Minimally helicity violating, maximally simple scalar amplitudes in N=4 SYM

TL;DR

This paper analyzes a special class of scalar amplitudes in planar N=4 SYM, deriving general formulas for tree and one-loop contributions with a simple ratio involving dual conformally invariant functions.

Contribution

It introduces a new class of scalar amplitudes with limited diagrams and an iterative structure, providing explicit formulas for any number of particles.

Findings

Derived a general formula for scalar amplitudes at tree and one-loop levels.

The one-loop to tree ratio involves dual conformally invariant box functions.

Established a new infinite sequence of one-loop amplitudes in N=4 SYM.

Abstract

In planar N=4 SYM we study a particular class of helicity preserving amplitudes. These are scalar amplitudes whose flavor configuration is chosen in such a way that only a limited number of diagrams is allowed, which exhibit an iterative structure. For such amplitudes we evaluate the tree level and one-loop contributions, providing a general formula valid for any number of particles. The ratio between the one-loop and tree level results is a simple combination of dual conformally invariant box functions with at most two massive legs. Along with the MHV and NMHV series, this constitutes the third known infinite sequence of one-loop amplitudes in N=4 SYM.