Academic year 2007-2008 University of Li`ege Faculty of Sciences AGO Department IFPA Exotic and Non-Exotic Baryon Properties on the Light Cone C¶edricLorc¶e E-mail: [email protected] Supervisor: Maxim Polyakov Thesis presented in ful¯llment of the requirements for the Degree of Doctor of Science Acknowledgment First I would like to warmly thank my supervisor M. Polyakov for accepting me as a Ph.D. student, for his faith in me and especially for his kindness. It was a genuine pleasure to work and discuss with him. Thanks to him I have learned a lot on physics and the scienti¯c world and met many very interesting people. Next I would like to express my gratitude towards J. Cugnon for his help, advice and support in all the necessary steps linked to the present thesis. I am especially grateful to K. Goeke and M. Hacke for the two years passed in Ruhr UniversitÄatBochum (Germany) where the biggest part of the present thesis has been achieved. I will forever remember the welcoming people of Theoretische Physik II group. I have particularly appreciated everyday K. Goeke's good humour. He was always whistling, laughing or in raptures about other physicists' research. Living in Germany was a unique and extraordinary experience for me. That is the reason why I address this sentence to all people met there: Ich danke euch fÄuralles. I would also like to thank D. Diakonov for his help, patience and disponibility. Beside being a great physicist he is also a man full of humanity. The other part of the present thesis has been achieved in Li`egeUniversity. I am thankful to members of the IFPA group. I am in fact also indebted to all my teachers and professors for the share of their knowledge and passion. A thesis work does not only consist of passing all the days in front of a computer, papers or drafts. Discussions about physics, pataphysics and metaphysics are also essential to proceed. So I am thankful for all the entertaining, pleasant, interesting, serious and less serious moments passed with friends and other people met. I cannot of course cite all of them: Alice D., Aline D., Christophe B., Daniel H., Danielle R., Delphine D., Denis F., Fr¶ed¶ericK., Geo®rey M., Ghil-Soek Y., Gr¶egoryA., Jacqueline M., Jean-Paul M., J¶er¶emieG., Kirill S., Lionel H., Luc L., Michel W., Nina G., Pauline M., Quentin J., Renaud V., Sophie P., St¶ephaneT., Thibaut M., Tim L., Virginie C., Virgine D., Xavier C. and many others. Finally I would like to express my gratitude to my family: my mother, my sister and my father for their love, presence, help and for giving me the possibility to reach my dreams. I have also special thanks for Pierrot Di Marco and his two sons Christophe and S¶ebastien. Thanks for all what they did for us. I am really happy and proud to consider them as genuine part of our family. Contents 1 Introduction 9 1.1 Hadron structure and QCD . 9 1.2 Models and degrees of freedom . 10 1.2.1 Constituent quark models . 10 1.2.2 Quark-antiquark pairs and the nucleon sea . 11 1.2.3 Chiral symmetry of QCD . 11 1.2.4 Importance of pions in models . 12 1.3 Baryon properties and experimental surprises . 13 1.3.1 Proton spin crisis . 14 1.3.2 Strangeness in nucleon and Dirac sea . 15 1.3.3 Shape of baryons . 16 1.3.4 Exotic baryons . 16 1.4 Motivations and Plan of the thesis . 18 2 Light-cone approach 21 2.1 Forms of dynamics . 21 2.2 Advantages of the light-cone approach . 22 2.3 Light cone v.s. In¯nite Momentum Frame . 25 2.4 Standard model approach based on Melosh rotation . 26 3 The Chiral Quark-Soliton Model 29 3.1 Introduction . 29 3.1.1 The e®ective action of ÂQSM . 29 3.2 Explicit baryon wave function . 30 3.3 Baryon rotational³ wave functions´ . 33 3.3.1 The octet 8; 1 + .................................... 33 ³2 ´ 3.3.2 The decuplet 10; 3 + .................................. 34 ³2 ´ 1 + 3.3.3 The antidecuplet 10; 2 ............................... 34 3.4 Formulation in the In¯nite Momentum Frame . 35 3.4.1 QQ¹ pair wave function . 35 3.4.2 Discrete-level wave function . 36 3.5 Baryon Fock components . 37 3.5.1 3Q component of baryons . 38 3.5.2 5Q component of baryons . 39 3.5.3 7Q component of baryons . 40 5 6 CONTENTS 3.5.4 nQ component of baryons . 40 3.6 Matrix elements, normalization and charges . 41 3.6.1 3Q contribution . 41 3.6.2 5Q contributions . 42 3.6.3 7Q contributions . 44 3.7 Scalar overlap integrals . 46 3.7.1 3Q scalar integrals . 46 3.7.2 5Q direct scalar integrals . 46 3.7.3 5Q exchange scalar integrals . 47 3.7.4 7Q scalar integrals . 48 4 Symmetry relations and parametrization 51 4.1 General flavor SU(3) symmetry relations . 51 4.2 Flavor SU(3) symmetry and magnetic moments . 53 4.2.1 Charge and U-spin . 53 4.2.2 More about SU(3) octet magnetic moments . 54 4.2.3 More about SU(3) decuplet and antidecuplet magnetic moments . 55 4.2.4 More about SU(3) transition magnetic moments . 55 4.3 Speci¯c SU(6) symmetry relations . 57 5 Vector charges and normalization 59 5.1 Introduction . 59 5.2 Vector charges on the light cone . 60 5.3 Scalar overlap integrals and quark distributions . 61 5.3.1 3Q scalar integral . 62 5.3.2 5Q scalar integrals . 62 5.3.3 7Q scalar integrals . 63 5.4 Combinatoric results . 63 5.4.1 Octet baryons . 63 5.4.2 Decuplet baryons . 65 5.4.3 Antidecuplet baryons . 66 5.5 Numerical results and discussion . 67 5.5.1 Octet content . 68 5.5.2 Decuplet content . 69 5.5.3 Antidecuplet content . 70 6 Axial charges 71 6.1 Introduction . 71 6.2 Axial charges on the light cone . 72 6.3 Scalar overlap integrals and quark distributions . 73 6.3.1 3Q scalar integral . 74 6.3.2 5Q scalar integrals . 74 6.3.3 7Q scalar integrals . 75 6.4 Combinatoric Results . 75 6.4.1 Octet baryons . 75 6.4.2 Decuplet baryons . 76 6.4.3 Antidecuplet baryons . 77 CONTENTS 7 6.5 Numerical results and discussion . 78 6.5.1 Octet content . 78 6.5.2 Decuplet content . 80 6.5.3 Antidecuplet content . 81 6.6 Pentaquark width . 83 7 Tensor charges 85 7.1 Introduction . 85 7.2 Tensor charges on the light cone . 86 7.3 Scalar overlap integrals and quark distributions . 87 7.3.1 3Q scalar integral . 88 7.3.2 5Q scalar integrals . 88 7.4 Combinatoric Results . ..