Length scale calibration for van der Meer scans at the LHCb experiment

The van der Meer scan is one of the main methods used in high-energy physics experiments to calibrate the luminosity. This method is based on moving the particle beams in precise positions to determine the beam profiles and thus the absolute luminosity scale. To verify that these beam movements are indeed accurate, each van der Meer scan (vdM) comprises a particular procedure called length scale calibration (LSC). The following thesis presents the analysis of the data from three length scale calibration procedures, conducted at the LHCb experiment. The purpose of these procedures is to check the consistency between the nominal beam displacements (∆xLHC , ∆yLHC ), with the effective beam displacements (∆xV ELO, ∆yV ELO). The compatibility of the two positions can be verified by checking if the quantities Cx and Cy, defined as the ratio between the measured and nominal beam displacement, minus one, are compatible with zero. To measure the effective displacements two different techniques were used: the constant beam separation method and the beam-gas imaging method. The results obtained with the constant beam separation method are as follows: • LSC 2022: Cx = −0.0141 ± 0.0005; Cy = −0.0057 ± 0.0007; • First LSC 2023: Cx = −0.0396 ± 0.0015; Cy = −0.0407 ± 0.0019; • Second LSC 2023: Cx = −0.0442 ± 0.0015; Cy = −0.0395 ± 0.0019. The results obtained with the beam-gas imaging method are as follows: • LSC 2022: – Beam 1: Cx = −0.010 ± 0.024; Cy = −0.020 ± 0.029; – Beam 2: Cx = −0.002 ± 0.032; Cy = 0.013 ± 0.044; • First LSC 2023: – Beam 1: Cx = 0.004 ± 0.034; Cy = 0.003 ± 0.027; – Beam 2: Cx = −0.003 ± 0.033; Cy = −0.004 ± 0.033; • Second LSC 2023: – Beam 1: Cx = −0.013 ± 0.032; Cy = −0.014 ± 0.027; – Beam 2: Cx = 0.001 ± 0.031; Cy = 0.002 ± 0.034. These measurements will be complemented by a comprehensive evaluation of systematic uncertainties and will serve as input for the LHCb vdM campaign.