In particle physics, quarkonium (from quark
and -onium, pl. quarkonia) designates a flavorless
meson whose constituents are a heavy quark
and its own antiquark, making it a neutral
particle and the antiparticle of themselves.
== Background ==
=== Light quarks ===
Light quarks (up, down, and strange) are much
less massive than the heavier quarks, and
so the physical states actually seen in experiments
(η, η′, and π0 mesons) are quantum mechanical
mixtures of the light quark states. The much
larger mass differences between the charm
and bottom quarks and the lighter quarks results
in states that are well defined in terms of
a quark–antiquark pair of a given flavor.
== Heavy quarks ==
Examples of quarkonia are the J/ψ meson (the
ground state of charmonium, cc) and the ϒ
meson (bottomonium, bb). Because of the high
mass of the top quark, toponium does not exist,
since the top quark decays through the electroweak
interaction before a bound state can form
(a rare example of a weak process proceeding
more quickly than a strong process). Usually,
the word "quarkonium" refers only to charmonium
and bottomonium, and not to any of the lighter
quark–antiquark states.
== Charmonium ==
In the following table, the same particle
can be named with the spectroscopic notation
or with its mass. In some cases excitation
series are used: Ψ' is the first excitation
of Ψ (for historical reasons, this one is
called J/ψ particle); Ψ" is a second excitation,
and so on. That is, names in the same cell
are synonymous.
Some of the states are predicted, but have
not been identified; others are unconfirmed.
The quantum numbers of the X(3872) particle
have been measured recently by the LHCb experiment
at CERN
. This measurement shed some light on its
identity, excluding the third option among
the three envised, which are :
a charmonium hybrid state;
a
D
0
D
¯
∗
0
{\displaystyle D^{0}{\bar {D}}^{*0}}
molecule.
a candidate for the 11D2 state;In 2005, the
BaBar experiment announced the discovery of
a new state: Y(4260). CLEO and Belle have
since corroborated these observations. At
first, Y(4260) was thought to be a charmonium
state, but the evidence suggests more exotic
explanations, such as a D "molecule", a 4-quark
construct, or a hybrid meson.
Notes:
* Needs confirmation.
† Predicted, but not yet identified.
† Interpretation as a 1−− charmonium
state not favored.
== Bottomonium ==
In the following table, the same particle
can be named with the spectroscopic notation
or with its mass.
Some of the states are predicted, but have
not been identified; others are unconfirmed.
Notes:
* Preliminary results. Confirmation needed.The
Υ(1S) state was discovered by the E288 experiment
team, headed by Leon Lederman, at Fermilab
in 1977, and was the first particle containing
a bottom quark to be discovered. The χb (3P)
state was the first particle discovered in
the Large Hadron Collider. The article about
this discovery was first submitted to arXiv
on 21 December 2011. On April 2012, Tevatron's
DØ experiment confirms the result in a paper
published in Phys. Rev. D.
== Toponium ==
The theta meson is not expected to be physically
observable, as top quarks decay too fast to
form mesons.
== QCD and quarkonia ==
The computation of the properties of mesons
in Quantum chromodynamics (QCD) is a fully
non-perturbative one. As a result, the only
general method available is a direct computation
using lattice QCD (LQCD) techniques. However,
other techniques are effective for heavy quarkonia
as well.
The light quarks in a meson move at relativistic
speeds, since the mass of the bound state
is much larger than the mass of the quark.
However, the speed of the charm and the bottom
quarks in their respective quarkonia is sufficiently
smaller, so that relativistic effects affect
these states much less. It is estimated that
the speed, v, is roughly 0.3 times the speed
of light for charmonia and roughly 0.1 times
the speed of light for bottomonia. The computation
can then be approximated by an expansion in
powers of v/c and v2/c2. This technique is
called non-relativistic QCD (NRQCD).
NRQCD has also been quantized as a lattice
gauge theory, which provides another technique
for LQCD calculations to use. Good agreement
with the bottomonium masses has been found,
and this provides one of the best non-perturbative
tests of LQCD. For charmonium masses the agreement
is not as good, but the LQCD community is
actively working on improving their techniques.
Work is also being done on calculations of
such properties as widths of quarkonia states
and transition rates between the states.
An early, but still effective, technique uses
models of the effective potential to calculate
masses of quarkonia states. In this technique,
one uses the fact that the motion of the quarks
that comprise the quarkonium state is non-relativistic
to assume that they move in a static potential,
much like non-relativistic models of the hydrogen
atom. One of the most popular potential models
is the so-called Cornell (or funnel) potential
V
(
r
)
=
−
a
r
+
b
r
{\displaystyle V(r)=-{\frac {a}{r}}+br}
where
r
{\displaystyle r}
is the effective radius of the quarkonium
state,
a
{\displaystyle a}
and
b
{\displaystyle b}
are parameters. This potential has two parts.
The first part,
a
/
r
{\displaystyle a/r}
corresponds to the potential induced by one-gluon
exchange between the quark and its anti-quark,
and is known as the Coulombic part of the
potential, since its
1
/
r
{\displaystyle 1/r}
form is identical to the well-known Coulombic
potential induced by the electromagnetic force.
The second part,
b
r
{\displaystyle br}
, is known as the confinement part of the
potential, and parameterizes the poorly understood
non-perturbative effects of QCD. Generally,
when using this approach, a convenient form
for the wave function of the quarks is taken,
and then
a
{\displaystyle a}
and
b
{\displaystyle b}
are determined by fitting the results of the
calculations to the masses of well-measured
quarkonium states. Relativistic and other
effects can be incorporated into this approach
by adding extra terms to the potential, much
in the same way that they are for the hydrogen
atom in non-relativistic quantum mechanics.
This form has been derived from QCD up to
O
(
Λ
QCD
3
r
2
)
{\displaystyle {\mathcal {O}}(\Lambda _{\text{QCD}}^{3}r^{2})}
by Y. Sumino in 2003. It is popular because
it allows for accurate predictions of quarkonia
parameters without a lengthy lattice computation,
and provides a separation between the short-distance
Coulombic effects and the long-distance confinement
effects that can be useful in understanding
the quark/anti-quark force generated by QCD.
Quarkonia have been suggested as a diagnostic
tool of the formation of the quark–gluon
plasma: both disappearance and enhancement
of their formation depending on the yield
of heavy quarks in plasma can occur.
== See also ==
OZI Rule
