Most of QCD is just fine. The spectrum of observed three quark baryon states, and of two quark meson states involving quarks of different flavors, largely matches the simple naive QCD expectation. The proton mass has been calculated from first principles to more than 1% accuracy. The strong force coupling constant at the Z boson mass is known to a four significant digit accuracy, and estimates of the masses of the top, bottom, and charm quark are improving in precision greatly compared to just a few years ago.
There is also no trouble on the horizon with our understanding of how QCD is involved in the nuclear binding force within atoms. There are, however, theoretical discussions of a couple of alternative understandings of it that implicate the meson spectrum issues discussed below. Traditionally pions have been tapped as the force carrier between protons and neutrons, but now, other light scalar mesons such as scalar meson f(500) have been suggested as alternative carriers of the residual nuclear force between nucleons in an atom.
Missing Exotic States Predicted By QCD
Current experiments have allowed us to observe hadrons up to 10 GeV. But, many "exotic" states that QCD naively seems to allow in the mass range where observations should be possible (including less exotic predicted quarkonium states discussed in the next section), have not yet been detected.
There have still not been definitive sighting of glueballs, of tetraquarks, of pentaquarks, or of H-dibaryons. The implication of our failure to see them despite the fact that QCD predicts their existence and properties with considerable precision, is that we may be missing a solid understanding of why QCD discourages or highly suppress these states. Such QCD rules might be emergent from the existing QCD rules of the Standard Model in a way that we have not yet understood, or it could reflect something missing in those equations or in the other rules of the Standard Model that are used to apply them.
Similarly, no well established resonances have JPC quantum number combinations (total angular momentum, parity and in the case of electrically neutral mesons, charge parity) that have no obvious source in any kind of quark model with purely qq mesons. In the case of hypothetical mesons with J=0, 1 or 2, these are the JPC quantum numbers: O--, O+-, 1-+ and 2+- to name just those with J=0, 1 or 2. As one professor explains: "These latter quantum numbers are known as explicitly exotic quantum numbers. If a state with these quantum numbers is found, we know that it must be something other than a normal, qq¯ meson." At higher levels of integer J, the combination +- is prohibited for even integer values and -+ is prohibited for odd integer values. These combinations might be created by bound states of a quark, antiquark and a gluon, each of which contribute to the J, P and C of the overall composite particle that are called "hybrid mesons" and are not observed. Lattice QCD has calculated masses, widths and decay channels for these hybrids, just as it has for glueballs (aka gluonium).
But, these well defined and predicted resonances are simply not observed at those masses in experiments, suggesting that for some unknown reason, there are emergent or unstated rules of QCD that prohibit or highly suppress resonances that QCD naively permits such as gluonium (aka glueballs), or hybrid mesons, or true tetraquarks or true pentaquarks, or H-dibaryon states (at least in isolation, as opposed to blended with other states in linear combinations that produce qq model consistent aggregate states).
A few resonances have been observed that are probably "meson molecules" in which two mesons are bound by residual strong force much like protons and neutrons in an atomic nucleus, however, have been observed. This is the least exotic and least surprising of the QCD structures other than plain vanilla mesons, baryons and atomic nuclei observed to date, since it follows obviously from the same principles that explain the nuclear binding force that derives from the strong force mediated by gluons between quarks based on their "color charge."
Not very surprisingly, because top quarks have a mean lifetime an order of magnitude shorter than the mean strong force interaction time, mesons or baryons that include top quarks have not been observed. Still, the mean lifetime of the top quark is not so short that one wouldn't expect at least some highly suppressed top quarks to briefly hadronize when they end up in rare cases having lives much longer than the mean lifetime, so while the suppression of top hadrons is unsurprising, the magnitude of that suppression is a bit of a surprise.
Surprising Meson Spectrums
Meanwhile, many mesons have been observed whose quantum numbers, decay patterns, and masses taken together are not a good fit for simple models in which mesons are made up of a particular quark and a particular anti-quark which have either aligned spins (and hence have total angular moment J=1 called vector mesons) or oppositely aligned spins (and hence have total angular momentum J=0 called pseudoscalar mesons).
The spectrum of quarks with a quark and anti-quark of the same type, called quarkonium, are particularly problematic.
These states were already the subject to an exception to the usual QCD rules governing hadron decay. We know that quarkonium states are usually suppressed in hardonic decays, due to the Zweig rule, also known as OZI suppression, which can also be stated in the form that "diagrams that destroy the initial quark and antiquark are strongly suppressed with respect to those that do not."
Quarkonium mesons easily blend into linear combinations with each other because (1) bosons can be in the same place at the same time, and (2) they have similar quantum numbers because all quarkonium mesons have zero electric charge, baryon number (quarks minus antiquarks), isospin (net number of up and down quarks and up and down antiquarks), strangeness (net number of strange and antistrange quarks), charm number (charm quarks minus charm antiquarks) and bottom number (bottom quarks minus bottom antiquarks).
There are no mesons that appear to have a purely uu, dd or ss composition. The neutral pion, the neutral rho meson, and the neutral omega meson are believed to be linear combinations of uu and dd mesons (the omitted one of four simple combinations of uu and dd may be a scalar meson). The eta meson and the eta prime meson are believed to be linear combinations of the uu, dd and ss mesons. Many of the lighter scalar and axial-vector meson states without charm or bottom quarks are also presumed to include linear combinatons of uu, dd, and ss quarkonium mesons. There have been proposed nonets of scalar mesons that are chiral partners of the pseudoscalar mesons, for example, although the issues of the quark compositions of these true scalar mesons is not well resolved.
The only meson in which a meson with a quark and anti-quark of different flavors are prominently described as being linear combinations of different combinations states is the neutral kaon made of a strange quark and anti-down quark or visa versa, with the particle and anti-particle added in the long form and subtracted from each other in the short form of this meson. This is a case where the hadron and its antiparticle have the same values for J, P and C, and it has a neutral electric charge and is a boson. But, unlike quarkonium, they differ in the sign of their isospin and strangeness. There may be other cases of linearly combined states with no single dominant qq pair when the quarks have different flavors, like the kaon, but I haven't heard of them.
The large masses of charm and bottom quarks relative to the non-quark "glue" mass of mesons makes it harder for the quark content of charmonium and bottomonium-like states to remain ambiguous. These mesons are called XYZ mesons. But, they continue to show signs that they may be mixings of quarkonium states, rather than always being composed of a simple quark-antiquark pair of the same flavor of quark There are about seven charmonium-like states that have been discovered that were not predicted by QCD, and a like number of such states that are predicted to exist but have not been observed. Bottomonium states present similar issues. The XYZ mesons have JPC quantum numbers of 0-+ (pseudo-scalar), 0++ (scalar), 1-- (vector), 1+- (pseudo-vector) and 2++ (tensor) in their J=0, 1 and 2 states. Mesons with combinations 1++ (axial vector) and 2-+ and 2-- are also theoretically permitted.
There are even some indications that there is a resonance that is made up of a proton-antiproton pair that is acting like a quarkonium mesons.
There are competing theories to describe and predict these quarkonium dominated meson spectrums.
Mr. Olsen concludes by stating that:
The QCD exotic states that are much preferred by theorists, such as pentaquarks, the H-dibaryon, and meson hybrids with exotic JPC values continue to elude confirmation even in experiments with increasingly high levels of sensitivity.
On the other hand, a candidate pp bound state and a rich spectroscopy of quarkoniumlike states that do not fit into the remaining unassigned levels for cc charmonium and bb bottomonium states has emerged.
No compelling theoretical picture has yet been found that provides a compelling description of what is seen, but, since at least some of these states are near D(*)D* or B(*)B* thresholds and couple to S-wave combinations of these states, molecule-like confi gurations have to be important components of their wavefunctions. This has inspired a new field of flavor chemistry" that is attracting considerable attention both by the experimental and theoretical hadron physics communities.Time For A Breakthrough?
Implicit in Olsen's discussion is the recognition that we have a sufficiently large body of non-conforming experimental evidence that we may be close to the critical moment where some major theoretical break through could in one fell sweep explain almost all of the data that is not a clean fit for existing QCD models with some sort of paradigm shift.
Other Issues with QCD
There are other outstanding issues in QCD beyond those identified by Olsen's paper. A few of these follow.
As I've noted previously, sometimes perturbative QCD predictions differ materially from observed results even at energy scales where it should be reliable, perhaps simply because the calculations are so hard to do right.
The infrared (i.e. low energy) structure of QCD that can be explored only with lattice QCD is also sometimes mysterious with different methods producing different results. Particularly important is the question of whether the QCD potential reaches a theoretical zero at zero distance, or has a "non-trivial fixed point." In the infrared, it also appears the gluons acquire dynamical mass.
We still aren't sure if there are any deep reasons for the fact that no CP violation is observed in QCD despite the fact that it is a chiral theory and that there is a natural term for it in the QCD Lagrangian. This is called the "strong CP problem."
Meanwhile, even basic QCD exercises like estimating a hadron's properties from its components, when they are well defined, suffers from issues of low precision, because while it is possible to measure observable hadron properties precisely, it is very hard to do QCD calculations with enough terms to make the theoretical work highly precise, and this in turn leads the values for input parameters like the strong coupling constant and quark masses to be fuzzy as well. Recent progress has been made, however, in using new calculation methods like Monte Carlo methods and the amplitudeheron, to reduce the computational effort associated with these calculations.
While QCD has not yet definitively failed any tests of the Standard Model theory, and instead, has been repeatedly validated, it has also been subject to much less precise experimental tests than any other part of the Standard Model. The absence of any really viable alternative to QCD has been key to its survival and lack controversy in beyond the Standard Model physics discussions.