27 September 2004 | John C. Collins, Davison E. Soper, George Sterman
This paper summarizes the standard factorization theorems for hard processes in Quantum Chromodynamics (QCD), describing their proofs. The factorization theorems allow the separation of long-distance and short-distance behavior in QCD processes, enabling perturbative calculations. The key idea is that the cross section for a process can be expressed as a product of a short-distance part, which is perturbatively calculable, and a long-distance part, which describes the distribution of partons in hadrons.
The factorization theorems are applied to processes involving hadrons, such as deeply inelastic scattering, single-particle inclusive annihilation, and the Drell-Yan process. In these processes, the cross section is factorized into a parton distribution function (which describes the distribution of partons in a hadron) and a hard scattering cross section (which is perturbatively calculable). The parton distribution functions are determined experimentally, while the hard scattering cross sections are calculated using perturbation theory.
The factorization theorems are based on the idea that the long-distance effects in QCD can be separated from the short-distance effects, which are governed by the strong coupling constant. This separation is possible due to the asymptotic freedom of QCD, which allows the coupling constant to become small at high energies. The factorization theorems are essential for making predictions in QCD, as they allow the calculation of cross sections for processes involving hadrons using perturbative methods.
The paper discusses the factorization theorems in detail, including their derivation in scalar field theory and in QCD. It also describes the application of these theorems to specific processes, such as deeply inelastic scattering, single-particle inclusive annihilation, and the Drell-Yan process. The paper concludes with a discussion of the relationship between factorization theorems and the parton model, which is a theoretical framework that describes hadrons as composed of partons. The parton model provides a useful intuition for understanding the factorization theorems, as it shows that the cross section for a process can be expressed as a product of a parton distribution function and a hard scattering cross section.This paper summarizes the standard factorization theorems for hard processes in Quantum Chromodynamics (QCD), describing their proofs. The factorization theorems allow the separation of long-distance and short-distance behavior in QCD processes, enabling perturbative calculations. The key idea is that the cross section for a process can be expressed as a product of a short-distance part, which is perturbatively calculable, and a long-distance part, which describes the distribution of partons in hadrons.
The factorization theorems are applied to processes involving hadrons, such as deeply inelastic scattering, single-particle inclusive annihilation, and the Drell-Yan process. In these processes, the cross section is factorized into a parton distribution function (which describes the distribution of partons in a hadron) and a hard scattering cross section (which is perturbatively calculable). The parton distribution functions are determined experimentally, while the hard scattering cross sections are calculated using perturbation theory.
The factorization theorems are based on the idea that the long-distance effects in QCD can be separated from the short-distance effects, which are governed by the strong coupling constant. This separation is possible due to the asymptotic freedom of QCD, which allows the coupling constant to become small at high energies. The factorization theorems are essential for making predictions in QCD, as they allow the calculation of cross sections for processes involving hadrons using perturbative methods.
The paper discusses the factorization theorems in detail, including their derivation in scalar field theory and in QCD. It also describes the application of these theorems to specific processes, such as deeply inelastic scattering, single-particle inclusive annihilation, and the Drell-Yan process. The paper concludes with a discussion of the relationship between factorization theorems and the parton model, which is a theoretical framework that describes hadrons as composed of partons. The parton model provides a useful intuition for understanding the factorization theorems, as it shows that the cross section for a process can be expressed as a product of a parton distribution function and a hard scattering cross section.