Reflection Identities of Harmonic Sums and pole decomposition of BFKL eigenvalue

BFKL Eigenvalue and Maximal Alternation of Harmonic Sums

We analyze the known results for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in the perturbative regime using the analytic continuation of harmonic sums from even positive arguments to the complex plane. The resulting meromorphic functions have poles at negative integer values of the argument. The typical classification of harmonic sums is determined by two major parameters: $a)$ the \textit{weight} - a sum of inverse powers of the summation indices; $b)$ the \textit{depth} - a number of nested summations. We introduce the third parameter: the \textit{alternation} - a n…

The analytic structure of the BFKL equation and reflection identities of harmonic sums at weight five

We analyze the structure of the eigenvalue of the color-singlet Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation in N=4 SYM in terms of the meromorphic functions obtained by the analytic continuation of harmonic sums from positive even integer values of the argument to the complex plane. The meromorphic functions we discuss have pole singularities at negative integers and take finite values at all other points. We derive the reflection identities for harmonic sums at weight five decomposing a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a p…

NNNLLA BFKL pomeron eigenvalue in the planar N=4 SYM theory

We find the eigenvalue of the kernel of BFKL equation in the next-to-next-to-next-to-leading logarithm approximation (NNNLLA) in the planar N=4 SYM theory by using the quantum spectral curve to compute values at fixed spin, and reconstructing the general result using the LLL-algorithm, which also was used for the reconstruction of the general result for the intercept function for arbitrary conformal spin at fourth order, computed earlier in paper 1802.06908 up to the rational part. We have found, that a new type of harmonic sums enter into results. Those sums have the argument multiplied by fa…

Real valued functions for BFKL eigenvalue

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in $N=4$ super Yang-Mills theory as a real valued function of two variables anomalous dimension and the conformal spin. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory.

具有纯虚指标的调和和在整数值附近的解析延拓

Analytic continuation of harmonic sums with purely imaginary indices near the integer values

本文提出一种代数方法及 MATHEMATICA 代码，用于纯虚或实整数指标调和和在整数附近的解析延拓，并应用于 ABJM 模型反常维数，验证斜率函数并预测次斜率函数的前三阶微扰项。

结合DGLAP和BFKL的开度角的演变

Evolution in opening angle combining DGLAP and BFKL logarithms

我们提出了一个演化方程，它同时总结了领先的BFKL和DGKL积分胶子分布的单变量，即胶子的发射角。这种形式的演化适用于高能pp（和p \bar{p}）相互作用事件的Monte Carlo模拟，特别是在采样小x事件的情况下。