Book contents
- Frontmatter
- Contents
- Acknowledgements
- 1 Introduction
- 2 Relativistic kinematics, electromagnetic fields and the method of virtual quanta
- 3 The harmonic oscillator and the quantum field
- 4 The vacuum as a dielectric medium; renormalisation
- 5 Deep inelastic scattering and the parton model
- 6 The classical motion of the massless relativistic string
- 7 The decay kinematics of the massless relativistic string
- 8 A stochastic process for string decay
- 9 The properties of the Lund model fragmentation formulas; the external-part formulas
- 10 The internal-part fragmentation formulas and their relations to the unitarity equations of a field theory; Regge theory
- 11 The dynamical analogues of the Lund model fragmentation formulas
- 12 Flavor and transverse momentum generation and the vector meson to pseudoscalar meson ratio
- 13 Heavy quark fragmentation and baryon production
- 14 The Hanbury-Brown-Twiss effect and the polarisation effects in the Lund model
- 15 The Lund gluon model, its kinematics and decay properties
- 16 Gluon emission via the bremsstrahlung process
- 17 Multigluon emission, the dipole cascade model and other coherent cascade models
- 18 The λ-measure in the leading-log and modified leading-log approximations of perturbative QCD
- 19 The parton model and QCD
- 20 Inelastic lepto-production in the Lund model, the soft radiation model and the linked dipole chain model
- References
- Index
10 - The internal-part fragmentation formulas and their relations to the unitarity equations of a field theory; Regge theory
Published online by Cambridge University Press: 23 September 2009
- Frontmatter
- Contents
- Acknowledgements
- 1 Introduction
- 2 Relativistic kinematics, electromagnetic fields and the method of virtual quanta
- 3 The harmonic oscillator and the quantum field
- 4 The vacuum as a dielectric medium; renormalisation
- 5 Deep inelastic scattering and the parton model
- 6 The classical motion of the massless relativistic string
- 7 The decay kinematics of the massless relativistic string
- 8 A stochastic process for string decay
- 9 The properties of the Lund model fragmentation formulas; the external-part formulas
- 10 The internal-part fragmentation formulas and their relations to the unitarity equations of a field theory; Regge theory
- 11 The dynamical analogues of the Lund model fragmentation formulas
- 12 Flavor and transverse momentum generation and the vector meson to pseudoscalar meson ratio
- 13 Heavy quark fragmentation and baryon production
- 14 The Hanbury-Brown-Twiss effect and the polarisation effects in the Lund model
- 15 The Lund gluon model, its kinematics and decay properties
- 16 Gluon emission via the bremsstrahlung process
- 17 Multigluon emission, the dipole cascade model and other coherent cascade models
- 18 The λ-measure in the leading-log and modified leading-log approximations of perturbative QCD
- 19 The parton model and QCD
- 20 Inelastic lepto-production in the Lund model, the soft radiation model and the linked dipole chain model
- References
- Index
Summary
Introduction
In this chapter we will consider the decay properties of a cluster. We start to derive some results from the internal-part formulas, Eqs. (8.41) and (8.43).
I1 If we sum over all available states in the decay formulas of a cluster of squared mass s we obtain asymptotically, i.e. for large values of s, the behaviour ∼ sa. We will consider these state equations both for the case of a single species of flavor and meson and also for the case of many flavors and many hadrons in each flavor channel.
I2 At the same time we will derive the finite-energy version, fs, of the fragmentation function f in Eqs. (8.16), (8.17). We will show that fs tends rapidly towards f when s is larger than a few squared hadron masses (just as Hs → H according to the results of Chapter 9).
The method we will use is to derive a set of integral equations and then to solve them. In that way we will find that there are some necessary relationships between the parameters a, b and the normalisation parameters that constitute a set of eigenvalue equations for the integral equations.
The whole procedure is very similar to that for obtaining the unitarity conditions for the S-matrix in a quantum field theory. We will exploit these relationships by showing that the results obtained under I1 are just the same as are obtained for the multiperipheral ladder equations in a quantum field theory.
- Type
- Chapter
- Information
- The Lund Model , pp. 177 - 191Publisher: Cambridge University PressPrint publication year: 1998