The W electroweak gauge boson was discovered in 1983 at the CERN SPS collider. Although the properties of the W boson have been studied for more than 30 years, precise measurement of its mass remains a major challenge. 

Figure: The ATLAS measurement of the W boson mass is compared to the Standard Model prediction from the electroweak fit, and to the combined values measured at the LEP and Tevatron colliders.

The measurement of the W mass is a very complex measurement. Achieving a high precision in the W mass measurement requires a detailed understanding of many components, both theoretical and experimental and is of prime importance for testing the consistency of the Standard Model or any deviations thereof that could provide indirect signs of new physics.

The Standard Model precisely relates the mass of the W boson to the other SM parameters, At the loop level, the W boson mass is connected with the top quark and the Higgs boson via the radiative corrections to the W mass. In theories beyond the SM, the W mass also receives contributions from new particles.

Previous limits come from electron-positron and proton-antiproton colliders, yielding a combined world average of 80385±15 MeV, driven by the Tevatron results. This measurement is consistent with the Standard Model expectation of 80358±8 MeV. LHC energies help to improve this precision with its complementarity to the previous machine and detectors.

In principle, this measurement can be performed using different methods using transverse variables: a)  the transverse momentum of the lepton, b) the neutrino transverse momentum (which is also referred sometimes to as the missing transverse energy measured by the calorimeter) and finally the transverse mass. The combination of these measurements can improve the precision on the W mass measurement. Each of these different methods provide a different balance between the experimental and theoretical level of precision.

The W mass measurement at the LHC follows a strategy similar to the Tevatron but faces different challenges. Specifically the higher pile-up environment that affects the resolution and calibration of the jets produced in association with the W boson. More specifically, the information stored in the detector when a W is produced is a lepton and a recoiling jet, both of which need to be measured precisely. The shape of the kinematic distributions must be known below the per mil level to get <10 MeV accuracy on the W mass.  To meet this challenge new techniques have being developed to calibrate the lepton momentum scale to this precision and a W-like measurement of the Z mass (using the Z events as test sample to measure the Z mass as if it was a W-like system). Consequently this also poses challenges in controlling the experimental set-up as well as in theoretical modelling.  

The ATLAS collaboration reported the first measurement of the W mass using LHC proton-proton collisions data at a centre-of-mass energy of 7 TeV and corresponding to an integrated luminosity of 4.6 fb-1. The measured value is 80370±19 MeV, consistent with the Standard Model prediction. It is also consistent with the combined values measured at the LEP and Tevatron colliders, and with the world average (see figure). The ATLAS result matches the best single-experiment measurement of the W mass performed by the CDF collaboration.

Probing different kinematic regions compared to the previous measurements from Tevatron (moving to 7 TeV from 2 TeV) means that the uncertainties related to the proton quark substructure are expected to be larger. The enhanced amount of heavy-quark-initiated production, and the ratio of valence and sea quarks in the proton, affect the W boson transverse momentum distribution and its polarisation. The mass measurement is thus particularly sensitive to the parton distribution functions of the proton. This is because the second generation quarks become relevant, as well as there is an  ambiguity between the sea and valence quarks while valence quarks also polarise the W decay along the z-direction.

In addition, the production of the W+ and W- is not symmetric at the LHC as it was in Tevatron where proton - antiproton beams were colliding. Therefore this is a charge dependent analysis that could lead to potentially larger theoretical uncertainties on the measurements. It required an enormous amount of effort to develop an analysis strategy that would minimise model dependence and to tune state of the art detector modelling in the whole range of the transverse momentum.

There are plans to push further for such measurements with the 13 TeV data and this is driven by the expected improvements in the physics modelling. Increased statistics that can indirectly improve not only the systematic experimental uncertainties but also the theoretical set-up for the W mass measurement. Moreover a 13 TeV measurement would probe a different kinematic region. Finally, a better knowledge of the parton distribution functions, and improved QCD and electroweak predictions of W and Z boson production are crucial for further reducing the theoretical uncertainties.