Measuring the W Boson Mass at Hadron Colliders

TL;DR

Measuring the $W$ boson mass $M_W$ at hadron colliders requires precise modeling of $W$ production and decay, including QCD resummation for the $W$ transverse momentum and electroweak radiative corrections. The paper reviews the traditional $M_T$-based method and evaluates detector and theoretical uncertainties, highlighting PDF constraints, recoil modeling, and the need for unified Monte Carlo tools that merge QCD and ${\cal O}(\alpha)$ EW corrections. It also discusses alternative approaches, such as $p_T$-fitting and the $W$–$Z$ ratio method, and provides projections for Run II Tevatron and LHC precision, emphasizing the potential ~30 MeV target per experiment and the importance of systematic control for Higgs-mass indirect constraints. The work underscores the practical challenges and suggests methodological improvements that are critical for achieving high-precision $M_W$ measurements in future hadron-collider experiments.

Abstract

We discuss the prospects for measuring the W mass in Run II of the Tevatron and at the LHC. The basic techniques used to measure M_W are described and the statistical, theoretical and detector-related uncertainties are discussed in detail.

Figures (6)

• Figure 1: The effects of resolution and the finite $p_T^W$ on $p_T(e)$ in $W$ boson decay. The histogram shows $p_T^W$ without detector smearing and for $p_T^W=0$. The dots include the effects of adding finite $p_T^W$, while the shaded histogram includes the effects of detector resolutions. The effects are calculated for the DØ Run I detector resolutions.
• Figure 2: The effects of resolution and the finite $p_T^W$ on $M_T$ in $W\to e\nu$. The histogram shows $M_T$ without detector smearing and for $p_T^W=0$. The dots include the effects of adding finite $p_T^W$, while the shaded histogram includes the effects of detector resolutions. The effects are calculated for the DØ Run I detector resolutions.
• Figure 3: Statistical uncertainties in Run I $M_W$ measurements. Each circle represents either a CDF or DØ measurement. The result of a straight line fit is shown. The shaded box is the approximate extrapolation to a 2 fb$^{-1}$ Run II result.
• Figure 4: Systematic uncertainties for each Run I $M_W$ measurement. The open squares are the four electron measurements from CDF and DØ, the circles are the scale uncertainties from two DØ electron measurements and the Run Ib CDF measurement, and the diamonds are the systematic uncertainties (excluding scale) for the CDF muon measurements. The large box is the position of the extrapolated statistical uncertainties to the Run II luminosity. The lines are linear fits to each set of points.
• Figure 5: (a) A comparison of the two sources of uncertainty on the derived $p_{T}^{W}$ distribution. (b) The $p_{T}^{W}$ distribution extracted for the CDF Run Ib $W\to\mu\nu$ mass measurement.