Discontinuities of multi-Regge amplitudes

Abstract

Abstract. In the BFKL approach, discontinuities of multiple production amplitudes in invariant masses of produced particles are discussed. It turns out that they are in evident contradiction with the BDS ansatz for n-gluon amplitudes in the planar N=4 SYM at n ≥ 6. An explicit expression for the NLO discontinuity of the two-to-four amplitude in the invariant mass of two produced gluons is is presented.

One-loop Lipatov vertex in QCD with higher $ε$-accuracy

“…The discontinuities of multiple gluon production amplitudes in the MRK are interesting also from another point of view. They can be used [32] for a simple demonstration of violation of the ABDK-BDS (Anastasiou-Bern-Dixon-Kosower -Bern-Dixon-Smirnov) ansatz [33,34] for amplitudes with maximal helicity violation (MHV) in Yang-Mills theories with maximal supersymmetry (N = 4 SYM) in the planar limit and for the calculations of the remainder functions to this ansatz. There are two hypothesis about the remainder functions: the hypothesis of dual conformal invariance [35,36], which asserts that the MHV amplitudes are given by products of the BDS amplitudes and that the remainder functions depend only on anharmonic ratios of kinematic invariants, and the hypothesis of scattering amplitude/Wilson loop correspondence [37][38][39][40], according to which the remainder functions are given by the expectation values of Wilson loops.…”