54. Mass and Width of the W Boson

1

54. Mass and Width of the W Boson
Revised April 2024 by M. Grünewald (University Coll. Dublin) and A. Gurtu (CERN; TIFRMumbai).
Precision determination of the W mass is of great importance in testing the internal consistencyof the Standard Model. From the time of its discovery in 1983, the W boson has been studied andits mass determined in pp̄ and e+ e− interactions; it is currently studied in pp interactions at theLHC. The mass and width definition used here corresponds to a Breit-Wigner with mass-dependent
width.
Production of on-shell W bosons at hadron colliders is tagged by the high pT charged lepton
from its leptonic decay modes. Owing to the unknown parton-parton effective energy and missing
energy in the longitudinal direction, the hadron collider experiments reconstruct the transverse
mass of the W boson, and derive the W mass from comparing the transverse mass distribution
with Monte Carlo predictions as a function of the mass mW . The transverse momentum of thecharged lepton itself and the transverse missing energy (arising from the neutrino in W decay) arealso sensitive to the W mass and used in its determination. These analyses use the electron andmuon decay modes of the W boson.
At the e+ e− collider LEP, a precise knowledge of the beam energy enables one to determine
the e+ e− → W + W − cross section as a function of center of mass energy, as well as to reconstruct
the W mass precisely from its decay products, even if one of them decays leptonically. Close to√the W + W − production threshold ( s = 161 GeV), the dependence of the W -pair production crosssection on mW is large, and this was used to determine mW . At higher centre-of-mass energies(172 to 209 GeV) this dependence is much weaker, thus W bosons were directly reconstructed andthe mass determined as the invariant mass of the decay products, improving the resolution with akinematic fit.
To compute the LEP average W mass, each experiment provided its measured W mass for theq q̄q q̄ and q q̄`ν, ` = e, µ, τ channels at each center-of-mass energy, along with a detailed decomposition of uncertainty contributions: statistical, uncorrelated, partially correlated and fully correlated
systematics [1]. This yielded a combined LEP average W mass of mW = 80.376±0.033 GeV. Errors
on mW due to uncertainties in the LEP beam energy (9 MeV), and possible effect of color reconnection (CR) and Bose-Einstein correlations (BEC) between quarks from different W bosons (8MeV) are included. Similarly the combined LEP average of the W boson total width is determined
to be ΓW = 2.195 ± 0.083 GeV [1].
In the past a similar procedure was followed for the measurements at hadron colliders. The twoTevatron experiments CDF [2] and D0 [3] identified common systematic errors: uncertainties dueto the parton distribution functions (PDF), radiative corrections, and choice of mass (width) in thewidth (mass) measurements were treated as correlated and the resultant mass [4] and width [5] of
the W were determined. The W boson total width obtained is ΓW = 2.046 ± 0.049 GeV. Similarly
the mass results from the two LHC experiments, ATLAS [6] and LHCb [7] were combined to obtain
an LHC average mass of the W , and an overall hadron collider average of the W mass was obtained
as well [8].
The results on mass and width published by the experiments are shown in Figures 54.1 and54.2, respectively. Until 2022, all measurements were in good agreement with each other and withthe world average [8]. In April 2022 the CDF collaboration published a result mW = 80.4335 ±0.0094 GeV [10], based upon their full Run-II dataset of 8.8 fb−1 . The result is of higher precision
than the 2022 world average, but the two results disagree significantly.11The 2022 CDF result includes the 2.2 fb−1 of data used for the previous CDF Run-II result of 80.387 ± 0.019 GeV
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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54. Mass and Width of the W Boson

2February 2024

6 LEP280.376 ± 0.033

D080.383 ± 0.023

4 ATLAS80.370 ± 0.019

LHCb80.354 ± 0.032

80.3692 ± 0.0133

2 World Avg

χ2/dof = 0.5/3

80.4335 ± 0.0094

CDF 2022
080.3

80.35

80.4

80.45

80.5mW [GeV]
Figure 54.1: Measurements of the W -boson mass by the LEP, Tevatron and LHC experiments.
The CDF 2022 result is not used in the world average. In March 2024, after the cut-off of results
for this review, the ATLAS Collaboration has submitted for publication a refined analysis of theirdata used in [6] and obtained a more precise mass value of 80.3665 ± 0.0159 GeV [9].
February 2024

86420

ALEPH

2.14 ± 0.11

DELPHI

2.40 ± 0.17

L32.18 ± 0.14

OPAL

2.00 ± 0.14

LEP22.1952± 0.083

CDF2.033 ± 0.064

D02.061 ± 0.068

χ /dof = 37/33

Tevatron

2.046 2± 0.049

World Avg

2.085 ± 0.042

χ /dof = 1.4/4

2

Γ W [GeV]

2.5

Figure 54.2: Measurements of the W -boson width by the LEP and Tevatron experiments. InMarch 2024, after the cut-off of results for this review, the ATLAS Collaboration has submitted forpublication a refined analysis of their data used in [6] and obtained a width value of 2.202±0.047 GeV[9].
[2]. Incorporating the improved understanding of PDFs and track reconstruction, the central value of the 2.2 fb−1
result is increased by 13.5 MeV to 80,400.5 MeV [10].
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354. Mass and Width of the W Boson

The LHC-TeV W-mass Working Group, including W-mass experts from all hadron collider
experiments, CDF, D0, ATLAS, CMS, LHCb, has been working to understand better the natureof this disagreement and suggest a way forward to obtain a world average value of the W mass.
Corrections, uncertainties and their correlations have been evaluated to a greater detail and usedin the combination: the central values are corrected to a common theory description and PDF,
and the uncertainties, especially due to PDFs, have been re-evaluated to account for correlations
properly. The group reports [11] that a combination of all W-mass measurements has a probabilityof compatibility of 0.5% only, and is therefore disfavoured. A 91% probability of compatibility isobtained when the CDF-II measurement is removed. The corresponding value of the W boson mass
is mW = 80369.2 ± 13.3 MeV, which we quote as the World Average. More details are given in [11].
The Standard Model prediction from an electroweak fit, including Z-pole data and the measured
masses of the top quark and of the Higgs boson but excluding results on mW and ΓW , implies aW -boson mass of mW = 80.353 ± 0.006 GeV and a W -boson width of ΓW = 2.089 ± 0.001 GeV;
see Section 10, Electroweak Model and Constraints on New Physics, J.Erler and A.Freitas, 2024,
this review. Note that the electroweak fit of Section 10 to all measurements uses slightly different
measurements of the W boson mass and width as explained there.
References[1] S. Schael et al. (ALEPH, DELPHI, L3, OPAL, LEP Electroweak Working Group), Phys. Rept.
532, 119 (2013), [arXiv:1302.3415].
[2] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 108, 151803 (2012), [arXiv:1203.0275].
[3] V. M. Abazov et al. (D0), Phys. Rev. Lett. 108, 151804 (2012), [arXiv:1203.0293].
[4] T. A. Aaltonen et al. (CDF, D0), Phys. Rev. D 88, 5, 052018 (2013), [arXiv:1307.7627].
[5] The Tevatron Electroweak Working Group, for the CDF and D0 Collaborations, March 2010,[arXiv:1003.2826].
[6] M. Aaboud et al. (ATLAS), Eur. Phys. J. C 78, 2, 110 (2018), [Erratum: Eur.Phys.J.C 78,898 (2018)], [arXiv:1701.07240].
[7] R. Aaij et al. (LHCb), JHEP 01, 166 (2022), [arXiv:2107.10090].
[8] R. L. Workman et al. (Particle Data Group), PTEP 2022, 083C01 (2022).
[9] G. Aad et al. (ATLAS) (2024), [arXiv:2403.15085].
[10] T. Aaltonen et al. (CDF), Science 376, 6589, 170 (2022).
[11] S. Amoroso et al. (LHC-TeV MW Working Group), Eur. Phys. J. C 84, 5, 451 (2024),[arXiv:2308.09417].

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