Lattice Computations of Small-x Parton Distributions in a Model of Parton Densities in Very Large Nuclei

Abstract

Using weak coupling methods McLerran and Venugopalan~\cite{LV1} expressed the parton distributions in large nuclei as correlation functions of a two dimensional Euclidean field theory. The theory has the dimensionful coupling $g^2\mu$, where ${\mu }^2\sim A^{1/3}$ is the valence quark color charge squared per unit area. We use a lattice regularization to investigate these correlation functions both analytically and numerically for the simplified case of $SU(2)$ gauge theory. In weak coupling ($g^2\mu L<<5$), where $L$ is the transverse size of the nucleus, the numerical results agree with the {\it analytic} lattice weak coupling results. For $g^2\mu L>>5$, no solutions exist at O($a^4$) where $a$ is the lattice spacing. This suggests an ill-defined infrared behavior for the two dimensional theory. A recent proposal of McLerran et al.~\cite{Kovner} for an {\it analytic} solution of the classical problem is discussed briefly.

21 pages in LaTex+six figures

References in corpus (7)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Green's Functions in the Color Field of a Large Nucleus
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions
• Gluon Production at High Transverse Momentum in the McLerran-Venugopalan Model of Nuclear Structure Functions
• Quantum Corrections to the Weizsäcker--Williams Distribution Function as Small x
• The Gluon Propagator in non-Abelian Weizsäcker-Williams fields

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