The discovery of the J/psi and upsilon families of new particles has had a
revolutionary effect upon particle physics. The rich array of states
observed with the psions and expected with the upsilons has given rise to
a new spectroscopy. This has encouraged the hope that heavy quark–antiquark
systems might serve as a "hydrogen atom" of hadron physics.
High-energy physics is concerned with the relativistic domain in which
particle creation and annihilation are routine. However it has frequently
been possible to find restricted situations in which nonrelativistic
quantum mechanics is useful. Some familiar illustrations are the
application of the Weisskopf–Wigner formalism to the mixing of short- and
long-lived kaons lnd the meson classification scheme lased on the
nonrelativistic harmonic oscillator model for quark–antiquark states.
Heavy quark-antiquark bound states —
experiment and theory: the left-hand side shows the observed spectra of
psions and upsilons (the psions labelled 13S1 and
23S1 correspond to the
J/ψ and ψ’). The right-hand side gives the predictions of a
non-relativistic quark-antiquark potential which behaves logarithmically.
In this picture, the level spacing between the ground state (1S) and the
first excited state (2S) is the same for psions and upsilons.
In scattering theory, nonrelativistic examples have been an important
source of inspiration for the relativistic domain. Regge poles, on which
the phenomenological description of high energy scattering is based, were
derived and understood in nonrelativistic theory and applied to the
relativistic problem by conjecture. Similarly, the Glauber multiple
scattering approach emerged from nonrelativistic theory and optics. With
the discovery of the psion and upsilon families, theorists are turning
again to nonrelativistic quantum mechanics for inspiration and
Candidate gauge theories of the
strong interactions (see November 1977 issue, page 380) suggest that the
between quarks is weak at short distances but becomes very strong at
large distances. This 'explains' the paradox where quarks appear to
behave as quasi-free particles
within hadrons but cannot be liberated from the hadrons. On the basis
of these arguments it was conjectured that heavy quarks would move nonrelativistically
within hadrons. Thus bound states of a heavy quark and
antiquark should be a hadronic analogue of the positronium system of a
bound electron and positron.
This so-called quarkonium system might then be interpreted according to
the familiar rules of nonrelativistic
quantum mechanics using a potential to describe the interquark force. An
explicit form for this potential has not yet been derived from the general
theory but forms for very short and very long distances can be suggested. At
very small distances, the potential is expected to take a form like the Coulomb
force, corresponding to the exchange of a single massless gluon. At very
large distances, a linear confining potential seems to be appropriate.
The first opportunity to test the applicability of atomic-physics ideas
to hadrons came with the discovery in 1974 of the J/ψ and ψ’,
which are long-lived by strong interaction standards. These particles
could readily be interpreted as the first two levels of a charm
quark–antiquark system. A natural starting point is to regard the
potential as a combination of the Coulomb and linear forms, and then to
vary potential strengths and the charmed quark mass to reproduce the
The masses of the psions are eigenvalues of the Schrödinger equation.
Another observable, the square of the charmonium wave function at the
origin, is measured by the leptonic decay widths of the spin-one levels
where the quark and antiquark have their spins pointing in the same direction.
In the quarkonium picture, the decay of a vector (spin one, negative
parity) meson into a lepton pair is described by the annihilation of the
quarks into a virtual photon, which subsequently decays into the lepton
pair. The rate of the process is governed by the probability for the
quarks to coincide, i.e., the square of the charmonium wave function at
Looked at from the left, this diagram represents the decay of a vector
meson, V0, into an electron and positron through an intermediate photon (wavy line). The
meson could be a psion, an upsilon, or any other heavy vector (spin one,
negative parity) particle. Looked at from right to left, the diagram shows
the production of the vector meson in an electron-positron collision, via
an intermediate photon.
Once adjusted to fit the J/ψ and ψ’ positions and
leptonic widths, the potential can predict the positions of other levels and rates
for radiative transitions among levels, along with other quantities. Many
of the predicted levels have been found with masses remarkably close to the
theoretical expectations. For those accustomed to a purely descriptive
hadron spectroscopy, this agreement supported the nonrelativistic
potential model approach. Inevitably, complications appeared in the form
of relativistic corrections, tensor forces, and coupled-channel
New opportunities arose with the discovery of the upsilon family. If these
particles are a heavier quarkonium family, the nonrelativistic approximation
should be more reliable than for the psions, because the new quark is
two or three times more massive than the charmed quark. The comparison of
the psion and upsilon families should provide an incisive probe of the
An elementary way to make this comparison is to exploit the variation in
behaviour due to different simple potentials. So far, the only data to
which these considerations can now be applied is the apparent equality of
the three lowest level spacings for the psion and upsilon families. This
disagrees with the prediction of the most popular charmonium potential,
but is reproduced instead by a logarithmic potential, which has been
adopted as a simple form useful for making predictions.
What lies ahead? Theorists are busily refining potential models and
calculating the potential from the presumed underlying field theory of the strong
interactions. Many useful
theorems can be proved and the use of special techniques to reconstruct
the potential from the data is an appealing dream. Experiment, of course,
will be the final arbiter of the value of the nonrelativistic approach.
With work continuing on the upsilon at Fermilab, DESY and the ISR, and
with the advent of higher energy electron–positron colliding beams at
PETRA, SLAC and CESR, the best is yet to come.