I thought I knew what single inclusive scattering was, but today when I went to look up a definition to check my memory, I couldn't find one. A Google search yielded no shortage of papers that use the term, but no definition or explanation in the first several pages of results. I'm asking here so I'll have something to look up if/when I forget again: what specifically does "single inclusive" mean in particle phenomenology?
In my opinion it is context dependent and that is why you do not find a definition.
Inclusive is used when a cross section in an interaction includes all channels that fulfil the criteria. The criteria are usually of picking one particle or reaction and measuring the crossection. Example: muon inclusive crossection in proton proton scattering will be looking at the number of muons hitting the muon detectors inclusively, i.e. regardless of the detail reactions in each event. In this context single inclusive would mean to find events that have only a single muon detected in the muon detectors. This should be clear from the context in the paper.