Luminosity calibration bias in van-der-Meer scan due to the beam-beam interaction for q-Gaussian beams

Abstract

The accuracy of luminosity calibration is an important problem in the operation of colliders, the successful solution of which determines the accuracy of the experiments performed. In hadron colliders, luminosity calibration is performed using van-der-Meer scanning, the goal of which is to measure the overlap of the colliding beams. When two beams collide, their electromagnetic interaction leads to a change in their overlap and, consequently, the luminosity calibration is biased. Typically, this effect is accounted for under the assumption that beams have a Gaussian particle distribution. However, it is known that the particle distribution in hadron collider beams differs from Gaussian and is more generally described by q-Gaussian functions. Accurate accounting of electromagnetic interaction becomes an urgent task as the requirements for the accuracy of luminosity measurements increase (for example, in the HL-LHC project the goal is an accuracy of 1 %). This paper presents a model of the electromagnetic interaction of beams with a q-Gaussian distribution of particles, and determines the influence of this interaction on the luminosity calibration using the van der Meer scanning method. Calculations were carried out for beams with conditions of the CMS and ATLA experiments.