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Neutrino mass generation in asymptotically safe gravity

Gustavo P. de Brito1,*, Astrid Eichhorn2,†, Antonio D. Pereira3,‡, and Masatoshi Yamada4,§

  • 1Departamento de Física, Universidade Estadual Paulista (Unesp), Campus Guaratinguetá, Avenida Doutor Ariberto Pereira da Cunha, 333, Guaratinguetá, São Paulo, Brazil
  • 2Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
  • 3Instituto de Física, Universidade Federal Fluminense, Campus da Praia Vermelha, Avenida Litorânea s/n, 24210-346, Niterói, Rio de Janeiro Brazil
  • 4Department of Physics and Astronomy, Kwansei Gakuin University, Sanda, Hyogo 669-1330, Japan

  • *Contact author: gp.brito@unesp.br
  • †Contact author: eichhorn@thphys.uni-heidelberg.de
  • ‡Contact author: adpjunior@id.uff.br
  • §Contact author: m.yamada@kwansei.ac.jp
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Phys. Rev. D 112, 066004 – Published 9 September, 2025

DOI: https://doi.org/10.1103/m137-zx8f

Abstract

There exist several distinct phenomenological models to generate neutrino masses. We explore which of these models can consistently be embedded in a quantum theory of gravity and matter. We proceed by invoking a minimal number of degrees of freedom beyond the Standard Model. Thus, we first investigate whether the Weinberg operator, a dimension-five operator that generates neutrino masses without requiring degrees of freedom beyond the Standard Model, can arise in asymptotically safe quantum gravity. We find a negative answer with far-reaching consequences: new degrees of freedom beyond gravity and the Standard Model are necessary to give neutrinos a mass in the asymptotic-safety paradigm. Second, we explore whether the type-I seesaw mechanism is viable and discover an upper bound on the seesaw scale. The bound depends on the mass of the visible neutrino. We find a numerical value of 1014  GeV for this bound when neglecting neutrino mixing for a visible mass of 10−10  GeV. Conversely, for the most “natural” value of the seesaw scale in a quantum-gravity setting, which is the Planck scale, we predict an upper bound for the neutrino mass of the visible neutrino of approximately 10−15  GeV. Third, we explore whether neutrinos could also be pseudo-Dirac neutrinos in asymptotic safety and find that this possibility can be accommodated.

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Phys. Rev. D 112, 066004– Published 9 September, 2025
  • Received 29 May 2025
  • Accepted 12 August 2025
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