How to Identify a Majoron: Effective Field Theories of Spontaneous Lepton Number Breaking
Abstract
We revisit the traditional type~I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global U(1) symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of $1−−10$~TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.
Related
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BibTeX
@misc{biggio2026identify,
title = {{How to Identify a Majoron: Effective Field Theories of Spontaneous Lepton Number Breaking}},
author = {Carla Biggio and Marta Fuentes Zamoro and Xu Li and Luca Merlo and Luca Ottonello},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.11522},
eprint = {2608.11522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11522},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - How to Identify a Majoron: Effective Field Theories of Spontaneous Lepton Number Breaking
AU - Carla Biggio
AU - Marta Fuentes Zamoro
AU - Xu Li
AU - Luca Merlo
AU - Luca Ottonello
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2608.11522
UR - https://arxiv.org/abs/2608.11522
AB - We revisit the traditional type~I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global U(1) symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of $1−−10$~TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.
ER -