OPERATOR EXPANSION FOR HIGH-ENERGY SCATTERING

OPERATOR EXPANSION FOR HIGH-ENERGY SCATTERING

September1995 | I.BALITSKY*
The paper discusses the high-energy behavior of QCD amplitudes, focusing on the leading logarithms that arise in the evolution of nonlocal operators, specifically gauge factors ordered along straight lines. These operators, known as Wilson-line operators, are crucial for understanding the small-x behavior of structure functions. The author demonstrates that the leading logarithms can be derived from the evolution of these operators with respect to the deviation of the Wilson lines from the light cone, which serves as a "renormalization point." This approach generalizes the BFKL equation and provides a more comprehensive description of high-energy processes, including the triple vertex of hard pomerons. The paper also delves into the high-energy limit of virtual photon scattering, where the amplitude is expressed as an integral over gluon fields. The analysis involves expanding the amplitude in powers of the external field and performing the functional integral over the gluon fields. The result is a decomposition of the amplitude into an impact factor and a matrix element of Wilson-line operators. The impact factor is found to be independent of the large energy scale, while the matrix element of the Wilson-line operators captures the high-energy behavior. Finally, the paper addresses the longitudinal divergence that arises in the matrix elements of Wilson-line operators and proposes a regularization scheme to handle this divergence. This regularization is essential for obtaining a well-defined and convergent expression for the high-energy scattering amplitude.The paper discusses the high-energy behavior of QCD amplitudes, focusing on the leading logarithms that arise in the evolution of nonlocal operators, specifically gauge factors ordered along straight lines. These operators, known as Wilson-line operators, are crucial for understanding the small-x behavior of structure functions. The author demonstrates that the leading logarithms can be derived from the evolution of these operators with respect to the deviation of the Wilson lines from the light cone, which serves as a "renormalization point." This approach generalizes the BFKL equation and provides a more comprehensive description of high-energy processes, including the triple vertex of hard pomerons. The paper also delves into the high-energy limit of virtual photon scattering, where the amplitude is expressed as an integral over gluon fields. The analysis involves expanding the amplitude in powers of the external field and performing the functional integral over the gluon fields. The result is a decomposition of the amplitude into an impact factor and a matrix element of Wilson-line operators. The impact factor is found to be independent of the large energy scale, while the matrix element of the Wilson-line operators captures the high-energy behavior. Finally, the paper addresses the longitudinal divergence that arises in the matrix elements of Wilson-line operators and proposes a regularization scheme to handle this divergence. This regularization is essential for obtaining a well-defined and convergent expression for the high-energy scattering amplitude.
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