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The irresistible call of $\tau=i$

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arxiv 2211.00659 v1 pith:24YACFHN submitted 2022-11-01 hep-ph hep-th

classification hep-phhep-th
keywords leptonmodularmultipletspointtermsuniversalactinganalyze
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We analyze a large set of modular invariant models of lepton masses and mixing angles, pointing out that many of them prefer to live close to the self-dual point $\tau=i$. We show that in the vicinity of this point a universal behavior naturally emerges, independently from details of the theory such as the finite modular group acting on the lepton multiplets, the weights of the matter multiplets and even the form of the kinetic terms, which are not required to be neither minimal nor flavour blind. The neutrino mass spectrum is normally ordered and universal relations describe the scaling of the physical observables in terms of the parameter $|\tau-i|$.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neutrino mass and leptogenesis in the non-SUSY modular $A^\prime_5$ inverse seesaw model

    hep-ph 2026-03 conditional novelty 6.0 of 10

    Three non-SUSY A5-prime modular inverse-seesaw models fit neutrino oscillation data and can generate the observed baryon asymmetry via TeV-scale resonant leptogenesis.

  2. Stringy Constraints on Modular Flavor Models

    hep-ph 2025-08 conditional novelty 6.0 of 10

    Heterotic one-loop threshold corrections imply upper bounds on the modulus in modular flavor models, ruling out tau near i infinity for typical dilaton and beta-function values and disfavoring tau = i at large volume.

  3. Flavor Symmetries and Winding Modes

    hep-th 2025-06 conditional novelty 6.0 of 10

    In the Z3 heterotic orbifold, the modular symmetry of the Kähler modulus is Gamma(3), and the discrete flavor symmetry Delta(27) arises from misaligned U(1) gauge symmetries that become massless at different critical points.

  4. CPon Dark Matter

    hep-ph 2024-11 conditional novelty 6.0 of 10

    A light scalar from spontaneous CP violation, the CPon, can be a viable dark matter candidate with a mass between about 10 meV and 1 MeV and a suppression scale above 10^12 GeV.

  5. Modular Symmetry with Weighton

    hep-ph 2025-05 conditional novelty 5.0 of 10

    A systematic classification of modular weighton models at levels 3, 4 and 5, with two T' benchmark fits that reproduce quark and lepton hierarchies, each requiring one admitted cancellation.

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