Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

October 1993 | Larry McLerran and Raju Venugopalan
The authors present a theoretical framework for computing the gluon distribution function for very large nuclei at small transverse momentum. They argue that this function can be expressed as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory, valid to all orders in the density of partons per unit area but to lowest order in \(\alpha_s\). The gluon distribution function is proportional to \(1/x\), and the finite density of partons modifies the dependence on transverse momentum for small values of \(x\). The paper reviews the previous work on the weakly coupled many-body theory and the scaling behavior of the gluon distribution function in the screened region. It also discusses the classical problem of solving the equations of motion for the gluon field in the presence of a delta-function source along the light cone. The authors show that the correlation functions can be computed using lattice Monte Carlo methods, and they expect the infrared behavior of these correlation functions to be finite at small \(k_t\). The study of the gluon and light quark propagators in this background field configuration is left for future analysis.The authors present a theoretical framework for computing the gluon distribution function for very large nuclei at small transverse momentum. They argue that this function can be expressed as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory, valid to all orders in the density of partons per unit area but to lowest order in \(\alpha_s\). The gluon distribution function is proportional to \(1/x\), and the finite density of partons modifies the dependence on transverse momentum for small values of \(x\). The paper reviews the previous work on the weakly coupled many-body theory and the scaling behavior of the gluon distribution function in the screened region. It also discusses the classical problem of solving the equations of motion for the gluon field in the presence of a delta-function source along the light cone. The authors show that the correlation functions can be computed using lattice Monte Carlo methods, and they expect the infrared behavior of these correlation functions to be finite at small \(k_t\). The study of the gluon and light quark propagators in this background field configuration is left for future analysis.
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