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Quantum Field Theory Approaches to Meson Structure

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Quantum Field Theory Approaches to Meson Structure Quantum Field Theory Approaches to Meson Structure Dissertation der Mathematisch–Naturwissenschaftlichen Fakult¨at der Eberhard Karls Universit¨at T¨ubingen zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) vorgelegt von Tanja Branz aus T¨ubingen T¨ubingen 2011 Tag der m¨undlichen Pr¨ufung: 24.02.2011 Dekan: Prof. Dr. Wolfgang Rosenstiel 1. Berichterstatter: Prof. Dr. Thomas Gutsche 2. Berichterstatter: Prof. Dr. Werner Vogelsang 3. Berichterstatter: Prof. Dr. Eulogio Oset Zusammenfassung Meson–Spektroskopie ist eines der interessantesten Themen in der Teilchenphysik. Vor allem durch die Entdeckung von zahlreichen neuen Zust¨anden im Charmo- nium Spektrum mit Eigenschaften, die nicht durch das Konstituenten Quark Modell erkl¨art werden k¨onnen, hat das Interesse zahlreicher theoretischer Untersuchungen auf dieses Thema gelenkt. In der vorliegenden Dissertation werden verschiedene Mesonstrukturen diskutiert, die von leichten und schweren Quark–Antiquark Mesonen bis hin zu gebundenen Zust¨anden von Hadronen, sogenannten Hadronischen Molek¨ulen, im leichten und schweren Sektor reichen. F¨ur die Untersuchung der Mesoneneigenschaften wie Massen- spektrum, totale und partielle Breiten sowie Produktionsraten verwenden wir drei verschiedene theoretische Modelle. Gebundene Zust¨ande von Mesonen werden zun¨achst in einem Modell untersucht, das auf gekoppelten Meson Kan¨alen basiert, bei der Meson–Meson Resonanzen dy- namisch generiert werden. Die Zerfallseigenschaften von Mesonmolek¨ulen werden anschließend in einem zweiten Modell analysiert. Die Basis dieses zweiten Zugangs bilden effektive Lagrangedichten, die die Wechselwirkung zwischen den hadronisch gebundenem Zustand und dessen Konstituenten beschreibt. Neben den Meson- molek¨ulen betrachten wir auch die radiativen und starken Zerfallseigenschaften her- k¨ommlicher Quark–Antiquark Mesonen in diesem ph¨anomenologischen Modell. Den Abschluss der drei theoretischen Methoden, die hier vorgestellt werden, wird von einem AdS/CFT Modell gebildet. Dieses holographische Modell unterscheidet sich fundamental von den beiden vorher diskutierten Ans¨atzen, da zus¨atzliche Di- mensionen und Elemente aus der String Theorie enthalten sind. Wir berechnen das Massenspektrum leichter und schwerer Mesonen und deren Zerfallskonstanten im Rahmen dieses Modells. Abstract Meson spectroscopy became one of the most interesting topics in particle physics in the last ten years. In particular, the discovery of new unexpected states in the charmonium spectrum which cannot be simply explained by the constituent quark model attracted the interest of many theoretical efforts. In the present thesis we discuss different meson structures ranging from light and heavy quark–antiquark states to bound states of hadrons—hadronic molecules. Here we consider the light scalar mesons f0(980) and a0(980) and the charmonium–like Y (3940), Y (4140) and Z±(4430) states. In the discussion of the meson properties like mass spectrum, total and partial decay widths and production rates we introduce three different theoretical methods for the treatment and description of hadronic structure. For the study of bound states of mesons we apply a coupled channel approach which allows for the dynamical generation of meson–meson resonances. The decay properties of meson molecules are further on studied within a second model based on effective Lagrangians describing the interaction of the bound state and its con- stituents. Besides hadronic molecules the effective Lagrangian approach is also used to study the radiative and strong decay properties of ordinary quark–antiquark (qq¯) states. The AdS/QCD model forms the completion of the three theoretical methods intro- duced in the present thesis. This holographic model provides a completely different ansatz and is based on extra dimensions and string theory. Within this framework we calculate the mass spectrum of light and heavy mesons and their decay constants. Contents 1. Introduction 9 1.1. Hadronic Structure ............................ 11 1.1.1. Constituent Quark Model .................... 11 1.1.2. Beyond the Quark Model ..................... 12 2. Meson Spectroscopy 15 2.1. Meson Spectroscopy in the Light Sector ................. 15 2.1.1. f0(980) and a0(980) ........................ 16 2.2. Meson Spectroscopy in the Charmonium Sector ............ 20 2.2.1. Y(3940) .............................. 24 2.2.2. Y(4140) .............................. 25 2.2.3. Z(4430) .............................. 26 2.3. Outline of the theory part ........................ 28 3. Dynamically generated resonances 31 3.1. Coupled channels ............................. 31 3.2. Coupled channels including charmed mesons .............. 38 3.2.1. Hidden–charm, open–strange sector ............... 45 3.2.2. Charm–strange resonances .................... 45 3.2.3. Flavor exotic resonances ..................... 50 3.2.4. Summary ............................. 55 3.3. Radiative decays of dynamically generated states ........... 57 3.3.1. Radiative decays of light mesons ................. 60 3.3.2. Radiative decays of hidden–charm mesons ........... 67 3.3.3. Summary ............................. 70 4. Effective Model for Hadronic Bound States 73 4.1. Formalism ................................. 74 4.1.1. Inclusion of the electromagnetic interaction ........... 77 4.2. Light meson bound states ........................ 80 4.2.1. a0(980) and f0(980) ........................ 80 4.2.2. Weak non–leptonic decays of hadron molecules ......... 98 4.3. Heavy Charmonium–like Hadronic Molecules ..............106 4.3.1. Y(3940) and Y(4140) .......................106 4.3.2. Z(4430) ..............................115 5 6 Contents 4.4. Two–photon decay of heavy hadron molecules .............125 4.5. Quark–antiquark mesons .........................131 4.5.1. Implementation of confinement .................133 4.5.2. Inclusion of the electromagnetic interaction ...........136 4.6. Basic properties of π and ρ mesons ...................138 4.7. An extension to strange, charm and bottom flavors ..........141 4.8. Dalitz decays ...............................144 4.9. Conclusions ................................150 5. Holographic model AdS/QCD 153 5.1. Basic approach ..............................153 5.1.1. Anti–de–Sitter space .......................155 5.1.2. Conformal field theory ......................157 5.1.3. Light front Fock representation .................158 5.2. AdS/QCD – the method .........................163 5.2.1. Action of a string .........................163 5.2.2. Matching procedure ........................165 5.2.3. One–gluon exchange and hyperfine–splitting ..........169 5.3. Properties of light and heavy mesons ..................171 5.3.1. Mass spectrum of light mesons ..................172 5.3.2. Mass spectrum of heavy–light mesons ..............175 5.3.3. Mass spectrum of heavy quarkonia ...............177 5.3.4. Leptonic and radiative meson decay constants .........180 5.4. Summary .................................183 6. Conclusions 185 A. Appendix: Effective Model for hadronic bound states 189 A.1. Loop Integrals ...............................189 A.1.1. Radiative transitions .......................189 A.1.2. Strong decays ...........................190 A.2. Gauge invariance .............................190 A.3. Coupling constants ............................191 ′ A.4. Coupling ratio gD1Dψ /gD1Dψ ......................193 A.5. Gauge invariance of the ρ0 γ transition amplitude .........195 → A.6. Loop integration techniques .......................197 B. Appendix: AdS/QCD 201 B.1. Evaluation of integrals in the heavy quark limit ............201 B.2. Decay constants ..............................202 Literature 215 Contents 7 List of Figures 218 List of Tables 220 1. Introduction Historically, mesons, i.e. pions, were first introduced by Yukawa [1] in 1935 as exchange bosons generating the strong interaction between nucleons. However, pions and nucleons did not remain the only hadron states but with the improvement of the accelerator facilities, which gave access to higher mass regions, numerous states of baryons and mesons have been observed, which needed to be interpreted in a systematic way. By arranging the nearly degenerate hadron states according to their quantum numbers such as total spin and parity, a specific pattern of multiplets emerged which was the starting point of the constituent quark model introduced in 1964 by Zweig and Gell–Mann. Mesons and baryons were interpreted as composite objects consisting of a valence quark–antiquark pair (qq¯) or three quarks (qqq), respectively. Up to now the constituent quark model is one of the most important models for hadron structure and provides a first reference point for newly observed states. The discovery of baryons with three identical quarks, as for example first the ∆++ (uuu) and then the Ω− (sss) state, required the introduction of an additional quan- tum number, which is the color charge, since otherwise these states would be for- bidden by the Pauli principle. The definition of the three colors and later on the experimental evidence for this color degree of freedom in deep inelastic scattering experiments provided the basis for quantum chromodynamics (QCD) which is the underlying theory of strong interaction. One of the major challenges in the applica- tion of QCD is how quarks and gluons combine to form composite particles called hadrons. In contrast to quantum electrodynamics, QCD becomes non–perturbative at large length scales and cannot be accessed
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