An inference method of the luminosity spectrum in a future e+e− linear collider

The high-luminosity e+e− linear collider has been studied as an energy frontier future project in high energy physics, and is expected to be a good place for the precision experiments. The high-luminosity e+e− linear collider no longer produces a monochromatic energy spectrum in the center of mass system, but a continuous and rather broad energy spectrum due to beamstrahlung of colliding e+ and e− beams. Without precise knowledge of this energy spectrum alias the luminosity spectrum, the precision experiment in the linear collider should be confronted with a crucial problem. A statistical method based on new developments in information technology is examined with a view of determining the luminosity spectrum. A statistical model is formulated and a likelihood fitting is carried out to determine the luminosity spectrum by using Bhabha events. The e+ and e− beam parameters, describing the luminosity spectrum, can be determined with an uncertainty of several percent by using 10 k Bhabha events under an ideal detector condition.