these corrections on the recoil $\phi$ distribution is illustrated in Figure
11(b).

((a))

((b))

Figure 11: Distributions of (a) $\Sigma\bar{E_{\textrm{T}}}$ and (b) azimuth
$\phi$ of the recoil in data and simulation for $Z\to\mu\mu$ events. The
$\Sigma\bar{E_{\textrm{T}}}$ distribution is shown before and after applying
the Smirnov-transform correction, and the $\phi$ distribution is shown before
and after the $u_{x,y}$ correction. The lower panels show the data-to-
prediction ratios, with the vertical bars showing the statistical uncertainty.

The transverse momentum of $Z$ bosons can be reconstructed from the decay-
lepton pair with a resolution of $1$–$2{\mathrm{\ Ge\kern-1.00006ptV}}$, which
is negligible compared to the recoil energy resolution. The recoil response
can thus be calibrated from comparisons with the reconstructed
$p_{\text{T}}^{\ell\ell}$ in data and simulation. Recoil energy scale and
resolution corrections are derived in bins of $\Sigma\bar{E_{\textrm{T}}}$ and
$p_{\text{T}}^{\ell\ell}$ at reconstruction level, and are applied in
simulation as a function of the particle-level vector-boson momentum
$p_{\text{T}}^{V}$ in both the $W$\- and $Z$-boson samples. The energy scale
of the recoil is calibrated by comparing the
$u_{\parallel}^{Z}+p_{\text{T}}^{\ell\ell}$ distribution in data and
simulation, whereas resolution corrections are evaluated from the
$u_{\perp}^{Z}$ distribution. Energy-scale correction factors
$b(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime})$ are defined as the
difference between the average values of the
$u_{\parallel}^{Z}+p_{\text{T}}^{\ell\ell}$ distributions in data and
simulation, and the energy-resolution correction factors
$r(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime})$ as the ratio of the
standard deviations of the corresponding $u_{\perp}^{Z}$ distributions.

The parallel component of $u_{\mathrm{T}}$ in simulated events is corrected
for energy scale and resolution, whereas the perpendicular component is
corrected for energy resolution only. The corrections are defined as follows:

$\displaystyle u^{V,\textrm{corr}}_{\parallel}$ $\displaystyle=$
$\displaystyle
u^{V,\textrm{MC}}_{\parallel}+b(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime})+(u^{V,\textrm{MC}}_{\parallel}+p_{\textrm{T}}^{V})\cdot
r(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime});$ (5) $\displaystyle
u^{V,\textrm{corr}}_{\perp}$ $\displaystyle=$ $\displaystyle
u^{V,\textrm{MC}}_{\perp}\cdot
r(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime}),$ (6)

where $V=W,Z$, $u^{V,\textrm{MC}}_{\parallel}$ and $u^{V,\textrm{MC}}_{\perp}$
are the parallel and perpendicular components of $u_{\mathrm{T}}$ in the
simulation, and $u^{V,\textrm{corr}}_{\parallel}$ and
$u^{V,\textrm{corr}}_{\perp}$ are the corresponding corrected values. Since
the resolution of $u_{\mathrm{T}}$ has a sizeable dependence on the amount of
pile-up, the correction procedure is defined in three bins of
$\left<\mu\right>$, corresponding to low, medium, and high pile-up conditions,
and defined by the ranges of $\left<\mu\right>\,\in[2.5,6.5]$,
$\left<\mu\right>\,\in[6.5,9.5]$, and $\left<\mu\right>\,\in[9.5,16.0]$,
respectively. The effect of the calibration is shown in Figure 12 for
$Z\rightarrow\mu\mu$ events. The level of agreement obtained after corrections
is satisfactory, and similar performance is observed for $Z\rightarrow ee$
events.

((a))  ((b))  ((c))  ((d))

Figure 12: Recoil distributions for (a) $u_{\parallel}^{Z}$, (b)
$u_{\parallel}^{Z}+p_{\text{T}}^{\ell\ell}$, (c) $u_{\perp}^{Z}$, and (d)
$u_{\textrm{T}}$ in $Z\rightarrow\mu\mu$ events. The data are compared to the
simulation before and after applying the recoil corrections described in the
text. The lower panels show the data-to-prediction ratios, with the vertical
bars showing the statistical uncertainty.

A closure test of the applicability of $Z$-based corrections to $W$ production
is performed using $W$ and $Z$ samples simulated with Powheg+Herwig 6, which
provide an alternative model for the description of hadronisation and the
underlying event. The procedure described above is used to correct the recoil
response from Powheg+Pythia 8 to Powheg+Herwig 6, where the latter is treated
as pseudodata. As shown in Figure 13, the corrected $W$ recoil distributions
in Powheg+Pythia 8 match the corresponding distributions in Powheg+Herwig 6.
For this study, the effect of the different particle-level $p_{\text{T}}^{W}$
distributions in both samples is removed by reweighting the Powheg+Pythia 8
prediction to Powheg+Herwig 6. This study is performed applying the standard
lepton selection cuts, but avoiding further kinematic selections in order to
maximize the statistics available for the test.

((a))  ((b))

Figure 13: Distributions of (a) $u_{\textrm{T}}$ and (b)
$u_{\parallel}^{\ell}$ in $W$ events simulated using Powheg+Pythia 8 and
Powheg+Herwig 6. The recoil response in Powheg+Pythia 8 is corrected to the
Powheg+Herwig 6 response using simulated $Z$ events following the method
described in the text. The $p_{\text{T}}^{W}$ distribution in Powheg+Pythia 8
is reweighted to the Powheg+Herwig 6 prediction. The lower panels show the
ratios of Powheg+Herwig 6 to Powheg+Pythia 8, with and without the response
correction in the Powheg+Pythia 8 sample.

###  8.3 Systematic uncertainties

The recoil calibration procedure is sensitive to the following sources of
systematic uncertainty: the uncertainty of the scale factor applied to the
$\left<\mu\right>$ distribution, uncertainties due to the Smirnov transform of
the $\Sigma\bar{E_{\mathrm{T}}}$ distribution, uncertainties in the correction
of the average value of the $u_{x,y}$ distributions, statistical uncertainties
in the residual correction factors and their $p_{\text{T}}$ dependence, and
expected differences in the recoil response between $Z$\- and $W$-boson
events.

The uncertainty from the $\left<\mu\right>$ scale-factor $\alpha$ is evaluated
by varying it by its uncertainty and repeating all steps of the recoil
calibration procedure. These variations affect the determination of $m_{W}$ by
less than $1{\mathrm{\ Me\kern-1.00006ptV}}$.

The systematic uncertainty related to the dependence of the
$\Sigma\bar{E_{\mathrm{T}}}$ correction on $p_{\text{T}}$ is estimated by
comparing with the results of a $p_{\text{T}}$-inclusive correction. This
source contributes, averaging over $W$-boson charges, an uncertainty of
approximately $1{\mathrm{\ Me\kern-1.00006ptV}}$ for the extraction of $m_{W}$
from the $p_{\textrm{T}}^{\ell}$ distribution, and $11{\mathrm{\
Me\kern-1.00006ptV}}$ when using the $m_{\textrm{T}}$ distribution.

The recoil energy scale and resolution corrections of Eqs. (5) and (6) are
derived from the $Z$-boson sample and applied to $W$-boson events. Differences
in the detector response to the recoil between $W$\- and $Z$-boson processes
are considered as a source of systematic uncertainty for these corrections.
Differences between the $u_{\perp}^{W}$ and $u_{\perp}^{Z}$ distributions
originating from different vector-boson kinematic properties, different ISR
and FSR photon emission, and from different selection requirements are,
however, discarded as they are either accurately modelled in the simulation or
already incorporated in the correction procedure.

To remove the effect of such differences, the two-dimensional distribution
$h^{W}_{\textrm{MC}}(p_{\text{T}},\Sigma\bar{E_{\textrm{T}}})$ in $W$-boson
simulated events is corrected to match the corresponding distribution in
$Z$-boson simulated events, treating the neutrinos in $W$-boson decays as
charged leptons to calculate $u_{\textrm{T}}$ as in $Z$-boson events. Finally,
events containing a particle-level photon from final-state radiation are
removed. After these corrections, the standard deviation of the $u_{\perp}$
distribution agrees within 0.03% between simulated $W$\- and $Z$-boson events.
This difference is equivalent to 6% of the size of the residual resolution
correction, which increases the standard deviation of the $u_{\perp}$
distribution by 0.5%. Accordingly, the corresponding systematic uncertainty
due to the extrapolation of the recoil calibration from $Z$\- to $W$-boson
events is estimated by varying the energy resolution parameter $r$ of Eqs. (5)
and (6) by 6%. The impact of this uncertainty on the extraction of $m_{W}$ is
approximately $0.2{\mathrm{\ Me\kern-1.00006ptV}}$ for the
$p_{\textrm{T}}^{\ell}$ distribution, and $5.1{\mathrm{\ Me\kern-1.00006ptV}}$
for the $m_{\textrm{T}}$ distribution. The extrapolation uncertainty of the
energy-scale correction $b$ was found to be negligible in comparison.

In addition, the statistical uncertainty of the correction factors contributes
$2.0{\mathrm{\ Me\kern-1.00006ptV}}$ for the $p_{\textrm{T}}^{\ell}$
distribution, and $2.7{\mathrm{\ Me\kern-1.00006ptV}}$ for the
$m_{\textrm{T}}$ distribution. Finally, instead of using a binned correction,
a smooth interpolation of the correction values between the bins is performed.
Comparing the binned and interpolated correction parameters
$b(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime})$ and
$r(p_{\text{T}}^{V},\Sigma\bar{E_{\textrm{T}}}^{\prime})$ leads to a
systematic uncertainty in $m_{W}$ of $1.4{\mathrm{\ Me\kern-1.00006ptV}}$ and
$3.1{\mathrm{\ Me\kern-1.00006ptV}}$ for the $p_{\text{T}}^{\ell}$ and
$m_{\mathrm{T}}$ distributions, respectively. Systematic uncertainties in the
$u_{x,y}$ corrections are found to be small compared to the other systematic
uncertainties, and are neglected.

The impact of the uncertainties of the recoil calibration on the extraction of
the $W$-boson mass from the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$
distributions are summarised in Table 6. The determination of $m_{W}$ from the
$p_{\text{T}}^{\ell}$ distribution is only slightly affected by the
uncertainties of the recoil calibration, whereas larger uncertainties are
estimated for the $m_{\mathrm{T}}$ distribution. The largest uncertainties are
induced by the $\Sigma\bar{E_{\mathrm{T}}}$ corrections and by the
extrapolation of the recoil energy-scale and energy-resolution corrections
from $Z$\- to $W$-boson events. The systematic uncertainties are in general
smaller for $W^{-}$ events than for $W^{+}$ events, as the
$\Sigma\bar{E_{\mathrm{T}}}$ distribution in $W^{-}$ events is closer to the
corresponding distribution in $Z$-boson events.

$W$-boson charge | $W^{+}$ | $W^{-}$ | Combined
---|---|---|---
Kinematic distribution | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$
$\delta m_{W}$ [MeV] |  |  |  |  |  |
$\left<\mu\right>$ scale factor | 0.2 | 1.0 | 0.2 | 1.0 | 0.2 | 1.0
$\Sigma\bar{E_{\textrm{T}}}$ correction | 0.9 | 12.2 | 1.1 | 10.2 | 1.0 | 11.2
Residual corrections (statistics) | 2.0 | 2.7 | 2.0 | 2.7 | 2.0 | 2.7
Residual corrections (interpolation) | 1.4 | 3.1 | 1.4 | 3.1 | 1.4 | 3.1
Residual corrections ($Z\to W$ extrapolation) | 0.2 | 5.8 | 0.2 | 4.3 | 0.2 | 5.1
Total | 2.6 | 14.2 | 2.7 | 11.8 | 2.6 | 13.0
Table 6: Systematic uncertainties in the $m_{W}$ measurement due to recoil
corrections, for the different kinematic distributions and $W$-boson charge
categories. Combined uncertainties are evaluated as described in Section 2.2.

##  9 Consistency tests with $Z$-boson events

The $Z\rightarrow\ell\ell$ event sample allows several validation and
consistency tests of the $W$-boson analysis to be performed. All the
identification requirements of Section 5.1, the calibration and efficiency
corrections of Sections 7 and 8, as well as the physics-modelling corrections
described in Section 6, are applied consistently in the $W$\- and $Z$-boson
samples. The $Z$-boson sample differs from the $W$-boson sample in the
selection requirements, as described in Section 5.2. In addition to the event-
selection requirements described there, the transverse momentum of the
dilepton system, $p_{\text{T}}^{\ell\ell}$, is required to be smaller than
$30{\mathrm{\ Ge\kern-1.00006ptV}}$.

The missing transverse momentum in $Z$-boson events is defined by treating one
of the two decay leptons as a neutrino and ignoring its transverse momentum
when defining the event kinematics. This procedure allows the
$p_{\text{T}}^{\text{miss}}$ and $m_{\mathrm{T}}$ variables to be defined in
the $Z$-boson sample in close analogy to their definition in the $W$-boson
sample. The procedure is repeated, removing the positive and negative lepton
in turn.

In the $Z$-boson sample, the background contribution arising from top-quark
and electroweak production is estimated using Monte Carlo samples. Each
process is normalised using the corresponding theoretical cross sections,
evaluated at NNLO in the perturbative expansion of the strong coupling
constant. This background contributes a 0.12% fraction in each channel. In the
muon channel, the background contribution from multijet events is estimated to
be smaller than 0.05% using simulated event samples of $b\bar{b}$ and
$c\bar{c}$ production, and neglected. In the electron channel, a data-driven
estimate of the multijet background contributes about a 0.1% fraction, before
applying the isolation selections, which reduce it to a negligible level.

Figure 14 shows the reconstructed distributions of $p_{\text{T}}^{\ell\ell}$
and $y_{\ell\ell}$ in selected $Z$-boson events; these distributions are not
sensitive to the value of $m_{Z}$. Figure 15 shows the corresponding
distributions for $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$, variables which
are sensitive to $m_{Z}$. Data and simulation agree at the level of 1–2%
percent in all the distributions.

((a))  ((b))  ((c))  ((d))

Figure 14: The (a,b) $p_{\text{T}}^{\ell\ell}$ and (c,d) $y_{\ell\ell}$
distributions in $Z$-boson events for the (a,c) electron and (b,d) muon decay
channels. The data are compared to the simulation including signal and
backgrounds. Detector calibration and physics-modelling corrections are
applied to the simulated events. Background events contribute less than 0.2%
of the observed distributions. The lower panels show the data-to-prediction
ratios, with the error bars showing the statistical uncertainty.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 15:  The $p_{\text{T}}^{\ell}$ distribution in the (a) electron and (b)
muon channels, and $m_{\mathrm{T}}$ distributions in the (c,e) electron and
(d,f) muon decay channels for $Z$ events when the (c,d) negatively charged, or
(e,f) positively charged lepton is removed. The data are compared to the
simulation including signal and backgrounds. Detector calibration and physics-
modelling corrections are applied to the simulated events. Background events
contribute less than 0.2% of the observed distributions. The lower panels show
the data-to-prediction ratios, with the error bars showing the statistical
uncertainty.

The mass of the $Z$ boson is extracted with template fits to the
$m_{\ell\ell}$, $p_{\text{T}}^{\ell}$, and $m_{\mathrm{T}}$ kinematic
distributions. The extraction of the $Z$-boson mass from the dilepton
invariant mass distribution is expected to yield, by construction, the value
of $m_{Z}$ used as input for the muon-momentum and electron-energy
calibrations, providing a closure test of the lepton calibration procedures.
The $p_{\text{T}}^{\ell}$ distribution is very sensitive to the physics-
modelling corrections described in Section 6. The comparison of the value of
$m_{Z}$ extracted from the $p_{\text{T}}^{\ell}$ distribution with the value
used as input for the calibration tests the physics modelling and efficiency
corrections. Finally, $m_{Z}$ measurements from the $m_{\mathrm{T}}$
distribution provides a test of the recoil calibration.

Similarly to the $W$-boson mass, the value of $m_{Z}$ is determined by
minimising the $\chi^{2}$ function of the compatibility test between the
templates and the measured distributions. The templates are generated with
values of $m_{Z}$ in steps of $4$ to $25{\mathrm{\ Me\kern-1.00006ptV}}$
within a range of $\pm 450{\mathrm{\ Me\kern-1.00006ptV}}$, centred around a
reference value corresponding to the LEP combined value,
$m_{Z}=91187.5{\mathrm{\ Me\kern-1.00006ptV}}$ [32]. The $\chi^{2}$ function
is interpolated with a second order polynomial. The minimum of the $\chi^{2}$
function yields the extracted value of $m_{Z}$, and the difference between the
extracted value of $m_{Z}$ and the reference value is defined as $\Delta
m_{Z}$. The ranges used for the extraction are $[80,100]{\mathrm{\
Ge\kern-1.00006ptV}}$ for the $m_{\ell\ell}$ distributions, $[30,55]{\mathrm{\
Ge\kern-1.00006ptV}}$ for the $p_{\text{T}}^{\ell}$ distribution, and
$[40,120]{\mathrm{\ Ge\kern-1.00006ptV}}$ for the $m_{\mathrm{T}}$
distribution. The extraction of $m_{Z}$ from the $m_{\mathrm{T}}$ distribution
is performed separately for positively and negatively charged leptons in the
event, by reconstructing $m_{\mathrm{T}}$ from the kinematic properties of one
of the two charged leptons and of the recoil reconstructed by treating the
other as a neutrino.

$Z$-boson mass fits are performed using the $m_{\mathrm{T}}$ and
$p_{\text{T}}^{\ell}$ distributions in the electron and muon decay channels,
inclusively in $\eta$ and separately for positively and negatively charged
leptons. The results of the fits are summarised in Figure 16 and Table 7. The
$p_{\text{T}}^{\ell}$ fit results include all lepton reconstruction systematic
uncertainties except the $Z$-based energy or momentum scale calibration
uncertainties; the $m_{\mathrm{T}}$ fit results include recoil calibration
systematic uncertainties in addition. Physics-modelling uncertainties are
neglected.

The value of $m_{Z}$ measured from positively charged leptons is correlated
with the corresponding extraction from the negatively charged leptons. The
$p_{\text{T}}^{\ell}$ distributions for positively and negatively charged
leptons are statistically independent, but the $m_{\mathrm{T}}$ distributions
share the same reconstructed recoil event by event, and are statistically
correlated. In both cases, the decay of the $Z$-boson induces a kinematical
correlation between the distributions of positively and negatively charged
leptons. The correlation is estimated by constructing two-dimensional
$\ell^{+}$ and $\ell^{-}$ distributions, separately for $p_{\text{T}}^{\ell}$
and $m_{\mathrm{T}}$, fluctuating the bin contents of these distributions
within their uncertainties, and repeating the fits for each pseudodata sample.
The correlation values are $-7\%$ for the $p_{\text{T}}^{\ell}$ distributions,
and $-12\%$ for the $m_{\mathrm{T}}$ distributions.

Figure 16: Summary of the $m_{Z}$ determinations from the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions in the muon and
electron decay channels. The LEP combined value of $m_{Z}$, which is used as
input for the detector calibration, is also indicated. The horizontal and
vertical bands show the uncertainties of the $m_{Z}$ determinations and of the
LEP combined value, respectively.

Accounting for the experimental uncertainties as described above, the combined
extraction of $m_{Z}$ from the $p_{\text{T}}^{\ell}$ distribution yields a
result compatible with the reference value within $0.9$ standard deviations.
The difference between the $m_{Z}$ extractions from positively and negatively
charged lepton distributions is compatible with zero within $1.4$ standard
deviations. For the extraction from the $m_{\mathrm{T}}$ distribution, the
compatibility with the reference value of $m_{Z}$ is at the level of $1.5$
standard deviations. Fits using the lepton pair invariant mass distribution
agree with the reference, yielding $\Delta m_{Z}=1\pm 3{\mathrm{\
Me\kern-1.00006ptV}}$ in the muon channel and $\Delta m_{Z}=3\pm 5{\mathrm{\
Me\kern-1.00006ptV}}$ in the electron channel, as expected from the
calibration procedure. In summary, the consistency tests based on the
$Z$-boson sample agree with the expectations within the experimental
uncertainties.

Lepton charge |  $\ell^{+}$ |  $\ell^{-}$ |  Combined
---|---|---|---
Distribution | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$
$\Delta m_{Z}$ [MeV] |  |  |  |  |  |
$Z\to ee$ | $13\pm 31\pm 10$ | $-93\pm 38\pm 15$ | $-20\pm 31\pm 10$ | $4\pm 38\pm 15$ | $-3\pm 21\pm 10$ | $-45\pm 27\pm 15$
$Z\to\mu\mu$ | $1\pm 22\pm\;\,8$ | $-35\pm 28\pm 13$ | $-36\pm 22\pm\;\,8$ | $-1\pm 27\pm 13$ | $-17\pm 14\pm\;\,8$ | $-18\pm 19\pm 13$
Combined | $5\pm 18\pm\;\,6$ | $-58\pm 23\pm 12$ | $-31\pm 18\pm\;\,6$ | $1\pm 22\pm 12$ | $-12\pm 12\pm\;\,6$ | $-29\pm 16\pm 12$

Table 7:  Difference between $Z$-boson mass, extracted from
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, and the LEP combined
value. The results are shown separately for the electron and muon decay
channels, and their combination. The first quoted uncertainty is statistical,
the second is the experimental systematic uncertainty, which includes lepton
efficiency and recoil calibration uncertainties where applicable. Physics-
modelling uncertainties are neglected.

##  10 Backgrounds in the $W$-boson sample

The $W$-boson event sample, selected as described in Section 5.2, includes
events from various background processes. Background contributions from
$Z$-boson, $W\rightarrow\tau\nu$, boson pair, and top-quark production are
estimated using simulation. Contributions from multijet production are
estimated with data-driven techniques.

###  10.1 Electroweak and top-quark backgrounds

The dominant sources of background contribution in the $W\rightarrow\ell\nu$
sample are $Z\rightarrow\ell\ell$ events, in which one of the two leptons
escapes detection, and $W\rightarrow\tau\nu$ events, where the $\tau$ decays
to an electron or muon. These background contributions are estimated using the
Powheg+Pythia 8 samples after applying the modelling corrections discussed in
Section 6, which include NNLO QCD corrections to the angular coefficients and
rapidity distributions, and corrections to the vector-boson transverse
momentum. The $Z\rightarrow ee$ background represents 2.9% of the $W^{+}\to
e\nu$ sample and 4.0% of the $W^{-}\to e\nu$ sample. In the muon channel, the
$Z\rightarrow\mu\mu$ background represents 4.8% and 6.3% of the
$W^{+}\to\mu\nu$ and $W^{-}\to\mu\nu$ samples, respectively. The $W\to\tau\nu$
background represents 1.0% of the selected sample in both channels, and the
$Z\to\tau\tau$ background contributes approximately 0.12%. The normalisation
of these processes relative to the $W$-boson signal and the corresponding
uncertainties are discussed in Section 4. A relative uncertainty of 0.2% is
assigned to the normalisation of the $W\rightarrow\tau\nu$ samples with
respect to the $W$-boson signal sample, to account for the uncertainty in the
$\tau$-lepton branching fractions to electrons and muons. In the determination
of the $W$-boson mass, the variations of $m_{W}$ are propagated to the
$W\rightarrow\tau\nu$ background templates in the same way as for the signal.

Similarly, backgrounds involving top-quark (top-quark pairs and single top-
quark) production, and boson-pair production are estimated using simulation,
and normalisation uncertainties are assigned as discussed in Section 4. These
processes represent 0.11% and 0.07% of the signal event selection,
respectively.

Uncertainties in the distributions of the $W\rightarrow\tau\nu$ and
$Z\rightarrow\ell\ell$ processes are described by the physics-modelling
uncertainties discussed in Section 6, and are treated as fully correlated with
the signal. Shape uncertainties for boson-pair production and top-quark
production are considered negligible compared to the uncertainties in their
cross sections, given the small contributions of these processes to the signal
event selection.

###  10.2 Multijet background

Inclusive multijet production in strong-interaction processes constitutes a
significant source of background. A fraction of multijet events contains
semileptonic decays of bottom and charm hadrons to muons or electrons and
neutrinos, and can pass the $W$-boson signal selection. In addition, inclusive
jet production contributes to the background if one jet is misidentified as
electron or muon, and sizeable missing transverse momentum is reconstructed in
the event. In-flight decays of pions or kaons within the tracking region can
mimic the $W$-boson signal in the muon channel. In the electron channel,
events with photon conversions and hadrons misidentified as electrons can be
selected as $W$-boson events. Due to the small selection probability for
multijet events, their large production cross section, and the relatively
complex modelling of the hadronisation processes, the multijet background
contribution cannot be estimated precisely using simulation, and a data-driven
method is used instead.

The estimation of the multijet background contribution follows similar
procedures in the electron and muon decay channels, and relies on template
fits to kinematic distributions in background-dominated regions. The analysis
uses the distributions of $p_{\text{T}}^{\text{miss}}$, $m_{\mathrm{T}}$, and
the $p_{\text{T}}^{\ell}/m_{\mathrm{T}}$ ratio, where jet-enriched regions are
obtained by relaxing a subset of the signal event-selection requirements. The
first kinematic region, denoted FR1, is defined by removing the
$p_{\text{T}}^{\text{miss}}$ and $m_{\mathrm{T}}$ requirements from the event
selection. A second kinematic region, FR2, is defined in the same way as FR1,
but by also removing the requirement on $u_{\mathrm{T}}$. Multijet background
events, which tend to have smaller values of $p_{\text{T}}^{\text{miss}}$ and
$m_{\mathrm{T}}$ than the signal, are enhanced by this selection. The
$p_{\text{T}}^{\ell}/m_{\mathrm{T}}$ distribution is sensitive to the angle
between the $p_{\text{T}}^{\ell}$ and $p_{\text{T}}^{\text{miss}}$ vectors in
the transverse plane. Whereas $W$-boson events are expected to peak at values
of $p_{\text{T}}^{\ell}/m_{\mathrm{T}}=0.5$, relatively large tails are
observed for multijet events.

Templates of the multijet background distributions for these observables are
obtained from data by inverting the lepton energy-isolation requirements.
Contamination of these control regions by electroweak and top production is
estimated using simulation and subtracted. In the muon channel, the anti-
isolation requirements are defined from the ratio of the scalar sum of the
$p_{\text{T}}$ of tracks in a cone of size $\Delta R<0.2$ around the
reconstructed muon to the muon $p_{\text{T}}$. The isolation variable
$p_{\text{T}}^{\mu,\textrm{cone}}$, introduced in Section 5.1, is required to
satisfy $c_{1}<p_{\text{T}}^{\mu,\textrm{cone}}/p_{\text{T}}^{\ell}<c_{2}$,
where the anti-isolation boundaries $c_{1}$ and $c_{2}$ are varied as
discussed below. In order to avoid overlap with the signal region, the lower
boundary $c_{1}$ is always larger than $0.1$. In the electron channel, the
scalar sum of the $p_{\text{T}}$ of tracks in a cone of size $\Delta R<0.4$
around the reconstructed electron, defined as $p_{\text{T}}^{e,\textrm{cone}}$
in Section 5.1, is used to define the templates, while the requirements on the
calorimeter isolation are omitted.

The multijet background normalisation is determined by fitting each of the
$p_{\text{T}}^{\text{miss}}$, $m_{\mathrm{T}}$, and
$p_{\text{T}}^{\ell}/m_{\mathrm{T}}$ distributions in the two kinematic
regions FR1 and FR2, using templates of these distributions based on multijet
events and obtained with several ranges of the anti-isolation variables. The
multijet background in the signal region is determined by correcting the
multijet fraction fitted in the FR1 and FR2 for the different efficiencies of
the selection requirements of the signal region. In the electron channel,
$c_{1}$ is varied from $4{\mathrm{\ Ge\kern-1.00006ptV}}$ to $9{\mathrm{\
Ge\kern-1.00006ptV}}$ in steps of $1{\mathrm{\ Ge\kern-1.00006ptV}}$, and
$c_{2}$ is set to $c_{2}=c_{1}+1{\mathrm{\ Ge\kern-1.00006ptV}}$. In the muon
channel, $c_{1}$ is varied from 0.1 to 0.37 in steps of 0.03, and $c_{2}$ is
set to $c_{2}=c_{1}+0.03$. Example results of template fits in the electron
and muon channels are shown in Figure 17. The results corresponding to the
various observables and to the different kinematic regions are linearly
extrapolated in the isolation variables to the signal regions, denoted by
$c_{1}=0$. Figure 18 illustrates the extrapolation procedure.

The systematic uncertainty in the multijet background fraction is defined as
half of the largest difference between the results extrapolated from the
different kinematic regions and observables. The multijet background
contribution is estimated separately in all measurement categories. In the
electron channel, the multijet background fraction rises from 0.58$\pm$0.08%
at low $|\eta_{\ell}|$ to 1.73$\pm$0.19% in the last measurement bin,
averaging the $W^{+}$ and $W^{-}$ channels. In the muon channel, the charge-
averaged multijet background fraction decreases from 0.72$\pm$0.07% to
0.49$\pm$0.03%, when going from low to high $|\eta_{\ell}|$. The uncertainties
in the multijet background fractions are sufficient to account for the
observed residual discrepancies between the fitted distributions and the data
(see Figure 17). The estimated multijet background yields are consistent
between $W^{+}$ and $W^{-}$, but the multijet background fraction is smaller
in the $W^{+}$ channels due to the higher signal yield.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 17: Example template fits to the (a,b) $p_{\text{T}}^{\text{miss}}$,
(c,d) $m_{\mathrm{T}}$, and (e,f) $p_{\text{T}}^{\ell}/m_{\mathrm{T}}$
distributions in the FR1 kinematic region, in the (a,c,e) electron and (b,d,f)
muon decay channels. Multijet templates are derived from the data requiring
$4{\mathrm{\ Ge\kern-1.00006ptV}}<p_{\text{T}}^{e,\textrm{cone}}<8{\mathrm{\
Ge\kern-1.00006ptV}}$ in the electron channel, and
$0.2<p_{\text{T}}^{\mu,\textrm{cone}}/p_{\text{T}}^{\ell}<0.4$ in the muon
channel. The data are compared to the simulation including signal and
background contributions.

Corrections to the shape of the multijet background contributions and
corresponding uncertainties in the distributions used to measure the $W$-boson
mass are estimated with a similar procedure. The kinematic distributions in
the control regions are obtained for a set of anti-isolation ranges, and
parameterised with linear functions of the lower bound of the anti-isolation
requirement. The distributions are extrapolated to the signal regions
accordingly. Uncertainties in the extrapolated distributions are dominated by
the statistical uncertainty, which is determined with a toy MC method by
fluctuating within their statistical uncertainty the bin contents of the
histograms in the various anti-isolation ranges. The resulting multijet
background distribution is propagated to the templates, and the standard
deviation of the determined values of $m_{W}$ yields the estimated uncertainty
due to the shape of the multijet background. Uncertainties due to the choice
of parameterisation are small in comparison and neglected.

Uncertainties in the normalisation of multijet, electroweak, and top-quark
background processes are considered correlated across decay channels, boson
charges and rapidity bins, whereas the uncertainty in the shape of multijet
background is considered uncorrelated between decay channels and boson
charges. The impact of the background systematic uncertainties on the
determination of $m_{W}$ is summarised in Table 8.

((a))  ((b))

Figure 18: Estimated number of multijet-background events as a function of the lower bound of the isolation-variable range used to define the control regions, for (a) electron and (b) muon decay channel. The estimation is performed for the two regions FR1 and FR2 and three distributions $p_{\text{T}}^{\text{miss}}$, $m_{\mathrm{T}}$, and $p_{\text{T}}^{\ell}/m_{\mathrm{T}}$, as described in the text. The linear extrapolations are indicated by the solid lines. The thick crosses show the results of the linear extrapolation of the background estimate to the signal region, including uncertainties from the extrapolation only. The thin crosses also include the uncertainty induced by the contamination of the control regions by EW and top-quark processes. Kinematic distribution | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$
---|---|---
Decay channel | $W\rightarrow e\nu$ | $W\rightarrow\mu\nu$ | $W\rightarrow e\nu$ | $W\rightarrow\mu\nu$
$W$-boson charge | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$ | $W^{+}$ | $W^{-}$
$\delta m_{W}$ [MeV] |  |  |  |  |  |  |  |
$W\rightarrow\tau\nu$ (fraction, shape) | 0.1 | 0.1 | 0.1 | 0.2 | 0.1 | 0.2 | 0.1 | 0.3
$Z\rightarrow ee$ (fraction, shape) | 3.3 | 4.8 | – | – | 4.3 | 6.4 | – | –
$Z\rightarrow\mu\mu$ (fraction, shape) | – | – | 3.5 | 4.5 | – | – | 4.3 | 5.2
$Z\rightarrow\tau\tau$ (fraction, shape) | 0.1 | 0.1 | 0.1 | 0.2 | 0.1 | 0.2 | 0.1 | 0.3
$WW$, $WZ$, $ZZ$ (fraction) | 0.1 | 0.1 | 0.1 | 0.1 | 0.4 | 0.4 | 0.3 | 0.4
Top (fraction) | 0.1 | 0.1 | 0.1 | 0.1 | 0.3 | 0.3 | 0.3 | 0.3
Multijet (fraction) | 3.2 | 3.6 | 1.8 | 2.4 | 8.1 | 8.6 | 3.7 | 4.6
Multijet (shape) | 3.8 | 3.1 | 1.6 | 1.5 | 8.6 | 8.0 | 2.5 | 2.4
Total | 6.0 | 6.8 | 4.3 | 5.3 | 12.6 | 13.4 | 6.2 | 7.4
Table 8: Systematic uncertainties in the $m_{W}$ measurement due to
electroweak, top-quark, and multijet background estimation, for fits to the
$p_{\textrm{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, in the electron
and muon decay channels, with positively and negatively charged $W$ bosons.

##  11 Measurement of the $W$-boson mass

This section presents the determination of the mass of the $W$ boson from
template fits to the kinematic distributions of the $W$-boson decay products.
The final measured value is obtained from the combination of measurements
performed using the lepton transverse momentum and transverse mass
distributions in categories corresponding to the electron and muon decay
channels, positively and negatively charged $W$ bosons, and absolute
pseudorapidity bins of the charged lepton, as illustrated in Table 1. The
number of selected events in each category is shown in Table 9.

$|\eta_{\ell}|$ range | 0–0.8 | 0.8–1.4 | 1.4–2.0 | 2.0–2.4 | Inclusive
---|---|---|---|---|---
$W^{+}\rightarrow\mu^{+}\nu$ | 1 283 332 | 1 063 131 | 1 377 773 | 885 582 | 4 609 818
$W^{-}\rightarrow\mu^{-}\bar{\nu}$ | 1 001 592 | 769 876 | 916 163 | 547 329 | 3 234 960
$|\eta_{\ell}|$ range | 0–0.6 | 0.6–1.2 |  | 1.8–2.4 | Inclusive
$W^{+}\rightarrow e^{+}\nu$ | 1 233 960 | 1 207 136 |  | 956 620 | 3 397 716
$W^{-}\rightarrow e^{-}\bar{\nu}$ | 969 170 | 908 327 |  | 610 028 | 2 487 525
Table 9: Numbers of selected $W^{+}$ and $W^{-}$ events in the different decay
channels in data, inclusively and for the various $|\eta_{\ell}|$ categories.

###  11.1 Control distributions

The detector calibration and the physics modelling are validated by comparing
data with simulated $W$-boson signal and backgrounds for several kinematic
distributions that are insensitive to the $W$-boson mass. The comparison is
based on a $\chi^{2}$ compatibility test, including statistical and systematic
uncertainties, and the bin-to-bin correlations induced by the latter. The
systematic uncertainty comprises all sources of experimental uncertainty
related to the lepton and recoil calibration, and to the background
subtraction, as well as sources of modelling uncertainty associated with
electroweak corrections, or induced by the helicity fractions of vector-boson
production, the vector-boson transverse-momentum distribution, and the PDFs.
Comparisons of data and simulation for the $\eta_{\ell}$, $u_{\mathrm{T}}$,
and $u^{\ell}_{\parallel}$ distributions, in positively and negatively charged
$W$-boson events, are shown in Figures 19 and 20 for the electron and muon
decay channels, respectively. Data and simulation agree for all distributions.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 19: The (a,b) $\eta_{\ell}$, (c,d) $u_{\mathrm{T}}$, and (e,f)
$u_{\parallel}^{\ell}$ distributions for (a,c,e) $W^{+}$ events and (b,d,f)
$W^{-}$ events in the electron decay channel. The data are compared to the
simulation including signal and background contributions. Detector calibration
and physics-modelling corrections are applied to the simulated events. The
lower panels show the data-to-prediction ratios, the error bars show the
statistical uncertainty, and the band shows the systematic uncertainty of the
prediction. The $\chi^{2}$ values displayed in each figure account for all
sources of uncertainty and include the effects of bin-to-bin correlations
induced by the systematic uncertainties.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 20: The (a,b) $\eta_{\ell}$, (c,d) $u_{\mathrm{T}}$, and (e,f)
$u_{\parallel}^{\ell}$ distributions for (a,c,e) $W^{+}$ events and (b,d,f)
$W^{-}$ events in the muon decay channel. The data are compared to the
simulation including signal and background contributions. Detector calibration
and physics-modelling corrections are applied to the simulated events. The
lower panels show the data-to-prediction ratios, the error bars show the
statistical uncertainty, and the band shows the systematic uncertainty of the
prediction. The $\chi^{2}$ values displayed in each figure account for all
sources of uncertainty and include the effects of bin-to-bin correlations
induced by the systematic uncertainties.

###  11.2 Data-driven check of the uncertainty in the $p_{\text{T}}^{W}$
distribution

The uncertainty in the prediction of the $u^{\ell}_{\parallel}$ distribution
is dominated by $p_{\textrm{T}}^{W}$ distribution uncertainties, especially at
negative values of $u^{\ell}_{\parallel}$ in the kinematic region
corresponding to $u^{\ell}_{\parallel}<-15{\mathrm{\ Ge\kern-1.00006ptV}}$.
This is illustrated in Figure 21, which compares the recoil distributions in
the Powheg+Pythia 8 and Powheg+Herwig 6 samples, before and after the
corrections described in Section 8.2 (the $p_{\text{T}}^{W}$ distribution
predicted by Powheg+Pythia 8 is not reweighted to that of Powheg+Herwig 6). As
can be seen, the recoil corrections and the different $p_{\text{T}}^{W}$
distributions have a comparable effect on the $u_{\textrm{T}}$ distribution.
In contrast, the effect of the recoil corrections is small at negative values
of $u^{\ell}_{\parallel}$, whereas the difference in the $p_{\text{T}}^{W}$
distributions has a large impact in this region.

((a))  ((b))

Figure 21: Distributions of (a) $u_{\textrm{T}}$ and (b)
$u_{\parallel}^{\ell}$ in $W\to\mu\nu$ events simulated using Powheg+Pythia 8
and Powheg+Herwig 6 after all analysis selection cuts are applied. The
Powheg+Pythia 8 distributions are shown before and after correction of the
recoil response to that of Powheg+Herwig 6. The lower panels show the ratios
of Powheg+Herwig 6 to Powheg+Pythia 8, with and without the recoil response
correction in the Powheg+Pythia 8 sample. The discrepancy remaining after
recoil corrections reflects the different $p_{\text{T}}^{W}$ distributions.

The sensitivity of the $u^{\ell}_{\parallel}$ distribution to the modelling of
the $p_{\textrm{T}}^{W}$ distribution is exploited to validate the theory-
driven estimate of the $p_{\textrm{T}}^{W}$ uncertainty, described in Section
6.5.2, with a data-driven procedure. The parton-shower factorisation scale
$\mu_{\textrm{F}}$ associated with the $c\bar{q}\to W$ processes constitutes
the main source of uncertainty in the modelling of the $p_{\text{T}}^{W}$
distribution. Variations of the $u^{\ell}_{\parallel}$ distribution induced by
changes in the factorisation scale of the $c\bar{q}\to W$ processes are
parameterised and fitted to the data. The initial range of variation of
$\mu_{\textrm{F}}$ corresponds to factors of $0.5$ and $2.0$ with respect to
the default setting, as described in Section 6.5.2. The $u^{\ell}_{\parallel}$
distribution is predicted for the two boundary values of $\mu_{\textrm{F}}$,
and assumed to vary linearly as a function of $\mu_{\textrm{F}}$. A linear
variable $s$ parameterises the variations induced by changes in
$\mu_{\textrm{F}}$ in units of the initially allowed range, i.e. $s=-1$
corresponds to half the variation from $\mu_{\textrm{F}}=m_{V}$ to
$\mu_{\textrm{F}}=m_{V}/2$, and $s=+1$ corresponds to half the variation from
$\mu_{\textrm{F}}=m_{V}$ to $\mu_{\textrm{F}}=2m_{V}$. The optimal value of
$s$ is determined by fitting the fraction of events which are in the kinematic
region $-30<u^{\ell}_{\parallel}<-15{\mathrm{\ Ge\kern-1.00006ptV}}$. The fit
accounts for all experimental and modelling uncertainties affecting the
$u^{\ell}_{\parallel}$ distribution, and gives a value of $s=-0.22\pm 1.06$.
The uncertainty on the determination of $s$ is dominated by the PDF and
recoil-calibration uncertainties, and matches the initial variation range of
$\mu_{\textrm{F}}$ used to estimate the modelling uncertainty.

This validation test supports the Pythia 8 AZ prediction of the
$p_{\textrm{T}}^{W}$ distribution and the theory-driven associated uncertainty
estimate. The data strongly disagree with the DYRES and Powheg MiNLO+Pythia 8
predictions, as illustrated in Figure 22 and mentioned in Section 6.3.

((a))  ((b))

Figure 22: Ratio between the predictions of Pythia 8 AZ, DYRES and Powheg
MiNLO+Pythia 8 to the data for the (a) $u_{\textrm{T}}$ and (b)
$u_{\parallel}^{\ell}$ distributions in $W\rightarrow\mu\nu$ events. The
$W$-boson rapidity distribution is reweighted according to the NNLO
prediction. The DYRES and Powheg MiNLO+Pythia 8 predictions are shown after
reweighting the $p_{\textrm{T}}^{W}$ distribution in Powheg+Pythia 8. The
error bars on the data points display the statistical uncertainty. The band on
the Pythia 8 AZ prediction represents its total systematic uncertainty,
including experimental and physics-modelling uncertainties.

###  11.3 Results for $m_{W}$ in the measurement categories

Measurements of $m_{W}$ are performed using the $p_{\text{T}}^{\ell}$ and
$m_{\mathrm{T}}$ distributions, separately for positively and negatively
charged $W$ bosons, in three bins of $|\eta_{\ell}|$ in the electron decay
channel, and in four bins of $|\eta_{\ell}|$ in the muon decay channel,
leading to a total of 28 $m_{W}$ determinations. In each category, the value
of $m_{W}$ is determined by a $\chi^{2}$ minimisation, comparing the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions in data and
simulation for different values of $m_{W}$. The templates are generated with
values of $m_{W}$ in steps of $1$ to $10{\mathrm{\ Me\kern-1.00006ptV}}$
within a range of $\pm 400{\mathrm{\ Me\kern-1.00006ptV}}$, centred around the
reference value used in the Monte Carlo signal samples. The statistical
uncertainty is estimated from the half width of the $\chi^{2}$ function at the
value corresponding to one unit above the minimum. Systematic uncertainties
due to physics-modelling corrections, detector-calibration corrections, and
background subtraction, are discussed in Sections 6–8 and 10, respectively.

The lower and upper bounds of the range of the $p_{\text{T}}^{\ell}$
distribution used in the fit are varied from $30$ to $35{\mathrm{\
Ge\kern-1.00006ptV}}$, and from $45$ to $50{\mathrm{\ Ge\kern-1.00006ptV}}$
respectively, in steps of $1{\mathrm{\ Ge\kern-1.00006ptV}}$. For the
$m_{\mathrm{T}}$ distribution, the boundaries are varied from $65$ to
$70{\mathrm{\ Ge\kern-1.00006ptV}}$, and from $90$ to $100{\mathrm{\
Ge\kern-1.00006ptV}}$. The total measurement uncertainty is evaluated for each
range, after combining the measurement categories as described in Section 11.4
below. The smallest total uncertainty in $m_{W}$ is found for the fit ranges
$32<p_{\text{T}}^{\ell}<45{\mathrm{\ Ge\kern-1.00006ptV}}$ and
$66<m_{\mathrm{T}}<99{\mathrm{\ Ge\kern-1.00006ptV}}$. The optimisation is
performed before the unblinding of the $m_{W}$ value and the optimised range
is used for all the results described below.

The final measurement uncertainty is dominated by modelling uncertainties,
with typical values in the range $25$–$35{\mathrm{\ Me\kern-1.00006ptV}}$ for
the various charge and $|\eta_{\ell}|$ categories. Lepton-calibration
uncertainties are the dominant sources of experimental systematic uncertainty
for the extraction of $m_{W}$ from the $p_{\text{T}}^{\ell}$ distribution.
These uncertainties vary from about $15{\mathrm{\ Me\kern-1.00006ptV}}$ to
about $35{\mathrm{\ Me\kern-1.00006ptV}}$ for most measurement categories,
except the highest $|\eta|$ bin in the muon channel where the total
uncertainty of about $120{\mathrm{\ Me\kern-1.00006ptV}}$ is dominated by the
muon momentum linearity uncertainty. The uncertainty in the calibration of the
recoil is the largest source of experimental systematic uncertainty for the
$m_{\mathrm{T}}$ distribution, with a typical contribution of about
$15{\mathrm{\ Me\kern-1.00006ptV}}$ for all categories. The determination of
$m_{W}$ from the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions in
the various categories is summarised in Table 10, including an overview of
statistical and systematic uncertainties. The results are also shown in Figure
23. No significant differences in the values of $m_{W}$ corresponding to the
different decay channels and to the various charge and $|\eta_{\ell}|$
categories are observed.

((a))  ((b))

Figure 23: Overview of the $m_{W}$ measurements in the (a) electron and (b)
muon decay channels. Results are shown for the $p_{\text{T}}^{\ell}$ and
$m_{\mathrm{T}}$ distributions, for $W^{+}$ and $W^{-}$ events in the
different $|\eta_{\ell}|$ categories. The coloured bands and solid lines show
the statistical and total uncertainties, respectively. The horizontal line and
band show the fully combined result and its uncertainty.

Channel | $m_{W}$ | Stat. | Muon | Elec. | Recoil | Bckg. | QCD | EW | PDF | Total
---|---|---|---|---|---|---|---|---|---|---
$m_{\mathrm{T}}$-Fit | [MeV] | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc.
$W^{+}\rightarrow\mu\nu,|\eta|<0.8$ | 80371.3 | 29.2 | 12.4 | 0.0 | 15.2 | 8.1 | 9.9 | 3.4 | 28.4 | 47.1
$W^{+}\rightarrow\mu\nu,0.8<|\eta|<1.4$ | 80354.1 | 32.1 | 19.3 | 0.0 | 13.0 | 6.8 | 9.6 | 3.4 | 23.3 | 47.6
$W^{+}\rightarrow\mu\nu,1.4<|\eta|<2.0$ | 80426.3 | 30.2 | 35.1 | 0.0 | 14.3 | 7.2 | 9.3 | 3.4 | 27.2 | 56.9
$W^{+}\rightarrow\mu\nu,2.0<|\eta|<2.4$ | 80334.6 | 40.9 | 112.4 | 0.0 | 14.4 | 9.0 | 8.4 | 3.4 | 32.8 | 125.5
$W^{-}\rightarrow\mu\nu,|\eta|<0.8$ | 80375.5 | 30.6 | 11.6 | 0.0 | 13.1 | 8.5 | 9.5 | 3.4 | 30.6 | 48.5
$W^{-}\rightarrow\mu\nu,0.8<|\eta|<1.4$ | 80417.5 | 36.4 | 18.5 | 0.0 | 12.2 | 7.7 | 9.7 | 3.4 | 22.2 | 49.7
$W^{-}\rightarrow\mu\nu,1.4<|\eta|<2.0$ | 80379.4 | 35.6 | 33.9 | 0.0 | 10.5 | 8.1 | 9.7 | 3.4 | 23.1 | 56.9
$W^{-}\rightarrow\mu\nu,2.0<|\eta|<2.4$ | 80334.2 | 52.4 | 123.7 | 0.0 | 11.6 | 10.2 | 9.9 | 3.4 | 34.1 | 139.9
$W^{+}\rightarrow e\nu,|\eta|<0.6$ | 80352.9 | 29.4 | 0.0 | 19.5 | 13.1 | 15.3 | 9.9 | 3.4 | 28.5 | 50.8
$W^{+}\rightarrow e\nu,0.6<|\eta|<1.2$ | 80381.5 | 30.4 | 0.0 | 21.4 | 15.1 | 13.2 | 9.6 | 3.4 | 23.5 | 49.4
$W^{+}\rightarrow e\nu,1,8<|\eta|<2.4$ | 80352.4 | 32.4 | 0.0 | 26.6 | 16.4 | 32.8 | 8.4 | 3.4 | 27.3 | 62.6
$W^{-}\rightarrow e\nu,|\eta|<0.6$ | 80415.8 | 31.3 | 0.0 | 16.4 | 11.8 | 15.5 | 9.5 | 3.4 | 31.3 | 52.1
$W^{-}\rightarrow e\nu,0.6<|\eta|<1.2$ | 80297.5 | 33.0 | 0.0 | 18.7 | 11.2 | 12.8 | 9.7 | 3.4 | 23.9 | 49.0
$W^{-}\rightarrow e\nu,1.8<|\eta|<2.4$ | 80423.8 | 42.8 | 0.0 | 33.2 | 12.8 | 35.1 | 9.9 | 3.4 | 28.1 | 72.3
$p_{\text{T}}$-Fit |  |  |  |  |  |  |  |  |  |
$W^{+}\rightarrow\mu\nu,|\eta|<0.8$ | 80327.7 | 22.1 | 12.2 | 0.0 | 2.6 | 5.1 | 9.0 | 6.0 | 24.7 | 37.3
$W^{+}\rightarrow\mu\nu,0.8<|\eta|<1.4$ | 80357.3 | 25.1 | 19.1 | 0.0 | 2.5 | 4.7 | 8.9 | 6.0 | 20.6 | 39.5
$W^{+}\rightarrow\mu\nu,1.4<|\eta|<2.0$ | 80446.9 | 23.9 | 33.1 | 0.0 | 2.5 | 4.9 | 8.2 | 6.0 | 25.2 | 49.3
$W^{+}\rightarrow\mu\nu,2.0<|\eta|<2.4$ | 80334.1 | 34.5 | 110.1 | 0.0 | 2.5 | 6.4 | 6.7 | 6.0 | 31.8 | 120.2
$W^{-}\rightarrow\mu\nu,|\eta|<0.8$ | 80427.8 | 23.3 | 11.6 | 0.0 | 2.6 | 5.8 | 8.1 | 6.0 | 26.4 | 39.0
$W^{-}\rightarrow\mu\nu,0.8<|\eta|<1.4$ | 80395.6 | 27.9 | 18.3 | 0.0 | 2.5 | 5.6 | 8.0 | 6.0 | 19.8 | 40.5
$W^{-}\rightarrow\mu\nu,1.4<|\eta|<2.0$ | 80380.6 | 28.1 | 35.2 | 0.0 | 2.6 | 5.6 | 8.0 | 6.0 | 20.6 | 50.9
$W^{-}\rightarrow\mu\nu,2.0<|\eta|<2.4$ | 80315.2 | 45.5 | 116.1 | 0.0 | 2.6 | 7.6 | 8.3 | 6.0 | 32.7 | 129.6
$W^{+}\rightarrow e\nu,|\eta|<0.6$ | 80336.5 | 22.2 | 0.0 | 20.1 | 2.5 | 6.4 | 9.0 | 5.3 | 24.5 | 40.7
$W^{+}\rightarrow e\nu,0.6<|\eta|<1.2$ | 80345.8 | 22.8 | 0.0 | 21.4 | 2.6 | 6.7 | 8.9 | 5.3 | 20.5 | 39.4
$W^{+}\rightarrow e\nu,1,8<|\eta|<2.4$ | 80344.7 | 24.0 | 0.0 | 30.8 | 2.6 | 11.9 | 6.7 | 5.3 | 24.1 | 48.2
$W^{-}\rightarrow e\nu,|\eta|<0.6$ | 80351.0 | 23.1 | 0.0 | 19.8 | 2.6 | 7.2 | 8.1 | 5.3 | 26.6 | 42.2
$W^{-}\rightarrow e\nu,0.6<|\eta|<1.2$ | 80309.8 | 24.9 | 0.0 | 19.7 | 2.7 | 7.3 | 8.0 | 5.3 | 20.9 | 39.9
$W^{-}\rightarrow e\nu,1.8<|\eta|<2.4$ | 80413.4 | 30.1 | 0.0 | 30.7 | 2.7 | 11.5 | 8.3 | 5.3 | 22.7 | 51.0

Table 10: Results of the $m_{W}$ measurements in the electron and muon decay
channels, for positively and negatively charged $W$ bosons, in different
lepton-$|\eta|$ ranges, using the $m_{\mathrm{T}}$ and $p_{\text{T}}^{\ell}$
distributions in the optimised fitting range. The table shows the statistical
uncertainties, together with all experimental uncertainties, divided into
muon-, electron-, recoil- and background-related uncertainties, and all
modelling uncertainties, separately for QCD modelling including scale
variations, parton shower and angular coefficients, electroweak corrections,
and PDFs. All uncertainties are given in MeV.

The comparison of data and simulation for kinematic distributions sensitive to
the value of $m_{W}$ provides further validation of the detector calibration
and physics modelling. The comparison is performed in all measurement
categories. The $\eta$-inclusive $p_{\text{T}}^{\ell}$, $m_{\mathrm{T}}$ and
$p_{\text{T}}^{\text{miss}}$ distributions for positively and negatively
charged $W$ bosons are shown in Figures 24 and 25 for the electron and muon
decay channels, respectively. The value of $m_{W}$ used in the predictions is
set to the overall measurement result presented in the next section. The
$\chi^{2}$ values quantifying the comparison between data and prediction are
calculated over the full histogram range and account for all sources of
uncertainty. The bin-to-bin correlations induced by the experimental and
physics-modelling systematic uncertainties are also accounted for. Overall,
satisfactory agreement is observed. The deficit of data visible for
$p_{\text{T}}^{\ell}\sim 40$–$42{\mathrm{\ Ge\kern-1.00006ptV}}$ in the
$W^{+}\rightarrow e^{+}\nu$ channel does not strongly affect the mass
measurement, as the observed effect differs from that expected from $m_{W}$
variations. Cross-checks of possible sources of this effect were performed,
and its impact on the mass determination was shown to be within the
corresponding systematic uncertainties.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 24: The (a,b) $p_{\text{T}}^{\ell}$, (c,d) $m_{\mathrm{T}}$, and (e,f)
$p_{\text{T}}^{\text{miss}}$ distributions for (a,c,e) $W^{+}$ events and
(b,d,f) $W^{-}$ events in the electron decay channel. The data are compared to
the simulation including signal and background contributions. Detector
calibration and physics-modelling corrections are applied to the simulated
events. For all simulated distributions, $m_{W}$ is set according to the
overall measurement result. The lower panels show the data-to-prediction
ratios, the error bars show the statistical uncertainty, and the band shows
the systematic uncertainty of the prediction. The $\chi^{2}$ values displayed
in each figure account for all sources of uncertainty and include the effects
of bin-to-bin correlations induced by the systematic uncertainties.

((a))  ((b))  ((c))  ((d))  ((e))  ((f))

Figure 25: The (a,b) $p_{\text{T}}^{\ell}$, (c,d) $m_{\mathrm{T}}$, and (e,f)
$p_{\text{T}}^{\text{miss}}$ distributions for (a,c,e) $W^{+}$ events and
(b,d,f) $W^{-}$ events in the muon decay channel. The data are compared to the
simulation including signal and background contributions. Detector calibration
and physics-modelling corrections are applied to the simulated events. For all
simulated distributions, $m_{W}$ is set according to the overall measurement
result. The lower panels show the data-to-prediction ratios, the error bars
show the statistical uncertainty, and the band shows the systematic
uncertainty of the prediction. The $\chi^{2}$ values displayed in each figure
account for all sources of uncertainty and include the effects of bin-to-bin
correlations induced by the systematic uncertainties.

###  11.4 Combination and final results

The measurements of $m_{W}$ in the various categories are combined accounting
for statistical and systematic uncertainties and their correlations. The
statistical correlation of the $m_{W}$ values determined from the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions is evaluated with the
bootstrap method [113], and is approximately 50% for all measurement
categories.

The systematic uncertainties have specific correlation patterns across the
$m_{W}$ measurement categories. Muon-momentum and electron-energy calibration
uncertainties are uncorrelated between the different decay channels, but
largely correlated between the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$
distributions. Recoil-calibration uncertainties are correlated between
electron and muon decay channels, and they are small for $p_{\text{T}}^{\ell}$
distributions. The PDF-induced uncertainties are largely correlated between
electron and muon decay channels, but significantly anti-correlated between
positively and negatively charged $W$ bosons, as discussed in Section 6. Due
to the different balance of systematic uncertainties and to the variety of
correlation patterns, a significant reduction of the uncertainties in the
measurement of $m_{W}$ is achieved by combining the different decay channels
and the charge and $|\eta_{\ell}|$ categories.

As discussed in Section 2, the comparison of the results from the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, from the different
decay channels, and in the various charge and $|\eta_{\ell}|$ categories,
provides a test of the experimental and physics modelling corrections.
Discrepancies between the positively and negatively charged lepton categories,
or in the various $|\eta_{\ell}|$ bins would primarily indicate an
insufficient understanding of physics-modelling effects, such as the PDFs and
the $p_{\text{T}}^{W}$ distribution. Inconsistencies between the electron and
muon channels could indicate problems in the calibration of the muon-momentum
and electron-energy responses. Significant differences between results from
the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions would point to
either problems in the calibration of the recoil, or to an incorrect modelling
of the transverse-momentum distribution of the $W$ boson. Several measurement
combinations are performed, using the best linear unbiased estimate (BLUE)
method [114, 115]. The results of the combinations are verified with the
HERAverager program [116], which gives very close results.

Table 11 shows an overview of the $m_{W}$ measurement combinations. In the
first step, determinations of $m_{W}$ in the electron and muon decay channels
from the $m_{\mathrm{T}}$ distribution are combined separately for the
positive- and negative-charge categories, and together for both $W$-boson
charges. The results are compatible, and the positively charged, negatively
charged, and charge-inclusive combinations yield values of $\chi^{2}/$dof
corresponding to $2/6$, $7/6$, and $11/13$, respectively. Compatibility of the
results is also observed for the corresponding combinations from the
$p_{\text{T}}^{\ell}$ distribution, with values of $\chi^{2}/$dof of $5/6$,
$10/6$, and $19/13$, for positively charged, negatively charged, and charge-
inclusive combinations, respectively. The $\chi^{2}$ compatibility test
validates the consistency of the results in the $W\rightarrow e\nu$ and
$W\rightarrow\mu\nu$ decay channels. The precision of the determination of
$m_{W}$ from the $m_{\mathrm{T}}$ distribution is slightly worse than the
result obtained from the $p_{\text{T}}^{\ell}$ distribution, due to the larger
uncertainty induced by the recoil calibration. In addition, the impact of PDF-
and $p_{\text{T}}^{W}$-related uncertainties on the $p_{\text{T}}^{\ell}$ fits
is limited by the optimisation of the fitting range. In the second step,
determinations of $m_{W}$ from the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$
distributions are combined separately for the electron and the muon decay
channels. The results are compatible, with values of $\chi^{2}/$dof of 4/5 and
8/5 in the electron channel for the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$
distributions, respectively, and values of 7/7 and 3/7 in the muon channel for
the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, respectively.
The $m_{W}$ determinations in the electron and in the muon channels agree,
further validating the consistency of the electron and muon calibrations.
Agreement between the $m_{W}$ determinations from the $p_{\text{T}}^{\ell}$
and $m_{\mathrm{T}}$ distributions supports the calibration of the recoil, and
the modelling of the transverse momentum of the $W$ boson.

The results are summarised in Table 11 and illustrated in Figure 26. The
combination of all the determinations of $m_{W}$ reported in Table 10 has a
value of $\chi^{2}/$dof of $29/27$, and yields a final result of

$\displaystyle m_{W}$ $\displaystyle=$ $\displaystyle 80369.5\pm 6.8{\mathrm{\
Me\kern-1.00006ptV}}(\textrm{stat.})\pm 10.6{\mathrm{\
Me\kern-1.00006ptV}}(\textrm{exp. syst.})\pm 13.6{\mathrm{\
Me\kern-1.00006ptV}}(\textrm{mod. syst.})$ $\displaystyle=$ $\displaystyle
80369.5\pm 18.5{\mathrm{\ Me\kern-1.00006ptV}},$

where the first uncertainty is statistical, the second corresponds to the
experimental systematic uncertainty, and the third to the physics-modelling
systematic uncertainty. The latter dominates the total measurement
uncertainty, and it itself dominated by strong interaction uncertainties. The
experimental systematic uncertainties are dominated by the lepton calibration;
backgrounds and the recoil calibration have a smaller impact. In the final
combination, the muon decay channel has a weight of 57%, and the
$p_{\text{T}}^{\ell}$ fit dominates the measurement with a weight of 86%.
Finally, the charges contribute similarly with a weight of 52% for $W^{+}$ and
of 48% for $W^{-}$.

Figure 26: Overview of the $m_{W}$ determinations from the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, and for the
combination of the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions,
in the muon and electron decay channels and for $W^{+}$ and $W^{-}$ events.
The horizontal lines and bands show the statistical and total uncertainties of
the individual $m_{W}$ determinations. The combined result for $m_{W}$ and its
statistical and total uncertainties are also indicated (vertical line and
bands).

Combined | Value | Stat. | Muon | Elec. | Recoil | Bckg. | QCD | EW | PDF | Total |  $\chi^{2}/$dof
---|---|---|---|---|---|---|---|---|---|---|---
categories | [MeV] | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | of Comb.
$m_{\mathrm{T}}$, $W^{+}$, $e$-$\mu$ | 80370.0 | 12.3 | 8.3 | 6.7 | 14.5 | 9.7 | 9.4 | 3.4 | 16.9 | 30.9 | 2/6
$m_{\mathrm{T}}$, $W^{-}$, $e$-$\mu$ | 80381.1 | 13.9 | 8.8 | 6.6 | 11.8 | 10.2 | 9.7 | 3.4 | 16.2 | 30.5 | 7/6
$m_{\mathrm{T}}$, $W^{\pm}$, $e$-$\mu$ | 80375.7 | 9.6 | 7.8 | 5.5 | 13.0 | 8.3 | 9.6 | 3.4 | 10.2 | 25.1 | 11/13
$p_{\text{T}}^{\ell}$, $W^{+}$, $e$-$\mu$ | 80352.0 | 9.6 | 6.5 | 8.4 | 2.5 | 5.2 | 8.3 | 5.7 | 14.5 | 23.5 | 5/6
$p_{\text{T}}^{\ell}$, $W^{-}$, $e$-$\mu$ | 80383.4 | 10.8 | 7.0 | 8.1 | 2.5 | 6.1 | 8.1 | 5.7 | 13.5 | 23.6 | 10/6
$p_{\text{T}}^{\ell}$, $W^{\pm}$, $e$-$\mu$ | 80369.4 | 7.2 | 6.3 | 6.7 | 2.5 | 4.6 | 8.3 | 5.7 | 9.0 | 18.7 | 19/13
$p_{\text{T}}^{\ell}$, $W^{\pm}$, $e$ | 80347.2 | 9.9 | 0.0 | 14.8 | 2.6 | 5.7 | 8.2 | 5.3 | 8.9 | 23.1 | 4/5
$m_{\mathrm{T}}$, $W^{\pm}$, $e$ | 80364.6 | 13.5 | 0.0 | 14.4 | 13.2 | 12.8 | 9.5 | 3.4 | 10.2 | 30.8 | 8/5
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{+}$, $e$ | 80345.4 | 11.7 | 0.0 | 16.0 | 3.8 | 7.4 | 8.3 | 5.0 | 13.7 | 27.4 | 1/5
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{-}$, $e$ | 80359.4 | 12.9 | 0.0 | 15.1 | 3.9 | 8.5 | 8.4 | 4.9 | 13.4 | 27.6 | 8/5
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{\pm}$, $e$ | 80349.8 | 9.0 | 0.0 | 14.7 | 3.3 | 6.1 | 8.3 | 5.1 | 9.0 | 22.9 | 12/11
$p_{\text{T}}^{\ell}$, $W^{\pm}$, $\mu$ | 80382.3 | 10.1 | 10.7 | 0.0 | 2.5 | 3.9 | 8.4 | 6.0 | 10.7 | 21.4 | 7/7
$m_{\mathrm{T}}$, $W^{\pm}$, $\mu$ | 80381.5 | 13.0 | 11.6 | 0.0 | 13.0 | 6.0 | 9.6 | 3.4 | 11.2 | 27.2 | 3/7
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{+}$, $\mu$ | 80364.1 | 11.4 | 12.4 | 0.0 | 4.0 | 4.7 | 8.8 | 5.4 | 17.6 | 27.2 | 5/7
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{-}$, $\mu$ | 80398.6 | 12.0 | 13.0 | 0.0 | 4.1 | 5.7 | 8.4 | 5.3 | 16.8 | 27.4 | 3/7
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{\pm}$, $\mu$ | 80382.0 | 8.6 | 10.7 | 0.0 | 3.7 | 4.3 | 8.6 | 5.4 | 10.9 | 21.0 | 10/15
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{+}$, $e$-$\mu$ | 80352.7 | 8.9 | 6.6 | 8.2 | 3.1 | 5.5 | 8.4 | 5.4 | 14.6 | 23.4 | 7/13
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{-}$, $e$-$\mu$ | 80383.6 | 9.7 | 7.2 | 7.8 | 3.3 | 6.6 | 8.3 | 5.3 | 13.6 | 23.4 | 15/13
$m_{\mathrm{T}}$-$p_{\text{T}}^{\ell}$, $W^{\pm}$, $e$-$\mu$ | 80369.5 | 6.8 | 6.6 | 6.4 | 2.9 | 4.5 | 8.3 | 5.5 | 9.2 | 18.5 | 29/27

Table 11: Results of the $m_{W}$ measurements for various combinations of
categories. The table shows the statistical uncertainties, together with all
experimental uncertainties, divided into muon-, electron-, recoil- and
background-related uncertainties, and all modelling uncertainties, separately
for QCD modelling including scale variations, parton shower and angular
coefficients, electroweak corrections, and PDFs. All uncertainties are given
in MeV.

The result is in agreement with the current world average of $m_{W}=80385\pm
15{\mathrm{\ Me\kern-1.00006ptV}}$ [29], and has a precision comparable to the
currently most precise single measurements of the CDF and D0 collaborations
[22, 23].

###  11.5 Additional validation tests

The final combination of $m_{W}$, presented above, depends only on template
fits to the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions. As a
validation test, the value of $m_{W}$ is determined from the
$p_{\text{T}}^{\text{miss}}$ distribution, performing a fit in the range
$30<p_{\text{T}}^{\text{miss}}<60{\mathrm{\ Ge\kern-1.00006ptV}}$. Consistent
results are observed in all measurement categories, leading to combined
results of $80364\pm 26(\textrm{stat}){\mathrm{\ Me\kern-1.00006ptV}}$ and
$80367\pm 23(\textrm{stat}){\mathrm{\ Me\kern-1.00006ptV}}$ for the electron
and muon channels, respectively.

Several additional studies are performed to validate the stability of the
$m_{W}$ measurement. The stability of the result with respect to different
pile-up conditions is tested by dividing the event sample into three bins of
$\left<\mu\right>$, namely $[2.5,6.5]$, $[6.5,9.5]$, and $[9.5,16]$. In each
bin, $m_{W}$ measurements are performed independently using the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions. This categorisation
also tests the stability of $m_{W}$ with respect to data-taking periods, as
the later data-taking periods have on average more pile-up due to the
increasing LHC luminosity.

The calibration of the recoil and the modelling of the $p_{\text{T}}^{W}$
distribution are tested by performing $m_{W}$ fits in two bins of the recoil
corresponding to $[0,15]{\mathrm{\ Ge\kern-1.00006ptV}}$ and
$[15,30]{\mathrm{\ Ge\kern-1.00006ptV}}$, and in two regions corresponding to
positive and negative values of $u_{\parallel}^{\ell}$. The analysis is also
repeated with the $p_{\text{T}}^{\text{miss}}$ requirement removed from the
signal selection, leading to a lower recoil modelling uncertainty but a higher
multijet background contribution. The stability of the $m_{W}$ measurements
upon removal of this requirement is studied, and consistent results are
obtained. All $m_{W}$ determinations are consistent with the nominal result.
An overview of the validation tests is shown in Table 12, where only
statistical uncertainties are given. Fitting ranges of
$30<p_{\text{T}}^{\ell}<50{\mathrm{\ Ge\kern-1.00006ptV}}$ and
$65<m_{\mathrm{T}}<100{\mathrm{\ Ge\kern-1.00006ptV}}$ are used for all these
validation tests, to minimise the statistical uncertainty.

Decay channel |  $W\rightarrow e\nu$ |  $W\rightarrow\mu\nu$ |  Combined
---|---|---|---
Kinematic distribution | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$ | $p_{\text{T}}^{\ell}$ | $m_{\mathrm{T}}$
$\Delta m_{W}$ [MeV] |  |  |  |  |  |
$\left<\mu\right>$ in $[2.5,6.5]$ | $8\pm 14$ | $14\pm 18$ | $-21\pm 12$ | $0\pm 16$ | $-9\pm\;\,9$ | $6\pm 12$
$\left<\mu\right>$ in $[6.5,9.5]$ | $-6\pm 16$ | $6\pm 23$ | $12\pm 15$ | $-8\pm 22$ | $4\pm 11$ | $-1\pm 16$
$\left<\mu\right>$ in $[9.5,16]$ | $-1\pm 16$ | $3\pm 27$ | $25\pm 16$ | $35\pm 26$ | $12\pm 11$ | $20\pm 19$
$u_{\mathrm{T}}$ in $[0,15]{\mathrm{\ Ge\kern-1.00006ptV}}$ | $0\pm 11$ | $-8\pm 13$ | $5\pm 10$ | $8\pm 12$ | $3\pm\;\,7$ | $-1\pm\;\,9$
$u_{\mathrm{T}}$ in $[15,30]{\mathrm{\ Ge\kern-1.00006ptV}}$ | $10\pm 15$ | $0\pm 24$ | $-4\pm 14$ | $-18\pm 22$ | $2\pm 10$ | $-10\pm 16$
$u_{\parallel}^{\ell}<0\,{\mathrm{\ Ge\kern-1.00006ptV}}$ | $8\pm 15$ | $20\pm 17$ | $3\pm 13$ | $-1\pm 16$ | $5\pm 10$ | $9\pm 12$
$u_{\parallel}^{\ell}>0\,{\mathrm{\ Ge\kern-1.00006ptV}}$ | $-9\pm 10$ | $1\pm 14$ | $-12\pm 10$ | $10\pm 13$ | $-11\pm\;\,7$ | $6\pm 10$
No $p_{\text{T}}^{\text{miss}}$-cut | $14\pm\;\,9$ | $-1\pm 13$ | $10\pm\;\,8$ | $-6\pm 12$ | $12\pm\;\,6$ | $-4\pm\;\,9$
Table 12: Summary of consistency tests for the determination of $m_{W}$ in
several additional measurement categories. The $\Delta m_{W}$ values
correspond to the difference between the result for each category and the
inclusive result for the corresponding observable ($p_{\text{T}}^{\ell}$ or
$m_{\mathrm{T}}$). The uncertainties correspond to the statistical uncertainty
of the fit to the data of each category alone. Fitting ranges of
$30<p_{\text{T}}^{\ell}<50{\mathrm{\ Ge\kern-1.00006ptV}}$ and
$65<m_{\mathrm{T}}<100{\mathrm{\ Ge\kern-1.00006ptV}}$ are used.

Finally, the stability of the measurement with respect to variations of the
kinematic ranges used for the template fits is studied. The lower and upper
bounds of the range of the $p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$
distributions are varied as in the optimisation procedure described in Section
11.3. The statistical and systematic uncertainties are evaluated for each
range, and are only partially correlated between different ranges. Figure 27
shows measured values of $m_{W}$ for selected ranges of the
$p_{\text{T}}^{\ell}$ and $m_{\mathrm{T}}$ distributions, where only the
uncorrelated statistical and systematic uncertainties with respect to the
optimal range are shown. The observed variations are all within two standard
deviations of the uncorrelated uncertainties, and small compared to the
overall uncertainty of the measurement, which is illustrated by the band on
Figure 27. The largest dependence on the kinematic ranges used for the fits is
observed for variations of the upper bound of the $p_{\text{T}}^{\ell}$
distribution in the $W^{+}\rightarrow e^{+}\nu$ channel, and is related to the
shape of the data-to-prediction ratio for this distribution in the region
$40<p_{\text{T}}^{\ell}<42{\mathrm{\ Ge\kern-1.00006ptV}}$, as discussed in
Section 11.3.

((a))  ((b))

Figure 27: Stability of the combined measurement of $m_{W}$ with respect to
variations of the kinematic ranges of (a) $p_{\text{T}}^{\ell}$ and (b)
$m_{\mathrm{T}}$ used for the template fits. The optimal $m_{\mathrm{T}}$
range is used for the $p_{\text{T}}^{\ell}$ variations, and the optimal
$p_{\text{T}}^{\ell}$ range is used for the $m_{\mathrm{T}}$ variations. The
effect on the result of symmetric variations of the fitting range boundaries,
and its dependence on variations of the lower (upper) boundary for two values
of the upper (lower) boundary for $p_{\text{T}}^{\ell}$ ($m_{\mathrm{T}}$) are
shown. The bands and solid lines respectively show the statistical and total
uncertainty on the difference with the optimal result.

###  11.6 Measurement of $m_{W^{+}}-m_{W^{-}}$

The results presented in the previous sections can be used to derive a
measurement of the mass difference between the positively and negatively
charged $W$ bosons, $m_{W^{+}}-m_{W^{-}}$. Starting from the $m_{W}$
measurement results in the 28 categories described above, 14 measurements of
$m_{W^{+}}-m_{W^{-}}$ can be constructed by subtraction of the results
obtained from the $W^{+}$ and $W^{-}$ samples in the same decay channel and
$|\eta|$ category. In practice, the $m_{W}$ values measured in $W^{+}$ and
$W^{-}$ events are subtracted linearly, as are the effects of systematic
uncertainties on these measurements, while the uncertainty contributions of a
statistical nature are added in quadrature. Contrarily to the $m_{W}$
measurement discussed above, no blinding procedure was applied for the
measurement of $m_{W^{+}}-m_{W^{-}}$.

In this process, uncertainties that are anti-correlated between $W^{+}$ and
$W^{-}$ and largely cancel for the $m_{W}$ measurement become dominant when
measuring $m_{W^{+}}-m_{W^{-}}$. On the physics-modelling side, the fixed-
order PDF uncertainty and the parton shower PDF uncertainty give the largest
contributions, while other sources of uncertainty only weakly depend on charge
and tend to cancel. Among the sources of uncertainty related to lepton
calibration, the track sagitta correction dominates in the muon channel,
whereas several residual uncertainties contribute in the electron channel.
Most lepton and recoil calibration uncertainties tend to cancel. Background
systematic uncertainties contribute as the $Z$ and multijet background
fractions differ in the $W^{+}$ and $W^{-}$ channels. The dominant statistical
uncertainties arise from the size of the data and Monte Carlo signal samples,
and of the control samples used to derive the multijet background.

The $m_{W^{+}}-m_{W^{-}}$ measurement results are shown in Table 13 for the
electron and muon decay channels, and for the combination. The electron
channel measurement combines six categories ($p_{\text{T}}^{\ell}$ and
$m_{\mathrm{T}}$ fits in three $|\eta_{\ell}|$ bins), while the muon channel
has four $|\eta_{\ell}|$ bins and eight categories in total. The fully
combined result is

$\displaystyle m_{W^{+}}-m_{W^{-}}$ $\displaystyle=$ $\displaystyle-29.2\pm
12.8{\mathrm{\ Me\kern-1.00006ptV}}(\textrm{stat.})\pm 7.0{\mathrm{\
Me\kern-1.00006ptV}}(\textrm{exp. syst.})\pm 23.9{\mathrm{\
Me\kern-1.00006ptV}}(\textrm{mod. syst.})$ $\displaystyle=$
$\displaystyle-29.2\pm 28.0{\mathrm{\ Me\kern-1.00006ptV}},$

where the first uncertainty is statistical, the second corresponds to the
experimental systematic uncertainty, and the third to the physics-modelling
systematic uncertainty.

Channel | $m_{W^{+}}-m_{W^{-}}$ | Stat. | Muon | Elec. | Recoil | Bckg. | QCD | EW | PDF | Total
---|---|---|---|---|---|---|---|---|---|---
| [MeV] | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc. | Unc.
$W\rightarrow e\nu$ | $-29.7$ | $17.5$ | $0.0\leavevmode\nobreak\ $ | $4.9$ | $0.9$ | $5.4$ | $0.5$ | $0.0$ | $24.1$ | $30.7$
$W\rightarrow\mu\nu$ | $-28.6$ | 16.3 | 11.7 | 0.0 | 1.1 | 5.0 | 0.4 | 0.0 | 26.0 | 33.2
Combined | $-29.2$ | 12.8 | 3.3 | 4.1 | 1.0 | 4.5 | 0.4 | 0.0 | 23.9 | 28.0

Table 13: Results of the $m_{W^{+}}-m_{W^{-}}$ measurements in the electron
and muon decay channels, and of the combination. The table shows the
statistical uncertainties; the experimental uncertainties, divided into muon-,
electron-, recoil- and background-uncertainties; and the modelling
uncertainties, separately for QCD modelling including scale variations, parton
shower and angular coefficients, electroweak corrections, and PDFs. All
uncertainties are given in MeV.

##  12 Discussion and conclusions

This paper reports a measurement of the $W$-boson mass with the ATLAS
detector, obtained through template fits to the kinematic properties of decay
leptons in the electron and muon decay channels. The measurement is based on
proton–proton collision data recorded in 2011 at a centre-of-mass energy of
$\sqrt{s}=7{\mathrm{\ Te\kern-1.00006ptV}}$ at the LHC, and corresponding to
an integrated luminosity of 4.6 fb-1. The measurement relies on a thorough
detector calibration based on the study of $Z$-boson events, leading to a
precise modelling of the detector response to electrons, muons and the recoil.
Templates for the $W$-boson kinematic distributions are obtained from the NLO
MC generator Powheg, interfaced to Pythia8 for the parton shower. The signal
samples are supplemented with several additional physics-modelling corrections
allowing for the inclusion of higher-order QCD and electroweak corrections,
and by fits to measured distributions, so that agreement between the data and
the model in the kinematic distributions is improved. The $W$-boson mass is
obtained from the transverse-momentum distribution of charged leptons and from
the transverse-mass distributions, for positively and negatively charged $W$
bosons, in the electron and muon decay channels, and in several kinematic
categories. The individual measurements of $m_{W}$ are found to be consistent
and their combination yields a value of

$\displaystyle m_{W}$ $\displaystyle=$ $\displaystyle 80370\pm
7\leavevmode\nobreak\ (\textrm{stat.})\pm 11\leavevmode\nobreak\ (\textrm{exp.
syst.})\pm 14\leavevmode\nobreak\ (\textrm{mod. syst.}){\mathrm{\
Me\kern-1.00006ptV}}$ $\displaystyle=$ $\displaystyle 80370\pm 19{\mathrm{\
Me\kern-1.00006ptV}},$

where the first uncertainty is statistical, the second corresponds to the
experimental systematic uncertainty, and the third to the physics-modelling
systematic uncertainty. A measurement of the $W^{+}$ and $W^{-}$ mass
difference yields $m_{W^{+}}-m_{W^{-}}=-29\pm 28{\mathrm{\
Me\kern-1.00006ptV}}$.

The $W$-boson mass measurement is compatible with the current world average of
$m_{W}=80385\pm 15{\mathrm{\ Me\kern-1.00006ptV}}$ [29], and similar in
precision to the currently leading measurements performed by the CDF and D0
collaborations [22, 23]. An overview of the different $m_{W}$ measurements is
shown in Figure 28. The compatibility of the measured value of $m_{W}$ in the
context of the global electroweak fit is illustrated in Figures 30 and 30.
Figure 30 compares the present measurement with earlier results, and with the
SM prediction updated with regard to Ref. [16] using recent measurements of
the top-quark and Higgs boson masses, $m_{t}=172.84\pm 0.70{\mathrm{\
Ge\kern-1.00006ptV}}$ [117] and $m_{H}=125.09\pm 0.24{\mathrm{\
Ge\kern-1.00006ptV}}$ [118]. This update gives a numerical value for the SM
prediction of $m_{W}=80356\pm 8{\mathrm{\ Me\kern-1.00006ptV}}$. The
corresponding two-dimensional 68% and 95% confidence limits for $m_{W}$ and
$m_{t}$ are shown in Figure 30, and compared to the present measurement of
$m_{W}$ and the average of the top-quark mass determinations performed by
ATLAS [117].

Figure 28: The measured value of $m_{W}$ is compared to other published
results, including measurements from the LEP experiments ALEPH, DELPHI, L3 and
OPAL [25, 26, 27, 28], and from the Tevatron collider experiments CDF and D0
[22, 23]. The vertical bands show the statistical and total uncertainties of
the ATLAS measurement, and the horizontal bands and lines show the statistical
and total uncertainties of the other published results. Measured values of
$m_{W}$ for positively and negatively charged $W$ bosons are also shown.

Figure 29: The present measurement of $m_{W}$ is compared to the SM prediction
from the global electroweak fit [16] updated using recent measurements of the
top-quark and Higgs-boson masses, $m_{t}=172.84\pm 0.70{\mathrm{\
Ge\kern-1.00006ptV}}$ [117] and $m_{H}=125.09\pm 0.24{\mathrm{\
Ge\kern-1.00006ptV}}$ [118], and to the combined values of $m_{W}$ measured at
LEP [119] and at the Tevatron collider [24].

Figure 30: The 68% and 95% confidence-level contours of the $m_{W}$ and
$m_{t}$ indirect determination from the global electroweak fit [16] are
compared to the 68% and 95% confidence-level contours of the ATLAS
measurements of the top-quark and $W$-boson masses. The determination from the
electroweak fit uses as input the LHC measurement of the Higgs-boson mass,
$m_{H}=125.09\pm 0.24{\mathrm{\ Ge\kern-1.00006ptV}}$ [118].

The determination of the $W$-boson mass from the global fit of the electroweak
parameters has an uncertainty of $8{\mathrm{\ Me\kern-1.00006ptV}}$, which
sets a natural target for the precision of the experimental measurement of the
mass of the $W$ boson. The modelling uncertainties, which currently dominate
the overall uncertainty of the $m_{W}$ measurement presented in this paper,
need to be reduced in order to fully exploit the larger data samples available
at centre-of-mass energies of $8$ and $13{\mathrm{\ Te\kern-1.00006ptV}}$.
Better knowledge of the PDFs, as achievable with the inclusion in PDF fits of
recent precise measurements of $W$\- and $Z$-boson rapidity cross sections
with the ATLAS detector [41], and improved QCD and electroweak predictions for
Drell–Yan production, are therefore crucial for future measurements of the
$W$-boson mass at the LHC.

## Acknowledgements

We thank CERN for the very successful operation of the LHC, as well as the
support staff from our institutions without whom ATLAS could not be operated
efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,
Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and
FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST
and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech
Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF,
Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China;
ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan;
CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland;
FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation;
JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South
Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and
Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC,
United Kingdom; DOE and NSF, United States of America. In addition, individual
groups and members have received support from BCKDF, the Canada Council,
CANARIE, CRC, Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada;
EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Actions,
European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne
and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany;
Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the
Greek NSRF; BSF, GIF and Minerva, Israel; BRF, Norway; CERCA Programme
Generalitat de Catalunya, Generalitat Valenciana, Spain; the Royal Society and
Leverhulme Trust, United Kingdom.

The crucial computing support from all WLCG partners is acknowledged
gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF
(Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA
(Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan),
RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG
resource providers. Major contributors of computing resources are listed in
Ref. [120].

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The ATLAS Collaboration

M. Aaboud${}^{\textrm{\scriptsize 137d}}$, G. Aad${}^{\textrm{\scriptsize
88}}$, B. Abbott${}^{\textrm{\scriptsize 115}}$, J.
Abdallah${}^{\textrm{\scriptsize 8}}$, O. Abdinov${}^{\textrm{\scriptsize
12}}$, B. Abeloos${}^{\textrm{\scriptsize 119}}$, S.H.
Abidi${}^{\textrm{\scriptsize 161}}$, O.S. AbouZeid${}^{\textrm{\scriptsize
139}}$, N.L. Abraham${}^{\textrm{\scriptsize 151}}$, H.
Abramowicz${}^{\textrm{\scriptsize 155}}$, H. Abreu${}^{\textrm{\scriptsize
154}}$, R. Abreu${}^{\textrm{\scriptsize 118}}$, Y.
Abulaiti${}^{\textrm{\scriptsize 148a,148b}}$, B.S.
Acharya${}^{\textrm{\scriptsize 167a,167b}}$,a, S.
Adachi${}^{\textrm{\scriptsize 157}}$, L. Adamczyk${}^{\textrm{\scriptsize
41a}}$, D.L. Adams${}^{\textrm{\scriptsize 27}}$, J.
Adelman${}^{\textrm{\scriptsize 110}}$, M. Adersberger${}^{\textrm{\scriptsize
102}}$, T. Adye${}^{\textrm{\scriptsize 133}}$, A.A.
Affolder${}^{\textrm{\scriptsize 139}}$, T. Agatonovic-
Jovin${}^{\textrm{\scriptsize 14}}$, C. Agheorghiesei${}^{\textrm{\scriptsize
28b}}$, J.A. Aguilar-Saavedra${}^{\textrm{\scriptsize 128a,128f}}$, S.P.
Ahlen${}^{\textrm{\scriptsize 24}}$, F. Ahmadov${}^{\textrm{\scriptsize
68}}$,b, G. Aielli${}^{\textrm{\scriptsize 135a,135b}}$, S.
Akatsuka${}^{\textrm{\scriptsize 71}}$, H. Akerstedt${}^{\textrm{\scriptsize
148a,148b}}$, T.P.A. Åkesson${}^{\textrm{\scriptsize 84}}$, A.V.
Akimov${}^{\textrm{\scriptsize 98}}$, G.L. Alberghi${}^{\textrm{\scriptsize
22a,22b}}$, J. Albert${}^{\textrm{\scriptsize 172}}$, M.J. Alconada
Verzini${}^{\textrm{\scriptsize 74}}$, M. Aleksa${}^{\textrm{\scriptsize
32}}$, I.N. Aleksandrov${}^{\textrm{\scriptsize 68}}$, C.
Alexa${}^{\textrm{\scriptsize 28b}}$, G. Alexander${}^{\textrm{\scriptsize
155}}$, T. Alexopoulos${}^{\textrm{\scriptsize 10}}$, M.
Alhroob${}^{\textrm{\scriptsize 115}}$, B. Ali${}^{\textrm{\scriptsize 130}}$,
M. Aliev${}^{\textrm{\scriptsize 76a,76b}}$, G.
Alimonti${}^{\textrm{\scriptsize 94a}}$, J. Alison${}^{\textrm{\scriptsize
33}}$, S.P. Alkire${}^{\textrm{\scriptsize 38}}$, B.M.M.
Allbrooke${}^{\textrm{\scriptsize 151}}$, B.W. Allen${}^{\textrm{\scriptsize
118}}$, P.P. Allport${}^{\textrm{\scriptsize 19}}$, A.
Aloisio${}^{\textrm{\scriptsize 106a,106b}}$, A.
Alonso${}^{\textrm{\scriptsize 39}}$, F. Alonso${}^{\textrm{\scriptsize 74}}$,
C. Alpigiani${}^{\textrm{\scriptsize 140}}$, A.A.
Alshehri${}^{\textrm{\scriptsize 56}}$, M. Alstaty${}^{\textrm{\scriptsize
88}}$, B. Alvarez Gonzalez${}^{\textrm{\scriptsize 32}}$, D. Álvarez
Piqueras${}^{\textrm{\scriptsize 170}}$, M.G. Alviggi${}^{\textrm{\scriptsize
106a,106b}}$, B.T. Amadio${}^{\textrm{\scriptsize 16}}$, Y. Amaral
Coutinho${}^{\textrm{\scriptsize 26a}}$, C. Amelung${}^{\textrm{\scriptsize
25}}$, D. Amidei${}^{\textrm{\scriptsize 92}}$, S.P. Amor Dos
Santos${}^{\textrm{\scriptsize 128a,128c}}$, A. Amorim${}^{\textrm{\scriptsize
128a,128b}}$, S. Amoroso${}^{\textrm{\scriptsize 32}}$, G.
Amundsen${}^{\textrm{\scriptsize 25}}$, C.
Anastopoulos${}^{\textrm{\scriptsize 141}}$, L.S. Ancu${}^{\textrm{\scriptsize
52}}$, N. Andari${}^{\textrm{\scriptsize 19}}$, T.
Andeen${}^{\textrm{\scriptsize 11}}$, C.F. Anders${}^{\textrm{\scriptsize
60b}}$, J.K. Anders${}^{\textrm{\scriptsize 77}}$, K.J.
Anderson${}^{\textrm{\scriptsize 33}}$, A. Andreazza${}^{\textrm{\scriptsize
94a,94b}}$, V. Andrei${}^{\textrm{\scriptsize 60a}}$, S.
Angelidakis${}^{\textrm{\scriptsize 9}}$, I. Angelozzi${}^{\textrm{\scriptsize
109}}$, A. Angerami${}^{\textrm{\scriptsize 38}}$, F.
Anghinolfi${}^{\textrm{\scriptsize 32}}$, A.V.
Anisenkov${}^{\textrm{\scriptsize 111}}$,c, N. Anjos${}^{\textrm{\scriptsize
13}}$, A. Annovi${}^{\textrm{\scriptsize 126a,126b}}$, C.
Antel${}^{\textrm{\scriptsize 60a}}$, M. Antonelli${}^{\textrm{\scriptsize
50}}$, A. Antonov${}^{\textrm{\scriptsize 100}}$,∗, D.J.
Antrim${}^{\textrm{\scriptsize 166}}$, F. Anulli${}^{\textrm{\scriptsize
134a}}$, M. Aoki${}^{\textrm{\scriptsize 69}}$, L. Aperio
Bella${}^{\textrm{\scriptsize 32}}$, G. Arabidze${}^{\textrm{\scriptsize
93}}$, Y. Arai${}^{\textrm{\scriptsize 69}}$, J.P.
Araque${}^{\textrm{\scriptsize 128a}}$, V. Araujo
Ferraz${}^{\textrm{\scriptsize 26a}}$, A.T.H. Arce${}^{\textrm{\scriptsize
48}}$, R.E. Ardell${}^{\textrm{\scriptsize 80}}$, F.A.
Arduh${}^{\textrm{\scriptsize 74}}$, J-F. Arguin${}^{\textrm{\scriptsize
97}}$, S. Argyropoulos${}^{\textrm{\scriptsize 66}}$, M.
Arik${}^{\textrm{\scriptsize 20a}}$, A.J. Armbruster${}^{\textrm{\scriptsize
145}}$, L.J. Armitage${}^{\textrm{\scriptsize 79}}$, O.
Arnaez${}^{\textrm{\scriptsize 32}}$, H. Arnold${}^{\textrm{\scriptsize 51}}$,
M. Arratia${}^{\textrm{\scriptsize 30}}$, O. Arslan${}^{\textrm{\scriptsize
23}}$, A. Artamonov${}^{\textrm{\scriptsize 99}}$, G.
Artoni${}^{\textrm{\scriptsize 122}}$, S. Artz${}^{\textrm{\scriptsize 86}}$,
S. Asai${}^{\textrm{\scriptsize 157}}$, N. Asbah${}^{\textrm{\scriptsize
45}}$, A. Ashkenazi${}^{\textrm{\scriptsize 155}}$, L.
Asquith${}^{\textrm{\scriptsize 151}}$, K. Assamagan${}^{\textrm{\scriptsize
27}}$, R. Astalos${}^{\textrm{\scriptsize 146a}}$, M.
Atkinson${}^{\textrm{\scriptsize 169}}$, N.B. Atlay${}^{\textrm{\scriptsize
143}}$, K. Augsten${}^{\textrm{\scriptsize 130}}$, G.
Avolio${}^{\textrm{\scriptsize 32}}$, B. Axen${}^{\textrm{\scriptsize 16}}$,
M.K. Ayoub${}^{\textrm{\scriptsize 119}}$, G. Azuelos${}^{\textrm{\scriptsize
97}}$,d, A.E. Baas${}^{\textrm{\scriptsize 60a}}$, M.J.
Baca${}^{\textrm{\scriptsize 19}}$, H. Bachacou${}^{\textrm{\scriptsize
138}}$, K. Bachas${}^{\textrm{\scriptsize 76a,76b}}$, M.
Backes${}^{\textrm{\scriptsize 122}}$, M. Backhaus${}^{\textrm{\scriptsize
32}}$, P. Bagiacchi${}^{\textrm{\scriptsize 134a,134b}}$, P.
Bagnaia${}^{\textrm{\scriptsize 134a,134b}}$, J.T.
Baines${}^{\textrm{\scriptsize 133}}$, M. Bajic${}^{\textrm{\scriptsize 39}}$,
O.K. Baker${}^{\textrm{\scriptsize 179}}$, E.M. Baldin${}^{\textrm{\scriptsize
111}}$,c, P. Balek${}^{\textrm{\scriptsize 175}}$, T.
Balestri${}^{\textrm{\scriptsize 150}}$, F. Balli${}^{\textrm{\scriptsize
138}}$, W.K. Balunas${}^{\textrm{\scriptsize 124}}$, E.
Banas${}^{\textrm{\scriptsize 42}}$, Sw. Banerjee${}^{\textrm{\scriptsize
176}}$,e, A.A.E. Bannoura${}^{\textrm{\scriptsize 178}}$, L.
Barak${}^{\textrm{\scriptsize 32}}$, E.L. Barberio${}^{\textrm{\scriptsize
91}}$, D. Barberis${}^{\textrm{\scriptsize 53a,53b}}$, M.
Barbero${}^{\textrm{\scriptsize 88}}$, T. Barillari${}^{\textrm{\scriptsize
103}}$, M-S Barisits${}^{\textrm{\scriptsize 32}}$, T.
Barklow${}^{\textrm{\scriptsize 145}}$, N. Barlow${}^{\textrm{\scriptsize
30}}$, S.L. Barnes${}^{\textrm{\scriptsize 36c}}$, B.M.
Barnett${}^{\textrm{\scriptsize 133}}$, R.M. Barnett${}^{\textrm{\scriptsize
16}}$, Z. Barnovska-Blenessy${}^{\textrm{\scriptsize 36a}}$, A.
Baroncelli${}^{\textrm{\scriptsize 136a}}$, G. Barone${}^{\textrm{\scriptsize
25}}$, A.J. Barr${}^{\textrm{\scriptsize 122}}$, L. Barranco
Navarro${}^{\textrm{\scriptsize 170}}$, F. Barreiro${}^{\textrm{\scriptsize
85}}$, J. Barreiro Guimarães da Costa${}^{\textrm{\scriptsize 35a}}$, R.
Bartoldus${}^{\textrm{\scriptsize 145}}$, A.E. Barton${}^{\textrm{\scriptsize
75}}$, P. Bartos${}^{\textrm{\scriptsize 146a}}$, A.
Basalaev${}^{\textrm{\scriptsize 125}}$, A. Bassalat${}^{\textrm{\scriptsize
119}}$,f, R.L. Bates${}^{\textrm{\scriptsize 56}}$, S.J.
Batista${}^{\textrm{\scriptsize 161}}$, J.R. Batley${}^{\textrm{\scriptsize
30}}$, M. Battaglia${}^{\textrm{\scriptsize 139}}$, M.
Bauce${}^{\textrm{\scriptsize 134a,134b}}$, F. Bauer${}^{\textrm{\scriptsize
138}}$, H.S. Bawa${}^{\textrm{\scriptsize 145}}$,g, J.B.
Beacham${}^{\textrm{\scriptsize 113}}$, M.D. Beattie${}^{\textrm{\scriptsize
75}}$, T. Beau${}^{\textrm{\scriptsize 83}}$, P.H.
Beauchemin${}^{\textrm{\scriptsize 165}}$, P. Bechtle${}^{\textrm{\scriptsize
23}}$, H.P. Beck${}^{\textrm{\scriptsize 18}}$,h, K.
Becker${}^{\textrm{\scriptsize 122}}$, M. Becker${}^{\textrm{\scriptsize
86}}$, M. Beckingham${}^{\textrm{\scriptsize 173}}$, C.
Becot${}^{\textrm{\scriptsize 112}}$, A.J. Beddall${}^{\textrm{\scriptsize
20e}}$, A. Beddall${}^{\textrm{\scriptsize 20b}}$, V.A.
Bednyakov${}^{\textrm{\scriptsize 68}}$, M. Bedognetti${}^{\textrm{\scriptsize
109}}$, C.P. Bee${}^{\textrm{\scriptsize 150}}$, T.A.
Beermann${}^{\textrm{\scriptsize 32}}$, M. Begalli${}^{\textrm{\scriptsize
26a}}$, M. Begel${}^{\textrm{\scriptsize 27}}$, J.K.
Behr${}^{\textrm{\scriptsize 45}}$, A.S. Bell${}^{\textrm{\scriptsize 81}}$,
G. Bella${}^{\textrm{\scriptsize 155}}$, L. Bellagamba${}^{\textrm{\scriptsize
22a}}$, A. Bellerive${}^{\textrm{\scriptsize 31}}$, M.
Bellomo${}^{\textrm{\scriptsize 89}}$, K. Belotskiy${}^{\textrm{\scriptsize
100}}$, O. Beltramello${}^{\textrm{\scriptsize 32}}$, N.L.
Belyaev${}^{\textrm{\scriptsize 100}}$, O. Benary${}^{\textrm{\scriptsize
155}}$,∗, D. Benchekroun${}^{\textrm{\scriptsize 137a}}$, M.
Bender${}^{\textrm{\scriptsize 102}}$, K. Bendtz${}^{\textrm{\scriptsize
148a,148b}}$, N. Benekos${}^{\textrm{\scriptsize 10}}$, Y.
Benhammou${}^{\textrm{\scriptsize 155}}$, E. Benhar
Noccioli${}^{\textrm{\scriptsize 179}}$, J. Benitez${}^{\textrm{\scriptsize
66}}$, D.P. Benjamin${}^{\textrm{\scriptsize 48}}$, M.
Benoit${}^{\textrm{\scriptsize 52}}$, J.R. Bensinger${}^{\textrm{\scriptsize
25}}$, S. Bentvelsen${}^{\textrm{\scriptsize 109}}$, L.
Beresford${}^{\textrm{\scriptsize 122}}$, M. Beretta${}^{\textrm{\scriptsize
50}}$, D. Berge${}^{\textrm{\scriptsize 109}}$, E. Bergeaas
Kuutmann${}^{\textrm{\scriptsize 168}}$, N. Berger${}^{\textrm{\scriptsize
5}}$, J. Beringer${}^{\textrm{\scriptsize 16}}$, S.
Berlendis${}^{\textrm{\scriptsize 58}}$, N.R. Bernard${}^{\textrm{\scriptsize
89}}$, G. Bernardi${}^{\textrm{\scriptsize 83}}$, C.
Bernius${}^{\textrm{\scriptsize 112}}$, F.U.
Bernlochner${}^{\textrm{\scriptsize 23}}$, T. Berry${}^{\textrm{\scriptsize
80}}$, P. Berta${}^{\textrm{\scriptsize 131}}$, C.
Bertella${}^{\textrm{\scriptsize 86}}$, G. Bertoli${}^{\textrm{\scriptsize
148a,148b}}$, F. Bertolucci${}^{\textrm{\scriptsize 126a,126b}}$, I.A.
Bertram${}^{\textrm{\scriptsize 75}}$, C. Bertsche${}^{\textrm{\scriptsize
45}}$, D. Bertsche${}^{\textrm{\scriptsize 115}}$, G.J.
Besjes${}^{\textrm{\scriptsize 39}}$, O. Bessidskaia
Bylund${}^{\textrm{\scriptsize 148a,148b}}$, M.
Bessner${}^{\textrm{\scriptsize 45}}$, N. Besson${}^{\textrm{\scriptsize
138}}$, C. Betancourt${}^{\textrm{\scriptsize 51}}$, A.
Bethani${}^{\textrm{\scriptsize 87}}$, S. Bethke${}^{\textrm{\scriptsize
103}}$, A.J. Bevan${}^{\textrm{\scriptsize 79}}$, R.M.
Bianchi${}^{\textrm{\scriptsize 127}}$, M. Bianco${}^{\textrm{\scriptsize
32}}$, O. Biebel${}^{\textrm{\scriptsize 102}}$, D.
Biedermann${}^{\textrm{\scriptsize 17}}$, R. Bielski${}^{\textrm{\scriptsize
87}}$, N.V. Biesuz${}^{\textrm{\scriptsize 126a,126b}}$, M.
Biglietti${}^{\textrm{\scriptsize 136a}}$, J. Bilbao De
Mendizabal${}^{\textrm{\scriptsize 52}}$, T.R.V.
Billoud${}^{\textrm{\scriptsize 97}}$, H. Bilokon${}^{\textrm{\scriptsize
50}}$, M. Bindi${}^{\textrm{\scriptsize 57}}$, A.
Bingul${}^{\textrm{\scriptsize 20b}}$, C. Bini${}^{\textrm{\scriptsize
134a,134b}}$, S. Biondi${}^{\textrm{\scriptsize 22a,22b}}$, T.
Bisanz${}^{\textrm{\scriptsize 57}}$, C. Bittrich${}^{\textrm{\scriptsize
47}}$, D.M. Bjergaard${}^{\textrm{\scriptsize 48}}$, C.W.
Black${}^{\textrm{\scriptsize 152}}$, J.E. Black${}^{\textrm{\scriptsize
145}}$, K.M. Black${}^{\textrm{\scriptsize 24}}$, D.
Blackburn${}^{\textrm{\scriptsize 140}}$, R.E. Blair${}^{\textrm{\scriptsize
6}}$, J.-B. Blanchard${}^{\textrm{\scriptsize 138}}$, T.
Blazek${}^{\textrm{\scriptsize 146a}}$, I. Bloch${}^{\textrm{\scriptsize
45}}$, C. Blocker${}^{\textrm{\scriptsize 25}}$, A.
Blue${}^{\textrm{\scriptsize 56}}$, W. Blum${}^{\textrm{\scriptsize 86}}$,∗,
U. Blumenschein${}^{\textrm{\scriptsize 79}}$, S.
Blunier${}^{\textrm{\scriptsize 34a}}$, G.J. Bobbink${}^{\textrm{\scriptsize
109}}$, V.S. Bobrovnikov${}^{\textrm{\scriptsize 111}}$,c, S.S.
Bocchetta${}^{\textrm{\scriptsize 84}}$, A. Bocci${}^{\textrm{\scriptsize
48}}$, C. Bock${}^{\textrm{\scriptsize 102}}$, M.
Boehler${}^{\textrm{\scriptsize 51}}$, D. Boerner${}^{\textrm{\scriptsize
178}}$, D. Bogavac${}^{\textrm{\scriptsize 102}}$, A.G.
Bogdanchikov${}^{\textrm{\scriptsize 111}}$, C. Bohm${}^{\textrm{\scriptsize
148a}}$, V. Boisvert${}^{\textrm{\scriptsize 80}}$, P.
Bokan${}^{\textrm{\scriptsize 168}}$,i, T. Bold${}^{\textrm{\scriptsize
41a}}$, A.S. Boldyrev${}^{\textrm{\scriptsize 101}}$, M.
Bomben${}^{\textrm{\scriptsize 83}}$, M. Bona${}^{\textrm{\scriptsize 79}}$,
M. Boonekamp${}^{\textrm{\scriptsize 138}}$, A.
Borisov${}^{\textrm{\scriptsize 132}}$, G. Borissov${}^{\textrm{\scriptsize
75}}$, J. Bortfeldt${}^{\textrm{\scriptsize 32}}$, D.
Bortoletto${}^{\textrm{\scriptsize 122}}$, V.
Bortolotto${}^{\textrm{\scriptsize 62a,62b,62c}}$, K.
Bos${}^{\textrm{\scriptsize 109}}$, D. Boscherini${}^{\textrm{\scriptsize
22a}}$, M. Bosman${}^{\textrm{\scriptsize 13}}$, J.D. Bossio
Sola${}^{\textrm{\scriptsize 29}}$, J. Boudreau${}^{\textrm{\scriptsize
127}}$, J. Bouffard${}^{\textrm{\scriptsize 2}}$, E.V. Bouhova-
Thacker${}^{\textrm{\scriptsize 75}}$, D. Boumediene${}^{\textrm{\scriptsize
37}}$, C. Bourdarios${}^{\textrm{\scriptsize 119}}$, S.K.
Boutle${}^{\textrm{\scriptsize 56}}$, A. Boveia${}^{\textrm{\scriptsize
113}}$, J. Boyd${}^{\textrm{\scriptsize 32}}$, I.R.
Boyko${}^{\textrm{\scriptsize 68}}$, J. Bracinik${}^{\textrm{\scriptsize
19}}$, A. Brandt${}^{\textrm{\scriptsize 8}}$, G.
Brandt${}^{\textrm{\scriptsize 57}}$, O. Brandt${}^{\textrm{\scriptsize
60a}}$, U. Bratzler${}^{\textrm{\scriptsize 158}}$, B.
Brau${}^{\textrm{\scriptsize 89}}$, J.E. Brau${}^{\textrm{\scriptsize 118}}$,
W.D. Breaden Madden${}^{\textrm{\scriptsize 56}}$, K.
Brendlinger${}^{\textrm{\scriptsize 45}}$, A.J.
Brennan${}^{\textrm{\scriptsize 91}}$, L. Brenner${}^{\textrm{\scriptsize
109}}$, R. Brenner${}^{\textrm{\scriptsize 168}}$, S.
Bressler${}^{\textrm{\scriptsize 175}}$, D.L. Briglin${}^{\textrm{\scriptsize
19}}$, T.M. Bristow${}^{\textrm{\scriptsize 49}}$, D.
Britton${}^{\textrm{\scriptsize 56}}$, D. Britzger${}^{\textrm{\scriptsize
45}}$, F.M. Brochu${}^{\textrm{\scriptsize 30}}$, I.
Brock${}^{\textrm{\scriptsize 23}}$, R. Brock${}^{\textrm{\scriptsize 93}}$,
G. Brooijmans${}^{\textrm{\scriptsize 38}}$, T. Brooks${}^{\textrm{\scriptsize
80}}$, W.K. Brooks${}^{\textrm{\scriptsize 34b}}$, J.
Brosamer${}^{\textrm{\scriptsize 16}}$, E. Brost${}^{\textrm{\scriptsize
110}}$, J.H Broughton${}^{\textrm{\scriptsize 19}}$, P.A. Bruckman de
Renstrom${}^{\textrm{\scriptsize 42}}$, D. Bruncko${}^{\textrm{\scriptsize
146b}}$, A. Bruni${}^{\textrm{\scriptsize 22a}}$, G.
Bruni${}^{\textrm{\scriptsize 22a}}$, L.S. Bruni${}^{\textrm{\scriptsize
109}}$, BH Brunt${}^{\textrm{\scriptsize 30}}$, M.
Bruschi${}^{\textrm{\scriptsize 22a}}$, N. Bruscino${}^{\textrm{\scriptsize
23}}$, P. Bryant${}^{\textrm{\scriptsize 33}}$, L.
Bryngemark${}^{\textrm{\scriptsize 84}}$, T. Buanes${}^{\textrm{\scriptsize
15}}$, Q. Buat${}^{\textrm{\scriptsize 144}}$, P.
Buchholz${}^{\textrm{\scriptsize 143}}$, A.G. Buckley${}^{\textrm{\scriptsize
56}}$, I.A. Budagov${}^{\textrm{\scriptsize 68}}$, F.
Buehrer${}^{\textrm{\scriptsize 51}}$, M.K. Bugge${}^{\textrm{\scriptsize
121}}$, O. Bulekov${}^{\textrm{\scriptsize 100}}$, D.
Bullock${}^{\textrm{\scriptsize 8}}$, H. Burckhart${}^{\textrm{\scriptsize
32}}$, S. Burdin${}^{\textrm{\scriptsize 77}}$, C.D.
Burgard${}^{\textrm{\scriptsize 51}}$, A.M. Burger${}^{\textrm{\scriptsize
5}}$, B. Burghgrave${}^{\textrm{\scriptsize 110}}$, K.
Burka${}^{\textrm{\scriptsize 42}}$, S. Burke${}^{\textrm{\scriptsize 133}}$,
I. Burmeister${}^{\textrm{\scriptsize 46}}$, J.T.P.
Burr${}^{\textrm{\scriptsize 122}}$, E. Busato${}^{\textrm{\scriptsize 37}}$,
D. Büscher${}^{\textrm{\scriptsize 51}}$, V. Büscher${}^{\textrm{\scriptsize
86}}$, P. Bussey${}^{\textrm{\scriptsize 56}}$, J.M.
Butler${}^{\textrm{\scriptsize 24}}$, C.M. Buttar${}^{\textrm{\scriptsize
56}}$, J.M. Butterworth${}^{\textrm{\scriptsize 81}}$, P.
Butti${}^{\textrm{\scriptsize 109}}$, W. Buttinger${}^{\textrm{\scriptsize
27}}$, A. Buzatu${}^{\textrm{\scriptsize 35c}}$, A.R.
Buzykaev${}^{\textrm{\scriptsize 111}}$,c, S. Cabrera
Urbán${}^{\textrm{\scriptsize 170}}$, D. Caforio${}^{\textrm{\scriptsize
130}}$, V.M. Cairo${}^{\textrm{\scriptsize 40a,40b}}$, O.
Cakir${}^{\textrm{\scriptsize 4a}}$, N. Calace${}^{\textrm{\scriptsize 52}}$,
P. Calafiura${}^{\textrm{\scriptsize 16}}$, A.
Calandri${}^{\textrm{\scriptsize 88}}$, G. Calderini${}^{\textrm{\scriptsize
83}}$, P. Calfayan${}^{\textrm{\scriptsize 64}}$, G.
Callea${}^{\textrm{\scriptsize 40a,40b}}$, L.P. Caloba${}^{\textrm{\scriptsize
26a}}$, S. Calvente Lopez${}^{\textrm{\scriptsize 85}}$, D.
Calvet${}^{\textrm{\scriptsize 37}}$, S. Calvet${}^{\textrm{\scriptsize 37}}$,
T.P. Calvet${}^{\textrm{\scriptsize 88}}$, R. Camacho
Toro${}^{\textrm{\scriptsize 33}}$, S. Camarda${}^{\textrm{\scriptsize 32}}$,
P. Camarri${}^{\textrm{\scriptsize 135a,135b}}$, D.
Cameron${}^{\textrm{\scriptsize 121}}$, R. Caminal
Armadans${}^{\textrm{\scriptsize 169}}$, C. Camincher${}^{\textrm{\scriptsize
58}}$, S. Campana${}^{\textrm{\scriptsize 32}}$, M.
Campanelli${}^{\textrm{\scriptsize 81}}$, A. Camplani${}^{\textrm{\scriptsize
94a,94b}}$, A. Campoverde${}^{\textrm{\scriptsize 143}}$, V.
Canale${}^{\textrm{\scriptsize 106a,106b}}$, M. Cano
Bret${}^{\textrm{\scriptsize 36c}}$, J. Cantero${}^{\textrm{\scriptsize
116}}$, T. Cao${}^{\textrm{\scriptsize 155}}$, M.D.M. Capeans
Garrido${}^{\textrm{\scriptsize 32}}$, I. Caprini${}^{\textrm{\scriptsize
28b}}$, M. Caprini${}^{\textrm{\scriptsize 28b}}$, M.
Capua${}^{\textrm{\scriptsize 40a,40b}}$, R.M. Carbone${}^{\textrm{\scriptsize
38}}$, R. Cardarelli${}^{\textrm{\scriptsize 135a}}$, F.
Cardillo${}^{\textrm{\scriptsize 51}}$, I. Carli${}^{\textrm{\scriptsize
131}}$, T. Carli${}^{\textrm{\scriptsize 32}}$, G.
Carlino${}^{\textrm{\scriptsize 106a}}$, B.T. Carlson${}^{\textrm{\scriptsize
127}}$, L. Carminati${}^{\textrm{\scriptsize 94a,94b}}$, R.M.D.
Carney${}^{\textrm{\scriptsize 148a,148b}}$, S. Caron${}^{\textrm{\scriptsize
108}}$, E. Carquin${}^{\textrm{\scriptsize 34b}}$, G.D. Carrillo-
Montoya${}^{\textrm{\scriptsize 32}}$, J. Carvalho${}^{\textrm{\scriptsize
128a,128c}}$, D. Casadei${}^{\textrm{\scriptsize 19}}$, M.P.
Casado${}^{\textrm{\scriptsize 13}}$,j, M. Casolino${}^{\textrm{\scriptsize
13}}$, D.W. Casper${}^{\textrm{\scriptsize 166}}$, R.
Castelijn${}^{\textrm{\scriptsize 109}}$, A. Castelli${}^{\textrm{\scriptsize
109}}$, V. Castillo Gimenez${}^{\textrm{\scriptsize 170}}$, N.F.
Castro${}^{\textrm{\scriptsize 128a}}$,k, A.
Catinaccio${}^{\textrm{\scriptsize 32}}$, J.R. Catmore${}^{\textrm{\scriptsize
121}}$, A. Cattai${}^{\textrm{\scriptsize 32}}$, J.
Caudron${}^{\textrm{\scriptsize 23}}$, V. Cavaliere${}^{\textrm{\scriptsize
169}}$, E. Cavallaro${}^{\textrm{\scriptsize 13}}$, D.
Cavalli${}^{\textrm{\scriptsize 94a}}$, M. Cavalli-
Sforza${}^{\textrm{\scriptsize 13}}$, V. Cavasinni${}^{\textrm{\scriptsize
126a,126b}}$, E. Celebi${}^{\textrm{\scriptsize 20a}}$, F.
Ceradini${}^{\textrm{\scriptsize 136a,136b}}$, L. Cerda
Alberich${}^{\textrm{\scriptsize 170}}$, A.S.
Cerqueira${}^{\textrm{\scriptsize 26b}}$, A. Cerri${}^{\textrm{\scriptsize
151}}$, L. Cerrito${}^{\textrm{\scriptsize 135a,135b}}$, F.
Cerutti${}^{\textrm{\scriptsize 16}}$, A. Cervelli${}^{\textrm{\scriptsize
18}}$, S.A. Cetin${}^{\textrm{\scriptsize 20d}}$, A.
Chafaq${}^{\textrm{\scriptsize 137a}}$, D. Chakraborty${}^{\textrm{\scriptsize
110}}$, S.K. Chan${}^{\textrm{\scriptsize 59}}$, W.S.
Chan${}^{\textrm{\scriptsize 109}}$, Y.L. Chan${}^{\textrm{\scriptsize 62a}}$,
P. Chang${}^{\textrm{\scriptsize 169}}$, J.D. Chapman${}^{\textrm{\scriptsize
30}}$, D.G. Charlton${}^{\textrm{\scriptsize 19}}$, A.
Chatterjee${}^{\textrm{\scriptsize 52}}$, C.C. Chau${}^{\textrm{\scriptsize
161}}$, C.A. Chavez Barajas${}^{\textrm{\scriptsize 151}}$, S.
Che${}^{\textrm{\scriptsize 113}}$, S. Cheatham${}^{\textrm{\scriptsize
167a,167c}}$, A. Chegwidden${}^{\textrm{\scriptsize 93}}$, S.
Chekanov${}^{\textrm{\scriptsize 6}}$, S.V. Chekulaev${}^{\textrm{\scriptsize
163a}}$, G.A. Chelkov${}^{\textrm{\scriptsize 68}}$,l, M.A.
Chelstowska${}^{\textrm{\scriptsize 32}}$, C. Chen${}^{\textrm{\scriptsize
67}}$, H. Chen${}^{\textrm{\scriptsize 27}}$, S. Chen${}^{\textrm{\scriptsize
35b}}$, S. Chen${}^{\textrm{\scriptsize 157}}$, X.
Chen${}^{\textrm{\scriptsize 35c}}$,m, Y. Chen${}^{\textrm{\scriptsize 70}}$,
H.C. Cheng${}^{\textrm{\scriptsize 92}}$, H.J. Cheng${}^{\textrm{\scriptsize
35a}}$, Y. Cheng${}^{\textrm{\scriptsize 33}}$, A.
Cheplakov${}^{\textrm{\scriptsize 68}}$, E.
Cheremushkina${}^{\textrm{\scriptsize 132}}$, R. Cherkaoui El
Moursli${}^{\textrm{\scriptsize 137e}}$, V. Chernyatin${}^{\textrm{\scriptsize
27}}$,∗, E. Cheu${}^{\textrm{\scriptsize 7}}$, L.
Chevalier${}^{\textrm{\scriptsize 138}}$, V. Chiarella${}^{\textrm{\scriptsize
50}}$, G. Chiarelli${}^{\textrm{\scriptsize 126a,126b}}$, G.
Chiodini${}^{\textrm{\scriptsize 76a}}$, A.S. Chisholm${}^{\textrm{\scriptsize
32}}$, A. Chitan${}^{\textrm{\scriptsize 28b}}$, Y.H.
Chiu${}^{\textrm{\scriptsize 172}}$, M.V. Chizhov${}^{\textrm{\scriptsize
68}}$, K. Choi${}^{\textrm{\scriptsize 64}}$, A.R.
Chomont${}^{\textrm{\scriptsize 37}}$, S. Chouridou${}^{\textrm{\scriptsize
9}}$, B.K.B. Chow${}^{\textrm{\scriptsize 102}}$, V.
Christodoulou${}^{\textrm{\scriptsize 81}}$, D. Chromek-
Burckhart${}^{\textrm{\scriptsize 32}}$, M.C. Chu${}^{\textrm{\scriptsize
62a}}$, J. Chudoba${}^{\textrm{\scriptsize 129}}$, A.J.
Chuinard${}^{\textrm{\scriptsize 90}}$, J.J.
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Cirotto${}^{\textrm{\scriptsize 106a,106b}}$, Z.H.
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Clark${}^{\textrm{\scriptsize 52}}$, B.L. Clark${}^{\textrm{\scriptsize 59}}$,
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Clement${}^{\textrm{\scriptsize 148a,148b}}$, Y.
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Cochran${}^{\textrm{\scriptsize 67}}$, L. Colasurdo${}^{\textrm{\scriptsize
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Colijn${}^{\textrm{\scriptsize 109}}$, J. Collot${}^{\textrm{\scriptsize
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Consorti${}^{\textrm{\scriptsize 51}}$, S.
Constantinescu${}^{\textrm{\scriptsize 28b}}$, G.
Conti${}^{\textrm{\scriptsize 32}}$, F. Conventi${}^{\textrm{\scriptsize
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Costa${}^{\textrm{\scriptsize 170}}$, D. Costanzo${}^{\textrm{\scriptsize
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Cowan${}^{\textrm{\scriptsize 80}}$, B.E. Cox${}^{\textrm{\scriptsize 87}}$,