## Friday, March 7, 2014

### The Trouble With QCD (updated March 9, 2014)

A recent pre-print by Stephen Lars Olsen of Seoul National University sums up a major unsolved problem in quantum chromodynamics (QCD), the Standard Model theory that explains how quarks interact with each other via the strong force as mediated by gluons.

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 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.  As discussed at greater length in the section on meson oscillation below where I discuss baryon number violating neutron oscillation, the Standard Model QCD rule that baryon number is conserved has held up to intense experimental scrutiny (as has the Standard Model principle that lepton number is conserved).

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.

But, as explored below at greater length, there are also areas where QCD is falling short.  It predicts that exotic hadrons which are not observed are possible, while not easily explaining a variety of neutral quark-anti-quark states (and hadrons that look like them) called mesons where different combinations of particular kinds of quarks and antiquarks seem to blend ito each other.

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).

Standard Model QCD is sophisticated enough to deal with the variations from a simpler model seen in neutral quarks that can experience matter-antimatter oscillations to great precision.  But, Standard Model QCD still struggled to explain a spectrum of mesons that appear to be made up of various forms of "quarkonium" (i.e. mesons made up of a quark and an anti-quark of the same quark flavor) which blend into each other in ways not fully understood or easily predicted. A variety of competing theories seek to explain these phenomena after the fact within the context of QCD, but nobody predicted how this would happen in advance.

Matter-Antimatter Meson Oscillations: Weird But Understood

Oscillations of neutral mesons with their anti-particles is a phenomena of quantum physics that has been known since 1955. M. Gell-Mann and A. Pais, “Behavior of Neutral Particles under Charge Conjugation,” Phys. Rev. 97, 1387 (1955). This seminal paper observed that:
[W]ithin the framework of the tentative schemes under consideration, the θ0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes[.]
This prediction was experimentally confirmed for neutral kaons in 1956. K. Lande, E. Booth, J. Impeduglia, L. Lederman, and W. Chinowsky, "Observation of Long Lived Neutral V Particles", Phys. Rev. 103, 1901 (1956).

It turns out that there are at least two dominant means of blending the particle and anti-particle state of the neutral kaon, K0. One have a mixed bound state that is the sum of the particle and anti-particle state (divided by the square root of two), which is called the long kaon, or KL, or a mixed bound state that is the difference between the particle and the anti-particle state (divided by the square root of two), which is called the short kaon, or KS.

It isn't clear to me the extent to which particle and anti-particle states of D0, B0, and B0s mesons mix into long and short bound states with distinct lifetimes and decays, in the way that the K0 meson does. It could be that this is discouraged by the mass gap between the up and charm quarks in the neutral D meson (about 554-1), between the down and bottom quarks in the neutral B meson (about 871-1), and between the strange and bottom quark in the neutral strange B meson (about 44-1) relative to the gap between the down and strange quark in the neutral kaon (a ratio of about 17-22 according to the PDG) lead these neutral mesons to mix their particle and antiparticle states less strongly than the K0meson.

In addition to the K0 meson, there are three other mesons which are bound states of a quark and an anti-quark of different flavors, and a neutral electric charge, which oscillate between matter and anti-matter states of the meson: the D0 (i.e. neutral D meson, made up of a charm quark and anti-strange quark), the B0(i.e. neutral B meson, made up of a down quark and anti-bottom quark)(reported in H. Albrecht et al. (ARGUS collaboration), Phys. Lett. B 192, 245 (1987)), and the B0s(i.e. neutral strange B meson, made up of a strange quark and anti-bottom quark)(reported in A. Abulencia et al. (CDF collaboration), Phys. Rev. Lett. 97, 242003 (2006)). The last of these oscillations to be observed experimentally was in the D0, which was announced in a March 5, 2013 paper from LHCb. This announcement was the culmination of prior studies starting in 2007. As an author of that paper explained: "First evidence came from both the BaBar and Belle Collaborations in 2007, with further proof soon supplied by the CDF Collaboration and other additional measurements. A global combination of these pioneering results established the existence of these oscillations. Now, LHCb has presented the first clear observation based on a single measurement."

While these oscillations appear at the hadron level as a case of matter turning into anti-matter, the conventional explanation for this phenomena, as explained by an LHCb investigator is that this is actually a second order weak force interaction.

For example, in the case of the D0oscillation, what happens is that the charm quark oscillates into an up quark via an intermediate virtual down, strange or bottom quark, while the anti-up quark oscillates into an anti-charm quark via a virtual anti-down, anti-strange, or anti-bottom quark. Usually, when a quark emits a W boson causing a flavor change, the W boson decays democratically (i.e. with equal probability into all quantum number neutral, electric charge one shifting pairs of decay products that are energy permitted) before it can be absorbed by another quark. But, in this process there are two W boson exchanges within the neutral mesons between the chain of matter particles and the chain of anti-matter particles, so there are no W boson decay products.

In neutral meson oscillation, the sum of the masses of the particles in the hadrons in the initial state and end state have exactly the same masses, because quarks and anti-quarks have the same mass. Also, the initial and end state charges of the particles in the matter chain and in the anti-matter chain are the same. Likewise, no matter actually gets changed into anti-matter at any point in the process (even though it naively looks like it does), so each chain of interactions preserves baryon number perfectly, although they do change the quark flavor numbers of the meson by +1 and -1 respectively, for the quarks in question.

These meson to anti-meson oscillations are "weird", but they do occur at rates predicted by the Standard Model using constants derived from other weak force interactions with quarks pursuant to the relevant Feynman diagrams for the interaction.

As I have discussed previously, it isn't entirely clear (at least to me) if neutrino oscillation similarly involves a second order weak force process through a virtual charged lepton and a virtual pair of W bosons that can be illustrated with a Feynman diagram, much like the interactions involved in meson to anti-meson oscillations, or if this occurs by some other mechanism.

Charged mesons (and baryons) don't mix in this manner, although charged mesons (and baryons) can, in principle, exhibit CP violation (see this review article at 8), just as neutral mesons are observed to experimentally.

An Aside Re Baryon to Anti-Baryon Oscillations: They Don't Happen

In contrast, neutral baryons do not appear to oscillate between particle and anti-particle states.

Unlike neutral meson oscillations, which can be understood to involve mere quark flavor changes, rather than true matter-antimatter oscillations, and oscillations of neutrinos to other flavors of neutrinos (but not to anti-neutrinos), there is no possible weak force interaction that could turn the three matter particles of a matter baryon into the three anti-matter particles of an anti-matter baryon.  (There are no baryons which are their own anti-particles, so there are no simple baryon equivalents to quarkonium mesons discussed below.)

Thus, while meson to anti-meson oscillations appear to occur according to Standard Model flavor changing W boson processes, and observed neutrino oscillations could occur via the same processes, baryon to anti-baryon oscillations, even if they occur, could not occur in that manner.

The data tend to confirm the naive Standard Model prediction that neutral baryons (there are no baryons that are their own antiparticles) do not oscillate with their neutral baryon anti-matter counterparts, a process that would violate baryon number conservation.

A 1994 study determined that if neutron-neutron oscillations occurred at all, they the oscillation period was greater than 8.6*107 seconds (i.e. about two and a half years), even though the mean lifetime of a free neutron is about 881.5 +/- 1.5 seconds (i.e. about 14 minutes and 42 seconds). Thus, if the neutron oscillates into an anti-neutron state at all, it oscillates at a rate about 100,000 times as slowly as it decays in a free state (neutrinos bound in atomic nuclei are stable).  More recent studies have dramatically increased the extent of that bound, such as a 2002 study that concluded that oscillations of bound neutrons had a mean period of more than 1.3*10^8 seconds, which was increased to 2.7*10^8 seconds in 2007 at the SuperK experiment.  In contrast, as I understand the matter, all four of the oscillating neutral mesons have mean oscillation times on a similar order of magnitude to their mean lifetimes which are 10-8 seconds or less.

Neutron oscillation, like neutrino-less double beta decay, proton decay, flavor changing neutral currents, and other baryon number violating decays, are baryon number violating processes that are theoretically attractive in new physics theories for a variety of reasons (particularly related to cosmology).  But, very precise tests have again and again demonstrated that baryon number violating phenomena don't happen to the highest modern limits of experimental accuracy.

CP Violation In Oscillating Neutral Mesons: A More Weird Aspect Of Already Weird Particles

Even the rather complicated notion of neutral mesons with anti-particles actually involving mixed oscillation states with equal contributions of matter and antimatter components, is actually not quite right.

For example, neutral kaons do not actually oscillate from a matter to an anti-matter state at exactly the same rate as they oscillate back from an anti-matter state to a matter state.  So, the already hard to fathom "canonical" description of the kaon of a blend of the "short kaon" which is the difference between the matter and anti-matter state, and the "long kaon" which is the sum of the matter and anti-matter state, while much closer to the truth is not quite right.  The real blend is not 50% matter and 50% anti-matter, taken as either a sum or a difference, but a bit more than 50% matter and a bit less than 50% anti-matter.

This phenomena, called CP violation, which is quantified in the Standard Model by the CP violating phase of the CKM matrix, was first observed indirectly in neutral kaons (in 1964) and has also been observed directly, in each of the oscillating mesons: in neutral kaons since 1999, in the neutral B mesons since 2001, and in the neutral D mesons since 2011.  Reasonably accurate estimates of the magnitude of CP violation in B mesons (within a factor of three) based on the Standard Model equations and the CP violation parameter determined from indirect measurements involving neutral kaon decays were in existence by 1980, if not sooner.  At 2008 measurement by the Belle experiment that suggested a modest but statistically significant difference in the CP violation parameter for charged and neutral B mesons has not been born out by further experiments.

CP violation via the CKM matrix is the only process in the Standard Model in which an arrow of time is present fundamentally (CP violation is equivalent to treating processes that go forward and backward in time differently), as opposed to in an emergent statistical manner (the Second Law of Thermodynamics). And, even at the level of the most suppressed and rare types of D meson decays and CP violations observed as of 2013, the Standard Model prediction of their frequency has been confirmed.

As a 2013 review article at the Particle Data Group site explains.  CP violation has been observed experimentally, only at slight levels and only in the decays of a small subset of mesons:
CP violation has not yet been observed in the decay of any baryon, nor in the decay of any unﬂavored meson (such as the η), nor in processes involving the top quark, nor in ﬂavor-conserving processes such as electric dipole moments, nor in the lepton sector.
The article notes that in addition to the four types of neutral pseduo-scalar meson decays where CP violation has been observed, CP violation has also been detected at the five sigma level, at approximately the predicted amounts, in the decays of charged pseudo-scalar B mesons (i.e. mesons made of a bottom quark and an anti-up quark and visa versa).  The LHCb experiment first reported CP violation in charged B meson decays in 2012, a result that has been confirmed by the BaBar experiment in both existence and magnitude.

A 2012 effort to detect CP violation in charged D meson decays did not find it at even a two sigma level, with a result dominated by statistical uncertainty (i.e. basically, by an insufficiently large data set of charged D meson decays).  Efforts to find CP violation in the decays of baryons with charm quarks have likewise failed to reach statistical significance as of 2012.

CP violation has not been observed at this time in the decays of scalar, vector, or axial-vector mesons, or in excited meson states such as tensor mesons, or in any charged mesons other than pseudo-scalar charged B mesons.

In neutral kaons, the decay-rate asymmetry is only at the 0.003 level, although it is greater in neutral B mesons, where it is about 0.7 (it is also present in neutral D mesons, but this CP violation had not been documented definitively in time for inclusion in the article).  It charged B mesons it is about 0.2.

CP violation in baryons with bottom quarks, which has not yet been observed, is predicted to be on the order of one part per 10^5 or less.

It is possible that there is CP violation in neutrino oscillation as well, but this has not yet been definitively observed although the current experimental hints disfavor zero CP violation in neutrino oscillation and suggest that neutrinos may engage in CP violation more strongly than quarks.

The largest CP violating term in the Wolfenstein parameterization of the CKM matrix is multiplied by A*(lambda^3) in Vtd and Vub elements, by A*(lambda^4) in the Vts element, and by A^2*(lambda^5) in the Vcd element. The CP violating terms in other elements are at the lambda^6 order or less (lambda is roughly 0.23 and A is roughly the square root of two-thirds).  The fit of the single CP violating parameter to the observed CP violation in experiments is sufficiently tight to show on a model-independent basis that even if there is some other additional new physics source of CP violation in meson decays, that the CKM matrix CP violating phase is the dominant source of CP violation in those systems (from here at 2).

An Aside Re CP Violation and Matter-Antimatter Asymmetry In the Universe.

The observed level of CP violation is mysterious, however, because, while it exists in the Standard Model, the measured magnitude of CP violation in the Standard Model seems to be too small to explain the matter-antimatter asymmetry of the universe (at least involving baryons and charged leptons) assuming that (1) the universe began at the Big Bang in a pure energy state with no matter or anti-matter bias, (2) baryon number and lepton number are conserved as they are in the Standard Model except in rare high energy sphaleron processes, and (3) the basic outlines of the standard model of cosmology are correct (also here).

The Standard Model also cannot explain how the aggregate baryon number in the universe became non-zero or reached its current estimate value that is known to about one significant digit. We don't know the aggregate lepton number of the universe, the sum of B+L, or the difference B-L, because we don't know the relative proportion of neutrinos and anti-neutrinos in the universe. But, if there are more than a tiny fraction of a percent more neutrinos than anti-neutrinos in the universe, then L is not equal to zero, B+L and B-L have a large absolute value, and the absolute value of L is much greater than the absolute value of B. Very limited experimental hints to date tend to favor the existence of far more anti-neutrinos than neutrinos, which would imply a large negative value of L and B+L, and a very large positive value of B-L.

The Quarkonium Spectrum

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 are also notable for being particles that are their own anti-particles. If they did oscillate between particle and anti-particle states, the two states would be indistinguishable.

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 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 are resonances that are made up of bound states of oscillating mesons and anti-mesons, or of proton-antiproton pairs, that act like 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.
A recent review pre-print by Choi reaches the same conclusion as Olsen: Evidence for exotic hadrons predicted by QCD is absent; evidence for hadronic states that QCD has not anticipated (essentially the same ones, with some minor differences) is abundant and has not yet been well explained theoretically.

Time For A Breakthrough?

Implicit in Olsen and Choi'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.

Infrared QCD

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."  The issue is closely related to one of the current unsolved "Millenium Problems" in mathematics.

More generally, there are various competing models to explain the internal structure of hadrons, most of which are adequate for some purposes, but not others.  We still don't have a definitive single picture that is superior in all circumstances to describe hadron structure.

Similarly, while experiment confirms that quarks are fundamental and point-like down to scales as small as 10^-20 meters, this implicitly contradicts general relativity at sub-Planckian distances well below 10^-34 meters and we can't rule out the possibility that there is some sort of composite structure to the fundamental particles of the Standard Model, or that particles are something distinct from the space-time background, or that there might be discrete structure space-time itself, at the quantum gravity Planck scale or smaller scales.

Right now, there is a "desert" of new physics both over many order of magnitude below the scale of QCD, and also for many orders of magnitude above the electroweak scale to the "GUT scale".

At also appears that in the infrared, it also appears the gluons, which have zero rest mass in the Standard Model, acquire dynamical mass in an amount that is a function of their momentum (higher momentum gluons in low energy QCD have less dynamical mass).

This is quite odd, because usually, in the world of general and special relativity, particles with higher momentum acquire greater relativistic mass.  The behavior that we do observe in the case of massive gluons seems more like the macro-scale phenomena in which friction falls in faster moving objects thereby making them easier to push.

The Strong CP Problem

We still aren't sure if there are any deep reasons for the fact that no CP violation is observed in QCD interactions (the CP violations in neutral mesons described above involve weak force interactions), 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."  Experimentally, the strongest bound on the QCD constant that would give rise to strong CP violation comes from the measured value of the electric-dipole moment of the neutron.  The measured value is tiny and consistent with zero CP violation in strong force interactions.

Of course, like the hierarchy problem, the Strong CP problem is to some extent a presumptuous and philosophical problem.  We know what the laws of nature are in this case and can express that by stating that the value of a particular QCD constant is zero or very nearly zero, rather than a number on the order of one that those who view this as a problem would have presumed it would be.  Those who see this as a problem presume that there is some good reason that Nature shouldn't have made this choice and are arguing with Her over it.  Maybe there is a deep reason for this, but maybe the value of this physical constant is just one more law of nature and we are really just exposing our ignorance of the overall pattern when our expectations don't line up with reality in this case.

Very Difficult Calculations

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.  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 amplituhedron, to reduce the computational effort associated with these calculations.  Often, a variety of other simplifying tricks, from using pure "Yang-Mills theory" rather than the specific real world case of Standard Model QCD, or estimating physical outcomes by extrapolating from models using different masses or numbers of quark flavors than we see in the real world, are also used to approximate the impossible to solve exactly and directly equations of Standard Model QCD.

Discrepancies Between Theory and Experiment.

As I've noted previously, sometimes perturbative QCD predictions differ materially from observed results even at energy scales where it should be reliable.  This may simply be because the calculations are so hard to do right as explained above.  None of the discrepancies that seem to be present at this point involve cases where we are sufficiently confident of our calculations of the exact QCD prediction to be newsworthy at this point.

Other Lattice QCD points

Another review of the status of QCD and in particular Lattice QCD can be found here.  It notes success in estimating hadron masses, and the problem that theoretical uncertainty in QCD contributions is the biggest contributor to uncertainty regarding the magnetic moment of the muon which differs quite a bit in terms of standard deviations, but very little in terms of absolute amount, from the theoretically predicted value.

Conclusion

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.  But, few areas of the Standard Model have more wiggle room for beyond the Standard Model new physics.