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