Supersymmetry The predictions for the proton lifetime and the weak mixing angle, discussed in the previous lecture on grand unified theories, can be Incorporated in a proposed symmetry between bosons and fermions called supersymmetry. According to the supersymmetry, every known elementary particle has a supersymmetric partner (called a superpartner), which is has the same quantum numbers, except for its spin, and same interactions.
Spin-1/2 fermions, leptons and quarks have spin-0 superpartners, while spin-1 bosons, like photons, have spin-1/2 superpartners. The supersymmetric partners of fermions are named by adding a prefix ‘s’ to the name of the fermion, while the supersymmetric partners of the bosons are named by adding the ending ‘ino’ to the root of the normal name. This is illustrated in Table 12.1 on the next slide, where we list the various fermions and gauge bosons of the standard model, together with their superpartners.
The superpartners are collectively called superparticles, or sparticles for short. Supersymmetry (2) Supersymmetry (3)
The situation for the Higgs boson in Supersymmetry is more complicated, since if one simply associates a superpartner with the standard model Higgs boson, it can be shown that the theory becomes inconsistent, so supersymmetry requires additional spin-0 Higgs bosons, as well as their spin-1/2 superpartners, called Higgsinos.
The simplest version of supersymmetry is called the minimal supersymmetric standard model (MSSM) because it contains the minimum number of new particles that are required for a consistent theory. There are other, more complicated version of the supersymmetric theories, so supersymmetry is not a well defined theory: it is rather a concept or a framework for many different theories. MSSM which we discuss here has 5 Higgs bosons: three neutral and two charged spin-0 Higgs bosons, together with two neutral and two charged Higgsinos Supersymmetry (4) The photino, zino and the neutral Higgsinos and are all spin-1/2 particles that interact by electroweak forces only. They are expected to mix together in the same way as neutrinos, to form four new particles, called neutralinos. In similar way, the charged Higgsinos can mix with the winos to form four particles, called charginos.
A useful way to characterize particles in Supersymmery as particles or superparticles is to introduce a new quantum number, called R parity, defined as R ≡ (−1)3(B−L)+2S (12.13) where B is the baryon number, L is the lepton number and S is the spin. One can verify that all the particles of the standard model have R = +1, while the sparticles have R = −1.
R parity can be introduced in different versions of supersymmetric theory (not just in MSSM), and this quantum number also may be conserved or not in some supersymmetric theories. Supersymmetry (5) If supersymmetry were exact, a particle and its supersymmetric partner would have exactly the same mass. This is not realized in nature since superparticles would have been detected long ago. The masses of the predicted superparticles are unknown.
A very rough limit on the degree of symmetry breaking is suggested by the so-called hierarchy problem. From the theory of radiative corrections, theorists expect that the large quantum contributions to the square of the Higgs boson mass would make the Higgs mass huge, comparable to the scale at which new physics appears, unless there is a cancellation (called fine-tuning) between the quadratic radiative corrections and the bare Higgs mass. Supersymmetry provides an explanation on how a tiny Higgs mass can be protected from quantum corrections, since it removes the power-law divergences of the radiative corrections to the Higgs mass as long as the supersymmetric particles are light (see diagrams providing cancellations on the next slide). Unfortunately from such calculations, we get only an estimate on the masses of supersymmetric particles: and they are roughlexpected be of the order of 1 Tev. Many versions of the supersymmetric theories are is still in agreement with the LHC experiments. Supersymmetry (6) Supersymmetry (7) Supersymmetry theories have several other attractive features, such theories may provide us also with natural explanations for other needed BSM extensions related to cosmology. One of the arguments for the supersymmetry was that it may improve the trend of running constants of interactions so that they can cross in one point, see e.g. the schematical Figures below. It has been also shown that the lightest (and stable) supersymmetric particle may be a natural candidate for the dark matter. Supersymmetry also may provide us with more of the needed and still missing value of the CP asymmetry. The last two questions will be discussed in more details in the next lecture.
Strings Supersymmetry is an important component in even more ambitious schemes to unify gravity with the other forces of nature at superunification scale where gravitational interactions are comparable in strength with those of the grand unified strong and electroweak interactions. The problems here are mathematically formidable, not the least of them being that the divergences encountered in trying to quantize gravity are far more severe than those in either QCD or the electroweak theory, and there is at present no successful ‘stand alone’ quantum theory of gravity analogous to the former two. In order to resolve this problem, the theories that have been proposed invariably replace the idea of point-like elementary particles with tiny quantised one-dimensional strings, and for reasons of mathematical consistency are formulated in many more dimensions (usually 10, including one time dimension) than we observe in nature. Such theories have a single free parameter – the string tension. However, we live in a four-dimensional world and one possibility to explain this is that the extra dimensions are ‘compactified’, that is reduced to an unobservably small size, so we are interested in the low energy limit of such theories. Strings (2) Unfortunately the low energy limit which can be compared with experiments is not unique. String theorists have discovered that there are more than 104 possible low-energy theories that could be a low energy limit of the string theories, each corresponding to a universe with a different set of fundamental particles, interactions and parameters. Unless there is a method of choosing between the vast possibilities offered by this ‘landscape’, string theories have been criticized for having little or no real predictive power. Still they have generated a lively philosophical debate. One controversial philosophical approach to the question of choice has been to invoke the so-called ‘anthropic principle’. There are various forms of this, but essentially it states that what we can expect to observe must be restricted by the conditions necessary for our presence as observers. In other words, the world is observed to be the way it is because that is the only way that humans could ever be here to consider such questions Strings (3) The self-consistency of string theories in 10 dimensions lead to the the existence of higher- dimensional objects called branes (short for membranes). Using branes it is possible to construct an even more fundamental theory in 11 dimensions in which the supersymmetric string theories are unified. This theory has a name – M theory, but again despite mathematical beauty, and unfortunately again there seems to be no way to test experimentally the predictions.
The string theories seem to be relevant to energies defined by the so-called Planck mass MP , constructed from the known physics constants:
At this energy gravity is expected to become strong. This energy is so large that it is difficult to think of a way that the theories could be tested at currently accessible energies. The appeal of string theories at present is mainly the mathematical beauty and ‘naturalness’.
There are many connections though, accessible or even confirmed experimentally, between the particle physics and cosmology, which includes the current theory of gravity (general relativity). These connections will be discussed in the next lecture.