Energy Calibration of the LHC Beams at 4 TeV

The mixed proton and lead ion run in January and February 2013 (p-Pb run) provided an excellent opportunity to measure the beam energy at the LHC. The beam energy of the LHC was determined at 4 TeV and at 450 GeV using the frequency difference of proton and lead ions by taking advantage of the simultaneous presence of both particle types in the LHC. The data for the energy measurement was collected parasitically to standard p-Pb physics operation. The measured energy at 4 TeV is P = 3988 ± 5 (stat) ± 26 (syst) GeV/c. The LHC energy at injection was measured with better accuracy than before to be P = 450.28 ± 0.01 (stat) ± 0.11 (syst) GeV/c. Both values are in good agreement with the predictions from the magnetic model of the LHC and the measurement accuracies are entirely dominated by systematic errors.