[Paper Review] Baryons from Mesons: A Machine Learning Perspective

Yarin Gal, Vishnu Jejjala+2 more|arXiv (Cornell University)|Mar 23, 2020

Particle physics theoretical and experimental studies31 references4 citations

TL;DR

This paper proposes a machine learning framework that predicts baryon and exotic hadron masses using only meson spectroscopic data, employing neural networks and Gaussian processes. It achieves 90.3% and 96.6% accuracy respectively—surpassing the constituent quark model—demonstrating that baryons may emerge as solitons in a weakly coupled meson effective theory.

ABSTRACT

Quantum chromodynamics (QCD) is the theory of the strong interaction. The fundamental particles of QCD, quarks and gluons, carry colour charge and form colourless bound states at low energies. The hadronic bound states of primary interest to us are the mesons and the baryons. From knowledge of the meson spectrum, we use neural networks and Gaussian processes to predict the masses of baryons with 90.3% and 96.6% accuracy, respectively. These results compare favourably to the constituent quark model. We as well predict the masses of pentaquarks and other exotic hadrons.

Motivation & Objective

• To investigate whether machine learning models trained on meson spectra can predict baryon masses with higher accuracy than traditional quark models.
• To test the hypothesis that baryons arise as solitons in a weakly coupled effective theory of mesons, as suggested by large-N QCD.
• To extend predictions to exotic hadrons such as tetraquarks and pentaquarks, assessing model robustness across quark composition hypotheses.
• To compare the performance of neural networks and Gaussian processes in extrapolating from mesonic to baryonic and exotic states.
• To explore whether machine learning can uncover hidden patterns in hadron spectroscopy consistent with theoretical frameworks like the Gell-Mann–Okubo formula.

Proposed method

• The input vector consists of 13 features: quark/antiquark counts (u, d, s, c, b), isospin (I), spin (J), and parity (P), encoding hadron composition and quantum numbers.
• Neural networks are trained on meson data to generalize to baryons and exotic states, using a feedforward architecture with multiple hidden layers.
• Gaussian processes are applied as a non-parametric Bayesian method to model uncertainty and provide predictive distributions with confidence intervals.
• The models are evaluated on known baryon masses, pentaquarks, tetraquarks, and resonances like $a_0(980)$, testing different quark composition hypotheses.
• Performance is quantified using mean absolute error and accuracy metrics, with comparisons to the constituent quark model and lattice QCD benchmarks.
• Theoretical consistency is assessed by checking whether predictions align with known symmetries, such as degeneracy in proton and neutron masses or $^2$H$^+$ and $^2$He$^{++}$.

Experimental results

Research questions

• RQ1 Can machine learning models trained solely on meson data accurately predict baryon masses, surpassing the constituent quark model?
• RQ2 Do the predictions support the theoretical idea that baryons are solitons in a weakly coupled meson effective field theory?
• RQ3 How do different machine learning architectures—neural networks versus Gaussian processes—perform in predicting masses of exotic hadrons with ambiguous quark compositions?
• RQ4 Can the models discriminate between different quark composition hypotheses for resonances like $a_0(980)$ and $f_0(980)$, or do they yield degenerate predictions?
• RQ5 To what extent can machine learning uncover or validate theoretical relations such as the Gell-Mann–Okubo formula from empirical data?

Key findings

• The Gaussian process model achieves 96.6% accuracy in predicting baryon masses, outperforming the constituent quark model and showing lower uncertainty than neural networks.
• Neural networks achieve 90.3% accuracy in baryon mass prediction, with significantly lower variance in predictions compared to the Gaussian process.
• For tetraquarks, the Gaussian process provides better predictions than the neural network, despite assigning nearly identical masses across different composition hypotheses.
• The neural network successfully discriminates between quark composition hypotheses for resonances like $D^*_{s0}(2317)$ and $f_2(1565)$, identifying the mesonic configuration as closest to measured masses.
• The Gaussian process fails to distinguish between different composition hypotheses for $a_0(980)$ and $f_0(980)$, predicting nearly identical masses, suggesting a mesonic nature for these states.
• Both models predict nearly degenerate masses for the proton and neutron, and for $^2$H$^+$ and $^2$He$^{++}$, reflecting isospin symmetry in the training data.