Dynamical generation of Majorana masses

Journal Article · Sat Sep 01 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.1699· OSTI ID:6478077

Abada, A; Le Yaouanc, A; Oliver, L; Pene, O; Raynal, J ^[1]

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1. Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris-Sud, Batiment 211, 91405 Orsay (France)

We address the general question of the dynamical generation of Majorana masses through quartic interactions of the Nambu--Jona-Lasinio (NJL) type that have both chiral and lepton-number invariances. We make composite the Higgs field of the schemes of spontaneous breaking of the leptonic number; we can thus assign to it a leptonic number {vert bar}{ital L}{vert bar}=2 in a natural way. We consider a Weyl field and write a quartic self-interaction for this field that dynamically breaks chiral and fermion-number invariances and exhibits a whole spectrum of composite particles with different quantum numbers, in addition to a Goldstone Majoron. We compare in detail the Dirac and the Majorana cases. The vacuum degeneracy is the same in both cases, but the vacuum invariances are not. For a single fermion species, we have for the Dirac case a U(1){sub {ital V}{minus}{ital A}}{times}U(1){sub {ital V}+{ital A}} invariance that breaks down to U(1){sub {ital V}} and for the Majorana case a single U(1) invariance that breaks down to the identity {ital open}1. In general the Schwinger-Dyson equation is not the same for both cases, since for Majorana fermions we have propagators of several types. However, in the particular case of a NJL {ital contact} interaction (for Majorana fermions this is {ital the} {ital only} {ital nonvanishing} {ital contact} {ital quartic}/{ital B} {ital interaction}), and with a convenient convention for the coupling, the Schwinger-Dyson equation turns out to have the same form for Dirac and for Majorana fermions. The bound-state boson spectrum is quite different in both cases: for the Dirac case, one has a spectrum {sup 2{ital S}+1}{ital L}{sub {ital J}}({ital S}=0,1) {ital J}{sup {ital P}{ital C}}=0{sup {minus}+},1{sup {minus}{minus}},0{sup ++},1{sup ++},1{sup +{minus}},2{sup ++},. . .

• OSTI ID: 6478077
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 42:5; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FERMIONS
MASS
BOUND STATE
CHIRAL SYMMETRY
COMPOSITE MODELS
GOLDSTONE BOSONS
HIGGS MODEL
LEPTON NUMBER
PROPAGATOR
QUANTUM NUMBERS
STANDARD MODEL
SU-2 GROUPS
SYMMETRY BREAKING
U-1 GROUPS
VACUUM STATES
BOSONS
ELEMENTARY PARTICLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
SU GROUPS
SYMMETRY
SYMMETRY GROUPS
U GROUPS
UNIFIED GAUGE MODELS
645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties
645300 - High Energy Physics- Particle Invariance Principles & Symmetries