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We present new variants of the Two Higgs-Doublet Model where all Yukawacouplings with physical Higgs bosons are controlled by the quark mixingmatrices of both chiralities, as well as, in one case, the ratio between thetwo scalar doublets' vacuum expectation values. We obtain these by imposingapproximate symmetries on the Lagrangian which, in one of the cases, clearlyreveals the model to be the electroweak remnant of the Minimal Left-RightSymmetric Model. We also argue for the benefits of the bidoublet notation inthe Two Higgs-Doublet Model context for uncovering new models.

Crossed two Higgs-doublet models: reduction of Yukawa parameters in the low-scale limit of left-right symmetry and other avatars