String theory's concept of supersymmetry is a fancy way of saying that each particle has a related particle called a superpartner. Keeping track of the names of these superpartners can be tricky, so here are the rules in a nutshell.
- The superpartner of a fermion begins with an s, so the superpartner of an electron is the selectron and the superpartner of the quark is the squark
- The superpartner of a boson ends in –ino, so the superpartner of a photon is the photino and of the graviton is the gravitino.
Supersymmetry (SUSY for short) is basic of superstring theory. So what is the deal with this additional symmetry now? In previous blog we saw symmetry being set for electroweak and strong forces as basis for GUT - from where does this supersymmetry comes now? |

The known elementary particles come in two kinds - fermions, such as quarks, electrons, muons, etc (matter particles), and bosons, such as photons, gluons, Ws and Zs (force carriers). The key feature of supersymmetry is that every matter particle (quark, electron, etc) has a boson counterpart (squark, selectron, etc) and every force carrier (photon, gluon) has a fermion counterpart (photino, gluino, chargino, neutralino, etc). This doubling of the particle gene pool is because supersymmetry is a quantum-mechanical enhancement of the properties and symmetries of the space-time of our everyday experience, such as translations, rotations and relativistic transformations. Three things tell apart a sparticle from its normal counterpart: the spin, the mass, and of course the "s-" in their name (such as in stop, sbottom, selectron, setcetera), which puts them in a different category and earns them a different value of a quantum number called "R-parity". If R-parity is conserved, as in most versions of SUSY, sparticles can only decay yielding other sparticles, such that the lightest of them is perfectly stable, and constitutes a perfect candidate to explain the dark matter in the universe. The particle-superparticle twinning can assuage several theoretical headaches, such as why the different forces - gravity and electromagnetism - appear to operate at such vastly different and apparently arbitrary scales ("the Hierarchy Problem"). The extra particles provided by supersymmetry are also natural candidates for exotica, such as the missing dark matter of the universe. But this is not the only supersymmetry out there.

Based on curious experiments involving light absorbed and emitted by atoms, it was determined that electrons' magnetic properties arise, like all magnetism, from the motion of electric charge. This implied that electrons rotate. However, their rotation is (surprise) a little different from the rotation we are used to - it is a constant intrinsic property of electrons, just as other rotational states are intrinsic properties of other particles. This property is called spin. More specifically, physicists found that all matter particles and their antimatter partners have spin -1/2. Messenger particles, those that transmit forces, generally have spin 1 - this applies to photons, gluons, and both types of weak-gauge bosons. However, the graviton is a special case - it has spin-2. In should be noted that, as with all particle properties under string theory, spin arises from a string's vibrational patterns.

Physicists calculated that, if the universe obeys another symmetry approach called supersymmetry, each particle should come with a partner called a superpartner whose spin differs by half a unit. At first, physicists thought this meant that the mass and force particles had been connected - but this thought was incorrect. In reality, if the universe obeys supersymmetry, each particle has another undiscovered superpartner whose spin is 1/2 unit less than its own. An interesting nomenclature has arisen from this; the theorized superpartner of the electron is the selectron (supersymmetric electron), the superpartner of the neutrino is the sneutrino and that of the quark, the squark. Since these are all mass particles, their superpartners should all have spin-0. For the force particles, the superpartners should have spin-1/2. The photon's superpartner is the photino; the gluon, the gluino; and for W and Z bosons, the wino and zino.

Supersymmetry is thus a symmetry between Bosons an Fermions, which drastically constrains possible properties of the theory and makes it very appealing for explaining observable phenomena and puzzles. To get an idea of supersymmetry history and its extension within SM including spin story, you can start with paper here and here and here. This plethora of particles led many to dismiss supersymmetry as being highly unlikely, since none of these particles had been discovered.

The Minimal Supersymmetric extension of the Standard Model (MSSM) is a subset of a class of theories -generically called supersymmetric- which build on the Standard Model of electroweak interactions to mend a very nagging shortcoming of the SM, called the problem of fine tuning. In two words, in the SM the Higgs boson mass is unnaturally small, since its value receives very large positive and negative contributions from virtual diagrams. This is as if you asked each of ten friends to give you a irrational positive or negative number of order unity, and upon adding the ten numbers, you found a result equal to 0.000000000000000000000000000000001 or so: you would guess that your friends played you some trick! They must have conjured to nullify the sum of their ten numbers. Supersymmetric theories solve that problem - the unnatural smallness of the sum of many different large contributions from virtual processes to the Higgs mass - quite elegantly. There, the Higgs boson mass is protected from those large contributions by the existence of a full class of additional particles, copies of the Standard Model quarks, leptons, and gauge bosons, but endowed with different values of spin. The figure above shows on the left side the SM particles (with 1 Higgs bosons though there should be five if we wish to go down to more details) and their corresponding s-particles on the right side.

Bosons will be fermions in the SUSY world, and fermions will be bosons: a really beautiful symmetry, but one which unfortunately is not realized fully in nature. No, it cannot work as is: because all these additional particles have never been seen in nature. So we need to "break the symmetry" between SM and SUSY, and hypothesize that some mechanism is at work to make the SUSY particle masses much larger than our present detection reach. So, in order to solve the problem of fine tuning of the SM, we have to assume that there exist more than twenty so-far-unseen elementary particles, and that these particles all have masses above our detection limits, but not too much so (lest their mending effect on the fine-tuning becomes more complicated to keep intact). Together with those additional particles, there are at least 105 new unknown parameters to buy in the package, which the theory does not explain: not just the particle masses, but their couplings, mixings, etc.

We already said electromagnetic and weak interactions "unify" at electroweak scale. Physicists believe that the same unification happens at a much higher energy scale - one directly unreachable by our experiments - between the three fundamental gauge couplings of the Standard Model. However, in the absence of supersymetry, the three gauge couplings do not seem to converge to a single point - this is why supersymmetry is required by GUT. As far as the Higgs boson is concerned, in the MSSM (which is a minimal version of the many different SUSY theories that can be formulated) there is not just one such particle, but five different ones; the three electrically neutral ones are called h,H, and A; and then there are H^{+} and H^{-}. The lightest neutral Higgs among these five particles does behave similarly to the Higgs boson of the Standard Model, so search techniques are pretty similar. Present searches have started to exclude significant portions of the parameter space of supersymmetric theories, by not finding a signal of SUSY Higgs bosons.

So, supersymmetry differs from all other symmetries in that it relates two classes of elementary particles which are so fundamentally different - the fermions and the bosons. According to supersymmetry, every "ordinary" particle has a companion particle - differing in spin by half a unit, but with otherwise identical properties. Furthermore, the strengths of the interactions of the superpartners are identical to those of the corresponding ordinary particle. Supersymmetry so simplifies the mathematics of quantum field theory and string theory that it allows theoriests to obtain solutions that would otherwise be far beyond their calculating ability. The general idea is for the unification of all forces of nature including quantum gravity. Since the graviton has spin 2, while the other gauge bosons have spin 1 and 0, supersymmetry is used to mix them. Starting with the graviton state of spine 2 and acting by supersymmetry generators we get the following chain of states: spin 2 spin 3/2 spin 1 spin 1/2 spin 0.

The standard model will only yield correct predictions if numerical input based on experimental data is carefully "fine-tuned" to better than one part in a million billion. The reason behind this is simple: each particle contributes to the quantum foam being generated. The fine-tuning cancels out the effects of this foam on the predictive power of the standard model. To get even more precise, the Higgs particle, which in theory gives the other particles their mass, cannot be more than about 1000 times a proton's mass in order for the standard model to work. However, quantum fluctuations have a tendency to greatly increase the calculated mass of this particle, sometimes causing it to seem on the Planck scale (about ten billion billion time the mass of a proton). Fine-tuning input cancels these effects, keeping the Higgs particle's mass within the limits set by the standard model. Supersymmetry solves this problem by ensuring that bosons (particles whose spin is a whole number) and fermions (particles whose spin is half of a whole) occur in pairs. Since the quantum jitters of bosons and fermions tend to cancel each other out, supersymmetry eliminates the need for careful fine-tuning of input into the standard model and thus is very attractive to physicists uncomfortable with the delicacy of the adjustments.

There are no direct indications on existence of supersymmetry in particle physics, however there are a number of theoretical and phenomenological issues that the SM fails to address adequately and SUSY should are:

- uniﬁcation with gravity
- uniﬁcation of gauge couplings
- hierarchy problem
- electroweak symmetry breaking

The history of supersymmetry is exceptional. In the past, virtually all major conceptual breakthroughs have occurred because physicists were trying to understand some established aspect of nature. In contrast, the discovery of supersymmetry in the early 1970s was a purely intellectual achievement, driven by the logic of theoretical development rather than by the pressure of existing data. Starting in the early 1980's, people began to realize that SUSY might indeed solve some basic problems of our world. Appeared a lot of SUSY correct predictions, some of them are:

- supersymmetry predicted in the early 1980s that the top quark would be heavy, because this was a necessary condition for the validity of the electroweak symmetry breaking explanation
- supersymmetric grand uniﬁed theories with a high fundamental scale accurately predicted the present experimental value of Weinberg angle before it was measured
- supersymmetry requires a light Higgs boson to exist, consistent with current precision measurements, which suggest Mh < 200 GeV

In extended supersymmetry there may be more than one superparticle for a given particle. For instance, with two copies of supersymmetry in four dimensions, a photon would have two fermion superpartners and a scalar superpartner. Many independent lines of cosmological evidence have led to the conclusion that the vast majority of matter in the universe is "dark" in the sense that it has evaded observation based on direct interaction with electromagnetic radiation. Nonbaryonic dark matter out-masses ordinary matter by a factor of about 8. The dominant class of dark matter candidates are "Weakly Interacting Massive Particles" (WIMPs). There have been a number of suggestions for dark matter particles, but it seems that the best candidate is the lightest "neutralino" that is provided by TeV-scale SUSY. Neutrolino is assumed to be 100 or even 1000 times heavier than the proton (i.e. its mass is in the range 100 GeV - 1 TeV). Another nice paper on subject btw...

Supersymmetry, as the fundamental symmetry, has not been observed in Nature so far. This means that (if it exist) it is broken, in a so called spontaneous way. A consequence of such breaking is that the superpartners have masses much larger than conventional elementary particles. This explains why the superpartners have not been captured so far in the experiment. They may have existed in the early universe, but as the universe cooled off and energy spread out after the big bang, these particles would have collapsed into the lower-energy states that we observe today. Of course, we may not think of our current universe as particularly low energy, but compared to the intense heat of the first few moments after the big bang, it certainly is. Nevertheless, powerful colliders should be able then to create SUSY particles. This would also provide support for this sort of prediction by string theory. While the speed with which the LHC may uncover new physics has surely been disappointing for many victims of a wishful thinking, it can't be excluded that some signs of new physics will emerge in a few months or years (aside from the Higgs boson(s), supersymmetry remains the most likely scheme that could appear as the first discovery - being confirmed or denied). Searches for supersymmetry have already removed a large chunk of parameter space to existing models. The allowed range of some of the parameters has shrunk considerably in the last few years, and yet the faith in SUSY of many scientists, both theorists and experimentalists, is unshaken.

Edward Witten once gave to a mixed audience of theorists and experimentalists seminar about physics beyond the SM; needles to say, string theory and SUSYfeatured prominently in his talk. At the questions session an experimentalist asked a rather obvious question, what if susy is not observed at the LHC? Witten's answer is one of the following two:

- Only a moron with a terribly ugly bad taste for physics would ask such a question. The problem with experimentalists is that they are all idiots. Even a mentally retarded infant would know by now that susy IS going to be observed by the LHC, just because string theory is a parameter-free theory of Nature all the way up to the Planck scale
- In that case further development will have to be experiment driven

The MSSM requires a Higgs boson below 140 GeV. In detail the signature would be different from the standard model Higgs boson. If there were a Higgs below about 130 GeV the vacuum would be unstable (actually 125 I believe is the lower threshold). On the other hand a 140 GeV Higgs can easily exist on its own and requires no new physics even at much higher energy scales.

For some some further reading I recommend mastercode site. LHC hold position to give more light on several topics - including supersymmetry models (supersymmetry is framework and not theory). We shall see - as they say...

Credits: Brian Greene, String Theory For Dummies, Dmitri Sorokin, Mary K. Gaillard, Bruno Zumino, Flip Tanedo, Wikipedia, Tommaso Dorigo

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