2 - Heavy quarks

Summary

The light u, d, and s quarks have masses m_q that are small compared to the scale of nonperturbative strong dynamics. Consequently, it is a good approximation to take the m_q → 0 limit of QCD. In this limit QCD has an SU(3)_L × SU(3)_R chiral symmetry, which can be used to predict some properties of hadrons containing these light quarks. For quarks with masses m_Q that are large compared with the scale of nonperturbative strong dynamics, it is a good approximation to take the m_Q → ∞ limit of QCD. In this limit QCD has spin-flavor heavy quark symmetry, which has important implications for the properties of hadrons containing a single heavy quark.

Introduction

The QCD Lagrangian in Eq. (1.82) describes the strong interactions of light quarks and gluons. As discussed in Sec. 1.4, there is a nonperturbative scale Λ_QCD that is dynamically generated by QCD. A color singlet state, such as a meson made up of a quark–antiquark pair, is bound by the nonperturbative gluon dynamics. If the quarks are light, the typical size of such a system is of the order of Λ⁻¹_QCD. Consider a Q meson that contains a heavy quark with mass m_Q ≫ Λ_QCD, and a light quark with mass m_q ≪ Λ_QCD. Such a heavy-light meson also has a typical size of the order of Λ⁻¹_QCD, as for mesons containing only light quarks. The typical momentum transfer between the heavy and light quarks in the Q meson arising from nonperturbative QCD dynamics is of the order of Λ_QCD.