Exotic And Heavy Hadron Mass Predictions

A new paper uses an improved neural network method to estimate the masses of various exotic hadrons (i.e. tetraquarks and pentaquarks) and doubly charmed and bottomed three valence quark baryons. It achieves results comparable to a couple of other analytical QCD methods and significantly improves on prior neural network methods.

The paper illustrates that while it is possible to make "reasonable predictions" of hadron masses, most of the approximations are quite crude compared to the experimental data, and even state of the art and computationally demanding lattice QCD methods still only approach parts per two thousand claimed accuracy.

A cynical person could argue that this method is merely trend fitting and doesn't reflect the underlying QCD physics that give rise to the result in any theoretically justifiable way, but given the great uncertainties and immense calculation efforts that go into theoretically justified QCD calculations of hadron masses with current methods and the fact that this approach can distinguish between hadrons that some of the alternatives cannot, this shortcoming is excusable for the time being.

Another important shortcoming of this method, however, is that the uncertainty in the estimates is not well quantified, although comparing experimental results to the predictions made can allow for a reasonable guess as to its order of magnitude (1%-11%), which is indeed competitive with alternative approaches that are currently viable such as older neural network methods, the Gaussian process method, and a Constituent Quark model approach. Also, the claimed error of some of the other predictions is not consistent with the experimental results.

The tables reprinted below also compactly review the valence quark structure of these hadrons (notwithstanding the fact that there is not complete consensus on this point) and the literature measuring and estimating their masses.

Deviation of prediction from best fit experimental results in MeV:

X(3872)  -44.5

Z(3900)  189.1

Z(4020)  273.8

Z(4430)    42.0

Y(4260) -180.9

Y(4360) -477.4

Y(4660) -530.1

P(4312) -140.9

P(4440) -292.4

P(4457)   -91.4

Z(100610) -204.1

Z(100650) -81.4

In the one experimental result (below) that can be compared to its doubly charmed and bottomed baryons, the error relative to the best fit value is 52.5 MeV high (better than 2% accuracy). 

Where only lattice QCD predictions are available for doubly charmed and bottomed baryons, three of the seven best fit values are consistent at the two sigma level (or at least very close) with the lattice QCD predictions, which implies that this method has significantly more uncertainty than lattice QCD.

The paper and its abstract are as follows:

Recently, there have been significant developments in neural networks; thus, neural networks have been frequently used in the physics literature. This work estimates the masses of exotic hadrons, doubly charmed and bottomed baryons from the meson and baryon masses using neural networks. Subsequently, the number of data has been increased using the artificial data augmentation technique proposed recently. We have observed that the neural network's predictive ability increases using augmented data. This study has shown that data augmentation techniques play an essential role in improving neural network predictions; moreover, neural networks can make reasonable predictions for exotic hadrons, doubly charmed, and doubly bottomed baryons. The results are also comparable to Gaussian Process and Constituent Quark Model.

Huseyin Bahtiyar, "Predicting Exotic Hadron Masses with Data Augmentation Using Multilayer Perceptron" arXiv:2208.09538 (August 19, 2022).