Light-by-light scattering at future $$e^+e^-$$ colliders

Abstract We study the sensitivity of possible CLIC and FCC-ee measurements light-by-light scattering to old new physics, including Heisenberg–Euler Lagrangian in Standard Model with contributions from loops additional charged particles or magnetic monopoles, Born–Infeld extension QED, effective dimension-8 operators involving four electromagnetic field strengths as could appear Effective Field Theory. find that at 365 GeV 350 would be sensitive physics scales half a TeV operator coefficients, 1.4 3 $$\sim 2$$ ∼ 2 5 95% CL, corresponding probing masses up 3.7$$ 3.7 for large charges and/or multiple species. Within theory, $$95\%$$ 95 % CL sensitivities range 300$$ 300 1.3 2.8 high-energy options. Measurements not exclude monopole production FCC-hh, except context theory.