Duality symmetry in high energy scattering

We discuss the duality symmetry of the linear(BFKL) and the non-linear(BK) high energy evolutions in the multicolor limit. We show that the usual color dipole picture is dual to the forward reggeized gluon formulation. The presented analysis is also generalized to the non-forward case where we suggest an extended version of the duality symmetry. We give it a physical interpretation as a symmetry under rotation of the Kernel in the transverse space from s-channel(dipoles) to t-channel(reggeized gluons). The duality symmetry is related to the integrability of the system. The duality symmetry of the BK equation found in the present study can be regarded as an indirect indication of its integrability.Comment: 13 pages, 6 figure

Reflection identities of harmonic sums of weight four

We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the argument. The pole decomposition demonstrates how the product of two simpler harmonic sums can build more complicated harmonic sums at higher weight. We list a minimal irreducible bilinear set of reflection identities at weight four which present the main result of the paper. We also discuss how other trilinear and quartic reflection identities can be easily constructed from our result with the use of well known shuffle relations for harmonic sums.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1808.0930

On the Analytic Solution of the Balitsky-Kovchegov Evolution Equation

The study presents an analytic solution of the Balitsky-Kovchegov~(BK) equation in a particular kinematics. The solution is written in the momentum space and based on the eigenfunctions of the truncated Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation in the gauge adjoint representation, which was used for calculation of the Regge~(Mandelstam) cut contribution to the planar helicity amplitudes. We introduce an eigenfunction of the singlet BFKL equation constructed of the adjoint eigenfunction multiplied by a factor, which restores the dual conformal symmetry present in the adjoint and broken in the singlet BFKL equations. The proposed analytic BK solution correctly reproduces the initial condition and the high energy asymptotics of the scattering amplitude.Comment: 8 page

Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function

We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by pole separation of a rather simple digamma function. This generates higher weight generalized polygamma functions at any given order of perturbative expansion. As a byproduct of our analysis we develop a general technique for calculating powers of the real part of digamma function in a pole separated form.Comment: 12 pages, 1 figur

Duality symmetry of BFKL equation: reggeized gluons vs color dipoles

We show that the duality symmetry of the BFKL equation can be interpreted as a symmetry under rotation of the BFKL Kernel in the transverse space from s-channel (color dipole model) to t-channel (reggeized gluon formulation). We argue that the duality symmetry holds also in the non-forward case due to a very special structure of the non-forward BFKL Kernel, which can be written as a sum of three forward BFKL Kernels. The duality symmetry is established by identifying the dual coordinates with the transverse coordinates of a non-diagonal dipole scattered off the target.Comment: 13 pages, 5 figure