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Doctoral Thesis
DOI
10.11606/T.55.2016.tde-09092016-144325
Document
Author
Full name
José Carlos Valencia Alvites
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Veiga, Paulo Afonso Faria da (President)
Jakel, Christian Dieter
Marar, Washington Luiz
Mencattini, Igor
Proença, Rodrigo Bissacot
Title in English
Rigorous results for the particle spectrum of lattice quantum chromodynamics moldels in the strong coupling regime
Keywords in English
Applied analysis
Energy-momentum spectrum
Mathematical physics
QCD
Spectral analysis
Abstract in English
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.
Title in Portuguese
Resultados rigorosos para o espectro de partículas de modelos de cromodinâmica quântica na rede, no regime de acoplamento forte
Keywords in Portuguese
Análise aplicada
Análise espectral
Espectro de energia-momento
Física-Matemática
QCD
Abstract in Portuguese
Nessa tese, usando métodos rigorosos, determinamos a parte inicial do espectro de energia-momento para o modelo de Cromodinâmica Quântica (QCD) na rede, em dimensão 3 + 1, com tempo imaginário e no regime de acoplamento forte. Consideramos o modelo de QCD com a ação de Wilson, três sabores de quarks e matrizes de spin de Dirac 4 X 4. Sob estas condições, reconsideramos a questão da demonstração da existência de bárions, no contexto do Eightfold Way de Gell-Mann e Ne ´eman. Complementando trabalhos anteriores onde a existência dos octetos de bárions foi demonstrada, aqui demonstramos a existência dos decupletos de bárions. Estas partículas são detectadas através de curvas de dispersão isoladas no espectro de energia-momento do modelo, considerando-se o subespaço H0, do espaço de Hilbert (quântico) físico H, com vetores com um número ímpar de férmions. Além disso, obtemos propriedades de suavidade destas curvas, assim como propriedade analíticas da medida espectral da correlação de dois bárions. Estes bárions são demonstrados ser os únicos estados espectrais no modelo, no subespaço ímpar, até o limiar de energia próximo do estado méson-bárion. Com os resultados obtidos nesta tese, podemos subir no espectro e validar, para o modelo completo, resultados espectrais envolvendo estados ligados de dois-bárion obtidos anteriormente na chamada aproximação escada (dominante).
 
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Publishing Date
2016-09-09
 
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