The search for supersymmetry, or other physics beyond the Standard Model (SM) is

becoming ever more tantalizing. The idea that the SM is theoretically incomplete is an old

one. There is now a whole range of innovative and experimentally striking suggestions for

this new physics that underlies the SM. A recent conference at CERN, Supersymmetry 2000,

surveyed the scene.

For all its spectacular experimental successes, the Standard Model (SM) fails to give us

solutions to such basic problems as why there are three copies (generations) of quarks and

leptons, why there are three different gauge forces (the strong, weak and electromagnetic,

with differing strengths), and how gravity should be included in a consistent quantum theory

along with the gauge forces.

Supersymmetry (SUSY) is the leading contender for

physics beyond the SM. Although SUSY has been around for some time and has so far had

no direct experimental support, indirect experimental hints and progress in understanding the

theoretical possibilities allowed for in a SUSY world have led to a new feeling of excitement.

With these new ideas on the market, the Supersymmetry 2000 (SUSY2K) conference, held

recently at CERN, attracted a large crowd and showed how the new SUSY ideas can

help.

SUSY makes precise predictions for the quantum numbers and selection rules for

many new particles. What is much more difficult is predicting the masses of these additional

supersymmetric particles. The reason for this is that SUSY must be a so-called “broken” or

hidden symmetry, and the mechanism of communication of SUSY breaking to the SM and

its superpartners is inevitably indirect, not well constrained, and is poorly

understood.

As a comparison, the unification of weak and electromagnetic gauge

forces in the electroweak sector is also “broken” or hidden – with the Higgs mechanism

leading to very different masses for the electromagnetic photon and the W and Z carriers of

the weak force.

For SUSY, such a direct coupling to the sector that breaks SUSY

(analogous to the direct coupling of the electroweak force to the Higgs) is not possible,

because such a coupling leads to sum rules for the masses of the unobserved superpartners

(see box) that are definitively excluded. Thus an indirect communication of SUSY breaking

must be employed.

### Mass communication

Many attractive new communication

mechanisms for SUSY breaking were reviewed at the SUSY2K conference. In “archetypal”

SUSY breaking, gravity takes on the role of communicating between the SUSY breaking

sector and the conventional world, and, until recently, this gravity-mediated SUSY breaking

was considered as the most plausible possibility.

However, during the last few years

many innovative new mechanisms have been proposed – “gauge mediation” (with heavy

messenger particles communicating the breaking), “anomaly mediation” (via symmetries that

are broken at the quantum but not at the classical level), and “gaugino mediation” (when the

SUSY partners of the SM gauge bosons take on the mediating role).

These different

mechanisms have characteristic mass spectra and experimental signatures. Supersymmetry

might not manifest itself as neutrino-like invisible events detectable only through “missing”

energy, but in several other ways, for example in events producing additional photons or

stable charged particles, or models with supersymmetric particles that are nearly degenerate

in mass. Experiments at LEP and elsewhere have been looking for these various possibilities,

but without any luck so far (see “Particles and sparticles” below).

### Particles and

sparticles

Standard Model (SM) particles come off the shelf in two kinds – fermions (matter

particles) such as quarks, electrons, muons, etc.) and bosons (force carriers) such as photons,

gluons, Ws and Zs. A feature of SUSY is that every matter particle (quark, electron…) has a

boson counterpart (squark, selectron…) and every force carrier (photon, gluon) has a fermion

counterpart (photino, gluino, chargino, neutralino…).

This doubling of the spectrum is

due to the fact that SUSY is a quantum-mechanical enhancement of the properties and

symmetries of the space-time of our everyday experience – such as translations, rotations and

Lorentz boosts.

SUSY introduces a new form of dimension – one that is only defined

quantum mechanically, and does not possess the classical properties we associate with a new

dimension, such as continuous “extent”.

The doubling of the particle population can fix

several of the problems afflicting today’s SM, for instance why the different forces – gravity,

electromagnetism, weak and strong – appear to operate at such vastly different and

apparently arbitrary scales (the “hierarchy problem”). The extra particles provided by SUSY

are also natural candidates for exotica such as the missing “dark matter” of the

universe.

### Problem solving

One of the theoretical motivations for these new

models is the “flavour problem”, namely that of understanding the relations between the

different generations of particles. Experiments observe many approximate flavour symmetries

in today’s non-SUSY SM; however, these symmetries are usually violated in typical

gravity-mediated SUSY breaking schemes.

Another motivation for some of the new

communication ideas (anomaly and gaugino mediation) has been provided by new ideas for

physics beyond the SM, such as extra dimensions beyond those accessible to us (see March p7) and multidimensional

“branes” (see Superstrings, black holes

and gauge theories; April 1999).

Many new ideas have also been stimulated by the

exact non-perturbative results that have allowed theorists to construct explicit models of

SUSY breaking, and motivated attempts to merge SUSY breaking with the visible particles.

One approach involves composite (sub-quark) models, where some of the SM states are

composites of a strongly interacting sector.

### Extra dimensions – are we the scum of

the universe?

A natural focus of the workshop was extradimensional models, in which the

world we experience is complemented by extra (but to us invisible) spatial dimensions. These

models have the common feature that our SM world is realized as localized degrees of

freedom living on a generalized 3-spatial-dimensional membrane (“3-brane”) embedded in a

universe possessing a larger number of dimensions.

In this approach, it is possible that

the fundamental scale of gravity might be the TeV scale, rather than the embarrassingly

distant Planck scale (10^{19} GeV), potentially eliminating the hierarchy problem

(see “Particles and sparticles”).

This requires a fundamental rethinking of cosmology

and the high-energy behaviour of SM physics. Many questions are being reformulated in

terms of the geometry of the extra dimensions – their sizes and shapes, and the fields localized

on them. In the same way that general relativity introduced geometry as the natural

explanation of gravity, so concepts of geometry and locality replace the ideas of symmetry

usually used in field theory.

Superstring theory naturally incorporates such branes and

gives, at least in toy models, explicit realizations of the brane-world idea. One major question

is the radiative stability of such models – that their predictions are compatible with

accompanying virtual quantum effects.

Without SUSY, the apparently haphazard

hierarchy of the different forces of nature, with each force having very different associated

mass scales, is not stable (or rather requires fine tuning). SUSY can take care of this problem,

and new light may be cast by brane physics.

At the moment there are two main

approaches to the construction of extra-dimensional models. Originally, it was thought that

the geometry of the extra coordinates should be distinct from our space – the universe at

large could be viewed as the product of two spaces. In this case, a solution to the hierarchy

problem requires large extra dimensions and quantum gravity physics at the TeV

scale.

In a more recent approach, highly-curved geometries have been proposed, which

tightly constrain the brane in which we live. In this very different geometry, gravity is

concentrated away from our world, explaining its observed weakness for us. Both schemes

have very specific signatures for experiments at high-energy colliders.

and/or extra dimensions. One of the crucial searches is for a Higgs boson: SUSY suggests

that one might well be visible at CERN’s LEP electron-positron collider.

Future

collider experiments are also gearing up to look for new particles. The Fermilab Tevatron will

resume the sparticle and Higgs searches after LEP is retired, and has quite good prospects. In

the longer run, the LHC is expected to produce Higgs bosons and any supersymmetric

particles. It will also be able to probe for extra dimensions at shorter scales than any previous

experiments. There is optimism that the next generation of collider experiments will break out

of the SM straitjacket.

The issue of the cosmological constant – the energy density of

free space – has been the most striking problem in quantum field theory for many years.

Experimentally, it has long been known that it is very close to zero. According to the latest

observations a (very) small non-zero value is now preferred, and this is further supported by

cosmic microwave background observations by the BOOMERANG and MAXIMA

collaborations.

However, the result of theoretical calculations in quantum field theory is

naturally a number at least 60 orders of magnitude bigger. SUSY has long held out the

promise of a resolution to this dilemma, but so far has not been able to claim a solution.

However, many new ideas of how to approach this problem are also suggested by brane

theories and were discussed at SUSY2K.

### Dark matter

If SUSY is correct then it

would have played an important role in the Big Bang. For example, SUSY might have

played a role in the generation of the observed matter in the universe. However, one of the

most important issues is that of possible SUSY remnants of the Big Bang, which could play

the role of the invisible “dark matter” known to pervade our universe. One of the most

attractive features of SUSY is that it provides quite naturally a candidate, the “neutralino”.

Experimental searches for such particle dark matter are just beginning to reach the range

suggested by theory. However, SUSY must also contend with the strong upper limits on

various unwanted supersymmetric particles such as gravitinos.

SUSY2K showed that

supersymmetry is assured of an exciting future.