EFFECTIVE FIELD THEORIES FOR VECTOR PARTICLES AND ...

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iv contents iii appendix 93 a notations and relations 95 a.1 The Special Unitary Group . . . . . . . . . . . . . . . . . . 95 a.2 One-loop Integrals . . . . . . . . . . . . . . . . . . . . . . 96 b technical details 99 b.1 Effective Field Theory Model in FeynArts . . . . . . . . . 99 b.2 Constraint Analysis in <strong>FOR</strong>M . . . . . . . . . . . . . . . . 101 c magnetic moment in detail 105 c.1 Feynman Rules . . . . . . . . . . . . . . . . . . . . . . . . 105 c.2 Fluxes of Large Momenta for Each Topology . . . . . . . 108 c.3 Ξ 1 and Ξ 2 for the Magnetic Moment . . . . . . . . . . . . 110 c.4 Non-renormalized Expressions per Diagram . . . . . . . 112 bibliography 117
LIST OF FIGURES Figure 4.1 Constraint analysis as a flowchart . . . . . . . . . . 29 Figure 5.1 Vector meson octet diagram . . . . . . . . . . . . . 38 Figure 6.1 One-loop contributions: three-point . . . . . . . . 61 Figure 6.2 One-loop contributions: four-point . . . . . . . . 63 Figure 7.1 Exemplary process for the magnetic moment . . . 71 Figure 7.2 Diagrams for the two-point function . . . . . . . . 75 Figure 7.3 Tree diagrams for the magnetic moment . . . . . 77 Figure 7.4 Loop diagrams for the magnetic moment . . . . . 78 Figure B.1 FeynArts for effective field theories . . . . . . . . . 100 Figure C.1 Fluxes of large momenta: two-point function . . . 108 Figure C.2 Fluxes of large momenta: three-point function . . 109 LIST OF TABLES Table 1.1 Firstly discovered vector mesons . . . . . . . . . . 6 Table 2.1 Overview of quark properties . . . . . . . . . . . . 10 Table 5.1 Determinant of M in detail, SU(3) . . . . . . . . . 40 Table 6.1 Coupling constants after U(1) invariance . . . . . 50 Table 6.2 Determinant of M in detail . . . . . . . . . . . . . 53 Table 6.3 Determinant of M in detail, SU(2) . . . . . . . . . 68 Table 7.1 Comparison with other theoretical predictions . . 87 Table C.1 Particular contributions to δZ ρ . . . . . . . . . . . 112 Table C.2 Particular contributions to f 1 (0) . . . . . . . . . . 113 Table C.3 Particular contributions to f 2 (0) . . . . . . . . . . 115 v
Page 1 and 2: EFFECTIVE FIELD THEORIES FOR VECTOR
Page 3: CONTENTS i introduction and theoret
Page 9 and 10: The main motivation for working in
Page 11 and 12: motivation and overview 5 in the tr
Page 13: motivation and overview 7 include v
Page 16 and 17: 10 qcd and chiral effective field t
Page 27 and 28: 3 POWER COUNTING AND REGULARIZATION
Page 29 and 30: 3.2 reformulated infrared regulariz
Page 31: 3.2 reformulated infrared regulariz
Page 34 and 35: 28 classical constraint analysis sy
Page 36 and 37: 30 classical constraint analysis 4.
Page 38 and 39: 32 classical constraint analysis Ne
Page 40 and 41: 34 classical constraint analysis wi
Page 43 and 44: 5 SU(3)-INVARIANT GENERAL LAGRANGIA
Page 45 and 46: su(3)-invariant general lagrangian
Page 47: su(3)-invariant general lagrangian
Page 50 and 51: 44 vector particles in the tensor m
Page 52 and 53: 46 vector particles in the tensor m
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48 vector particles in the tensor m
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7 MAGNETIC MOMENT OF THE RHO MESON
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7.2 power counting 73 which transfo
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7.3 two-point function 75 π c ρ c
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7.4 magnetic moment 77 γ γ ρ 3
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7.4 magnetic moment 79 γ γ γ π
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7.4 magnetic moment 81 This result
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7.5 reformulated infrared regulariz
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7.5 reformulated infrared regulariz
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7.6 discussion of results 87 Method
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SUMMARY AND CONCLUSION 8 This chapt
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summary and conclusion 91 cross-che
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NOTATIONS AND RELATIONS A In this c
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A.2 one-loop integrals 97 The two-p
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TECHNICAL DETAILS B This chapter gi
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B.2 constraint analysis in form 101
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B.2 constraint analysis in form 103
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106 magnetic moment in detail π a
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108 magnetic moment in detail c.2 f
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110 magnetic moment in detail c.3
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112 magnetic moment in detail c.4 n
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114 magnetic moment in detail Diagr
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116 magnetic moment in detail Diagr
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118 bibliography [18] M. R. Schindl
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120 bibliography [56] J. Wess and B
Page 128:
122 bibliography [95] F. Cardarelli
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EFFECTIVE FIELD THEORIES FOR VECTOR PARTICLES AND ...

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