New multiple soft theorem from split-helicity amplitude decomposition

We investigate the soft decomposition of tree-level gluon amplitudes with split-helicity configurations. First, we show how any split-helicity amplitude can be fully fixed from inverse soft limit using BCFW calculation. We show how the double and triple soft theorems can manifest beyond perturbative calculations through split-helicity decomposition. Next, we obtain a compact formula for the corresponding soft operator which is a simple combination of individual single soft operators. Then we generate the leading and sub-leading soft factors using soft momentum expansion, to compare with results derived from standard calculation.