Non-invertible symmetry from the minimal Fibonacci fusion rule forbids tree-level VEVs for multi-Higgs fields H4 and H5, generating them radiatively at one-loop with naturally small values of 10^{-3}-10^{-2} GeV that satisfy the rho parameter.
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A general prescription is formulated for spurion analysis of commutative non-invertible fusion algebras in particle physics, unifying prior specific cases and enabling systematic tracking of coupling constants in tree- and loop-level processes without requiring faithful realization or exclusive use.
A one-loop Dirac neutrino mass model stabilized by a non-invertible fusion rule from Z3 x Z3' accommodates oscillation data and provides a viable bosonic dark matter candidate.
Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.
Dynamical generation of leptonic CP violation and light sterile neutrino masses via radiative breaking of non-invertible selection rules, illustrated in the Inverse Seesaw model.
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More about modular symmetries and non-invertible properties in magnetized compactifications
Incomplete zero-mode multiplets under Scherk-Schwarz phases in magnetized compactifications violate modular symmetry as a group but retain control over couplings via full modular forms.