We Don't Understand High Energy Hadronic Physics

Lately, the story of high energy physics has been one ultra-precise confirmation of Standard Model predictions after another, interrupted occasionally by improved measurements of neutrino physics parameters.

Today, a short and very understated high energy physics preprint from the Belle collaboration measuring the exclusively hadronic branching fractions in two kinds of systems is a rare exception to that trend.  The abstract doesn't even mention the deviation between theory and experiment, and no conclusions or analysis in the short four page paper discusses why this discrepancy could arise.

The Experiments Conducted

Upsilon Decays

One system studied was the decay of two kinds of upsilon mesons (i.e. mesons composed of bottom quark and anti-bottom quark pairs), one more excited than the other, into one of seven combinations of pions, kaons, rho mesons and omega mesons.

Electron-Positron Decays

The other measured decays from an electron-positron annihilation into five different sets of mesons:

(1) a spin-1 (i.e. vector) omega meson with a quark content of (up anti-up plus down anti-down)/sqrt(2) and spin-0 (i.e. pseudo-scalar) neutral pion, with a quark content of (up anti-up minus down anti-down)/sqrt(2).

(2) a neutral vector kaon (down quark and an anti-strange quark) with a ground state 892 MeV mass and a neutral anti-kaon (a linear combination of the short kaon with a quark content of (down anti-strange minus strange anti-down/sqrt(2)), and the long kaon with a quark content of (down anti-strange plus strange anti-down)/sqrt(2))

(3) a negatively charged vector kaon with a ground state 892 MeV mass (a strange quark and an anti-up quark) and a positively charged kaon (an up quark and an anti-strange quark),

(4) an excited spin-2 vector kaon with an excited state 1430 MeV mass (a strange quark and an anti-up quark) and a neutral anti-kaon  (a linear combination of the short kaon with a quark content of (down anti-strange minus strange anti-down/sqrt(2)), and the long kaon with a quark content of (down anti-strange plus strange anti-down)/sqrt(2)), and

(5) a negatively charged excited spin-2 vector kaon with an excited state 1430 MeV mass (a strange quark and an anti-up quark) and a positively charged kaon (an up quark and an anti-strange quark).

The Results

For the most part, these measured branching fractions of the upsilon decays aren't greatly different from the theoretical QCD predictions in decay paths where there is enough data to provide a statistically significant result, although there were some tensions between the predicted values and measured values for

But, in the case of the electron-positron decays, the experimental results were grossly at odds with the perturbative QCD predictions.

In a model where SU(3) flavor symmetry is perfect, the ratio of decay path (2) above to decay path (3) above should be 2-1, and it should be 6-1 in a model where SU(3) flavor symmetry is broken.  Instead, the ratio of these decay rates was greater than 9-1 at the sqrt(s)=3.67 GeV energy scale and greater than 33-1 at the 3.773 GeV energy scale.

Other measured decay cross sections, at energies of sqrt(s)=10.52 Gev, 10.58 GeV and 10.876 GeV were similarly grossly at odds with the predictions of both the SU(3) perfect flavor symmetry model and of the SU(3) broken flavor symmetry model.  At 10.52 GeV there is a 7 sigma excess in decay channel (2).  At 10.58 GeV there is a 6.7 sigma excess in decay channel (1), and a greater than 10 sigma excess in decay channels (2) and (5).  At 10.876 GeV there is a 7.2 sigma excess in decay channel (2) and a 4.5 sigma excess in decay channel (5).

On the other hand, none of the six measurements of decay channels (3) and (4) were more than 2.1 sigma from the predicted values, and the 10.52 GeV value for decay channel (1) and (5) were not more than 2.1 sigma (there was no measurement of decay channel (1) at 10.876 GeV).

Thus, six data points are 4.5 sigma or more from the predicted values, while five data points are 2.1 sigma or less from the predicted values.  If the theoretical prediction was correct, we would expect an average deviation of 1 sigma.

Analysis

This result is grossly at odds with theoretical predictions.  This is particularly notable because the energy scales of these experiments are sufficiently high that they are in the range where perturbative QCD should not be materially inferior to lattice QCD predictions that are used at low (aka infrared) energy scales for pQCD breaks down.

The results have a "who ordered that?" character, as no leading beyond the Standard Model theory predicted this kind of gross discrepancy between theory and experiment.

Clearly, either something is seriously awry at the Belle experiment and causing huge systemic errors, or something is deeply flawed in the approach used to calculate the theoretical predictions for these decays.

This doesn't necessarily mean that new physics are necessary to solve the problem.  It could be that there is a flaw either in how perturbative QCD was applied, or in how perturbative QCD approximates the complete QCD calculations of the Standard Model in this context for some reason.

For example, perhaps there are intermediate decay paths to unknown linearly combined meson states that impact the decay cross-sections materially that QCD permits but which theorists have omitted in an oversimplifying assumption.

But, results like these do remind us that physicists have plenty to learn and discover, particularly when it comes to the hadronic physics of mesons, before they can claim to really understand QCD.