Studies of theoretical uncertainties on the measurement of the mass of the $W$ boson at the LHC

The measurement of the mass of the $W$ boson at the LHC requires control of both theoretical and experimental uncertainties. The extraction of the $W$-boson mass from the transverse momentum spectrum of electrons and muons produced in the leptonic decay of the $W$ boson, is likely to be limited by theoretical uncertainties. Uncertainties arising from the incomplete knowledge of the parton density functions and from the modelling of the low transverse momentum of the $W$ boson are estimated, accounting for the resolution effects of the ATLAS detector. Emphasis is given to the study of the physical origin of the uncertainties, so as to provide useful information for further reduction of the uncertainties.