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Doctoral Thesis
DOI
10.11606/T.43.1993.tde-12122013-153759
Document
Author
Full name
Carlos Antonio da Rocha
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1993
Supervisor
Committee
Robilotta, Manoel Roberto (President)
Borges Filho, Jose de Sá
Coelho, Helio T
Hussein, Mahir Saleh
Piza, Antonio Fernando Ribeiro de Toledo
Title in Portuguese
Potencial nucleon-nucleon devido à troca de dois píons: o papel da simetria quiral
Keywords in Portuguese
Física de partículas
Interação NN com dinâmica quiral
Potencial nucleon-nucleon
Simetria quiral
Troca de píons
Abstract in Portuguese
O presente trabalho consiste no estudo do papel da simetrial quiral no potencial nucleon-nucleon devido à troca de dois píons. Para o calculo do potencial foi levada em consideração a troca de dois píons não-correlacionados, envolvendo contribuicões com até um loop. A simetria quiral é introduzida no potencial através da sua realização não-linear, utilizando-se a Lagrangiana fenomenológica quiral de Weinberg. Os diagramas de Feynman construidos com os vértices dessa Lagragiana são ordenadas segundo potencias crescentes do momento, e calculados covariantemente. Os diagramas divergentes são regularizados covariantemente. Partindo do formalismo da equação de Bethe-Salpeter, relacionamos, em uma primeira etapa, as amplitudes de transição covariantes com o potencial, através do princípio da unitariedade elástica. O potencial, covariante e relativístico, e obtido no espaço dos momentos e é não-local e dependente da energia. Em uma segunda etapa, efetuamos a redução não-relativística do potencial e sua transformada de Fourier, obtendo um potencial local e independente da energia, que pode ser usado na equação de Schrödinger. O potencial obtido possui contribuições central, spin-orbita, tensorial e spin-spin. A parte dependente de isospin e semelhante à do potencial de Lemon e Partovi, sendo que as maiores modificações aparecem na parte isoescalar, principalmente no canal central, onde um substancial aumento de atração na região de 1.2 a 2.0 fm é observada. A fim de compararmos nosso potencial com a literatura, fixamos o valor de A como sendo 50 GeV, fazendo com que os efeitos do parâmetro de corte fiquem restritos à região r 0.5 fm. Os resultados obtidos foram comparados com o potencial fenomenológico de Argonne e revelaram razoável compatibilidade na maioria dos canais. Entretanto, existem discrepâncias importantes, possivelmente devidas a efeitos não estudados neste trabalho, tais como os devidos às ressonâncias A e p.
Title in English
Nucleon-nucleon potential due to the exchange of two pions: the role of chiral symmetry
Keywords in English
Chiral symmetry
Exchange of pions
NN Interaction with chiral dynamics
Nucleon-nucleon potential
Particle physics
Abstract in English
This work is devoted to the study of the role of chiral symmetry in the two pion exchange nucleon-nucleon potential. We consider only non-correlated two pion exchanges due to one loop contributions. Chiral symmetry is implemented in the potential through its non-linear realization, given by Weinberg's phenomenological Lagrangian. Feynman diagrams derived from this Lagrangian are arranged according to increasing powers of the momentum, and calculated covariantly. Divergent diagrams are regularizated covariantly. Starting from the Bethe-Salpeter equation, we relate the covariant transition amplitudes with the potential, using the elastic unitarity principle. The potential in momentum space is covariant, relativistic, non-local and energy dependent. Next, we perform its nonrelativistic reduction and Fourier transform, obtaining a potential which is local, energy independent and that can be used in the Schrödinger equation. This potential has central, spin-orbit, tensor and spin-spin components. The isospin dependent part is similar to that of the Lomon and Partovi potential, but important differences appear in the isoscalar part, especially in the central channel, where a substantial increase of attraction in the 1.2 to 2.0 fm region is observed. In order to compare our potential with the literature, we fixed the cutoff parameter at A = 50 GeV, restricting its effects to the r 0.5 fm region. Our results are compared with Argonne phenomenological potential, and a reasonable compatibility in most of the channels is found. However, there are also important discrepancies which may be due to effects not considered in this work, such as those due to A and the p ressonances.
 
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Publishing Date
2014-02-21
 
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