integration strategy and fixed-target brem

Dear Olivier,

I am in validating different methods of simulating e- + N -> e- + N + V, where V is a massive vector (i.e. a dark photon with coupling to EM currents), N is a nucleus whose coupling to
photons contains an atomic form factor that is proportional to t at small t, where t is the photon virtuality. I'm using MG v 3.4.0

I found that the default MG options (default t_strat and sde_strat 2) gave wrong results for cross-sections and distributions of the emitted V at high initial beam energies. This is of course a challenging region of phase space (and with no cuts on V), but I was able to get correct results by using sde_strat 1 t_strat 2 following your discussion in https://arxiv.org/pdf/2102.00773.pdf.
(here's a plot showing a cross-section comparison, each run here had 50000 points: https://www.dropbox.com/s/mw59tr1nzpbe7bp/generator_brem_xsec_vs_energy_comparison_mV_100_MeV_Z_6.pdf?dl=0)

Can you share any insight into why this might be happening? My understanding is that changing sde_strat to 2 allows madgraph to use the full matrix element (including the form factor) to compute the channel weights (alpha_i in your paper), as opposed to just using the propagator denominators. Since F(t)/t is regular whereas 1/t is singular at small t, the channels weights could be different, and the result could be biased. On the other hand, F(t)/t is present in every diagram, so this should cancel in normalizing the channel weights.

Thank you in advance!