Measurement of the W-boson mass with the ATLAS detector at the LHC

The present work shows the current status of the determination of the $W$-boson mass, using the LHC datasets in proton-proton collisions collected by the ATLAS detector at 5.02, 7 and 13 TeV. To achieve this, dedicated calibration procedures of the ATLAS Inner Detector (ID) and Muon Spectrometer (MS) have been designed and applied, and the $W$-boson mass measurement strategy has been optimised. The ID calibration procedure considers possibles biases in the muon track sagitta, geometrical deformations and magnetic field distortions. In the case of the MS, the alignment residuals between the ID and MS have been investigated, and the residual toroidal magnetic field present in the calorimeters has been re-evaluated. A dedicated muon momentum calibration has been implemented. After these corrections, the data-to-simulation agreement is found to be at the per mile level, and the corresponding uncertainties are propagated to the $W$-boson mass measurement. The present work also includes a detailed study of the $W$-boson mass fitting strategy. An analytical Profile Likehood fit in the Gaussian limit has been implemented, allowing a proper decomposition of the fit uncertainties, improving over the usual "impacts". In this scenario, the actual contribution of each systematic source to the final measurement uncertainty can be determined. The resulting measurement data can then be used consistently for further combinations and fits. The analytical fit was used to obtain a $W$ mass measurement at 7 TeV with value $80366.5\pm15.9$ MeV, in good agreement with numerical fits. For the low pile-up dataset, the improved calibration and optimised fitting strategy result in an expected precision of 14.3 MeV. Combining with the 7 TeV data an ultimate precision of 10.3 MeV can be obtained. The compatibility and combination of the world $W$-boson mass using the new ATLAS 2024 measurement at 7 TeV with other measurements (LEP, CDF, D0, and LHCb) was studied. The combination yields $m_W = 80388.4 \pm 10.3$ MeV with 0.2% compatibility when CDF is included, and $m_W = 80366.1 \pm 11.7$ MeV with 92% compatibility when CDF is removed, differing from the CDF result by $3.8\sigma$.