## Thursday, December 23, 2010

### Single-Higgs-doublet supersymmetric standard models

In the old-fashioned supersymmetric extensions of the Standard Model, we need at least two Higgs doublets: see why the God particle may have five faces.

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.

#### 5 comments:

1. Well, this goes across the lines we discussed a week ago, does it? The only requeriment of any Supersymmetric Standard Model is to have three spare scalars, coming from the chiral supermultiplet that each W and Z supermultiplet will eat to get mass; the other scalar in each chiral pet goes to the helicity 0 state of the boson, as usual.

And then over this agnostic SSM, you can add MSSM or NMSSM or whatever mechanism, including topcolor, extra dimensions, etc. But the first thing to look for should be the spin 1/2 and spin 0 components of the gauge supermultiplets.

2. Apologies, Alejandro, I just don't have a clue what you're saying. The "only requirement" for a model to work is to have three scalars? I can enumerate 60+ other requirements for a model to work.

But even if I pretended that the remaining 59+ ones don't exist, I don't know what you're saying. You just seem to be saying "anything goes" in any sentence - and every statement of this sort is just self-evidently wrong, for a new reason.

What I see is an incoherent sequence of nonsense. Merry Christmas.

3. Sorry Lubos, I was referring to some comment here two weaks ago. We discussed that any massless gauge supermultiplet get mass by eating a chiral supermultiplet. The two bosons of such chiral multiplet are, I believe, part of the higgs in the usual setup; but even in a higgless theory (say, technicolor) this chiral multiplet is still needed, to build a massive gauge multiplet.

Or, said more plainly, a massive gauge multiplet has one Dirac Fermion, one massive gauge and one scalar, always, higgs or not higgs.

So I was telling that the only requirement commont to all Supersymmetric Standard Models (and not in the non-susy SM) is the existence of those three bosons.

4. Ah, Merry Christmas, too.

5. Dear Alejandro, you were saying it, but unlike Arvind et al., you didn't have any evidence for your statement - that there can be supersymmetric models with a single doublet, or any "details" how it could happen, for that matter. You were also saying lots of things that are false.