Introduction
The ultimate goal of particle physics is to discover the World Formula.

What is a World Formula?
The World Formula is a mathematical description of the smallest components
of matter (often called "elementary particles"). Besides describing the
smallest component of matter, it also contains the information about
their "interaction", i.e. what these smallest components do to each other.
Below there is an example of a small piece of the World Formula in our current
understanding (the World Formula is often called "L"):
The formula describes an electron (labeled "e^{}") that emits
a photon (a particle of light), labeled with "gamma"). The electron does not
change its nature while emitting the photon, but it stays an electron.
What the formula describes is also depicted right below: an electron comes from
the left, emits a photon, but stays an electron. This is actually the
experimentally observed behavior of electrons and photons. It happens e.g.
if a light bulb shines. Its just electrons emitting photons.

Is it clear that a World Formula exists?
No, this is not clear. However, the history of physics has shown us that
a mathematical description of nature is possible.
Therefore it is a common believe and hope that something like the
World Formula exists. Looking back at the history of physics, one can
see the following important steps towards something like the World Formula:

In the beginning, physicists discoved gravity, and somewhat later
electricity. It has been found that they can be described with the same
type of formula (but not really the same one).

Electricity and magnetism were discovered centuries ago. Later it was found that
they are actually two aspects/versions of the same thing, i.e. they
are described by the very same Formula (now called "electromagnetism").

Later electromagnetism and another force found in nature (see below)
were found to be described by the same Formula.

How can we find the World Formula?
A formula describing nature can be found in the following way:
In this way (in step D/agreement) a more and more advanced version
of the World Formula is being found.

What do we know about the World Formula so far?
Particle physicists have a quite good guess already about a World
Formula. It is a mathematical formula that describes all known smallest
particles (the "elementary particles") and what they do to each other
(the "interaction"). This formula is called the "Standard Model" of
particle physics.
The World Formula so far describes
 The smallest components of matter (elementary particles), the
so called quarks and leptons.
 There are six quarks in our world, called d, u, s, c, b, t quark.
 And there are six leptons in our world, too, called
e, mu, tau, e neutrino, mu neutrino, tau neutrino.
The normal world around us just contains three of all of these,
the u and d quark and the electron (e).
 The particles responsible for the force, the "interaction" of the
matter particles. These are
 the photon (responsible for the light, the electromagnetic force)
 the W and the Z particle (responsible for radioactive
decay)
 the gluon (responsible for holding the u and d quarks together
in the protons and neutrons that make up the atomic nucleus)
All above named particles are put together in this table:
 But the World Formula contains one more piece:
a mysterious particle that is needed to make the whole formula work,
the Higgs particle (named after its "inventor", Peter Higgs).
It is the Higgs particle that makes the other particles massive. If
it would not exist, the World Formula could only describe particles
with zero mass.
These are all the components of our current version of the World Formula.
It then looks something like this:
 The first piece again describes an electron emitting a photon.
 The second piece describes an u quark emitting a W. Here the u quark
changes its nature (as has been observed in experiments) and becomes a
d quark.
 The third piece describes the interaction of a W with the Higgs particle.
 The ellipses show that our current version of the World Formula
is actually somewhat longer.
This does not mean that all these things happen at the same time.
The World Formula just describes everything that can happen on the
level of the smallest components, on the level of elementary particles.
The one missing piece of the World Formula is the Higgs particle.
This particle is probably the most searched particle in the world,
it leads the "most wanted" list. Many physicists, involved in big
high energy experiments, are looking for traces of this particle.
However, so far they have not been successful. But the search goes on
right now at Fermilab (in Batavia, IL, USA). The search will then
be continued in 2007 at the CERN laboratory, Geneva, Switzerland.
This machine will either find the Higgs particle or rule out
its existence. In the first case, we would know that our current guess
about the World Formula was quite good. In the latter case, we would have
to make a quite new guess about the World Formula.

An improved guess about the World Formula: Supersymmetry
It is a common believe that our current version of the World Formula
is not the ultimate one. There are several reasons:
 Gravitation is not included.
 The Formula contains many (too many?) "free parameters".
(A "free parameter" is a constant parameter in the formula whose
value can only be determined in an experiment, but cannot be derived
from the formula itself.)
 Why are there so many quarks and leptons?
 How and why does the Higgs particle work?
 What is the Dark Matter made of that has been observed by
the astronomers in space?
(To be more explicit: astronomers have observed the movement of
galaxies that can only be understood if there is about 10 times
"more" than the galaxies itself.
This "more" must be some kind of particles that we do
not know yet. It is not contained in the stars or the planets. It must
be spread throughout the space; and it is not described by our
World Formula  yet.)
Many particle physicists believe that the road to a better understanding,
to road to the true World Formula involves a new idea, called
Supersymmetry (SUSY).
If the world would be supersymmetric, it would contain
 SUSY partners to all quarks and leptons, called squarks and sleptons.
 SUSY partners to all force particles
 SUSY partners to the Higgs particle
 not one Higgs particle, but at least five of them
None of the SUSY partners have been observed so far. (Because they are
too heavy?)
But these particles are being searched for right now at Fermilab
(in Batavia, IL, USA). The search will then (as for the Higgs)
be continued in 2007 at the CERN laboratory, Geneva, Switzerland.
If SUSY is the right way to the ultimate World Formula, we will learn
about it within the next 6 or 7 years.

How are we advancing the World Formula right now?
Particle physicists all over the world are currently working on improving the
World Formula.

Some physicists are searching for the Higgs or the SUSY particles (at
Fermilab or the CERN laboratory, see
above). They try to figure out what guess for the World Formula is correct.

Some others are trying to make new guesses of how a more advanced Formula
might look like and what their consequences could be (e.g. new particles
that can be searched for).

From time to time physicists from all over the world gather at a
conference, a big meeting and discuss their new findings.

New results are made public. They are presented at the conferences
and printed in journals.
All these different activities
bring us (every day) a tiny bit closer to the World Formula.
Sven
Heinemeyer
LMU Munich, Germany
Sven.Heinemeyer@cern.ch
