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Mixing of Pseudoscalar-Baryon and Vector-Baryon in Meson-Baryon Interaction and the Generation of Resonances

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Mixing of Pseudoscalar-Baryon and Vector-Baryon in Meson-Baryon Interaction and the Generation of Resonances Facultat de F´ısica Departamento de F´ısica Te´orica Ph.D. THESIS: MIXING OF PSEUDOSCALAR-BARYON AND VECTOR-BARYON IN MESON-BARYON INTERACTION AND THE GENERATION OF RESONANCES A Thesis submitted by Eugenio Javier Garz´on Alama for the degree of Doctor of Philosophy in the University of Valencia Supervised by: Eulogio Oset Baguena I “With the lightest meson, with the heaviest baryon, No Hadron shall escape my sight. Let those who worship the Quark Model Beware my power, Chiral Perturbation Theory!” II III D. Eulogio Oset B´aguena, Catedr´atico de F´ısica Te´orica de la Universi- dad de Valencia, CERTIFICA: Que la presente Memoria Mixing of pseudoscalar- baryon and vector-baryon in meson-baryon interaction and the generation of resonances ha sido realizada bajo mi direcci´on en el Departamento de F´ısica Te´orica de la Universidad de Valencia por Eugenio Javier Garz´on Alama como Tesis para obtener el grado de Doctor en F´ısica Y para que as´ıconste presenta la referida Memoria, firmando el presente certificado. Fdo: Eulogio Oset B´aguena IV Contents Agradecimientos IX 1 Introduction 1 1.1 Effective Lagrangians and Chiral Perturbation Theory . .. 2 1.2 Dynamicallygeneratedresonances. 3 2 Formalism 5 2.1 Thehiddengaugeformalism . 7 2.2 FormalismforVVinteraction . 8 2.3 Lagrangians of the meson-baryon interaction . 11 2.4 Convolutionoftheloopfunction. 14 2.5 Polesandcouplings. 15 3 RadiativedecayofS=1/2resonances 19 3.1 Introduction............................ 19 3.2 Framework............................. 21 3.3 Radiativedecay .......................... 24 3.4 Radiative decays into γ andbaryondecuplet . 26 3.4.1 S = 0,I =1/2channel.................. 26 3.4.2 S = 0,I =3/2channel.................. 28 3.4.3 S = 1,I =0channel .................. 28 − 3.4.4 S = 1,I =1channel .................. 28 − 3.4.5 S = 2,I =1/2channel ................. 29 − 3.4.6 S = 3,I =0channel .................. 29 − 3.5 Radiative decays into γ andbaryonoctet. 30 3.5.1 S =0,I =1/2channel .................. 30 3.5.2 S = 1,I =0channel .................. 30 − 3.5.3 S = 1,I =1channel .................. 33 − V VI CONTENTS 3.5.4 S = 2,I =1/2channel ................. 33 − 3.6 Helicityamplitudes . 33 3.7 Conclusions ............................ 39 4 The box diagram 41 4.1 Introduction............................ 41 4.2 Formalism............................. 43 4.3 Theboxdiagram ......................... 47 4.4 ContacttermsVPBBfortheboxdiagrams . 51 4.5 Results............................... 55 4.6 Comparisontodata. 61 4.7 Conclusions ............................ 66 P 5 N ∗ resonances with J =3/2− 69 5.1 Introduction............................ 69 5.2 Formalism............................. 70 5.3 TheoreticalApproach. 71 5.4 Fittingthedata.......................... 73 5.5 Results............................... 75 5.6 Conclusions ............................ 81 P 6 N ∗ resonances with J =1/2− 83 6.1 Introduction............................ 83 6.2 Formalism............................. 84 6.3 Fittingthedata.......................... 87 6.4 Results............................... 88 6.5 Conclusions ............................ 92 7 Limits to the Fixed Center Approximation to Faddeev equa- tions: the case of the φ(2170). 95 7.1 Introduction............................ 95 7.2 Fixed center approximation formalism to the φf0(980) scattering 97 7.3 Fieldtheoreticalcalculation . 101 7.4 Beyond the FCA: excitation of the f0 in intermediate states . 103 7.5 Results...............................105 7.6 Conclusions ............................109 8 Strategies for an accurate determination of the X(3872) en- ergyfromQCDlatticesimulations 111 8.1 Introduction............................111 8.2 TheX(3872)inthecontinuumlimit. 112 CONTENTS VII 8.3 Formalisminfinitevolume . .115 8.4 Twochannelcase .........................119 8.5 Theinverseproblem . .120 8.6 Results...............................121 8.7 Conclusions ............................127 9 Conclusions 129 10 Resumen en espa˜nol 135 10.1 Introducci´on. .135 10.1.1 Lagrangianos efectivos y Teor´ıa de Perturbaciones Quiral136 10.1.2 Resonancias din´amicamente generadas . 137 10.2Formalismo ............................138 10.2.1 Elformalismodehiddengauge . 140 10.2.2 Formalismo para la interacci´on VV . 141 10.2.3 Lagrangianos de la interacci´on mes´on-bari´on . 144 10.2.4 Convoluci´on de la funci´on loop . 147 10.2.5 Polosyacoplamientos . .148 10.3 Conclusiones. .150 A Spin degeneracy of VB considering the VB VB transition157 → B Matrix elements of the ~σ~ǫ operator 163 C ExpressionoftheBoxdiagramintegral 165 D Coefficients of the Baryon octet - pseudoscalar mesons inter- action 167 ECoefficientsoftheboxintegral 171 F Evaluation the vertices 177 Bibliography 183 VIII CONTENTS Agradecimientos La vida est´acompuesta de etapas, etapas que est´an llenas de momentos, de personas y de metas. Hoy una de esas etapas termina, pero eso no es algo por lo que entristecerse ya que significa que se ha llegado al final con los objetivos cumplidos y que una nueva etapa comienza. Sin embargo, el llegar al final no es el verdadero objetivo, si no que es el recorrer ese camino lo que nos da la aut´entica recompensa y lo que nos hace aprender del esfuerzo y del tiempo invertido. Por ello el ver nuestra meta en el horizonte es lo que nos hace avanzar. Lo importante durante todo el camino es estar rodeado de gente que te apoye y que ande contigo. Y por ello quiero agradecer a todas esas personas que han contribuido mucho o poco a que este d´ıa haya llegado. Primero, el que m´as ha contribuido a que esto salga adelante ha sido Eulogio. El me ha orientado, ayudado y ense˜nado todo lo que ha hecho posible esta tesis. Gracias a ´el he podido formarme no solo como cient´ıfico si no tambi´en como persona y de ´el he aprendido mucho que seguro que me ser´amuy ´util en el futuro. Por ´el he podido viajar, descubrir nuevas culturas y conocer gente interesante. Adem´as me ha ense˜nado que el esfuerzo y la constancia tiene su recompensa, que hay que defender con firmeza tus convicciones cuando se est´aseguro de ello, siempre desde el respeto y la humildad. Por todo ello: Gracias Eulogio. Tambi´en a mi familia, a mi madre, a mi padre, a mi hermana y a mi abuela, que siempre est´an ah´ıy desean lo mejor para m´ı. Aunque por m´as que se lo explique, nunca entienden que es eso de “potrones” y quarks que hago, siempre se han interesado y preocupado de como va el trabajo, cuando lees la tesis, te han contestado ya de ese art´ıculo, a donde te manda Eulogio este a˜no, cuando lees la tesis (si, lo he puesto dos veces), vamos lo que es ser una familia que te quiere y se preocupa. Adem´as porque me han dado la oportunidad y los medios de haber podido estudiar, tener una carrera y llegar hasta donde estoy hoy. IX X Agradecimientos A la gente del grupo, en especial a Juan y a Manolo, que han sido como un par de padres extras durante estos a˜nos. A Juan por estar siempre tan pendiente y preocupado por mi, pregunt´andome a todas horas que c´omo estaba. A Manolo por todo lo que me ha ense˜nado de matem´aticas o de programaci´on, y por hacer que a partir de las diez, mirara en reloj cada dos por tres esperando escuchar ese “cafeto”, que indicaba que´ıbamos a almorzar y as´ıpoder descansar despegando los ojos de la pantalla. Agradecer tambi´en a la gente que de alguna forma u otra ha pasado por el grupo, dejando su huella no solo profesionalmente si no tambi´en de forma personal como Kanchan y Alberto, que han sido colegas pero tambi´en les considero amigos. Fueron las primeras personas que conoc´ıdel grupo y me hablaron de lo bien que te trataban, como en una familia. Y ten´ıan raz´on. Tambi´en a Raquel, que se convirti´oen una hermana mayor y en una amiga, y que desde el primer viaje a Jap´on estuvo ah´ıy me ayud´oen lo que necesitaba. Manolo Pav´on fue durante un tiempo el compa˜nero de despacho m´as divertido que se puede pedir, elevando el nivel de “frikismo” en el despacho hasta l´ımites insospechados. Durante este tiempo tambi´en pasaron por el grupo dos chicas que por su sencillez, alegr´ıa y bondad, dieron un gran cambio al grupo. Junko con su humildad, era apreciada por todo el grupo y se convirti´oen una improvisada profesora de mi rudimentario japon´es. Melahat lleg´om´as tarde y su alegr´ıa nos inund´oa todos. Ha sido una excelente compa˜nera y amiga. Muchos otros como Jorge Mart´ın Camalich, Dani Gamermann, Nacho Ruiz, Ju-Jun Xie, Chu-Wen Xiao, En Wang, Luis Alvarez Ruso, Carlos Hidalgo, Tim Ledwig, tambi´en han formado parte de este proyecto. Agradecer tambi´en el apoyo de colegas que me ha ayudado de muchas formas diversas, como Angels Ramos, Michael D¨oring, Laura Tolos, Atsushi Hosaka, Daisuke Jido, Makoto Oka, Tetsuo Hyodo, Bao Xi Sun y Lian Rong Dai. Poco a poco la gente va llegando a este d´ıa y se va marchando, pero otros vienen, y de repente te encuentras con un grupo de gente fant´astica donde menos te lo esperas. Francesca se convirti´oen una estupenda compa˜nera de despacho con la que compartir risas y miradas de complicidad. Tambi´en Uchino ha sido un excelente compa˜nero de cervezas, mientras uno al otro nos ense˜n´abamos japon´es y espa˜nol y coment´abamos las divertidas diferencias culturales entre Jap´on y Espa˜na. Despu´es llegaron Astrid y Jorgivan con los que conect´eenseguida y pasamos muy buenos ratos. Agradecer tambi´en a todos mis compa˜neros de Aikido, que son demasia- dos para ponerlos a todos aqu´ı, por haber sido el lugar donde poder evadirme de mis problemas y ser gente maravillosa con la que poder practicar y tomarse una cervecita para reponerse despu´es de haberse pasado la tarde haciendo “kokyus”.
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