Strong Interactions in Spacelike and Timelike Domains

Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach provides the theoretical basis for the description of the strong interactions in the spacelike and timelike domains. The book primarily focuses on the hadronic vacuum polarization function, R-ratio of electron-positron annihilation into hadrons, and the Adler function, which govern a variety of the strong interaction processes at various energy scales. Specifically, the book presents the essentials of the dispersion relations for these functions, recaps their perturbative calculation, and delineates the dispersively improved perturbation theory. The book also elucidates the peculiarities of the continuation of the spacelike perturbative results into the timelike domain, which is indispensable for the studies of electron-positron annihilation into hadrons and the related processes.

• Covers the topics that play an essential role in contemporary particle physics and future collider projects
• Applicable for self-education alongside standard textbooks
• Makes the subject easily accessible without the need of an extensive theoretical background

Graduate and postgraduate students, university lecturers, and researchers working in the fields of high energy physics, particle physics, quantum chromodynamics, and mathematical physics

Chapter 1: Basic Dispersion Relations

• Abstract
• 1.1 R-Ratio of Electron-Positron Annihilation Into Hadrons
• 1.2 Hadronic Vacuum Polarization Function Π(q2)
• 1.3 Adler Function D(Q2)

Chapter 2: Perturbative QCD Invariant Charge

• Abstract
• 2.1 Renormalization Group Equation
• 2.2 One-Loop Perturbative QCD Running Coupling
• 2.3 QCD Invariant Charge at Higher Loop Levels

Chapter 3: Functions Π(q2), R(s), and D(Q2) Within Perturbative Approach

• Abstract
• 3.1 Hadronic Vacuum Polarization Function Within Perturbative Approach
• 3.2 Adler Function Within Perturbative Approach
• 3.3 R-Ratio Within Perturbative Approach

Chapter 4: Dispersive Approach to QCD

• Abstract
• 4.1 Unified Integral Representations for Functions Π(q2), R(s), and D(Q2)
• 4.2 Spectral Density
• 4.3 Note on the Massless Limit

Chapter 5: Functions Π(q2), R(s), and D(Q2) Within Dispersive Approach

• Abstract
• 5.1 Hadronic Vacuum Polarization Function Within DPT
• 5.2 R-Ratio Within DPT
• 5.3 Adler Function Within DPT

Chapter 6: R-Ratio at High Energies

• Abstract
• 6.1 Appearance of the π2-Terms
• 6.2 General Features
• 6.3 Higher-Order Estimations

Conclusions

Appendix A: Perturbative QCD Running Coupling

Appendix B: Perturbative Spectral Function

Appendix C: Perturbative Approximation of R-Ratio