Luminosity spectrum reconstruction at linear colliders

A good knowledge of the luminosity spectrum is mandatory for many measurements at future $\mathrm {e}^{+}\mathrm {e}^{-}$ colliders. As the beam-parameters determining the luminosity spectrum cannot be measured precisely, the luminosity spectrum has to be measured through a gauge process with the detector. The measured distributions, used to reconstruct the spectrum, depend on Initial State Radiation, cross-section, and Final State Radiation. To extract the basic luminosity spectrum, a parametric model of the luminosity spectrum is created, in this case the spectrum at the 3 TeV compact linear collider. The model is used within a reweighting technique to extract the luminosity spectrum from measured Bhabha event observables, taking all relevant effects into account. The centre-of-mass energy spectrum is reconstructed within 5 % over the full validity range of the model. The reconstructed spectrum does not result in a significant bias or systematic uncertainty in the exemplary physics benchmark process of smuon pair production.