ALP-ttbar Toy MC v1.1: Magnetic-Field Separation, Photon-Conversion Backgrounds and Vertex Resolution for Displaced Light ALP → e+e− (companion to arXiv:2610.38932)

Personal, numpy-only toy Monte Carlo written after reading arXiv:2610.38932 (J. Alimena et al., "Hunting for Long-Lived ALPs in Top Events via Displaced Dielectron Pairs at the LHC"). It explores effects that the paper explicitly leaves outside its generator-level scope: (1) magnetic-field separation of highly collimated e+e- pairs, (2) photon conversions in tracker material as a background for the lightest ALPs, and (3, new in v1.1) the vertex resolution of nearly collinear pairs and how strongly the conversion veto depends on it. v1.1 adds a per-pair vertex-resolution model, an optimised material-veto width and a resolution-tail test (new Figure 4). Pairs below a few hundred MeV vertex about as poorly as photon conversions (about 3 mm in the pixel region, 8-10 mm in the strip region). At 17 MeV the conversion-induced loss in reach ranges from about 2x to about 60x, depending mainly on resolution tails, so the v1.0 conclusion that a mass window plus material veto recovers most of the reach holds only under optimistic assumptions; at 100-200 MeV the result is stable (about 1.5-7x). All v1.0 results are reproduced unchanged. Files: 4-page summary (PDF) and a complete snapshot (zip) with code, figures and printed numbers; ./run_all.sh reproduces everything in about 1 minute with fixed seeds. Disclaimer: personal project, not affiliated with the paper's authors or the CMS Collaboration. Kinematics are parametrised and detector numbers assumed; only qualitative trends and ratios are meaningful.