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Five faces of the God particle

One month ago, Fermilab's D0 Collaboration claimed the evidence for a new source of CP-violation in their comparison of muon-muon and antimuon-antimuon final states.

If the signal is real, supersymmetry is the most sensible explanation of this observation. In particular, a model based on "uplifted supersymmetry" has been proposed and advocated by Dobrescu, Fox, and Martin.

However, the media are more obsessed with the Higgs boson. So even though the discovery of supersymmetry - that is getting more likely these days - would be more revolutionary an event than the almost certain confirmation of the last unverified part of the Higgs mechanism, the media are rephrasing even supersymmetry itself in terms of the God particles.

Their favorite interpretation is that the D0 observations may point to five flavors of the God particle. It sounds incredible but the actual reason why there should be five Higgs bosons - and this reason is not only more fundamental but also more relevant for the D0 observations - namely supersymmetry - is not even mentioned in many articles about the "five faces of the God particles".

For example, National Geographic and The Telegraph, among others (such as The Escapist Magazine), wrote stories about the five Higgs bosons but they haven't mentioned the word "supersymmetry" in any form.

Jennifer Ouellette's article in Discovery News doesn't suffer from this lethal flaw. It's sensible, reasonably playful, and contains some key ideas, too. She may still have been affected by her husband, Sean Carroll, who hates the term "God particle", so she claims to hate it, too. But that's just her personal idiosyncrasy I have no serious problem with.

By the way, one week ago, a self-appointed committee of physicists who hate both God as well as Leon Lederman's creative ideas decided to eliminate God from the Higgs sector of particle physics. The victorious replacement for the term "God particle" was invented by Mr or Ms TigerRepellingRock - sounds like a distinguished name :-). (Papertiger is, of course, a much stronger a nickname because - as you should remember - paper covers and defeats rock.) The new popular term that is supposed to supersede the "God particle" is "the Champagne bottle boson".

So far, the new term only has 2-3 Google hits. Compare it to 150,000 hits for the "God particle". I wish the authors of the new name good luck. They will need lots of it. :-) By the way, they not only want to rename God. They also want to rename the "Mexican hat potential" which is known as the "Landau buttocks potential" in the former socialist bloc. That's a pretty ambitious P.R. project, indeed.

Why the God particle has five faces

Why does supersymmetry predict five Higgs particles?

In the (non-supersymmetric) Standard Model, the SU(2) symmetry has to be broken by a field that transforms as the complex (well, pseudoreal) 2-dimensional representation of SU(2). Its matter content is equivalent to 4 real scalar bosons.

However, these fields are the key players in the Higgs mechanism. Originally, we start with massless photons, W+, W-, and Z bosons. However, after the Higgs mechanism - after the spontaneous symmetry breaking -, the last three bosons (W+,W-,Z) have to become massive.

The massless particles - and photons remain massless - only have two (transverse) physical polarizations (imagine either the two linear ones; or the left-handed and right-handed circular polarizations). However, massive vector particles such as W+,W-,Z bosons must have three polarizations. In their rest frame, the polarization vector is an ordinary three-dimensional vector and it must have 3 components.

Where does the new, third (longitudinal) polarization come from?

It comes from the degree of freedom that previously belonged to the Higgs fields. Technically, we say that the gauge fields are "eating" the Higgs fields in order to become massive; the "eating" metaphor works if you care about the mass and if you care about the counting of the degrees of freedom, too. As a result, three of the four components of the Higgs doublet are "eaten" by the W+,W-,Z bosons, so that these three bosons become massive. Only the fourth component of the Higgs doublet survives.

It gives rise to the single God particle of the Standard Model. The key identity here is

4 - 3 = 1.
Analogously, in the Minimal Supersymmetric Standard Model (see e.g. Why supersymmetry should be seen at the LHC), we have to start with two Higgs doublets, a fact I will discuss later. Instead of 4 real components of scalar fields, it is equipped with 8 of them: the total content of the degrees of freedom gets doubled. However, the gauge fields remain unchanged because the gauge groups are fixed. So there are still W+,W-,Z bosons and only three components of the Higgs fields are "eaten". As a result,
8 - 3 = 5
five components of the Higgs fields are left. When you only care about the counting and the electric charges of the five Higgs fields, you may imagine that there's still one neutral Higgs boson from the Standard Model and a whole new doublet added on top of it. The doublet has 1 electrically neutral complex component and 1 charged complex component. The doublet therefore gives you a new positive charged Higgs, a new negatively charged Higgs, and two new neutral Higgses.

Why there must be two doublets in MSSM

There are two main reasons. Both of them are technical but kind of simple.

The first argument is based on anomalies. The Standard Model could have some potential anomalies - lethal violations of the gauge symmetries - induced by one-loop triangular diagrams. These anomalies arise from chiral (left-right asymmetric) particles - which inevitably means chiral fermions in 4 dimensions.

However, all the anomalies of the Standard Model cancel between quarks and leptons. For the Standard Model to be consistent, it is necessary to include both quarks and leptons: the Standard Model wouldn't work if you omitted one of the groups (or if the numbers of leptonic and quark generations differed).

When you include all of them, things are OK. Anomalies cancel. The total anomalies are zero.

On the other hand, supersymmetry requires that each particle is supplemented with its superpartner. For spin-zero Higgs bosons, the relevant superpartners are spin-1/2 higgsinos (which are subsequently mixed with other, neutral or electrically charged new spin-1/2 fermions, to produce neutralinos and charginos, respectively). And the minimum "packages" that act as partners for the Higgs bosons are chiral (Weyl) fermions, much like neutrinos.

Such higgsinos would contribute to the anomalies, much like the leptons and quarks do. If you only added one Higgs doublet, the lepton-quark balance would be destroyed and the anomalies would reappear. Two Higgs doublets eliminate the anomalies in a simple way: the two doublets have the opposite charges so that they cancel. Alternatively, you may complex conjugate one of the doublets and say that both doublets have the same charges but one of the higgsinos is left-handed while the second one is right-handed. Again, non-chiral (left-right-symmetric, or full Dirac) fermions contribute no anomalies and everything is fine.

Another, less fundamental but more popular argument explaining why two Higgs doublets are needed has something to do with the quark masses. All quark flavors we know are massive. In the Standard Model, the masses arise from the quarks' cubic ("Yukawa") interactions with the God particle. Once the God particle develops a vacuum condensate - it can be replaced by "v+h" where "v" is a number - the cubic term because a quadratic ('mass") term for the quarks. Without the Higgs mechanism, the quarks and leptons would have to be massless.

In the Standard Model, the Higgs doublet transforms as a 2-dimensional representation of SU(2) which is pseudoreal. It means that its complex or Hermitean conjugate is equivalent to itself and you may couple it both to upper and lower quarks. That's important because the hypercharge conservation requires different values of the hypercharge of the Higgs boson that produces the upper quark masses from the value of Y of the Higgs boson responsible for the lower quark masses.

However, when you consider a supersymmetric theory, the complex conjugation of the Higgs doublet does several things. It still transforms "2" to another "2", an equivalent representation of SU(2) - while flipping the sign of the hypercharge Y. However, it also changes a chiral superfield - a field in superspace that only depends on "theta's" - to an antichiral superfield that only depends on "theta_bar's". So if you could have inserted the former Higgs superfield into your superpotential coupling, you can't insert the latter, and vice versa.

Again, you need both types of the Higgs doublets to be able to produce all the Yukawa superpotential couplings that are needed for all the quark flavors to receive their desired masses.

Five Higgses in minimal supersymmetric models. The lightest neutral "h" field is the most similar one to the Standard Model Higgs but it has another, equally CP-even neutral but heavier brother, "H". There's a new CP-odd neutral Higgs boson, "A", and a pair of charged ones, "H+" and "H-" (that are related to one another by CP). The masses are close to the TRF best estimates as of mid July 2010. Click the picture to zoom in.

Supersymmetry is a highly constrained property of the Universe that may or may not be seen by the LHC. It predicts some new phenomena but the tightly organized system controlling all the new particles and interactions actually makes supersymmetric extensions the most conservative models of new physics that you may add to the Standard Model.

That's not enough to feel confident that the LHC should observe the supersymmetry. But if you're competent, if you understand how supersymmetry (at some scale) follows from (i.e. is predicted by) all realistic vacua of string theory, if you appreciate how it helps to produce the dark matter candidate particles and to preserve the gauge coupling unification, and how it helps to solve the hierarchy problem (the puzzle why the Higgs doesn't want to become as heavy as the Planck scale), you may start to understand why it seems more likely than not that the LHC should actually observe SUSY.

It's still a huge claim. We will see whether it's true.

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reader Plato said...

Lubos you should read sometime Leon Lederman's book on Symmetry and the beautiful Universe.

Out of exhaustive attempts to explain on my part the origination of the term "God Particle" the Fly's eye experiment, it is an attempt at a definition that is lacking. That one might revert too, such a name of something existing at certain energies, yet, can happen "ever so often" and be identified as it's decay is generated back too a sensible value in our human domain. It's a stepping stone from the "oblivious to the obvious," because it is an everyday thing, we understand there will always be these moments?

It is what makes us human, the mysterious and the idea of the unobtainable?:)


reader Andrew Oh-Willeke said...

In defense of the popular press, newspapers are written at the 5th grade level, and magazines are usually written at the 9th grade level. In a short, breaking news article, there isn't time to let a reader know enough to understand a term like supersymmetry or SUSY.

The science press and blogs did use the terms.

reader Lumo said...

Dear Andrew, thanks for the description of the elementary school equivalents to the genres of press. ;-)

Still, it's true that the popular press has explained SUSY at their level as well. Well, there's a partner for everyone with a different spin.

In this case, the actual observation of the CP-violation, if real, actually depends on SUSY rather than the Higgs sector per se. So it's just awkward to say that the phenomenon is explained by 5 Higgses.

The observation would actually be a consequence of SUSY, much like the 5-multiplicity of the Higgses would be a consequence of SUSY. But the observation wouldn't really be a consequenc of the multiplicity of Higgses only - even though, it's true, one could also try to design non-SUSY theories with 2 doublets. But they're not really studied in the papers so it's an additional speculation.