snorkack said:
"Molecule" implies a bound system which, for the first, is bound largely by electrostatic force - but so are atoms - and which, in contrast to atoms, contains at least three bound particles of which at least two are "heavy".
This is not what the term "molecule" means in the context of systems of four or more quarks that have sub-system structure. As I explained above, while this expectation is a natural one for the what the term should mean, a hadronic molecule uses the term molecule in a manner that is a
false friend.
One common definition of the term
mesonic molecule is that:
A
mesonic molecule is a set of two or more
mesons bound together by the
strong force.
[1][2] Unlike
baryonic molecules, which form the nuclei of all elements in nature save
hydrogen-1, a mesonic molecule has yet to be definitively observed.
[3] The
X(3872) discovered in 2003 and the
Z(4430) discovered in 2007 by the
Belle experiment are the best candidates for such an observation.
So, all atomic nuclei are also hadron molecules, even though they, like many or all meson molecules, they are bound by the "residual strong force" rather than directly by gluonic interactions with each other that way that quarks and gluons within a simple hadron are bound.
In contrast, the term "molecule" is not applied to a purely electromagnetically bound system made up purely of leptons, such as
muonium which is commonly described as kind of
exotic atom (i.e. "an otherwise normal
atom in which one or more sub-atomic particles have been replaced by other particles of the same
charge. For example,
electrons may be replaced by other negatively charged particles such as
muons (muonic atoms) or
pions (pionic atoms).") rather than as a molecule.
To the extent that pionium is bound solely by the electromagnetic force, by definition, it is only an exotic atom and is not a meson molecule.
But, it does not appear to me that pionium is bound solely by the electromagnetic force as an atomic nucleus and the charged leptons associated with it are in a an atom, since its properties require consideration of
both QED and QCD terms, and since it does not decay to positively and negatively charged particles as it would have to in the absence of QCD terms. So, it isn't obvious to me that pionium isn't both an exotic atom and a meson molecule. I acknowledge, however, that I don't have an in depth understanding of the forces at work binding charged pions together into pionium.
snorkack said:
Does any wording of the new nomenclature exclude pionium from being a tetraquark?
While one could argue that
pionium should count as a meson molecule, a
2011 paper on the subject states that it is an exotic atom :
Pionium (A2π) is the π +π − hydrogen-like atom, with 378 f m Bohr radius, which decays predominantly into π0π0 . The alternative γγ [i.e. diphoton] decay accounts for only ∼ 0.4% of the total rate.
In particular, pionium is a subset of exotic atoms known as
hadronic atoms (in which the substitute particles are hadrons).
Pionium is also part of a subset of exotic atoms known as
onium:
An
onium (plural:
onia) is the bound state of a particle and its antiparticle. The classic onium is
positronium, which consists of an electron and a positron bound together as a
metastable state, with a relatively long lifetime of 142 ns in the triplet state. Positronium has been studied since the 1950s to understand bound states in quantum field theory. A recent development called
non-relativistic quantum electrodynamics (NRQED) used this system as a proving ground.
Pionium, a bound state of two oppositely-charged
pions, is useful for exploring the
strong interaction. This should also be true of
protonium, which is a proton–antiproton bound state. Understanding bound states of pionium and protonium is important in order to clarify notions related to
exotic hadrons such as
mesonic molecules and
pentaquark states.
Kaonium, which is a bound state of two oppositely charged kaons, has not been observed experimentally yet.
The true analogs of positronium in the theory of strong interactions, however, are not exotic atoms but certain
mesons, the
quarkonium states, which are made of a heavy quark such as the
charm or
bottom quark and its antiquark. (
Top quarks are so heavy that they decay through the
weak force before they can form bound states.) Exploration of these states through non-relativistic quantum chromodynamics (NRQCD) and
lattice QCD are increasingly important tests of
quantum chromodynamics.
Muonium, despite its name, is
not an onium containing a muon and an antimuon, because IUPAC assigned that name to the system of an antimuon bound with an electron. However, the production of a muon–antimuon bound state, which
is an onium (called
true muonium), has been theorized.
The preference for describing pionium as an atom rather than a molecule reflects my observation in Post #13 in this thread that:
The term "molecule-like" really primarily reflects the visual appearance of a diagram of its structure, rather than reflecting the exact nature of that structure.
But the distinction between a 2011 paper's use of the term "atom" and the frequent use of the term meson molecule in some more recent papers, may also reflect, in part, an evolution in the terminology in common use between 2011, when meson molecules were largely hypothetical while exotic atoms like muonium and muonic hydrogen were well known were more familiar, and the present, when there are numerous tetraquarks and pentaquarks that have been observed, some of which are meson molecule candidates.
The proposed
new naming rules for hadrons (mostly tetraquarks and pentaquarks) from the LHCb aren't particular clear about how one distinguishes a tetraquark or pentaquark from a hadronic molecule on their face. One needs to either look in the interpretative fine print of
the full paper, or resort to rules about what counts as a hadron that predate the new naming rules.
My understanding has been that a true (simple?) hadron is a composite particle directly by gluonic interactions with each other that way that quarks and gluons, while a hadron molecule is one that is bound instead by the "residual strong force", in which case pionium is not a tetraquark even if it is a meson molecule, since the terms tetraquark and pentaquark are usually reserved only for true simple hadrons as distinct from hadron molecules. But, I can't at this time find an authority to cite or quote that is squarely on point regarding this distinction.