Factorization and Effective Action for High-Energy Scattering in QCD

I demonstrate that the amplitude of the high-energy scattering can be factorized in a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering.Comment: Talk presented at the workshop "Continuous Advances in QCD", (Minneapolis), April 1998. 15 pages, 3 eps figures, Latex using sprocl.sty and psfig.te

Factorization for high-energy scattering

I demonstrate that the amplitude of the high-energy scattering can be factorized in a product of two independent functional integrals over "fast" and "slow" fields which interact by means of Wilson-line operators -- gauge factors ordered along the straight lines.Comment: 4 pages, Latex, 1 postscript figure, to appear in PR

Rapidity factorization and evolution of gluon TMDs

I discuss how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at small $x\ll 1$ to linear evolution at moderate $x\sim 1$.Comment: 10 pages, contribution to Proceedings of QCD Evolution Workshop 201

Scattering of color dipoles: from low to high energies

A dipole-dipole scattering amplitude is calculated exactly in the first two orders of perturbation theory. This amplitude is an analytic function of the relative energy and the dipoles' sizes. The cross section of the dipole-dipole scattering approaches the high-energy BFKL asymptotics starting from a relatively large rapidity $\sim 5$.Comment: 13 pages, 10 postscript figures, typos correcte

Photon impact factor in the next-to-leading order

An analytic coordinate-space expression for the next-to-leading order photon impact factor for small-$x$ deep inelastic scattering is calculated using the operator expansion in Wilson lines.Comment: 5 pages, 3 figure

Rapidity evolution of Wilson lines at the next-to-leading order

At high energies particles move very fast so the proper degrees of freedom for the fast gluons moving along the straight lines are Wilson-line operators - infinite gauge factors ordered along the line. In the framework of operator expansion in Wilson lines the energy dependence of the amplitudes is determined by the rapidity evolution of Wilson lines. We present the next-to-leading order hierarchy of the evolution equations for Wilson-line operators.Comment: 5 pages and 2 figures, PRD version with typos correcte

High-enegy effective action from scattering of QCD shock waves

At high energies, the relevant degrees of freedom are Wilson lines - infinite gauge links ordered along straight lines collinear to the velocities of colliding particles. The effective action for these Wilson lines is determined by the scattering of QCD shock waves. I develop the symmetric expansion of the effective action in powers of strength of one of the shock waves and calculate the leading term of the series. The corresponding first-order effective action, symmetric with respect to projectile and target, includes both up and down fan diagrams and pomeron loops.Comment: 15 pages, 10 eps figure

High-energy amplitudes in N=4 SYM in the next-to-leading order

The high-energy behavior of the N=4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. 1. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four $Z^2$ currents in the first two orders in perturbation theory.Comment: 10 pages, 3 figure

NLO evolution of color dipoles

The small-$x$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities. We calculate the gluon contribution to small-x evolution of Wilson lines (the quark part was obtained earlier).Comment: 43 pages, 12 figure

Photon Impact Factor and \u3csub\u3eT\u3c/sub\u3e Factorization in the Next-To-Leading Order

The photon impact factor for the BFKL pomeron is calculated in the next-to-leading order (NLO) approximation using the operator expansion in Wilson lines. The result is represented as a NLO kT-factorization formula for the structure functions of small-x deep inelastic scattering