We Still Don't Really Understand Scalar Mesons

From the introduction and conclusion of a new short preprint (abstract here) from the STAR collaboration:

Searching for exotic state particles and studying their properties have furthered our understanding of quantum chromodynamics (QCD). Currently the structure and quark content of f(0)(980) are unknown with several predictions being a qq state, a qqqq state, a KK molecule state, or a gluonium state. In contrast to the vector and tensor mesons, the identification of the scalar mesons is a long-standing puzzle. Previous preliminary experimental measurements on the yield of f(0)(980) at RHIC and theoretical calculation suggest that it could be a KK stat[e]. In this analysis, the empirical number of constituent quark (NCQ) scaling is used to investigate the constituent quark content of f0(980). . . .

The extracted quark content of f(0)(980) is n(q) = 3.0 ± 0.7 (stat) ± 0.5 (syst). More data are needed to understand whether f(0)(980) is a qq, qqqq, KK molecule, gluonium state, or produced through ππ coalescence.

In other words, we still really have no idea what a well established common, light scalar meson is made out of, despite decades of experiments and theoretical work by many independent collaborations and researchers. But, the authors somewhat favor a KK (kaon-kaon) state. As I note below, this is a sensible suggestion.

What Makes Sense?

Of the leading possibilities identified in the preprint, two of them, the KK molecule, and a qqqq state with a strange quark component, seem to make the most sense as an explanation for the f(0)(980) scalar meson. 

A process of elimination analysis to reach that conclusion is as follows.

Not Three Valence Quarks

The "best fit" value of the study, by the way, with three valence quarks (with a combined uncertainty of ± 0.86), can't be correct. 

A hadron with three valence quarks couldn't have spin-0 as the f(0)(980) does, although it could have either two or four quarks, which the results do not favor one way or the other. 

But, this preprint tends to disfavor either zero valence quarks, or a hexquark interpretation.

Not Gluonium a.k.a. a Glueball

The three quark result therefore disfavors pure gluonium state (with zero valence quarks). Also a glueball with the quantum number properties of this light scalar meson is predicted by QCD calculations to have a mass of about 1700 MeV, a value inconsistent with the 980 MeV of the f(0)(980), even allowing for a very significant uncertainty in this QCD calculation which is particularly prone to be accurate since fewer physical constant uncertainties are involved and there is a high degree of symmetry. In contrast, another observed scalar meson, the f(0)(1710) is a much better candidate for a pure or nearly pure glueball.

No Charm, Bottom Or Top Quark Component

The f(0)(980) can't have charm quark or bottom quark components because one such quark is much more massive than the meson as a whole, and can't have a top quark component because top quarks don't hadronize.

The Trouble With A Strangeless qq State

The trouble with a qq state without a strange quark component is that it isn't obvious why it would be so much more massive than a neutral pion qq state with no strange quarks, which has a mass of about 135.0 GeV. A charge pion mass is 139.6 MeV (2 times which is 279.4 MeV), so even a ππ molecule should have enough binding energy to approach 980 MeV.

But pions are the only known mesons with a known valence quark composition without a strange quark component. 

Also, there is the f(0)(500) scalar meson out there as well, the would be a more likely candidate for a ππ molecule or for a tetraquark with only up and/or down quarks and antiquarks as valence quarks than the f(0)(980).

The Trouble With Three Or More Pions

A ππ coalescence involving more than two pions would have six or more valence quarks, inconsistent with this paper's bottom line conclusion that there are probably either two or four valence quarks.

The Trouble With Strangonium (An ss State)

The only qq state that would make sense in terms of the f(0)(980) scalar meson's mass is strangonium (made up of a strange quark and an anti-strange quark), something which isn't observed experimentally unblended with up and anti-up, as well as down and anti-down components mixed with it. 

But, a pure strangonium meson ought to be a pseudoscalar meson rather than a scalar meson, if it existed (i.e. odd rather than even parity), since it is asymmetrical. 

The eta prime meson, a pseudoscalar meson with an equal mix of a uu, dd, and ss state, has a mass of 957.8 MeV which is in the right ballpark for the f(0)(980) potentially to have a strange quark component. 

The eta prime meson mass (and the kaon mass discussed below) also supports the intuition that a pure strangonium qq state, if it existed, might very well have a mass of more than 980 MeV, although this is not a very firm intuition.

The KK Molecule Possibility

A charged kaon (with an up quark and anti-strange quark or an anti-up quark and a strange quark) has a mass of 493.7 MeV (2 times which would be 987.4 MeV) and a neutral kaon (with a down quark and anti-strange quark or an anti-down quark and a strange quark) has a mass of 497.6 MeV (2 times which would be 995.2 MeV). 

So, if a KK molecule had some negative binding energy, these could be in the right mass ballpark. 

Both charged kaons and the "short" neutral kaon (which is usually observed blended with a "long" neutral kaon that does not decay to pions), like the f(0)(980), often decays to pions. A KK molecule is consistent with this paper's results, as it would also have four valence quarks. Officially the "short" kaon and "long" kaon are listed as having the same mass, but that is partially because the masses of the two states can't be determined experimentally in isolation from each other. If the "short" kaon were actually lighter than the "long" kaon, and an f(0)(980) were a molecule of a "short" neutral kaon and its antiparticle, that could be an even better fit.

A qqqq State With A Strange Quark Component

A tetraquark with the same quark composition as a KK molecule (i.e. a strange quark and an anti-strange quark, together with either an up quark and anti-up quark, or a down quark and an anti-down quark, or perhaps a mixture of both light quark anti-quark pairs), would also have the right number of valence quarks to be consistent with the paper's conclusion. And, the case for a tetraquark to have slightly less mass than a KK molecule is also very plausible.

See also my previous post from October 28, 2021.