the Dirac equation in the background of a stringlike configuration in an extension of the standard model that accommodates the most general fermionic mass matrix for neutrinos. If either the left- or the right-handed Majorana mass vanishes, neutrino and electron zero modes are found to exist. If the harmonic mean of the neutrino Majorana masses is large compared to the Dirac mass, we can prove that normalizable neutrino zero modes cease to exist. This leads to an odd number of fermionic zero modes—namely, only the electron zero mode—which we argue implies that the bosonic background is in a topologically distinct sector from the vacuum. This is confirmed by noting that the bosonic sector of the model involves the breaking of a global (Formula presented) symmetry and hence possesses topological global (Formula presented) strings.

Original language | English (US) |
---|---|

Number of pages | 1 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 65 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*65*(6). https://doi.org/10.1103/PhysRevD.65.065003

**Zero modes of fermions with a general mass matrix.** / Starkman, Glenn; Stojkovic, Dejan; Vachaspati, Tanmay.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 65, no. 6. https://doi.org/10.1103/PhysRevD.65.065003

}

TY - JOUR

T1 - Zero modes of fermions with a general mass matrix

AU - Starkman, Glenn

AU - Stojkovic, Dejan

AU - Vachaspati, Tanmay

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We analyze zero energy solutions of the Dirac equation in the background of a stringlike configuration in an extension of the standard model that accommodates the most general fermionic mass matrix for neutrinos. If either the left- or the right-handed Majorana mass vanishes, neutrino and electron zero modes are found to exist. If the harmonic mean of the neutrino Majorana masses is large compared to the Dirac mass, we can prove that normalizable neutrino zero modes cease to exist. This leads to an odd number of fermionic zero modes—namely, only the electron zero mode—which we argue implies that the bosonic background is in a topologically distinct sector from the vacuum. This is confirmed by noting that the bosonic sector of the model involves the breaking of a global (Formula presented) symmetry and hence possesses topological global (Formula presented) strings.

AB - We analyze zero energy solutions of the Dirac equation in the background of a stringlike configuration in an extension of the standard model that accommodates the most general fermionic mass matrix for neutrinos. If either the left- or the right-handed Majorana mass vanishes, neutrino and electron zero modes are found to exist. If the harmonic mean of the neutrino Majorana masses is large compared to the Dirac mass, we can prove that normalizable neutrino zero modes cease to exist. This leads to an odd number of fermionic zero modes—namely, only the electron zero mode—which we argue implies that the bosonic background is in a topologically distinct sector from the vacuum. This is confirmed by noting that the bosonic sector of the model involves the breaking of a global (Formula presented) symmetry and hence possesses topological global (Formula presented) strings.

UR - http://www.scopus.com/inward/record.url?scp=85038311747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038311747&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.65.065003

DO - 10.1103/PhysRevD.65.065003

M3 - Article

VL - 65

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

ER -