Upper Limits on the Charge in Satellite Bunches for the October 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. Protons in the satellite bunches enter the measured beam currents but the luminosity calibrations relying on tracking are not sensitive to collisions that originate from the crossing of a satellite bunch with a nominal bunch. 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 October 2010, by studying the position of reconstructed vertices. We set upper limits on the fraction of protons in satellite bunches leading or trailing each beam not exceeding $10^{-3}$. We conclude that the corrections needed for the luminosity calibration due to satellite collisions within $100$~cm of the nominal interaction point are negligible.