Abstract

Superheavy particles near the unification threshold introduce modifications to precise grand-unified-theory (GUT) predictions. We establish a very useful and general theorem valid in a class of models possessing the custodial symmetry SU(2${)}_{\mathit{L}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathit{R}}$\ifmmode\times\else\texttimes\fi{}SU(4${)}_{\mathit{C}}$\ifmmode\times\else\texttimes\fi{}P at the highest intermediate scale, according to which the one-loop GUT-threshold contribution to ${\mathrm{sin}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\mathit{W}}$ by every class of superheavy particles (gauge bosons, Higgs scalars, and additional fermions) vanishes. The result also applies with supersymmetry, infinite towers, or higher-dimensional operators, and is independent of other intermediate symmetries at lower scales.

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