Measurement of the Rate of Collisions from Satellite Bunches for the April-May 2010 LHC Luminosity Calibration

The LHC luminosity measurement relies on a precise determination of the beam currents contributing to colliding bunch pairs. Satellite bunches occur when protons diffuse from a high-intensity bunch into a neighboring RF bucket. At the LHC, colliding bunches are nominally separated by 25 ns, while RF buckets occur every 2.5 ns. Hence, between two nominal colliding bunches there are nine potential "slots'' for satellite bunches. At least part of the latter are effectively included in beam current measurements for luminosity calibrations. On the other hand, proton-proton collisions that originate from the crossing of a satellite bunch with a nominal bunch do not enter standard ATLAS analyses because they occur displaced from the nominal collision point. Therefore, the rate of satellite collisions needs to be measured with a dedicated study to assess systematic uncertainties from this loss of luminosity. In this note we look for satellite collisions in data collected during beam separation ("van-der-Meer'') scans performed in April and May 2010, by studying the position of reconstructed vertices. Significant contributions are found during the two LHC fills of the May 2010 scans. The relative fraction of such collisions, with respect to proton-proton collisions of the nominal main bunches, is about 3.6 x 10^{-3} and 1.5 x 10^{-3} in LHC fills 1089 and 1090, respectively. For the April 2010 scans, limits of the order of 10^{-4} are s et. We conclude that the corrections needed for the luminosity calibration due to satellite collisions within 100 cm of the nominal interaction point are negligible.