PHYSICISTS often act as if they had the world of very tiny things more or
less wrapped up. Ask them what something is made of, and they will answer
confidently. Molecules are made of atoms, atoms are made of protons, neutrons
and electrons, and inside protons and neutrons lurk still smaller
particles鈥攖he quarks. But just because you know what something is made of
doesn鈥檛 mean that you understand it very well. After all, a living cell is made
of atoms and molecules, but that doesn鈥檛 say much about its structure鈥攐r
why it lives.
Subatomic particles such as protons and neutrons are a bit like cells,
too鈥攌nowing what they are made from is only a beginning. Quarks don鈥檛 sit
still inside a proton. They zip about at speeds approaching that of light, going
back and forth some 1023 times each second, and filling out a hazy, buzzing
cloud of action鈥攚hat we call the proton. Why is that cloud as big as it
is? And why does it weigh 1836 times as much as an electron?
The answers to these and other questions may quite literally lie trapped in
the bewildering mathematics of a theory called quantum chromodynamics (QCD), a
theory born in the 1970s and so a relative latecomer to the quantum world. Its
raison d鈥檈tre is to explain how quarks interact and come together to
form more complicated objects. Physicists believe that QCD might be a
staggeringly powerful and accurate theory鈥攊f only it wasn鈥檛 so complicated
that no one could solve its equations.
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But now researchers are finally making some progress using supercomputers and
a rather brutal mathematical trick. Their idea is to treat space-time, which
seems perfectly continuous to us, as if it were really a grid of discrete
points. This allows them to slap the equations of QCD on the world鈥檚 biggest
computers. By letting these computers run for many months, physicists are
finally getting a better picture of the weird interactions that take place
between quarks, and explaining why some particles are the size and weight they
are.
Even more exciting, this 鈥渓attice QCD鈥� approach is helping plot where exotic
new particles are likely to be discovered in the future.
Physicists have been driven to this seemingly desperate shredding of
space-time by the unruly nature of the strong force. As the glue that works
everywhere鈥攖ying quark to quark within protons and neutrons, and protons
and neutrons together within atomic nuclei鈥攊t is quite similar to the
electric and magnetic forces of everyday life. Physicists are confident that QCD
should鈥攅ventually鈥攑rove to be an excellent theory for the strong
force since its mathematical skeleton is modelled directly on that of quantum
electrodynamics (QED), the astonishingly accurate quantum theory of the
electromagnetic force.
QED views the force between two particles鈥攁 pair of electrons, for
example鈥攁s arising from the exchange of photons between the two. Particle
exchange also lies behind the notion of force in QCD, where two quarks interact
by trading photon-like particles called gluons. But there the similarity ends.
Inside a proton, where a trio of quarks flit about, QCD envisions a stormy
maelstrom of gluon lightning flashing to and fro and keeping the proton whole.
In contrast to the electrons and photons of QED, however, no one has ever seen a
free quark or gluon. Nature seems to have a kind of cosmic legislation against
them existing in their own right.
This difference is crucial, and it stems from a simple but profound feature
of QCD. Photons don鈥檛 carry any of the charge that creates electrical forces in
the first place. But in QCD, gluons do carry some of the same 鈥渃olour charge鈥� as
the quarks. This charge is the source of the strong force and is somewhat like
ordinary electrical charge, except that it comes in three different
types鈥攔ed, green and blue鈥攔ather than just one. Since gluons carry
colour charge, any pair of them can exchange gluons, just like a pair of quarks.
And these exchanged gluons can exchange still further gluons.
This proliferation of gluons prevents quarks and gluons from ever going off
on their own. In QED, an electron and positron generate a billowing electric
field between them that resembles the wings of a butterfly
(see Diagram, p 34).
Pull the particles apart and the field grows thinner, eventually breaking into
two haloes centred around now separated particles. In QCD, however, because the
fields (streams of gluons) carry colour charge, they create yet more fields
which create further fields.
These fields ultimately gather together into a 鈥渃olour flux tube鈥� that
stretches like an elastic band between the two particles and keeps them
together. Pull these particles apart and the vacuum simply churns up a new
quark-antiquark pair somewhere in-between. The band snaps, but the result is two
new quark-antiquark pairs connected by their own flux tubes, rather than free
quarks.
This determined stringiness is what makes the strong force strong, and is
also what makes QCD so hard to handle as a theory. In QED it is sensible to ask
what a free electron looks like, and straightforward to work out the answer.
When an electron moves through space it interacts with ghostly electron-positron
pairs and photons that pop in and out of existence all the time. These
interactions alter the electron鈥檚 behaviour. Even so, these 鈥渧acuum
fluctuations鈥� have only a minor influence on the electron鈥檚 properties so it is
not hard for physicists to include them.
But doing the same thing for a quark is a plain headache because in QCD the
effects of empty space are always huge. This is clear from the mere fact that
free quarks don鈥檛 exist. A quark鈥檚 interactions with the vacuum causes such a
commotion that its face is obliterated by a cloud of swarming gluons and other
quarks. We see only the enveloping cloud鈥攚hich appears as a proton, for
example, or some other 鈥渇undamental鈥� particle.
Because the vacuum in QCD is so messy, theorists trying to calculate
something like the mass of the proton have to include all sorts of complicated
interactions. Hence the need for supercomputers, which are now becoming so fast
that we can build new theoretical predictions on top of the sturdy scaffolding
of understanding that the basic structure of QCD already provides.
The bare framework of QCD can explain some very basic facts鈥攕uch as why
we see most of the particles that we do. According to the theory, only a group
of objects with no overall colour charge can exist on its own. Such colourless
clusters are called hadrons, and in QCD there are many ways to make colourless
clusters by mixing coloured quarks together.
Physicists know of six different kinds or 鈥渇lavours鈥� of quarks鈥攗p,
down, strange, charmed, bottom and top鈥攁nd so far, every one of the more
than a hundred hadrons discovered is made out of quarks of the first five
flavours. (The top quark is much heavier than the others, and decays into
lighter quarks as soon as it is formed.) Some of the known hadrons, such as the
proton, are called baryons and are made of a trio of quarks. Others, such as the
pion or the kaon, are called mesons, and are made from quark-antiquark
pairs.
Just three months ago, physicists from Fermilab, in Illinois, finally
succeeded in teasing enough information out of mounds of data to confirm their
sighting of the 鈥渓ast of the mesons鈥�. This elusive Bc meson contains a
charmed quark and a bottom antiquark, and is very energy-intensive to make
because its quarks are so much heavier than the more common up and down quarks
that occur in protons and neutrons. Mesons corresponding to all the possible
pair combinations of the five lightest quarks have now been found鈥攁nd this
classification of hadrons according to their quark content is a great victory
for QCD.
But the theory should tell us much more. We should be able to use it to
calculate the masses of all the hadrons and to examine what the quarks are doing
inside them. In the lattice QCD made possible by supercomputers, the quarks
exist only at the lattice points and the gluons only on the links between the
points. To calculate the mass of a hadron, theorists use this lattice to
simulate the seething quark-gluon gas of the vacuum. First, they generate
randomly a representative 鈥渟napshot鈥� of this vacuum which includes lots of
quark-antiquark pairs and gluons streaming about. Then, in the case of the
proton, the computer drops three quarks on the lattice and simulates their
movements and interactions according to the rules of QCD
(see Diagram, p 35).
Repeat this many times so that the calculations capture the 鈥渁verage鈥� behaviour
of the quarks, and the proton鈥檚 mass can be worked out.
Sounds simple. But doing it requires a huge amount of computation even on the
world鈥檚 speediest supercomputers. A lattice QCD calculation would take everyone
in the world, each doing one sum per second and working in unison, several
years. It takes supercomputers several months. Things can be speeded up by
simulating smaller regions of space, but the box has to be much larger than the
hadron you鈥檙e interested in, otherwise it will squeeze the particle unnaturally
and give an inaccurate answer for the mass. The spacing between points on the
lattice also has to be as small as possible because space-time is really
continuous.
Unfortunately, the size of the calculation grows with the number of points in
the space-time lattice. The only way to check whether the space-time region used
is big enough and the spacing small enough is to do a calculation, and then
repeat it with a larger region and smaller spacing and see if you get the same
result. That takes a lot of time. From recent calculations, it now seems that a
box about twice the diameter of a proton is usually adequate, if the lattice
points are one tenth of a proton鈥檚 width apart.
So does lattice QCD produce the right masses for the hadrons that we already
know? Does it give us a picture of what quarks are really doing inside those
particles? Sadly, running accurate lattice computations for the proton still
isn鈥檛 quite possible with today鈥檚 computers. Prohibitive computation time is
still the problem, and results obtained so far use the 鈥渜uenched approximation鈥�.
This is a mathematical gimmick that reduces computation time by a factor of
hundreds by ignoring the quark-antiquark pairs which can pop in and out of the
vacuum, and pretending that such things happen only with gluons. This is clearly
incorrect, and estimates show that it could contribute a 20 per cent error to
results. Computations for hadrons such as the proton or pion, which contain the
light up and down quarks, are most affected by this error, as most
quark-antiquark pairs in the vacuum are made of these quarks.
To reduce the error, physicists are testing QCD by calculating the properties
of slightly more exotic hadrons that are made of the heavy bottom or charmed
quarks. These can be produced in particle collision experiments at CERN, and
experimentalists have measured their properties. So they make nice test cases
for QCD.
Bottomonium, for example, is what you get by putting together a bottom quark
(b) and its antiquark 鈥�b, pronounced 鈥渂 bar鈥�. These can come together to
form a number of different mesons, depending on how they move relative to one
another. The simplest is known as the 鈥渦psilon鈥�. It has the lowest
energy鈥攁nd so the smallest mass鈥攂ecause the b and 鈥�b quarks
rotate about one another as slowly as is possible. Set these quarks rotating
more vigorously, and you get other mesons with larger masses. Using the rules of
QCD, lattice computations made by groups in Britain and the US in the past
couple of years can account for the masses of all these particles to an accuracy
of 10 per cent.
But there are other uses for lattice QCD. Since the particles we already know
are all made of either two or three quarks, it is natural to wonder whether
there might be more complex hadrons that we have yet to see. Some might have
more than three quarks, or have some gluons in them as well. Instead of a quark
and an antiquark, a particle might contain a quark, an antiquark and a gluon to
make what is called a hybrid. Then again, there could exist hadrons made purely
out of gluons, called glueballs.
Just as with ordinary hadrons, the objects within hybrids and glueballs
should be able to revolve around one another in all sorts of patterns, leading
to an abundance of particles. Physicists are now trying to use lattice QCD to
predict the precise properties of these 鈥渆xotic鈥� hadrons so they can identify
them by their signatures in experiments. Predicting the masses of such particles
before they are discovered would be an enormous triumph for lattice
QCD鈥攁nd for QCD per se.
The lightest glueball mass that theorists have found so far is slightly more
than one and a half times the mass of the proton. In 1996, researchers at CERN
found a particle called the f0 with a mass one and a half times that of
the proton, which seems to behave more like a glueball than anything else
(鈥淪tuck on a glueball鈥�, New Scientist,
15 February 1997, p 32 ). But
the theoretical result was obtained using the quenched approximation. As a
result, the predicted mass of the glueball is uncertain, and confirmation of its
discovery will have to wait for better calculations.
Two years ago, theorists in Britain and the US calculated the mass of the
lightest hybrid to be close to twice the mass of the proton, also using the
quenched approximation. Last summer, researchers at the Brookhaven National
Laboratory in the US announced what they believe is an exotic particle with a
mass less than one and a half times that of the proton. They found it by
studying the hadrons that come out of collisions between pions and protons. The
mass they find is worryingly smaller than the lattice calculations, although
more experiments are needed to be sure of the mass. And again, the quenched
approximation may be skewing the calculated mass.
At this point, all that is holding us back is want of a larger, faster
computer. There could be even stranger conglomerates of quarks and gluons
lurking out there. But we won鈥檛 know until we have managed to make the lattice
churn at much higher speeds.
