Scale Anomaly and "Soft" Pomeron in QCD

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Abstract

We propose a new non-perturbative approach to hadronic interactions at high energies and small momentum transfer, which is based on the scale anomaly of QCD and emphasizes the role of semi-classical vacuum fields. We find that the hadron scattering amplitudes exhibit Regge behavior and evaluate the intercept alpha(0) of the corresponding trajectory. Both the intercept and the scale for the slope of the trajectory appear to be determined by the energy density of non-perturbative QCD vacuum (the gluon condensate). Numerically, we find Delta = alpha(0) - 1 = 0.08 -0.1, consistent with the values ascribed phenomenologically to the ``soft'' Pomeron. For arbitrary numbers of colors N_c and flavors N_f, Delta is found to be proportional to (N_f/N_c)^2; however, in the large N_c (N_f fixed) limit, Delta \sim N_c^0.

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Ultraviolet Behavior of Non-Abelian Gauge Theories

David Gross, Frank Wilczek (1973)

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Green's Functions in the Color Field of a Large Nucleus

Raju Venugopalan, Larry McLerran (1994)

We compute the Green's functions for scalars, fermions and vectors in the color field associated with the infinite momentum frame wavefunction of a large nucleus. Expectation values of this wavefunction can be computed by integrating over random orientations of the valence quark charge density. This relates the Green's functions to correlation functions of a two dimensional, ultraviolet finite, field theory. We show how one can compute the sea quark distribution functions, and explictly compute them in the kinematic range of transverse momenta, \(\alpha_s^2 \mu^2 << k_t^2 << \mu^2\), where \(\mu^2\) is the average color charge squared per unit area. When \(m_{quark}^2 << \mu^2 \sim A^{1/3}\), the sea quark contribution to the infinite momentum frame wave function saturates at a value that is the same as that for massless sea quarks.