Generating invariant mass spectrum by combining multiple intervals

Dear developers,

I wanted to write this question in order to validate whether my approach is correct.

I'm working on generating an invariant mass spectrum for the dilepton channel in top quark production, aiming to extend up to 6 TeV. Initially, without imposing any minimum and maximum mass cuts, the spectrum quickly decays before reaching 400 GeV, which is far below my target energy range. My goal was then to generate multiple histograms at overlapping intervals (overlapping mass cuts) and later combining them.

First, I generate multiple .lhe files through MG5 with overlapping cuts and then using those as the input to perform a detector simulation using Delphes+Pythia8 to get simulation files. After that, I run an ROOT macro for event selection, each simulation file being an input, to generate invariant mass histograms (mainly those for muon and electron) and applying appropriate cross-section weights to each histogram to reflect the varying event rates across the spectrum. Then I use a macro to merge/combine all the separate histograms in order to get a combined spectrum.

The challenge arises when attempting to merge these histograms to form a continuous, combined spectrum. At the intersections of these intervals, the data points are distorted or lack smooth overlap, leading to a non-uniform spectrum.

My question is that is the approach to generate such a spectrum correct? My expectation was to get a smooth spectrum, so is it feasible to use .lhe files generated from MG5 in this context? Or is there a simpler/correct way to generate a mass spectrum for such a region, in which case is 6 TeV.

I appreciate any insights or suggestions you might have,
Thank you for your time.