Rigorous results for the particle spectrum of lattice quantum chromodynamics moldels in the strong coupling regime

Author(s)

José Carlos Valencia Alvites

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação
• Defense date: 04 fev. 2016

Examining board members

Paulo Afonso Faria da Veiga; Christian Dieter Jakel; Washington Luiz Marar; Igor Mencattini; Rodrigo Bissacot Proença

• Advisor: Paulo Afonso Faria da Veiga

Abstract

In this thesis, using rigorous methods, we determine the low-lying energy-momentum spectrum of a lattice Quantum Chromodynamics model (QCD) in dimension 3 + 1, imaginary time and in the strong coupling regime. We consider a QCD model with the Wilson action, three quark avors and 4 X 4 Dirac spin matrices. Under these conditions, we reanalyze que question about the existence of baryon particles in the context of the Gell-Mann and Ne´eman Eightfold Way. Completing previous works, where the octet baryons where shown to exist, here we prove the existence of the decuplet baryons detected by showing the existence of isolated dispersion curves in the energy-momentum espectrum restricted to the subspace of the physical quantum-mechanical Hilbert H of the model, associated with states with an odd number of fermions. Besides, we obtain some smoothness properties veried by these curves, as well as analytical properties of the spectral measure for the two-baryon correlations. Also, the octet and the decuplet baryons are shown to be the only states in the odd subspace up to near the energy threshold of the meson-baryon bound state. Using the results obtained here, we can go up in the spectrum and validate some previously obtained results on the two-baryon bound state spectrum beyond the so called ladder approximation, for the complete model. (AU)

• FAPESP's process: 12/00156-8 - Rigorous results for the particle spectrum for Lattice Quantum Chromodynamics models in the strong coupling regime
• Grantee: José Carlos Valencia Alvites
• Support type: Scholarships in Brazil - Doctorate