However, Arvind Rajaraman and two Californian collaborators whom I don't know argue that it doesn't have to be this way:Does Supersymmetry Require Two Higgs Doublets?People usually parrot two reasons why the two Higgs doublets are needed: one has to bring masses to upper and lower quarks and leptons; and gauge anomalies have to cancel which wouldn't be true with a single chiral Higgs doublet added to the Standard Model.
However, as the three authors explain, both conditions may be rather naturally circumvented. The down-type Higgs doublet may be absent and the down-type fermion masses may come from higher-dimension operators that have some extra factors of the fields that broke SUSY.
And the anomalies may be canceled by other fields, namely by a truncated fourth mirror generation. Take a fourth generation but erase its lepton part. The missing mirror leptons' anomaly cancels the missing down-type Higgs doublet's anomaly and everything is fine.
A reason why I think that these ideas to separate leptons and quarks deserve to be studied is the bbb three-sigma signal from the Tevatron that indicates some SUSY while the corresponding expected signal in the b-tau-tau channel is absent, potentially screwing the MSSM interpretation.
A different behavior of the leptons and quarks in new physics could be experimentally desirable. However, there is only one Higgs doublet in the new model so there's no new genuine "tan(beta)", either. The predictions of their model for the bbb and b-tau-tau channel would have to be recalculated.
Of course, a disadvantage of the new model is that such irregular matter contents seem less compatible with the grand unification: one needs at least three different types of chiral multiplets - ordinary generations; screwed mirror generation; Higgs doublet - to be added into the spectrum. But maybe this is actually OK from a GUT viewpoint.
Oh, holy crap, isn't the truncated fourth generation plus the single Higgs doublet an ordinary mirror generation? In that case, it would only differ from a normal generation by having a vev - and the electroweak symmetry would be simply broken by the fourth generation sneutrino, wouldn't it? Is that really possible? A sneutrino would normally have a negative R-parity so its vev would break R-parity; but one may revert the signs of R-parity for the fourth generation particles, sounds good.
In the context of string theory building, I guess that people would have eliminated the models if they produced a similar spectrum: they didn't realize they were viable and because there were other known viable "patterns", new patterns were not carefully checked for their viability. I actually don't know particular string vacua that produce this spectrum but it's plausible that they exist. (Update: there exists a Calabi-Yau with "(h11, h12) = (3,1)". It could be relevant to produce 3 normal generations and 1 antigeneration in the most straightforward way.)
All the RG running has to be calculated again in these models.
