This paper makes mass predictions for a huge number of three and five valence quark hadrons (in both ground states and excited states) made by both traditional methods from the literature and AI models, producing multiple estimates by different methods for each hadron considered. It is mostly a pattern recognition exercise, rather than a set of calculations from QCD first principles. It predicts several hundred composite particle masses.
This is easier for baryons (i.e. half-integer spin fermions) than for mesons (i.e. integer spin bosons) because baryons have far fewer quirky exceptions to general rules that flow, in part, from different mesons blending into each other, which is something that baryons don't do.
One observation is that these several hundred heavy baryons (in the broad sense of half integer spin hadrons, rather than the narrow sense of three valence quark hadrons) fill a pretty narrow range of masses, with the lightest having a mass of about 1.5 GeV, the heaviest having a mass of 11.4 GeV, and most of the predicted masses bunching up in the middle, with more than 4 GeV and less than 10 GeV. The lightest pentaquarks are a bit over 4 GeV.
Given that there are only a handful of possible quantum numbers for each hadron, the experimental task of distinguishing one heavy baryon from another would be challenging, with many possibilities near any given mass.
While experimental mass measurement of heavy baryons typically have uncertainties of a few MeV, the uncertainties in the theoretical mass predictions are much greater. The theoretical uncertainties of the predictions range from about 100 to 2000 MeV, with most in the range of about 450 to 1200 MeV. The differences between theoretical mass predictions methods for the same hadron also frequently exceed the combined claimed uncertainties in the predictions, however, so the uncertainties are probably underestimated.
Since it is easy to make predictions if they are vague enough, which makes it easy for the predictions to be consistent with the experimentally observed values, the significance of these models shouldn't be exaggerated. They are making very ballpark estimates based upon very general considerations.
But because it is so comprehensive, this is still somewhat useful in winnowing down candidates for a particular observed resonance with a particular observed mass from several hundred possibilities to perhaps a few dozen likely candidates of similar mass, which can be narrowed down further with measurements of the resonances spin, charge, and other quantum numbers to perhaps a dozen or fewer candidates.
In this article, we use two different methods for studying the mass spectra of fully-heavy baryons and pentaquarks.
In the first section, we use state-of-the-art machine learning methods, such as deep neural networks and the Particle Transformer model architecture, to predict baryon masses directly from their quantum numbers, based on experimental information on hadrons from the Particle Data Group (PDG). We use this data-driven approach for the case of fully heavy baryons, and a large number of exotic pentaquark states, going much beyond the well-known P+c(4380) and $ P_c^+(4457) candidates. Subsequently, we extend the Gürsey-Radicati mass formula to incorporate the contributions of charm and bottom quarks, enabling analytical calculations for both ground and radially excited states of baryons and pentaquarks.
The results obtained from both approaches demonstrate strong agreement with experimental data where available and make predictions for a number of unobserved states, including higher radial excitations. By addressing the question through both data-driven prediction and analytical modeling in different frameworks, this study offers complementary insights into the mass spectrum of conventional and exotic hadrons, guiding future experimental searches.