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Supersymmetry physics on (and off) the brane

1 December 2000

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 (1019 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.All current major high-energy collider experiments are desperately seeking SUSY
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.

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