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The brochure of the John von Neumann Institute for Computing
is available in English and in German. It can be ordered at the NIC secretariat
(nic@fz-juelich.de).
deutsche Broschüre (pdf) | English brochure (pdf)
 Elementary Particle Physics
The world as we see it today has a long history with a rather turbulent childhood. In its evolution
since the Big Bang it has passed through the cosmological phase transitions of the electroweak
theory and quantum chromodynamics (QCD). These phase transitions transformed the world
from one where the particles were massless and the quarks were free to the one in which we now
live with massive quarks and electrons and strongly bound proton and neutron states.
We believe that these complicated patterns can be explained by interactions
between only a small
number of constituent particles: the six quarks (up, down, strange, bottom, charm, top),
the three
leptons (electron, muon, tau) with their three corresponding neutrinos, and the
mediators of the
forces between them, the gluons, the photon and the W and Z bosons. It is one
of the fascinating
aspects of elementary particle physics that the plethora of physical phenomena observed in
experiments can be described by basically two kinds of interactions, the electroweak and the
strong interactions. Our theoretical description of these interactions is the Standard Model,
comprising the electroweak theory and quantum chromodynamics. It should not be forgotten that
the mysterious Higgs particle that is needed to make the Standard Model complete has still
escaped experimental detection. A particular role is played by the gravitational
force, for which a
consistent theoretical description on the quantum level has not yet been found.
Although the Standard Model can be analyzed by analytical tools such as perturbation theory,
many phenomena cannot be computed in this way. These are, for instance, the properties of the
cosmological phase transitions, the masses of the hadron bound states,
the masses of the quarks
and the strength of the strong coupling to give only a few examples.
The reason for these non-
perturbative phenomena is either the (spontaneous) breaking of a
symmetry as happens at a phase
transition (in very close analogy to the water-ice phase transition),
or the coupling of the model
becoming so strong that any kind of expansion in the coupling is rendered unreliable.
In 1974 Nobel laureate Kenneth Wilson suggested that our
standard continuum of space-time should
be replaced by a 4-dimensional grid of lattice points in order to study non-perturbative
phenomena. In this way, the problem can be made finite and the complicated equations
describing the interaction of the elementary particles can be solved on a computer.
In the late
1970s, Michael Creutz, following this approach, performed the first "computer experiments" in
which he showed that physical quantities of QCD can be evaluated using numerical simulation
techniques.
The success of these early simulations in simple models was followed by world-wide activity,
and more and more often when non-perturbative information is needed to interpret experimental
data, it is the lattice community that provides the relevant input. This
led lattice field theory to
become an integral part of theoretical high energy physics even including simulations of
supersymmetric theories.
However, it was also realized that in this "lattice approach" a number of
systematic errors have to
be controlled. For example, the initial discretization has to be removed
so that again we reach the
continuum theory ("continuum limit"). Hence, the mesh of lattice points has to be chosen finer
and finer, corresponding to more and more lattice points, thus rendering the simulation more
expensive. Other examples are the effects of a finite volume ("finite size effects") and the
extrapolation of the data to values of quark masses as estimated from experiments ("chiral
extrapolation"). The lattice community has developed a number of strategies to control such
systematic errors and is now ready to quote values for important physical quantities.
A major stumbling block remains, however: the sheer cost of the simulations.
The inherent
numerical problem is the solution of a set of linear equations with a
coefficient matrix that is of
the order of a million times a million and larger. During the simulation,
the coefficients change
and this large system has to be solved over and over again several thousand
times to obtain only
one single data point. As said above, when the mesh is made finer,
the system size even grows
leaving us with a real challenge for the numerical computations.
Fortunately, the models considered require only nearest neighbor interaction. This allows a
straightforward domain decomposition and a rather trivial parallelization of the problem. In
addition, the basic numerical ingredients are only floating point operations.
This suggests that,
first of all, massively parallel architectures are most suitable for lattice
simulations and, second,
that many features of highly developed general purpose machines may not
necessarily be needed,
for example, to generate the field configuration.
This triggered the development of specialized massively parallel computer architectures for
quantum chromodynamics simulations. One is the QCDOC machine (QCD on Chip) in the USA,
the other the APE machine (Array Processor Experiment) in Europe. At NIC, the specialized
APE computer (situated at DESY, Zeuthen) and the general purpose machines in Jülich are
exploited together in a symbiotic way in that different aspects of the numerical problems are
solved on these different architectures.
The progress in lattice field theory and the development of computer
architectures that today
have reached the multi-teraflops regime led to many physical results
that are increasingly finding
their way into the particle data booklet, the "bible" for high
energy physicists. Examples are the
value of the strong coupling, the quark masses, hadronic matrix elements,
form factors, the
glueball spectrum and even a random number generator. Another field
where lattice results are
essential is matter under extreme conditions, i.e. in heavy ion collisions
or neutron stars. Here,
the lattice provides quantitative information about, for example,
the critical temperature, the
pressure, and the particle spectrum. Thus, lattice results already play
a significant and important
role in the interpretation of experimentally obtained data. For a
selection of such results from
several groups in Germany, see the figures and their description.
In Germany, lattice physicists from more than 20 universities and research
laboratories founded a
Lattice Forum (LatFor) to discuss and coordinate the physics program, to
share the computer
resources and data and to identify the requirements of future simulations.
As a result it was found
that computer architectures in the multi-teraflops range are necessary to
implement the physics
program of the next few years. However, in order to provide precise numbers
and to understand
quantum field theory on a quantitative level, future machines that are able
to reach 100 and more
teraflops will be mandatory.
(Karl Jansen, NIC DESY-Zeuthen)
A section through a lattice showing a quark wavefunction density versus one
space and the time
axis of lattice. The quark wavefunction is strongly localized, which suggests
that it is correlated
with local topological objects of the lattice fields such as instantons or
monopoles. These objects
are believed to play an important role in the understanding of the confinement and chiral
symmetry breaking mechanisms.
(Source: Chi LF collaboration)
The phase diagram of strongly interacting particle matter as
function of temperature and baryon
number density is studied theoretically in lattice calculations
as well as experimentally in heavy
ion collision experiments at Brookhaven, USA (RHIC) and future
European accelerators at
CERN, Geneva (LHC) and the GSI in Darmstadt. Current
investigations of the phase diagram
suggest a strong dependence of the properties of the
transition on the baryon number density.
While the transition is a smooth crossover at low density
it is expected to be first order at high
density. The two regions are separated by a second order
transition point (critical point). In lattice
calculations the phase diagram is being intensively
studied in Germany by groups in Bielefeld
and Wuppertal.
The masses of the quarks are fundamental parameters of the Standard Model, but cannot be
measured directly by experiment. The plot shows data points for quark masses from lattice
simulations in the "quenched approximation". The label "light" denotes the
average of the up and
down quark masses. Green shaded areas show the error bands quoted by the particle data group,
also using techniques other than lattice calculations.
(Source: ALPHA collaboration)
Lattice results for the fields between a quark-antiquark pair.
Shown are a static quark q and
antiquark q¯, separated by a distance of about one fermi. The
figure on the left shows the color
electric flux lines, while the figure on the right shows the
(solenoidal) color magnetic monopole
currents. The picture leads to the interpretation of a dual
superconductor with condensed
monopoles. By means of the dual Meissner effect the electric
flux is constricted into a narrow
tube. The result is a linear confining potential between quark and antiquark.
(Gerrit Schierholz, DESY-Zeuthen, for the QCDSF collaboration)
The quantum mechanical vacuum generates and destroys virtual quark-antiquark pairs according
to Heisenberg's uncertainty principle. As a consequence, the narrow
flux tube is pulled to pieces,
as sketched in the left figure. Recently, the SESAM Collaboration demonstrated "string
breaking" by computing the crossing of the ground state and the
excited state potential, where the
gap at r/a=15 in the figure on the right is a clear signature for the
occurrence of dynamical string breaking.
(Thomas Lippert, NIC-ZAM, Jülich, for the SESAM Collaboration)
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