Farewell to Reality (27 page)

The symmetry in question is called a
supersymmetry.

We should be clear that the original motive for developing theories of supersymmetry (which we abbreviate to SUSY) was
not
driven by a compelling desire to solve all the problems of the standard model. For a hard—nosed pragmatist, demanding to know the cost of everything (and so, to quote Oscar Wilde, thereby knowing the
value
of nothing), it might be a little difficult to come to terms with the simple fact that theorists often develop theories simply because these things are interesting and form structures of great intrinsic
beauty.

And yet this was the situation in the early 1970s, when the first theories of supersymmetry were developed by a number of Soviet physicists based in Moscow and Kharkov. The theory was independently rediscovered in 1973 by CERN physicists Julius Wess and Bruno Zumino.
^*
As these theorists had not set out to solve the problems of the standard model, for a time SUSY was regarded (as was laser technology in the 1960s) as a solution in search of a problem. And yet it has become one of the most logical and compelling ways to transcend standard model physics.

SUSY is not a GUT. It is probably best to think of it as an important stepping stone. If it can be shown that the world is indeed
supersymmetric, then some (not all) of the problems of the present standard model go away and the path to a GUT is clearer. SUSY, however, is like life. It involves a big compromise. In return for some potentially neat solutions, what we get is a
shedload
of new particles.

As Noether discovered, continuous transformations of spacetime symmetries — of time, space and rotation — are associated with the conservation of energy and linear and angular momentum. An important theorem developed in the late 1960s suggested that this was it — there could be no further spacetime symmetries. However, it soon became apparent that the theorem was not watertight; it contained a big loophole. It assumed that in any symmetry transformation, fermions would continue to be fermions and bosons would continue to be bosons.

This brings us to an important assumption.

It is essential to our understanding of what follows that we grasp the significance of this last sentence.

The standard model of particle physics and the great variety of experimental data that has been gathered to validate it offer no real clues as to how its rather obvious failings can be addressed and corrected. Physicists have no real choice therefore but to go with their instincts.

And their instincts tell them that at the heart of the solution must lie some kind of fundamental symmetry. As Gordon Kane, a leading spokesperson for supersymmetry, explained:

Supersymmetry is the idea, or hypothesis, that the equations of [a unified theory] will remain unchanged even if fermions are replaced by bosons, and vice versa, in those equations in an appropriate way. This should be so in spite of the apparent differences between how bosons and fermions are treated in the standard model and in quantum theory … It should be emphasized
that supersymmetry is the
idea
that the laws of nature are unchanged if fermions [are interchanged with] bosons.
⁶

Assumption, idea, hypothesis. Call it what you will, SUSY is basically an enormous bet. With no real clues as to how physics beyond the standard model should be developed, physicists have decided that they must take a gamble.

Okay, but if we're going to bet the farm on Lucky Boy, running in the 3.15 at Chepstow, we will typically need a damn good reason. Why pin all our hopes on a fundamental spacetime symmetry between fermions and bosons? For the simple reason that a symmetry of this kind offers exactly the kind of cancellation required to fine—tune the Higgs mass.

Stephen Martin again:

Comparing [these equations] strongly suggests that the new symmetry ought to relate fermions and bosons, because of the relative minus sign between fermion loop and boson loop contributions to [the Higgs mass] … Fortunately, the cancellation of all such contributions to scalar masses is not only possible, but is actually unavoidable, once we merely assume that there exists a symmetry relating fermions and bosons, called a
supersymmetry.
⁷

Superpartners and supersymmetry-breaking

In fact, supersymmetry is not so much a theory as a
property
of a certain class of theories. There are therefore many different kinds of supersymmetric theories. To keep things reasonably simple, I propose to explore some of the consequences of supersymmetry by reference to something called the Minimal Supersymmetric Standard Model, usually abbreviated as the MSSM. This was first developed in 1981 by Howard Georgi and Greek physicist Savas Dimopoulos,
^*
and is the simplest supersymmetric extension to the current standard model of particle physics.

So, what are the consequences of assuming a symmetry relation between fermions and bosons in the MSSM? The answer is, perhaps, relatively unsurprising. In the MSSM, the various particle states form
supermultiplets,
each of which contains both fermions and bosons which are ‘mirror images' of each other.

Every particle in the standard model has a
superpartner
in the MSSM. For every fermion (half-integral spin) in the standard model, there is a corresponding so-called scalar fermion, or
sfermion,
which is actually a boson (zero spin). For every boson in the standard model, there is a corresponding
bosino,
which is actually a fermion with spin ½.

To generate the names of fermion superpartners we prepend an ‘s' (for scalar). So, the superpartner of the electron is the scalar electron, or selectron. The muon is superpartnered by the smuon. The superpartner of the top quark is the stop squark, and so on.

To generate the names of the boson superpartners we append ‘-ino'. The superpartner of the photon is the photino. The W and Z particles are partnered by winos
^*
and zinos. Gluons are partnered by gluinos. The Higgs boson is partnered by the Higgsino (actually, several Higgsinos). Once you've grasped the terminology, identifying the names and the properties of the superpartners becomes relatively straightforward. The superpartners of the standard model particles are summarized in Figure 6.

This all seems rather mad. And yet we've come across something very similar once already in the history of quantum and particle physics. There are precedents for this kind of logic. Recall that Paul Dirac discovered — from purely theoretical considerations — that for every particle there must exist an anti-particle. A negatively charged electron must be ‘partnered' by a positive electron. The positron was discovered shortly after Dirac's discovery, and anti—particles are now familiar components of the standard model.

The symmetry between particle and anti-particle, between positive and negative and negative and positive, is an exact symmetry. This means that a positron has precisely the same mass as an electron and is to all intents and purposes identical to an electron but for its charge. Similarly for all other particle—anti-particle pairs.

Figure 6
Supersymmetry predicts that every particle in the standard model must possess a corresponding superpartner. Matter particles — leptons and quarks (which are fermions) — are partnered by sleptons and squarks (bosons). Force particles (bosons) are partnered by bosinos (fermions), such as the photino, wino, zino and gluinos. The Higgs boson is partnered by the Higgsino.

But supersymmetry cannot be an exact symmetry. If the symmetry between fermions and bosons were exact, then we would expect the superpartners to have precisely the same masses as their standard model counterparts. In such a situation, we wouldn't be talking about assumptions, ideas or hypotheses, because our world would be filled
with selectrons and massless photinos.
^*
These super—particles (or ‘sparticles') would already be part of our experience. And, consequently, they would already form part of our theoretical models.

You can guess where this is going. The fact that the world is not already filled with superpartners that impress themselves on our experience and shape our empirical reality suggests that the exact symmetry between partners and superpartners no longer prevails. Something must have happened to force a distinction between the standard model particles and their superpartners. In other words, at some time, presumably shortly after the big bang, the supersymmetry must have been broken.

We assume that the superpartners gained mass in this process, such that they are all (rather conveniently) much heavier than the more familiar particles of the standard model, and have so far stayed out of reach of terrestrial particle colliders.

Cynicism is cheap, and not altogether constructive. It's certainly true that we seem to be building assumptions on top of assumptions.
If
superpartners exist then they
must
be massive. But, to a certain extent, suggesting that there must exist — from purely theoretical considerations — massive superpartners for every particle in the standard model is no different in principle to Dirac's discovery of antimatter.

Before we go on to consider what the MSSM predicts and how it might be tested, it's useful to review the potential of the theory to resolve many of the current problems with the standard model.

SUSY and the hierarchy problem

It is already apparent that one of the most compelling arguments in favour of SUSY is that it provides a perfectly logical, natural resolution of the hierarchy problem, at least in terms of stabilizing the electro-weak Higgs mass.

Recall from the last chapter that the hierarchy problem has two principal manifestations. There is the inexplicable gulf between the energy scale of the weak force and electromagnetism and the Planck scale. And then there is the problem that quantum corrections to the
Higgs mass should in principle cause it to mushroom in size all the way to the Planck mass, completely at odds with the electro-weak energy scale and recent experiments at the LHC which suggest a Higgs boson with a mass of 125 GeV.

At a stroke, SUSY eliminates the problems with the radiative corrections. The Higgs mass becomes inflated through interactions particularly with heavy virtual particles, such as virtual top quarks. The top quark is a fermion, and in the MSSM we must now include radiative corrections arising from interactions with its corresponding sfermion, the stop squark.

Now, I have very limited experience and virtually no ability as a mathematician. But what experience I do have allows me the following insight. If, when grappling with a complex set of mathematical equations, you are able to show that all the terms cancel beautifully and the answer is zero, the result is pure, unalloyed joy.

And this is what happens in SUSY. The positive contributions from radiative corrections arising from interactions with virtual particles are cancelled by negative contributions from interactions with virtual sparticles.
^*

The cancellation is not exact because, as I mentioned above, the symmetry between particles and sparticles cannot be exact. This is okay; the theory can tolerate some inexactness. However, force-fitting a light Higgs mass and broken supersymmetry does place some important constraints on the theory. Most importantly, the masses of many of the superpartners cannot be excessively large. If they exist, then they must possess masses of the order of a few hundred billion electron volts up to a trillion electron volts. Much heavier, and they couldn't serve the purpose of stabilizing the Higgs at the observed mass, and hence establishing the scale of the weak force and electromagnetism.

This has important implications for the testability of the theory, which I will go on to examine below.

SUSY and the convergence of subatomic forces

In 1974, Stephen Weinberg, Howard Georgi and Helen Quinn showed that the interaction strengths of the electromagnetic, weak and strong nuclear forces become near equal at energies around 200,000 billion GeV. The operative term here is ‘near equal'. As Figure 7(a) shows, extrapolating the standard model interaction strengths up to this scale shows that they become similar, but do not converge.

We tend to assume that the subatomic forces that we experience today are the result of symmetry-breaking applied to a unified electro-nuclear force shortly after the big bang. If this is really the case, then it seems logical to expect that the interaction strengths of these forces should converge on the energy that prevailed at the end of the grand unified epoch. Although this is a sizeable extrapolation — we're trying to predict behaviour at energies about 14 orders of magnitude beyond our experience — the fact that the standard model interaction strengths do not converge is perhaps a sign that something is missing from the model.