Comprehensive mass predictions: from triply heavy baryons to pentaquarks

Abstract 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 $$P_c^+(4380)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4380</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and $$P_c^+(4457)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4457</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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.