This paper looks at two of the biggest sources of error when measuring the total data collected (the integrated luminosity) at future electron–positron colliders running at the Z boson energy. The goal for these machines is extremely tight: a relative uncertainty below 10−4. The usual measurement uses small‑angle Bhabha scattering (SABS), a well understood electron–positron process seen at very small angles. The authors study a complementary channel, two‑photon (diphoton) events, and they also attack a separate bias that comes from beam electromagnetic deflection — the bending of outgoing particles by the opposing particle bunches.

To reduce particle identification errors in the forward detector region, the team simulated events and trained a gradient boosted decision tree (BDTG) to tell photons, electrons/positrons, and neutral hadrons apart. They compare two detector setups: the standard ILD LumiCal and an upgraded, highly granular design called GLIP. They find that both designs can reject neutral hadrons, but only the GLIP upgrade can reduce the contamination from misidentified SABS events down to the 10−4 target. Quantitatively, neutral hadron misidentification impacts the luminosity by about 2×10−5 for the ILD LumiCal and about 6×10−6 for GLIP. Previous work had shown a residual Bhabha contamination of 35×10−4 for the standard LumiCal setup and 0.01×10−4 for GLIP.

The authors also identified a new background process for the diphoton channel: low‑invariant‑mass radiative hadrons (e+e−→qq̄γ) where the hadronic system is very light and can mimic a single photon. They estimate this radiative hadron cross section at roughly 3 pb compared with about 100 pb for diphotons. Their hadronization modeling suggests that about 20% of these forward radiative‑hadron events could fake photons in the calorimeter. The authors caution that this hadronization simulation is not precise in the low‑mass regime and that the 20% number should be treated as an order‑of‑magnitude estimate.