Hadron Form Factors

From Basic Phenomenology to QCD Sum Rules

Alexander Khodjamirian

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9781032173030
• eBook ISBN: 9781351392976
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Nuclear Physics

This book introduces the phenomenology and theory of hadron form factors in a consistent manner, deriving step-by-step the key equations, defining the form factors from the matrix elements of hadronic transitions and deriving their symmetry relations. Explained are several general concepts of particle theory and phenomenology exemplified by hadron form factors. The main emphasis here is on learning the analytical methods in particle phenomenology. Many examples of hadronic processes involving form factors are considered, from the pion electromagnetic scattering to heavy B-meson decays. In the second part of the book, modern techniques of the form factor calculation, based on the method of sum rules in the theory of strong interactions, quantum chromodynamics, are introduced in an accessible manner.

This book will be a useful guide for graduate students and early-career researchers working in the field of particle phenomenology and experiments.

Features:

• The first book to address the phenomenology of hadron form factors at a pedagogical level in one coherent volume

• Contains up-to-date descriptions of the most important form factors of the electroweak transitions investigated in particle physics experiments

CHAPTER 1

QCD, Quark Currents, and Hadrons

1.1 BASIC ELEMENTS OF QCD

1.1.1 QCD Lagrangian

Within the Standard Model (SM) of elementary particles, quantum chromodynamics (QCD) describes the interactions of quarks and antiquarks with gluons. QCD is a quantum field theory that bears certain similarities with quantum electrodynamics (QED), the theory of electromagnetic interactions of electrons and positrons with photons. Quarks and antiquarks, similar to the electron and positron, have spin 1/2 and are described by Dirac equation. Gluons, similar to the photon, are massless, have spin 1 and two polarization states. The color charge in quark-gluon interactions is similar to the electric charge in the electromagnetic interactions.

But there are also striking differences between QCD and QED. The most important one is the self-interaction of gluons which has far reaching consequences and essentially shapes QCD. This phenomenon originates due to the specific properties of the color charge. Each quark field in QCD has N_c = 3 different states of the color charge. An antiquark field, correspondingly, has three states of the conjugated color charge. The quark-gluon interaction alters the color state of a quark or antiquark. Due to color-charge conservation, the emitted or absorbed gluon has to compensate for this change and, hence, itself carries one of the possible Nc2−1=8 combinations of color charges. Therefore, a gluon can emit and absorb other gluons.

Interactions of the quark and gluon fields are encoded in the QCD Lagrangian density which has the following compact form:

LQCD(x)=−14Gμνa(x)Gaμν(x)+∑q=u,d,s,c,b,tq¯i(x)(iDμjiγμ−mqδji)qj(x),	(1.1)

with a summation over the color indices a = 1, 2,…8; i, j = 1, 2, 3 and Lo...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Introduction
• CHAPTER 1: QCD, QUARK CURRENTS, AND HADRONS
• CHAPTER 2: MESON FORM FACTORS
• CHAPTER 3: BARYON FORM FACTORS
• CHAPTER 4: HADRONIC RADIATIVE TRANSITIONS
• CHAPTER 5: FORM FACTORS IN THE TIMELIKE REGION
• CHAPTER 6: NONLOCAL HADRONIC MATRIX ELEMENTS
• CHAPTER 7: FORM FACTOR ASYMPTOTICS
• CHAPTER 8: QCD SUM RULES
• CHAPTER 9: LIGHT-CONE EXPANSION AND DISTRIBUTION AMPLITUDES
• CHAPTER 10: QCD LIGHT-CONE SUM RULES
• Appendix A: Collection of useful formulas
• Appendix B: Decay amplitudes and widths
• Appendix C: Parameterization and z-expansion of form factors
• Appendix D: The pion light-cone distribution amplitudes
• Bibliography
• Index