Non-perturbative Effective Interactions in the Standard Model

✍ Scribed by Boris A. Arbuzov

• Publisher: De Gruyter
• Year: 2014
• Tongue: English
• Leaves: 236
• Series: De Gruyter Studies in Mathematical Physics; 23
• Category: Library

✦ Synopsis

This monograph is devoted to the nonperturbative dynamics in the Standard Model (SM), the basic theory of allfundamental interactions in nature except gravity. The Standard Model is divided into two parts: the quantum chromodynamics (QCD) and the electro-weak theory (EWT) are well-defined renormalizable theories in which the perturbation theory is valid. However, for the adequate description of the real physics nonperturbative effects are inevitable. This book describes how these nonperturbative effects may be obtained in the framework of spontaneous generation of effective interactions. The well-known example of such effective interaction is provided by the famous Nambu-Jona-Lasinio effective interaction. Also a spontaneous generation of this interaction in the framework of QCD is described and applied to the method for other effective interactions in QCD and EWT. The method is based on N.N. Bogoliubov's conception of compensation equations. As a result we then describe the principal features of the Standard Model, e.g. Higgs sector, and significant nonperturbative effects including recent results obtained at LHC and TEVATRON.

✦ Table of Contents

Preface
1 Elementary particles and fields
1.1 Conventions and notations
1.2 Particles and interactions
1.3 Quantum electrodynamics
1.4 Quantum chromodynamics
1.5 Bethe–Salpeter equation
1.6 Effective interactions
1.6.1 Preliminaries
1.6.2 The model NJL
2 The standard model
2.1 The electro-weak theory
2.1.1 Feynman rules for the electro-weak interaction
2.1.2 Higgs scalar search
2.2 Status of the standard model
2.3 Properties of nonrenormalizable equations, instructive example
3 Bogoliubov compensation
3.1 Origin of the approach
3.2 Application to QFT
3.3 A spontaneous generation of the Nambu–Jona-Lasinio interaction
3.4 Justification of the model choice
3.5 Compensation equation in a six-dimensional scalar model
3.6 Bethe–Salpeter equation and zero excitation
3.7 Compensation equation for scalar field mass
3.8 Estimate of nonlinearity influence
3.9 Conclusions of simple scalar model
3.10 Appendix
4 Three-gluon effective interaction
4.1 Compensation equation
4.2 Running coupling
4.3 The gluon condensate
4.4 The glueball
4.5 Conclusion
5 Nambu–Jona-Lasinio effective interaction
5.1 Introduction
5.2 Effective NJL interaction
5.3 Scalar and pseudo-scalar states
5.4 Spontaneous breaking of the chiral symmetry
5.5 Pion mass and the quark condensate
5.6 Numerical results and discussion
5.7 Vector mesons
5.7.1 Compensation equations for effective form-factors
5.7.2 Wave functions of vector states
5.7.3 Results and discussion
5.8 Necessary formulae
6 Three-boson interaction
6.1 Compensation equation for anomalousthree-boson interaction
6.2 Effective strong interaction in the weak gauge sector
6.3 Scalar bound state of two W-s
6.4 Muon g-2
7 Possible four-fermion interaction of heavy quarks
7.1 Four-fermion interaction of heavy quarks
7.2 Doublet bound state ΨL TR
7.3 Stability problem
7.4 Possible effects of the heavy quarks interaction
8 Overall conclusion
8.1 Short review of achievements of the compensation approach
8.2 Examples of additional relations in the compensation approach
8.3 Weinberg mixing angle and the fine structure constant
8.4 Expectations
8.5 A possible effective interaction in the general relativity
8.6 Appendix
Bibliography
Index