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-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

Next-to-Leading Order Evolution of Color Dipoles

The small-x deep inelastic scattering in the saturation region is governed by the nonlinear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the Balitsky-Kovchegov equation for the evolution of color dipoles. In the next-to-leading order the Balitsky-Kovchegov 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 the small-x evolution of Wilson lines (the quark part was obtained earlier)

Regularization of the Light-Cone Gauge Gluon Propagator Singularities Using Sub-Gauge Conditions

Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the theta-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator's light-cone poles. The obtained sub-gauge condition for the PV case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges. Our method does not allow one to construct a sub-gauge condition corresponding to the well-known Mandelstam-Leibbrandt prescription for regulating the gluon propagator poles.Comment: 19 pages, 2 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

Classical Gluon Production Amplitude for Nucleus-Nucleus Collisions: First Saturation Correction in the Projectile

We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g^3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtaining an analytic expression for the first projectile saturation correction to the gluon production cross section in nucleus-nucleus collisions.Comment: 37 pages, 24 figure

Conformal Kernel for the Next-to-Leading-Order BFKL equation in = 4 Super Yang-Mills Theory

Using the requirement of Möbius invariance of = 4 super Yang-Mills amplitudes in the Regge limit, we restore the explicit form of the conformal next-to-leading-order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel out of the eigenvalues known from the forward next-to-leading-order BFKL result

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

The photon impact factor for the Balitsky-Fadin-Kuraev-Lipatov pomeron is calculated in the next-to-leading order approximation using the operator expansion in Wilson lines. The result is represented as a next-to-leading order T-factorization formula for the structure functions of small- deep inelastic scattering