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The present work reviews the various aspects of the extension of the large-$N_c$ approach, as had been proposed and developed by 't Hooft, to the case of tetraquark states, which are a category of the general class of exotic states, also called multiquark states, whose internal valence-quark structure does not match with that of ordinary hadrons, and which have received, in recent years, many experimental confirmations. The primary question of describing, or probing, on theoretical grounds, multiquark states is first examined. The signature of such states inside Feynman diagrams in relation with their singularities is highlighted. The main mechanisms of formation of tetraquark states, provided by the diquark model and the molecular scheme, are considered together with their specific implications. The properties of tetraquark states at large $N_c$ are analyzed through the Feynman diagrams that describe two-meson scattering amplitudes. It turns out that, in that limit, the possible formation of tetraquark states is mainly due to the mutual interactions of their internal mesonic clusters. These essentially arise from the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel meson-meson scattering amplitudes, one may expect the occurrence of two independent tetraquark states, each having priviledged couplings with the two mesons of their dominant channel. The question of the energy balance of various schemes in the static limit is also analyzed. The clarification of the mechanisms that are at work in the formation of tetraquarks is the main outcome from the large-$N_c$ approach to this problem., Comment: 132 pages, 53 figures. Review article. v2: Sections 2.7 and 5.4 have been slightly extended; a few clarifying comments have been added in other sections; figure 43 has been completed; references have been added

Se investigan las propiedades de los bariones excitados pertenecientes al primer multipletede paridad negativa en el marco de la expansión en la inversa del número de colores dela Cromodinámica Cuántica. En particular, se busca realizar un análisis de las masas y losdecaimientos de los correspondientes bariones no-extra˜nos y sentar las bases para la inclusiónen dicho análisis de los bariones con extra˜neza. Para investigar las propiedades de los barionesen la expansión en la inversa del número de colores, primero se determinan las funcionesde onda debidamente simetrizadas de los bariones relevantes cuando el número de colores esgrande. Una vez establecidas dichas funciones de onda, se procede a calcular los elementos dematriz de los operadores que aparecen en distintos observables. De esta manera se obtienensus dependencias con el número de colores. A partir de los elementos de matriz relevantesse hallan los coeficientes libres que acompa˜nan a cada uno de los operadores que aparecena un cierto orden de potencia en 1/Nc. Para ello se ajustan los observables calculados a losdatos empíricos disponibles. Se busca realizar un análisis global de estos observables ya que,en general, las posibles mezclas entre estados con los mismos números cuánticos vinculan adichos observables entre sí. Determinamos que un estudio numérico simultáneo de las masasy los anchos de decaimiento fuerte y electromagnéticos de los bariones del sector no-extra˜nopredice valores de los ángulos de mezcla que son compatibles con los obtenidos en los análisisindependientes para los decaimientos electromagnéticos y fuertes. Además se observa que ladegeneración presente en las soluciones para los estudios independientes de masas y decaimientosfuertes desaparece en el análisis simultáneo. Por último, se llega a una conclusiónsobre el problema de la asignación de los estados teóricos con los estados físicos, que sepuede dar de cuatro maneras diferentes. Se encuentra que hay una asignación favorecida. Encuanto a la inclusión en el análisis de los bariones con extra˜neza, se consideran primeramentelos decaimientos fuertes en forma independiente, ya que no existían estudios previos de estetipo. Para ello se debieron considerar operadores de decaimiento que tuvieran en cuenta losefectos de ruptura de simetría debido a la diferencia entre las masas de los quarks “up” y “down” con la del “strange”. Entre otras conclusiones se obtuvo que en algunos casos losefectos de ruptura de simetría son importantes y que los operadores de 1-cuerpo son los másrelevantes, a pesar que los de 2-cuerpos son importantes para obtener un mejor ajuste. Porúltimo realizamos un primer estudio consistente de las masas y los decaimientos fuertes delmultiplete completo de bariones en el marco de un esquema perturbativo para el tratamientode la ruptura de simetría en las masas previamente utilizado en la literatura. Los resultadosobtenidos indican que si bien las características generales de los ajustes independientes sesiguen conservando en el ajuste global realizado, las dificultades encontradas para describir algunos decaimientos sugieren la necesidad de considerar mejores aproximaciones en futuroscálculos. We investigate the properties of excited baryons belonging to the first negative paritymultiplet within the inverse color number expansion formalism of Quantum Chromodynamics. In particular, we seek to make an analysis of the masses and decays of the correspondingnon-strange baryons and to set the base for the inclusion in this analysis of strange baryons. To investigate the baryon properties using the inverse colour number expansion, first theproperly symmetrized wave functions are determined, for the relevant baryons when thenumber of colours is large. Once such wavefunctions are established, the matrix elements ofthe operators appearing in different observables are calculated, obtaining in this way, theirdependence on color number. Starting from the relevant matrix elements, we find the freecoefficients of each operator at a given order of a power of 1/Nc. For that purpose, the calculatedobservables are fitted to available empirical data. A global analysis of these observablesis sought for, since, in general, the possible mixtures between states with equal quantumnumbers relate these observables amongst themselves. It is found that a simultaneous numericalstudy of the masses and the strong and electromagnetic decay widths of baryons in thenon-strange sector predicts mixing angles that are compatible with those obtained from theindependent analysis of the electromagnetic and strong decay widths. Also, it is observedthat the degeneracy present in the solutions for the independent studies of the masses andstrong decays disappears in the simultaneous analysis. Finally a conclusion is reached for theproblem of assigning the theoretical states to the physical states, which can be done in fordifferent ways. It is found that there is one favoured assignment. Concerning the inclusionin the analysis of strange baryons, we first consider strong decays independently, since therewere no previous studies of this kind. For this purpose we had to consider the decay operatorsthat took into account the effects of symmetry breaking due to the differences between theup and down quark masses and that of the strange quark. Amongst other conclusions, weobtained that in some cases the effects of simmetry breaking are important and that the onebody operators are the most relevant, even though the two body operators are important toobtain a better fit. Finally, we make a first consistent study of the masses and strong decaysof the complete baryon multiplet within a perturbative scheme for the treatment of symmetrybreaking in the masses previously used in the literature. The results obtained indicatethat even though the general characteristics of the independent fits are still conserved in theglobal fit, difficulties are found to describe some decays, which suggests the need to considerbetter approximations in future calculations. Fil: González de Urreta, Emiliano José. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

The model with the meson spectrum, consisting of zero-width equidistant resonances, is considered with connection to current correlators in coordinate space. The comparison of the explicit expressions for the correlators, obtained in this model, with the experimental data of ALEPH collaboration on tau-decay is made and good agreement is found., LaTeX, 8 pages, 3 figures