An extension of the Standard Model is proposed, where the Higgs field is valued in the complex projective plane \( {\mathbbm{CP}}^2 \) , rather than ℂ2. Its geometry is consistent with U(2) ≃ (SU(2) × U(1))/ℤ2 electroweak gauge symmetry. The leading terms in the Lagrangian, beyond those of the Standard Model, are much more tightly constrained than in general SMEFTs, and the custodial SO(4) symmetry of the Higgs sector is mildly broken. The predicted tree-level deviations from Standard Model phenomenology depend on a single large mass parameter M. Current experimental data imply that M is a few TeV or larger.
