Baryons, most prominent among them the proton
and the neutron, belong to the particle family of the
hadrons. They are made up of quarks, the last known
constituents of matter. The forces that determine their
behavior are described within Quantum
Chromodynamics (QCD). While QCD is solvable with
arbitrary precision for high energies, there are still no
satisfying solutions for middle and low energies. One
must resort to effective theories or models, and one
promising approach is relativistic constituent quark
models. The aim is to set up models for baryons that
allow for an effective description of their properties (like
mass) and reactions based on QCD, and in accordance
with all available experimental data for the low and
middle energy regime.
3.1. Constituent Quark Models
A typical CQM is based on a Hamilton operator, which
consists of a kinetic energy term and a quark-quark
interaction. The latter consists in turn of a confinement
and a hyperfine interaction. Finding appropriate
expressions for the interaction between quarks has been
the focus of interest for decades.
Quarks in nature are only found confined within
hadrons; in QCD this is known as confinement. The
form of the confinement potential depends on the model
used, but generally it increases when one tries to
separate two quarks.
The hyperfine interaction was first modeled by a
gluon exchange potential, which eventually failed to
reproduce the mass spectra of light and strange baryons:
One cannot model all excitation levels at the same time
to fit experimental data. Similar problems occurred
when modeling the hyperfine interaction with a
superposition of gluon and meson exchange [7], and
later on with the instanton-induced interaction. Some
years ago the Graz research group suggested a hyperfine
interaction based on the exchange of Goldstone bosons
[10, 5]. This model is well suited to reproduce the
ordering of energy levels by parity, better than the
models given above.
The models we chose for sonification exploration are
the Goldstone-Boson Exchange model, the One-Gluon
Exchange model, and for reference, a Confinement
model which does not include a hyperfine interaction.
3.2. Baryon Classification
Calculating baryon spectra is a typical few body
problem, which is solved in terms of relativistic
quantum mechanics. Here is a short explanation of the
quantum numbers of baryons, which classify baryon
states and determine its baryon wave function.
When visualizing the masses and thus the excitation
spectra of baryons, we use a classification scheme as in
Fig. 2. A baryon is characterized by a specific name,
which derives from the flavor F, a total momentum J,
and the parity P. A baryon state is thus called e.g.
N1/2+, meaning a nucleon with a total momentum of
1/2 and positive parity.
There are six flavors of quarks: up, down, strange,
charm, bottom and top. Up and down are very light,
strange is a little heavier, and the others are very heavy.
In Constituent Quark Models, mainly the baryons
consisting of light and strange quarks have been
investigated. The combination of three quarks with their
flavors determines the name of each baryon type: The
strange and light baryons can form nucleon N, delta A,
lambda A, sigma I, xi E and omega Q particles.
I....
Figure 2. Multiplet structure of the decuplet baryons
as one example of baryon flavor symmetries. The lowest
layer represents the sector of light and strange baryons.
The total momentum or Spin of a baryon always is a
multiple of 1/2, and the parity can be positive or
negative.
3.3. Initial Sonification Questions
While the basic properties of all these models can be
read and interpreted from baryon spectra, there are a
number of open research questions where we expect
sonification to be helpful. We have started by
identifying phenomena that are likely to be discernible
in basic sonification experiments:
Is it possible to distinguish e.g. the spectrum of an
N1/2+ nucleon from, a delta D3/2+ by listening only?
Is there a common family sound character for groups
of particles, or for entire models?
In the confinement model, the intentionally absent
hyperfine interaction causes data points to merge into
one: is this clearly audible?
3.4. Data Details
Three specially made data files have been used so far, all
of which contain mass spectra for nucleon and delta for
one model each: file 1 is from a Goldstone-Boson
exchange CQM, file 2 is from a One-Gluon exchange,
and file 3 from a Confinement model. Each data file is
made up of 20 lists, and each list refers to nucleon (or
delta) for one value of J^P. The data sets are different
lengths (22 - 2 entries), because we chose a mass limit
for each data file. While the total number of data points
is thus rather low, the interrelations and symmetries in
the data are quite complex. In the current experiments,
most of these symmetries are not portrayed yet.
The most interesting dimension to start with is that
of the mass differences, the level ordering. Because the
energy level of the nucleon in its fundamental state is
known to be 939 MeV in nature, one can shift all
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