Measuring the Beam Energy with Radiative Return Events

The beam energy at the ILC is needed to a precision of around 10−4 for accurate mass determinations of the top quark, the Higgs boson and in supersymmetry [1]. This measurement will mainly be done with a magnetic spectrometer [2]. However the absolute calibration of such a spectrometer is difficult and in addition the luminosity weighted centre of mass energy is not necessarily identical to twice the beam energy. It is thus very useful to have a method to measure the luminosity weighted centre of mass energy directly from annihilation data. Fortunately this is possible using radiative return events to the Z using the fact that the Z mass is known to very high precision. The method was already pioneered at LEP2, where it was however limited by the available statistics [3, 4, 5].