data are shown in Table 12, which gives the partial $\chi^{2}$ for each
dataset included in the fit (i.e. the contribution of that dataset to the
total $\chi^{2}$) and the total $\chi^{2}$ for each fit. The partial
$\chi^{2}$ values indicate that the $t\bar{t}$ data are well-described by the
PDF derived from the combined fit, and that the description of the HERA I+II
data is not degraded by the inclusion of the $t\bar{t}$ data, i.e. there is no
tension between the two datasets. The ratios of the fitted gluon PDF central
values with and without the $t\bar{t}$ data included are shown in Figure
15(a), together with the corresponding uncertainties. The ratio of relative
uncertainties in the PDFs with and without the $t\bar{t}$ data are shown in
Figure 15(b). The inclusion of the $t\bar{t}$ data reduces the uncertainty by
typically 10–25 % over most of the relevant $x$ range.

Datasets fitted | HERA I+II | HERA I+II + $t\bar{t}$
---|---|---
Partial $\chi^{2}$ / $N_{\mathrm{point}}$ |  |
\- HERA I+II | 1219 / 1056 | 1219 / 1056
\- $t\bar{t}$ (et al., $|y^{e\mu}|$, $E^{e}+E^{\mu}$) | - | 27 / 25
Total $\chi^{2}$ / $N_{\mathrm{dof}}$ | 1219 / 1042 | 1247 / 1067
Table 12: Results of the PDF fit to HERA I+II data (left column), and to HERA
I+II data plus the normalised differential $t\bar{t}$ cross-sections as a
function of et al., $|y^{e\mu}|$ and $E^{e}+E^{\mu}$ (right column). The
partial $\chi^{2}$ and number of data points for the datasets used in each fit
are given, together with the overall $\chi^{2}$ and total number of degrees of
freedom for each fit.

(a)

(b)

Figure 15: (a) Ratio of the gluon PDF determined from the fit using HERA I+II
data plus the normalised differential cross-section distributions as a
function of et al., $|y^{e\mu}|$ and $E^{e}+E^{\mu}$ in $t\bar{t}$ events, to
the gluon PDF determined from the fit using HERA I+II data alone, as a
function of Bjorken-$x$. The uncertainty bands are shown on the two PDFs as
the blue and red shading. (b) Ratio of the relative uncertainty in the gluon
PDF determined from the fit to HERA I+II plus $t\bar{t}$ data to that from
HERA data alone. The PDFs are shown evolved to the scale
$Q^{2}=\mbox{$m_{t}$}^{2}$ in both cases.

The gluon PDF obtained from this procedure is compared to the gluon PDFs from
the CT14 [103] and NNPDF 3.0 [105] global PDF sets in Figure 16. These PDF
sets, shown by the green bands, both have a larger high-$x$ gluon than
preferred by the HERA I+II data, with or without the addition of the
$t\bar{t}$ data from this analysis. The impact of the $t\bar{t}$ data on the
global PDF sets was investigated using a profiling procedure [113, 118, 119],
extending the $\chi^{2}$ definition of Eq. (7) to incorporate a vector
${\mathbf{b}}_{\mathrm{th}}$ of nuisance parameters $b_{k,{\mathrm{th}}}$
expressing the dependence of the theoretical prediction
$\varsigma_{i}^{\mathrm{th}}$ on the uncertainties for a particular PDF set.
In this formulation, the $\chi^{2}$ definition becomes:

$\displaystyle\chi^{2}(\mbox{${\mathbf{b}}_{\mathrm{exp}}$},\mbox{${\mathbf{b}}_{\mathrm{th}}$})=\sum_{i}\frac{\left(\mbox{$\varsigma_{i}^{\mathrm{exp}}$}+\sum_{j}\mbox{$\gamma_{ij}^{\mathrm{exp}}$}\mbox{$b_{j,{\mathrm{exp}}}$}-\mbox{$\varsigma_{i}^{\mathrm{th}}$}-\sum_{k}\mbox{$\gamma_{ik}^{\mathrm{th}}$}\mbox{$b_{k,{\mathrm{th}}}$}\right)^{2}}{d_{ii}^{2}}+\sum_{j}\mbox{$b_{j,{\mathrm{exp}}}$}^{2}+\sum_{k}\mbox{$b_{k,{\mathrm{th}}}$}^{2}+L\
,$ (9)

where $\mbox{$b_{k,{\mathrm{th}}}$}=\pm 1$ corresponds to the $\pm 1$ standard
deviation change of the PDF values according to the $k$th eigenvector of the
PDF error set. The values and uncertainties of the nuisance parameters
$b_{k,{\mathrm{th}}}$ after minimisation of the $\chi^{2}$ of Eq. (9) give the
profiled PDF with modified central values and uncertainties according to the
effect of the $t\bar{t}$ differential cross-section distributions. These
profiled PDFs are shown as the orange bands in Figure 16. Both the CT14 and
NNPDF 3.0 gluon PDFs are shifted downwards at high $x$ (corresponding to a
softer gluon distribution). The effect is larger in the case of CT14, which
has larger uncertainties in the gluon PDF in this region.

(a)

(b)

Figure 16: Ratios of various gluon PDFs and their uncertainty bands to the
gluon PDF determined from HERA I+II data alone (red shading). The blue shaded
band shows the gluon PDF from the fit to HERA I+II data plus the normalised
differential cross-section distributions as a function of et al., $|y^{e\mu}|$
and $E^{e}+E^{\mu}$ in $t\bar{t}$ events. The green band shows the gluon PDF
from the CT14 [103] PDF set in (a) and the NNPDF 3.0 [105] PDF set in (b). The
orange bands show the result of profiling these PDFs to the $t\bar{t}$
normalised differential cross-section data.

##  8 Extraction of the top quark mass

The normalised lepton $p_{\mathrm{T}}^{\ell}$ and dilepton
$p_{\mathrm{T}}^{e\mu}$, $m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$
and $E^{e}+E^{\mu}$ differential distributions are sensitive to the value of
the top quark mass, as already shown in Figure 5(a) for
$p_{\mathrm{T}}^{\ell}$ and Figure 5(b) for $p_{\mathrm{T}}^{e\mu}$. Provided
that other theoretical uncertainties in the predictions (as discussed in
Section 6) can be kept under control, fitting these distributions offers a
complementary way to measure $m_{t}$ compared to more traditional
determinations from complete reconstruction of the top quark decay products
[33, 34, 35, 36]. Ref. [32] explores such an approach in detail, arguing that
measurements from normalised lepton distributions are less sensitive to the
modelling of perturbative and non-perturbative QCD, and are closer to the
ideal of a measurement of the top quark pole mass $m_{t}^{\mathrm{pole}}$ than
those employing a direct measurement of the top quark decay products. It also
stresses the importance of using several different leptonic observables to
probe for inadequacies in the theoretical descriptions of the distributions
which may introduce biases in the extracted $m_{t}$ values. Experimentally,
the double-tagging technique employed here results in measurements with little
uncertainty from the hadronic components of the $t\bar{t}$ system, again
reducing the exposure to QCD modelling compared to the measurements based on
reconstructing the top quark decay products.

Several sets of top mass determinations are reported here, based either on
predictions from the NLO matrix element event generator Powheg interfaced to
Pythia6 and the CT10 PDFs as described in Section 2, or on fixed-order
predictions with NLO descriptions of the $t\bar{t}$ production and top quark
decay from the MCFM program with various PDF sets, as described in Section
6.3. In the first case, $m_{t}$ is extracted either by using a template fit
parameterising the predictions as a function of $m_{t}$ and finding the value
which minimises the $\chi^{2}$ with respect to the measured data (described in
Section 8.1), or by calculating moments of the distributions in data and
comparing them to the corresponding moments of the predicted distributions for
different values of $m_{t}$ (Section 8.2). In the template fit method, the
comparisons between data and predictions are performed at particle level, in
contrast to the template fits used for the ATLAS $m_{t}$ measurements based on
reconstruction of the top quark decay products [120], where the comparisons
are performed at detector level using the reconstructed distributions and
fully-simulated Monte Carlo events. The template fit method uses the complete
information from the measured distribution, taking into account the
uncertainty in each bin, whereas the moments method, advocated in Ref. [32],
allows different features of the distribution shapes to be emphasised via the
comparisons of moments of different order. The results from these two methods
are discussed and compared in Section 8.3.

In the mass determination from QCD fixed-order calculations, described in
Section 8.4, $\chi^{2}$ values are calculated for the comparison of data with
predictions at different $m_{t}$ values using the formalism of Eq. (9), and
the best-fit $m_{t}$ is found by polynomial interpolation. This approach is
similar to the template fit discussed above; the use of moments was not
pursued as it does not exploit the full information of each distribution and
does not allow the reduction of uncertainties via constrained nuisance
parameters. The $m_{t}$ value used in the fixed-order predictions corresponds
to a well-defined renormalisation scheme, which is the pole mass
($m_{t}^{\mathrm{pole}}$) scheme within the MCFM implementation. Both the QCD
scale uncertainties, representing the effects of missing higher-order
corrections beyond NLO, and the PDF uncertainties, are included in the
$\chi^{2}$ formalism in a natural way. This formalism also allows $m_{t}$ to
be determined using several distributions simultaneously, giving the most
precise results from any of the techniques explored here. The results from
this method are discussed in Section 8.5 and are used to define the final
measurement of the top quark mass from the distributions measured in this
paper.

###  8.1 Mass extraction using template fits

In the template fit method, the best fit top quark mass for each measured
distribution was obtained by minimising the $\chi^{2}$ for the comparison of
that distribution with predictions at different values of $m_{t}$, defined
analogously with Eq. (5):

$\displaystyle\chi^{2}(\mbox{$m_{t}$})={\mathbf{\Delta}}_{(n-1)}^{T}(\mbox{$m_{t}$})\
{\mathbf{S}}^{-1}_{(n-1)}\ {\mathbf{\Delta}}_{(n-1)}(\mbox{$m_{t}$})\ ,$ (10)

where ${\mathbf{\Delta}}_{(n-1)}(\mbox{$m_{t}$})$ represents the vector of
differences between the measured normalised differential cross-section value
and the prediction for a particular value of $m_{t}$. The latter were obtained
from a set of seven particle-level $t\bar{t}$ samples generated using Powheg +
Pythia6 with $\mbox{$h_{\mathrm{damp}}$}=\infty$ and the CT10 PDF set, for
values of $m_{t}$ ranging from 165–180 GeV in 2.5 GeV steps. The variation of
the cross-section in each bin was parameterised with a second-order polynomial
in $m_{t}$, allowing predictions for arbitrary values in the considered range
to be obtained by interpolation. An additional multiplicative correction was
applied to the predictions in each bin, based on the ratio of predictions from
Powheg + Pythia6 samples with $\mbox{$h_{\mathrm{damp}}$}=\mbox{$m_{t}$}$ and
$\mbox{$h_{\mathrm{damp}}$}=\infty$, in order to correspond to the baseline
event generator choice with $\mbox{$h_{\mathrm{damp}}$}=\mbox{$m_{t}$}$. As
shown in Table 13, the effects of this correction range from $-1.3$ to 3.0 GeV
depending on the distribution fitted, and were assumed to be independent of
$m_{t}$. As the predictions include the simulation of leptons from
$W\rightarrow\tau\rightarrow e/\mu$ decays, the comparisons are made with the
experimental results including leptons from $\tau$ decays, as in Section 6.2.

Mass shift [GeV] | $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
Powheg ($\mbox{$h_{\mathrm{damp}}$}=\infty)\rightarrow(\mbox{$h_{\mathrm{damp}}$}=\mbox{$m_{t}$})$ | 0.9 | 3.0 | -1.3 | 0.9 | 0.5
Top $p_{\text{T}}$ NNLO reweighting | 1.8 | 0.3 | 2.2 | 1.3 | 1.3
Table 13: Changes in the top quark mass fitted in data from each lepton or
dilepton distribution using the template fit method. The first row shows the
shifts when changing the Powheg parameter $h_{\mathrm{damp}}$ from $\infty$ to
$m_{t}$, a correction which is applied to the results quoted in Table 14. The
second row shows additional shifts when reweighting the top quark
$p_{\text{T}}$ in Powheg + Pythia6 to the NNLO prediction of Ref. [25].

The template fit method was tested with pseudo-experiments based on fully-
simulated $t\bar{t}$ samples with $m_{t}$ values in the range 165–180 GeV plus
non-$t\bar{t}$ backgrounds. The pseudo-data were processed through the
complete analysis procedure starting from the observed event counts in each
bin, using the methodology described in Section 4.3. The baseline Powheg +
Pythia6 $t\bar{t}$ sample with $\mbox{$m_{t}$}=172.5$ GeV was used as
reference for the calculation of $G^{i}_{e\mu}$, $C^{i}_{b}$,
$N_{1}^{i,\mathrm{bkg}}$ and $N_{2}^{i,\mathrm{bkg}}$. No statistically
significant biases were found for the fits based on the
$p_{\mathrm{T}}^{\ell}$, $p_{\mathrm{T}}^{e\mu}$ and $m^{e\mu}$ distributions,
but biases of up to 0.6 GeV for $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and
0.9 GeV for $E^{e}+E^{\mu}$ were found in pseudo-experiments with true $m_{t}$
values 5 GeV away from the 172.5 GeV reference, still small compared to the
expected statistical uncertainties using these distributions. These biases
were corrected in the fit results from data discussed in Section 8.3 below.
The pseudo-experiments were also used to check the statistical uncertainties
returned by the fit via the pull distributions, which were generally found to
be within $\pm 5$ % of unity.

Both the data statistical uncertainty and experimental systematic
uncertainties on the measurements of the differential distributions are
included in the matrix ${\mathbf{S}}_{(n-1)}$ in Eq. (10). Further
uncertainties in the extracted $m_{t}$ value arise from the choices of PDFs
and event generator setup for the predictions. The PDF uncertainties were
assessed from the variations in normalised $t\bar{t}$ differential cross-
section distributions predicted by MC@NLO + Herwig reweighted using the error
sets of the CT10, MSTW and NNPDF 2.3 PDF sets as described in Section 5.1. The
event generator setup uncertainties were assessed as the quadrature sum of a
$t\bar{t}$ generator uncertainty and a QCD radiation uncertainty. The former
was obtained from the comparison of results using Powheg + Pythia6
($\mbox{$h_{\mathrm{damp}}$}=\mbox{$m_{t}$}$) and MC@NLO + Herwig samples
(thus varying both the matrix element and parton shower generator). The latter
was defined as half the variation from fits using the Powheg + Pythia6 samples
with radLo and radHi tunes discussed in Section 2. In all cases, the
uncertainties were defined from the difference in $m_{t}$ values obtained when
fitting the two samples as pseudo-data, using the full experimental covariance
matrix from the data measurement and the standard templates obtained from the
Powheg + Pythia6 samples as discussed above.

###  8.2 Mass extraction using moments

Top quark mass information can also be derived from a measured distribution by
calculating Mellin moments of the distribution, and comparing the values
observed to a calibration curve obtained from predictions with different
values of $m_{t}$ [32]. The $k$th order Mellin moment $\mu^{(k)}$ for a
distribution $D(x)\equiv\mathrm{d}\sigma/\mathrm{d}x$ as a function of a
kinematic variable $x$ is defined as:

$\displaystyle\mbox{$\mu^{(k)}$}=\frac{1}{\sigma_{\mathrm{fid}}}\int
x^{k}D(x)\,\mathrm{d}x\,,$ (11)

where the integral is taken over the fiducial region, and the total fiducial
cross-section $\sigma_{\mathrm{fid}}=\int D(x)\,\mathrm{d}x$. These moments
can in principle be evaluated without binning the data, since for leptonic
observables, the value $x$ for each individual event is measured with high
precision. However, for the purpose of this analysis, these moments were
approximated by binned moments $\Theta^{(k)}$ evaluated as:

$\displaystyle\mbox{$\Theta^{(k)}$}=\sum_{i}\mbox{$\varsigma^{i}_{t\bar{t}}$}X_{i}\,,\
X_{i}=<x^{k}>\mathrm{in\ bin}\ i\,,$ (12)

where $\varsigma^{i}_{t\bar{t}}$ is the fraction of the total fiducial
$t\bar{t}$ cross-section in bin $i$ (Eq. (2)) and $X_{i}$ is the mean value of
$x$ for all the events falling in bin $i$. The values of $X_{i}$, which act as
weights for each bin $i$ of each kinematic distribution when calculating the
moment $k$, were evaluated using the baseline Powheg + Pythia6 sample and kept
constant when evaluating moments for the data and all simulation samples.
Calibration curves for the first, second and third moments $\Theta^{(1)}$,
$\Theta^{(2)}$ and $\Theta^{(3)}$ were derived using the same set of Powheg +
Pythia6 samples with top quark masses in the range 165–180 GeV as used for the
template analysis. The dependencies of $\Theta^{(k)}$ on $m_{t}$ were found to
be well-described by second-order polynomials
$\mbox{$\Theta^{(k)}$}(\mbox{$m_{t}$})=P_{2}(\mbox{$m_{t}$})$. A constant
offset in each moment was used to correct to the calibration appropriate for
$\mbox{$h_{\mathrm{damp}}$}=\mbox{$m_{t}$}$ samples, and the polynomial
inverted to obtain the $m_{t}$ value corresponding to a given measured $k$th
moment $\Theta^{(k)}$.

The extraction procedure was tested for bias with pseudo-experiments in the
same way as for the template fit. The observed biases were of similar size to
those in the template fit, and were corrected in the same way. Experimental
systematic uncertainties were evaluated by calculating the moments from the
normalised cross-section distribution with each bin shifted by one standard
deviation of each systematic, and translating the resulting shift in
$\Theta^{(k)}$ to a shift in $m_{t}$. Uncertainties in the predictions due to
the choice of PDFs, $t\bar{t}$ generator and radiation settings were assessed
in the same way, i.e. from the shifts in $\Theta^{(k)}$ predicted by each of
the alternative samples.

###  8.3 Results from the template and moment methods

The results of applying the template and first, second and third moment
methods to each of the $p_{\mathrm{T}}^{\ell}$, $p_{\mathrm{T}}^{e\mu}$,
$m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and $E^{e}+E^{\mu}$
distributions using predictions from Powheg + Pythia6 and CT10 PDFs are shown
in Table 14 and Figure 17. The table shows the $\chi^{2}$ at the best fit mass
for each distribution, and the breakdown of uncertainties into statistical,
experimental systematic and theoretical contributions, evaluated as discussed
in Section 8.1. For the template fits, the data statistical uncertainty was
evaluated from a $\chi^{2}$ minimisation of Eq. (10) with only statistical
uncertainties included in the covariance matrix S. The experimental systematic
uncertainty was evaluated as the quadrature difference between the total
uncertainty (when including both statistical and experimental systematic
uncertainties in S), and the data statistical uncertainty. For the moments
method, the statistical and experimental systematic uncertainties were
evaluated directly on the moments $\Theta^{(k)}$ as discussed in Section 8.2.

Template | $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
$\chi^{2}/N_{\mathrm{d}of}$ | 8.1/8 | 7.5/7 | 13.9/10 | 8.0/6 | 12.5/8
$m_{t}$ [GeV] | $168.4\pm 2.3$ | $173.0\pm 2.1$ | $170.6\pm 4.2$ | $169.4\pm 2.0$ | $166.9\pm 4.0$
Data statistics | $\pm\,1.0$ | $\pm\,0.9$ | $\pm\,2.0$ | $\pm\,0.9$ | $\pm\,1.3$
Expt. systematic | $\pm\,1.6$ | $\pm\,1.0$ | $\pm\,3.1$ | $\pm\,1.6$ | $\pm\,1.5$
PDF uncertainty | $\pm\,1.0$ | $\pm\,0.2$ | $\pm\,1.6$ | $\pm\,0.6$ | $\pm\,3.4$
$t\bar{t}$ generator | $\pm\,0.4$ | $\pm\,1.4$ | $\pm\,1.4$ | $\pm\,0.4$ | $\pm\,1.1$
QCD radiation | $\pm\,0.7$ | $\pm\,0.8$ | $\pm\,0.5$ | $\pm\,0.2$ | $\pm\,0.2$

Moment 1 | $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
$m_{t}$ [GeV] | $168.2\pm 2.9$ | $172.4\pm 3.8$ | $166.6\pm 6.5$ | $168.4\pm 2.9$ | $160.8\pm 7.9$
Data statistics | $\pm\,1.0$ | $\pm\,1.0$ | $\pm\,2.4$ | $\pm\,1.1$ | $\pm\,2.2$
Expt. systematic | $\pm\,2.1$ | $\pm\,1.6$ | $\pm\,3.8$ | $\pm\,2.1$ | $\pm\,3.1$
PDF uncertainty | $\pm\,1.2$ | $\pm\,0.3$ | $\pm\,2.9$ | $\pm\,1.1$ | $\pm\,6.7$
$t\bar{t}$ generator | $\pm\,0.2$ | $\pm\,1.3$ | $\pm\,3.4$ | $\pm\,0.2$ | $\pm\,2.0$
QCD radiation | $\pm\,1.2$ | $\pm\,3.0$ | $\pm\,1.4$ | $\pm\,1.1$ | $\pm\,0.2$

Moment 2 | $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
$m_{t}$ [GeV] | $168.1\pm 3.2$ | $172.2\pm 4.5$ | $166.9\pm 6.9$ | $167.9\pm 3.3$ | $159.9\pm 9.2$
Data statistics | $\pm\,1.2$ | $\pm\,1.1$ | $\pm\,2.8$ | $\pm\,1.3$ | $\pm\,2.6$
Expt. systematic | $\pm\,2.3$ | $\pm\,2.0$ | $\pm\,4.3$ | $\pm\,2.4$ | $\pm\,3.4$
PDF uncertainty | $\pm\,1.3$ | $\pm\,0.4$ | $\pm\,3.3$ | $\pm\,1.3$ | $\pm\,7.8$
$t\bar{t}$ generator | $\pm\,0.4$ | $\pm\,1.2$ | $\pm\,3.2$ | $\pm\,0.4$ | $\pm\,2.4$
QCD radiation | $\pm\,1.2$ | $\pm\,3.7$ | $\pm\,0.7$ | $\pm\,1.3$ | $\pm\,0.2$

Moment 3 | $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
$m_{t}$ [GeV] | $168.3\pm 3.5$ | $172.0\pm 5.6$ | $166.4\pm 9.1$ | $167.6\pm 3.8$ | $160.9\pm 9.5$
Data statistics | $\pm\,1.5$ | $\pm\,1.4$ | $\pm\,4.2$ | $\pm\,1.6$ | $\pm\,3.0$
Expt. systematic | $\pm\,2.5$ | $\pm\,2.6$ | $\pm\,6.0$ | $\pm\,2.7$ | $\pm\,3.7$
PDF uncertainty | $\pm\,1.5$ | $\pm\,0.6$ | $\pm\,4.1$ | $\pm\,1.4$ | $\pm\,7.8$
$t\bar{t}$ generator | $\pm\,0.6$ | $\pm\,1.1$ | $\pm\,3.5$ | $\pm\,0.7$ | $\pm\,2.4$
QCD radiation | $\pm\,1.1$ | $\pm\,4.6$ | $\pm\,0.2$ | $\pm\,1.4$ | $\pm\,0.2$

Table 14:  Measurements of the top quark mass from individual template fits to
the lepton $p_{\mathrm{T}}^{\ell}$ and dilepton $p_{\mathrm{T}}^{e\mu}$,
$m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and $E^{e}+E^{\mu}$
distributions, and using the first, second and third moments of these
distributions. The data are compared to predictions from Powheg + Pythia6 with
the CT10 PDF set. The $\chi^{2}$ value at the best-fit mass for each
distribution (for the template fits only), the fitted mass with its total
uncertainty, and the individual uncertainty contributions from data
statistics, experimental systematics, and uncertainties in the predictions due
to the choice of $t\bar{t}$ event generator and the modelling of QCD radiation
are shown. Figure 17: Measurements of the top quark mass using templates
derived from Powheg + Pythia6 with the CT10 PDF set. The results from fitting
templates of the single lepton $p_{\mathrm{T}}^{\ell}$ and dilepton
$p_{\mathrm{T}}^{e\mu}$, $m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$
and $E^{e}+E^{\mu}$ distributions, and from the first, second and third
moments of these distributions, are shown. For comparison, the world-average
of mass measurements from reconstruction of the top quark decay products and
its uncertainty [121] is shown by the cyan band.

The ratios of predictions to data at the best-fit top quark mass found by the
application of the template fit method to each distribution are shown in
Figure 18. The data are generally well-described by these predictions, as can
also be seen from the $\chi^{2}$ values in Table 14, except for the
$E^{e}+E^{\mu}$ distribution. This distribution is quite sensitive to PDFs as
well as $m_{t}$, and is better described by the HERAPDF PDFs than the CT10
PDFs used here to extract $m_{t}$, resulting in a low fitted value with a
large PDF uncertainty, and a large variation between the template and moment
fit results. Total uncertainties in $m_{t}$ of about 2 GeV are obtained from
the template fits to the $p_{\mathrm{T}}^{\ell}$, $p_{\mathrm{T}}^{e\mu}$ and
$p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ distributions. These results have
relatively small theoretical uncertainties, and the experimental uncertainties
are dominated by $t\bar{t}-Wt$ interference and the electron energy scale. The
$m^{e\mu}$ distribution is intrinsically less sensitive to $m_{t}$, having
larger statistical, experimental and theoretical systematic uncertainties. The
results from the extraction based on moments have larger uncertainties than
those from the template fit, reflecting that the moments do not take into
account the relative precision on the different bins of the distributions, and
that the higher moments are more sensitive to the tails of the distributions,
which are less precisely measured and subject to larger theoretical
uncertainties. Within each distribution, the $m_{t}$ values from the different
moments are close, though 3–4 GeV lower than the template fit results for
$m^{e\mu}$, and up to 7 GeV lower in the case of $E^{e}+E^{\mu}$.

(a)

(b)

(c)

(d)

(e)

Figure 18: Ratios of predictions of normalised differential cross-sections to
data as a function of (a) $p_{\mathrm{T}}^{\ell}$, (b)
$p_{\mathrm{T}}^{e\mu}$, (c) $m^{e\mu}$, (d)
$p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and (e) $E^{e}+E^{\mu}$, with the
prediction taken from Powheg + Pythia6 with the CT10 PDF at the best-fit top
quark mass $m_{t}$ for each distribution. The data statistical uncertainties
are shown by the black error bars around a ratio of unity, and the total
experimental uncertainties by the cyan band.

The central values of the template fit results from the five distributions
exhibit a spread (envelope) of about 6 GeV. The results from the fits of
$p_{\mathrm{T}}^{\ell}$ and $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ lie 4–5
GeV below that from $p_{\mathrm{T}}^{e\mu}$, which is close to the world-
average mass value from reconstruction of top quark decay products of
$173.34\pm 0.76$ GeV [121]. The consistency of the fit results was assessed by
combining them using the best linear unbiased estimate (BLUE) technique [122].
Correlations in the statistical uncertainties were assessed using pseudo-
experiments as described in Section 4.3. Correlations between systematic
uncertainties were determined by assuming the effects on $m_{t}$ from each
individual experimental or theoretical component to be fully correlated
between distributions. PDF uncertainties were assessed using the eigenvector
pairs of the CT10 PDF only. The combination of all five distributions has a
$\chi^{2}$ probability of 4 %, indicating that the systematic uncertainties
may be underestimated.

The Powheg + Pythia6 $t\bar{t}$ samples used here do not provide a good
modelling of the top quark $p_{\text{T}}$ spectrum [18, 19, 20, 22, 23],
potentially biasing the results. The size of this possible bias was explored
by fitting the distributions from the Powheg + Pythia6 baseline sample
reweighted to the top quark $p_{\text{T}}$ spectrum calculated at NNLO
precision in Ref. [25]. The reweighted sample gives a better description of
the $p_{\mathrm{T}}^{\ell}$ and $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$
distributions, as can be seen from the $\chi^{2}$ values for ‘Powheg + PY6
$p_{\text{T}}$ NNLO’ in Table 8. The mass shifts between the baseline and
reweighted samples, representing the amount that the top quark mass measured
in data would be shifted upwards if the templates were based on reweighted
samples, are shown in Table 13. These shifts are larger (1.3–1.8 GeV) for
$p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and $p_{\mathrm{T}}^{\ell}$ than for
$p_{\mathrm{T}}^{e\mu}$ (0.3 GeV), and would bring the results shown in Figure
17 into closer agreement with each other. However, given that this reweighting
is relatively crude, and does not take into account the potential NNLO effects
on other distributions important for modelling the lepton and dilepton
kinematics (e.g. the invariant mass and rapidity of the $t\bar{t}$ system),
the shifts are taken to be purely indicative, and no attempt has been made to
correct the quoted central values for these effects. The predictions for the
$p_{\mathrm{T}}^{\ell}$ and $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$
distributions are also sensitive to the choice of PDF. The PDF uncertainties
shown for $p_{\mathrm{T}}^{\ell}$ and
$p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ in Table 14 are significantly larger
than those for $p_{\mathrm{T}}^{e\mu}$, and as shown in Section 6.2, the
Powheg + Pythia6 sample generated using HERAPDF 1.5 instead of CT10 gives a
significantly better description of both distributions at
$\mbox{$m_{t}$}=172.5$ GeV.

The predictions from Powheg + Pythia6, based on NLO matrix elements interfaced
to parton showers, hence suffer from significant uncertainties due to missing
NNLO corrections and lack of knowledge of the PDFs. Consequently, they do not
have sufficient precision to extract the top quark mass from individual
distributions with a theoretical uncertainty better than about 2 GeV, slightly
larger than the uncertainties corresponding to the precision of the
experimental measurements. These limitations are addressed by the approach
discussed below, where several distributions are fitted simultaneously to
extract $m_{t}$ whilst constraining the uncertainties in the theoretical
predictions.

###  8.4 Mass extraction using fixed-order predictions

The NLO fixed-order predictions for each distribution were generated using
MCFM as discussed in Section 6.3, for top quark masses in the range 161–180
GeV in steps of 0.5 GeV, with various PDF choices. The $\chi^{2}$ for the
consistency of each prediction with the data was calculated using Eq. (9),
incorporating both PDF and QCD scale uncertainties into the theoretical
uncertainties represented by the nuisance parameters
${\mathbf{b}}_{\mathrm{th}}$. The central scales were again chosen to be
$\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$, with the values varying with $m_{t}$ in
the mass scan, and independent variations of $\mu_{F}$ and $\mu_{R}$ by
factors of two and one-half defining the one standard deviation up and down
scale variations. The $\chi^{2}$ was evaluated at each mass point, and
interpolated using a fourth-order polynomial. The asymmetric uncertainty in
the fitted value of $m_{t}$ was defined as the points at which the $\chi^{2}$
increases by one unit either side of the minimum point. This uncertainty
naturally includes both experimental statistical and systematic uncertainties
in the measurements, and theoretical uncertainties due to PDFs and QCD scale
choices.

In this method, the top quark mass can be extracted from each measured
distribution individually, or from the combination of several distributions,
where the sum $i$ in Eq. (9) runs over the bins of all considered
distributions, and the experimental covariance matrix includes both
statistical and systematic correlations between bins of the same and different
distributions, evaluated as discussed in Section 6.2. When fitting several
distributions simultaneously, the system is over-constrained, profiling the
various sources of theoretical uncertainty. For example, when including all
eight measured distributions, the et al. and $|y^{e\mu}|$ distributions have
little sensitivity to $m_{t}$, but constrain the PDF parameters. The
$\Delta\phi^{e\mu}$ distribution constrains the QCD scale parameters $\mu_{F}$
and $\mu_{R}$, under the assumption that uncertainties in higher-order QCD
corrections are parameterised by $\mu_{F}$ and $\mu_{R}$ in a way that can be
transported from one distribution to another. Two alternative dynamical scale
choices were also tested in order to probe this assumption, as discussed in
Section 8.5 below.

Potential biases in the method were checked by using predictions with
$\mbox{$m_{t}$}=172.5$ GeV as pseudo-data, and considering both experimental
and theoretical uncertainties in the $\chi^{2}$ definition. The resulting
fitted values of $m_{t}$ were within 0.1 GeV of the input value for all five
fitted individual distributions ($p_{\mathrm{T}}^{\ell}$,
$p_{\mathrm{T}}^{e\mu}$, $m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$
and $E^{e}+E^{\mu}$), and 0.01 GeV from the input value for a combined fit of
all eight distributions, also including et al., $|y^{e\mu}|$ and
$\Delta\phi^{e\mu}$. The widths of the pull distributions were found to be
compatible with unity, confirming the validity of the uncertainty estimates
from the fits.

###  8.5 Mass results from fixed-order predictions

The results of the fits to NLO QCD fixed-order predictions with MCFM and the
CT14 PDF set are shown for the individual distributions in Table 15, and the
results using the CT14, MMHT, NNPDF 3.0, HERAPDF 2.0, ABM 11 [123] and NNPDF
3.0_nojet [105] PDF sets are shown in Figure 19. As shown in Section 7, the
constraint on the gluon PDF from the leptonic $t\bar{t}$ measurements is
consistent with the PDF determination from DIS data. The use of the NNPDF
3.0_nojet PDF set, which does not include Tevatron and LHC jet production
data, allows the effects on $m_{t}$ of any possible tension between DIS and
jet data in the determination of the gluon PDF to be tested. The results from
combined fits to all eight distributions, using predictions from all six PDF
sets, are shown in Table 16 and Figure 19. In Tables 15 and 16, the
decomposition of the total uncertainty from each mass fit into statistical,
experimental and theoretical (PDF and QCD scales) uncertainties was obtained
in analogy to the numerical procedure outlined in Ref. [124]. For each
individual source of statistical or systematic uncertainty (corresponding to a
nuisance parameter $b_{j,{\mathrm{exp}}}$ or $b_{k,{\mathrm{th}}}$ in Eq.
(9)), the data were shifted by plus or minus one standard deviation, and a new
$m_{t}$ value obtained by re-minimising the $\chi^{2}$ function. The resulting
shifts in $m_{t}$ were added in quadrature to obtain the decomposition into
the various categories. The quadrature sum of the decomposed uncertainties
agrees with the total to within 10 % in all cases, the residual differences
being due to non-linearity between the uncertainty sources and the extracted
values of $m_{t}$.

| $p_{\mathrm{T}}^{\ell}$ | $p_{\mathrm{T}}^{e\mu}$ | $m^{e\mu}$ | $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ | $E^{e}+E^{\mu}$
---|---|---|---|---|---
$\chi^{2}/N_{\mathrm{d}of}$ | 9/8 | 5/7 | 11/10 | 11/6 | 8/8
$m_{t}^{\mathrm{pole}}$ [GeV] | $169.7\,^{+2.9}_{-2.7}$ | $175.1\pm 1.9$ | $174.5\,^{+5.1}_{-5.3}$ | $170.3\pm 2.1$ | $168.5\,^{+3.2}_{-3.3}$
Data statistics | $\pm\,2.0$ | $\pm\,1.4$ | $\,{}^{+3.8}_{-4.0}$ | $\pm\,1.4$ | $\pm\,2.3$
Expt. systematic | $\,{}^{+2.5}_{-2.3}$ | $\pm\,0.9$ | $\,{}^{+2.9}_{-3.3}$ | $\,{}^{+1.5}_{-1.6}$ | $\pm\,2.0$
PDF uncertainty | $\pm\,0.5$ | $\pm\,0.1$ | $\pm\,1.1$ | $\pm\,0.5$ | $\pm\,1.4$
QCD scales | $\pm\,1.1$ | $\,{}^{+0.7}_{-0.8}$ | $\pm\,2.6$ | $\,{}^{+0.4}_{-0.5}$ | $\pm\,0.7$
Table 15:  Measurements of the top quark mass from individual fits to the lepton $p_{\mathrm{T}}^{\ell}$ and dilepton $p_{\mathrm{T}}^{e\mu}$, $m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and $E^{e}+E^{\mu}$ distributions, using fixed-order predictions from MCFM with the CT14 PDF set. The $\chi^{2}$ value at the best-fit mass for each distribution, the fitted mass with its total uncertainty, and the individual uncertainty contributions from data statistics, experimental systematics, and uncertainties in the predictions from PDF and QCD scale effects are shown. | CT14 | MMHT | NNPDF 3.0 | HERAPDF 2.0 | ABM 11 | NNPDF nojet
---|---|---|---|---|---|---
$\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$ |  |  |  |  |  |
$\chi^{2}/N_{\mathrm{d}of}$ | 71/68 | 70/68 | 67/68 | 67/68 | 71/68 | 64/68
$m_{t}^{\mathrm{pole}}$ [GeV] | $173.5\pm 1.2$ | $173.4\pm 1.2$ | $173.2\pm 1.2$ | $172.9\pm 1.2$ | $172.8\,^{+1.3}_{-1.2}$ | $173.1\pm 1.2$
Data statistics | $\pm\,0.9$ | $\pm\,0.9$ | $\pm\,0.9$ | $\pm\,0.9$ | $\pm\,0.9$ | $\pm\,0.9$
Expt. systematic | $\,{}^{+0.7}_{-0.8}$ | $\pm\,0.8$ | $\pm\,0.8$ | $\pm\,0.9$ | $\,{}^{+0.9}_{-0.8}$ | $\pm\,0.8$
PDF uncertainty | $\pm\,0.1$ | $\pm\,0.1$ | $\,{}^{+0.1}_{-0.2}$ | $\pm\,0.1$ | $\pm\,0.1$ | $\pm\,0.4$
QCD scales | $\pm\,0.1$ | $\pm\,0.1$ | $\,{}^{+0.1}_{-0.0}$ | $\pm\,0.1$ | $\pm\,0.1$ | $\pm\,0.0$
$\mu_{F}=\mu_{R}=H_{T}/4$ |  |  |  |  |  |
$\chi^{2}/N_{\mathrm{d}of}$ | 69/68 | 67/68 | 64/68 | 61/68 | 66/68 | 60/68
$m_{t}^{\mathrm{pole}}$ [GeV] | $173.6\pm 1.3$ | $173.4\pm 1.3$ | $173.2\pm 1.3$ | $173.6\pm 1.3$ | $173.7\,^{+1.3}_{-1.2}$ | $173.2\,^{+1.3}_{-1.4}$
$\mu_{F}=\mu_{R}=E_{T}/2$ |  |  |  |  |  |
$\chi^{2}/N_{\mathrm{d}of}$ | 71/68 | 70/68 | 66/68 | 64/68 | 68/68 | 64/68
$m_{t}^{\mathrm{pole}}$ [GeV] | $174.7\pm 1.4$ | $174.5\,^{+1.5}_{-1.4}$ | $174.3\,^{+1.5}_{-1.4}$ | $173.6\,^{+1.3}_{-1.2}$ | $173.4\,^{+1.2}_{-1.1}$ | $174.0\,^{+1.5}_{-1.4}$
Table 16:  Measurements of the top quark mass from combined fits to all eight
lepton and dilepton distributions, using fixed-order predictions from MCFM
with the CT14, MMHT, NNPDF 3.0, HERAPDF 2.0, ABM 11 and NNPDF 3.0_nojet PDF
sets, and various choices for the central QCD factorisation and
renormalisation scales $\mu_{F}$ and $\mu_{R}$. The upper section of the table
gives the results for $\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$, showing the
$\chi^{2}$ values at the best-fit mass for each PDF set, the fitted mass with
its total uncertainty, and the breakdown of individual uncertainty
contributions from data statistics, experimental systematics, and
uncertainties in the predictions from PDF and QCD scale effects. Uncertainties
given as ‘0.0’ are smaller than 0.05 GeV. The lower parts of the table give
the $\chi^{2}$ values, fitted mass and total uncertainty for alternative scale
choices of $\mu_{F}=\mu_{R}=H_{T}/4$ and $E_{T}/2$. Figure 19: Measurements of
the top quark mass using predictions derived from MCFM with the CT14, MMHT,
NNPDF 3.0, HERAPDF 2.0, ABM 11 and NNPDF 3.0_nojet PDF sets. The central
factorisation and renormalisation scales are set to
$\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$. The results from fitting templates of the
single lepton $p_{\mathrm{T}}^{\ell}$ and dilepton $p_{\mathrm{T}}^{e\mu}$,
$m^{e\mu}$, $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ and $E^{e}+E^{\mu}$
distributions one at a time, and of a combined fit to these five distributions
plus the et al., $|y^{e\mu}|$ and $\Delta\phi^{e\mu}$ distributions together,
are shown. For comparison, the world-average of mass measurements from
reconstruction of the top quark decay products and its uncertainty [121] is
shown by the cyan band.

The MCFM fixed-order results for individual distributions shown in Table 15
and Figure 19 show some similar patterns to those from the Powheg +
Pythia6-based template fits shown in Table 14 and Figure 17. The results from
$p_{\mathrm{T}}^{\ell}$ and $p_{\mathrm{T}}^{e}+p_{\mathrm{T}}^{\mu}$ are
close, the largest $m_{t}$ values come from $p_{\mathrm{T}}^{e\mu}$, the
smallest from $E^{e}+E^{\mu}$ and the least precise determination is obtained
from $m^{e\mu}$. The envelope of the central values is similar (6 GeV), but
all values are shifted up by a few GeV compared to the corresponding Powheg +
Pythia6-based template fit results for the same distribution. The $\chi^{2}$
values are reasonable, indicating a satisfactory description of the data by
the predictions at the best-fit $m_{t}$ values. The various distributions show
different relative sensitivities to the PDF and QCD scale uncertainties.

As shown in Table 16, the combination of all eight measured distributions
(including et al., $|y^{e\mu}|$ and $\Delta\phi^{e\mu}$ which are not
sensitive to $m_{t}$) significantly reduces the theoretical uncertainties due
to both PDF and QCD scale effects. The $\chi^{2}$ values for the combined
description of all eight distributions are reasonable for all PDFs, implying
that there is no significant tension between the mass fit results from the
individual distributions, once the correlations between the distributions are
taken into account. Several additional tests using the predictions based on
NNPDF 3.0 were performed to probe the compatibility of the top quark mass
values extracted from the different distributions, and the accuracy of the
physics modelling used to perform the extraction. The combined fit was
repeated removing one distribution at a time. The largest shift of $-1.4\pm
1.1$ GeV was observed when removing the $p_{\mathrm{T}}^{e\mu}$ distribution,
where the uncertainty corresponds to the quadrature difference of the fit
uncertainties with and without the $p_{\mathrm{T}}^{e\mu}$ distribution
included. The removal of any other single distribution changed the result by
less than 0.3 GeV, and a fit to only the five distributions directly sensitive
to $m_{t}$ (excluding et al., $|y^{e\mu}|$ and $\Delta\phi^{e\mu}$) gave a
result of $173.1\pm 1.2$ GeV, corresponding to a shift of $-0.1$ GeV with
respect to the eight-distribution result. Finally, the individual measurements
from the five directly-sensitive distributions were combined using the
HAverager program [125, 126]. Correlated statistical and systematic
uncertainties were taken into account using nuisance parameters, but post-fit
correlations between these nuisance parameters were neglected, unlike in the
simultaneous fit approach with xFitter. The average of the five measurements
is $173.4\pm 1.6$ GeV with a $\chi^{2}$ of $6.4/4$, in reasonable agreement
with the result from the simultaneous fit of the five distributions. No
additional uncertainty was included as a result of these tests.

The combined-fit $\chi^{2}$ values in Table 16 are smallest for the HERAPDF
2.0 and NNPDF 3.0_nojet PDF sets, which do not include the constraints on the
gluon PDF from LHC and Tevatron jet data in the region relevant for $t\bar{t}$
production. However, the $m_{t}$ values resulting from the NNPDF 3.0 and NNPDF
3.0_nojet PDFs are close, indicating that the results are not sensitive to
whether the jet data are included or not. Amongst the ‘global fit’ PDF sets
incorporating a larger set of experimental data, the smallest $\chi^{2}$
values result from the fit with NNPDF 3.0, though the values from the other
PDFs are also reasonable. The results using NNPDF 3.0 were therefore used to
define the central $m_{t}$ value from the combined fit to all eight
distributions, and an additional uncertainty of 0.3 GeV, corresponding to half
the difference of the envelope encompassing all the other PDFs, was added in
quadrature to the PDF uncertainty from NNPDF 3.0 alone. The effect of the
uncertainty in the value of $\alpha_{\text{S}}$ was found to be 0.01 GeV. The
residual dependence of the measured differential cross-sections on the top
quark mass assumed in the simulation (see Section 5.1) is very small. A $\pm
5$ GeV variation around the baseline value of $\mbox{$m_{t}$}=172.5$ GeV was
assumed, giving a 0.1 GeV change on the result of the combined fit.

The choice of a fixed central scale, $\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$ is
expected to provide a good description of the inclusive $t\bar{t}$ cross-
section and differential distributions in the kinematic regions dominated by
top quarks with relatively low $p_{\text{T}}$. However, dynamical scales,
which vary as a function of the top quark kinematics, are expected to be more
appropriate for modelling the regions with high $p_{\text{T}}$ [107]. Two
alternative dynamical central scale choices for the $t\bar{t}$ production
process were explored to test the sensitivity of the results to this choice:

  * •

$\mu_{F}=\mu_{R}=H_{T}/4$ where $H_{T}$ is defined as
$\sqrt{\mbox{$m_{t}$}^{2}+p_{\text{T}}(t)^{2}}+\sqrt{\mbox{$m_{t}$}^{2}+p_{\text{T}}(\bar{t})^{2}}$
and $p_{\text{T}}(t)$ and $p_{\text{T}}(\bar{t})$ are the transverse momentum
of the top quark and antiquark, corresponding to one of the dynamical scales
suggested in Ref. [107].

  * •

$\mu_{F}=\mu_{R}=E_{T}/2$ where $E_{T}$ is defined as
$\sqrt{\mbox{$m_{t}$}^{2}+p_{\text{T}}(t\bar{t})^{2}}$ and
$p_{\text{T}}(t\bar{t})$ is the $p_{\text{T}}$ of the $t\bar{t}$ system,
analogously to a scale $\sqrt{m_{W}^{2}+p_{\text{T}}(W)^{2}}$ used in the
description of jet production in association with $W$ bosons [127, 128].

In both cases, the central scale for the top quark decay process $t\rightarrow
b\ell\nu+X$ was fixed at $\mbox{$m_{t}$}/2$. The corresponding predictions for
the top quark $p_{\text{T}}$ spectrum from MCFM with NNPDF 3.0 and these scale
choices are shown in Figure 20, and compared to the ATLAS $\sqrt{s}=8$ TeV
measurement using $t\bar{t}$ events with a lepton and at least four jets [20].
Unlike the predictions of Powheg + Pythia6 used in Section 8.3, the MCFM
predictions with central scale choices of $\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$,
$H_{T}/4$ and $E_{T}/2$ provide good descriptions of the measured top quark
$p_{\text{T}}$ spectrum, whereas $\mu_{F}=\mu_{R}=\mbox{$m_{t}$}$ is too hard.

Figure 20: Measurement of the top quark $p_{\text{T}}$ spectrum in $pp$
collisions at $\sqrt{s}=8$ TeV from ATLAS events with a lepton and at least
four jets [20], compared to the predictions from MCFM as used in this analysis
with NNPDF 3.0, $\mbox{$m_{t}$}=173.3$ GeV, and QCD scale choices of
$\mu_{F}=\mu_{R}=\mbox{$m_{t}$}/2$, $H_{T}/4$ and $E_{T}/2$, as well as with
$\mu_{F}=\mu_{R}=\mbox{$m_{t}$}$. The measurement uncertainties are
represented by the yellow band, with the uncorrelated component shown by the
black error bar. The lower plots show the ratios of the different predictions
to the data.

The results from the combined fit to all eight distributions with these scale
choices and all six PDF sets are shown in the lower part of Table 16, and
displayed graphically in Figure 21. In the same way as for the fixed central
scale, the actual factorisation and normalisation scales used in the
predictions were allowed to vary independently around the dynamical central
scales, with one standard deviation variations corresponding to factors of two
and one-half. The $\chi^{2}$ values for the fits with a central scale of
$H_{T}/4$ are all improved compared to those for $\mbox{$m_{t}$}/2$,
reflecting a generally better description of the high-$p_{\text{T}}$ tails of
the distributions. The $\chi^{2}$ values from the $E_{T}/2$ fits lie between
the other two choices. The largest difference in the $m_{t}$ values from a
dynamical scale and the fixed scale with any PDF (1.1 GeV for $E_{T}/2$ vs.
$\mbox{$m_{t}$}/2$ with the CT14 PDF) was used to define an additional
theoretical uncertainty due to the choice of the functional form of the QCD
scales.

Figure 21: Measurements of the top quark mass using predictions derived from
MCFM with the CT14, MMHT, NNPDF 3.0, HERAPDF 2.0, ABM 11 and NNPDF 3.0_nojet
PDF sets, and the central QCD factorisation and renormalisation scales
$\mu_{F}$ and $\mu_{R}$ set to $\mbox{$m_{t}$}/2$, $H_{T}/4$ and $E_{T}/2$.
The results are derived from a combined fit to all eight lepton and dilepton
distributions. For comparison, the world-average of mass measurements from
reconstruction of the top quark decay products [121] is shown by the cyan
band.

The final top quark mass value from the combination of all distributions is:

$\mbox{$m_{t}^{\mathrm{pole}}$}=173.2\pm 0.9\pm 0.8\pm
1.2\,\text{Ge\kern-1.00006ptV},$

where the three uncertainties arise from data statistics, experimental
systematic effects, and uncertainties in the theoretical predictions, giving a
total uncertainty of $1.6$ GeV. The theoretical uncertainty is dominated by
the comparison of results with different QCD central scale choices. Figure 22
shows a comparison with previous determinations of the top quark pole mass
from the inclusive $t\bar{t}$ production cross-section [40, 13, 15] and from
the invariant mass distribution of the $t\bar{t}$ plus one jet system [41].
The present result is in agreement with these other results, all of which have
larger uncertainties. It is also in agreement with the Tevatron and LHC
average measurement of $173.34\pm 0.76$ GeV from reconstruction of the top
quark decay products [121], as well as with more precise recent results using
similar techniques [129, 35, 36]. However, the precision of the present pole
mass result is not sufficient to probe potential differences between it and
the other techniques at the 1 GeV level.

Figure 22: Result of the top quark pole mass determination from the combined
fit to eight leptonic distributions (shown by the red point and grey band),
compared to other determinations from inclusive and differential cross-section
measurements in $t\bar{t}$ events [40, 13, 15, 41]. The statistical
uncertainties are shown separately by the thick error bars where available.

The theoretical uncertainty of 1.2 GeV on the final result using fixed-order
predictions is significantly smaller than the uncertainties due to $t\bar{t}$
modelling and potential NNLO effects in the top quark $p_{\text{T}}$ spectrum
for the fits based on Powheg + Pythia6 templates. In the fixed-order approach,
the potential missing NNLO corrections are absorbed into the variations of the
QCD scales $\mu_{F}$ and $\mu_{R}$, which are significantly constrained by the
fit to the complete set of distributions, including those with little
sensitivity to $m_{t}$. However, there remains a significant uncertainty of
about 1 GeV due to the choice of the functional form of the QCD scales,
limiting the gain from the combined fit. This approach would therefore benefit
significantly from the availability of fixed-order calculations including NNLO
effects in the top quark production and decay [130], which should reduce the
uncertainties due to scale choices. Off-shell and interference effects in the
$pp\rightarrow WWb\bar{b}\rightarrow e\mu\nu\bar{\nu}b\bar{b}+X$ process
(including both $t\bar{t}$ and single top $Wt$ contributions) [131, 132, 133,
134, 135, 136, 137], as well as NLO electroweak corrections [138, 139], were
not considered in this analysis. They are expected to be small compared to the
theoretical uncertainties of the current result, but likely cannot be
neglected in a determination of $m_{t}$ based on NNLO QCD predictions. These
theoretical advances would allow the power of the full set of distributions to
be utilised more effectively, especially in view of the likely reduction in
the experimental statistical and systematic uncertainties from the larger
$t\bar{t}$ samples now becoming available from LHC running at $\sqrt{s}=13$
TeV.

##  9 Conclusions

Lepton and dilepton differential cross-section distributions have been
measured in $t\bar{t}\rightarrow e\mu\nu\bar{\nu}b\bar{b}$ events selected
from 20.2 fb-1of $pp$ collisions at $\sqrt{s}=8$ TeV recorded by the ATLAS
detector at the LHC. The absolute and normalised cross-sections were measured
using opposite-charge $e\mu$ events with one or two $b$-tagged jets, and
corrected to a fiducial volume corresponding to the experimental acceptance of
the leptons and no requirements on jets. Eight single lepton and dilepton
differential distributions were measured, with relative uncertainties varying
in the range 1–10 %, and presented with and without the contribution from
leptonic decays of $\tau$-leptons produced in the $W$ decays.

The results were compared to the predictions of various $t\bar{t}$ NLO and LO
multileg matrix element event generators interfaced to several parton shower
and hadronisation models. These generally give a good description of the
distributions, though some distributions are modelled poorly by certain event
generators. Those involving rapidity information are better described by the
HERAPDF PDF sets than the CT10 set used as default. The distributions also
show some sensitivity to NNLO corrections in the description of the top quark
$p_{\text{T}}$ spectrum. The data are sensitive to the gluon PDF around
$x\approx 0.1$ and have the potential to reduce PDF uncertainties in this
region.

Several of the measured distributions are sensitive to the top quark mass, in
a way which is complementary to traditional measurements of $m_{t}$ using the
invariant mass of the reconstructed top quark decay products. Various
techniques for extracting the top quark mass from the measured distributions
were explored, including fits using templates from Powheg + Pythia6 simulated
samples, mass determinations based on moments of the distributions, and fits
to fixed-order NLO QCD predictions, giving access to the top quark pole mass
in a well-defined renormalisation scheme as implemented in MCFM. The most
precise result was obtained from a fit of fixed-order predictions to all eight
measured distributions simultaneously, extracting $m_{t}^{\mathrm{pole}}$
whilst simultaneously constraining uncertainties due to PDFs and QCD scales.
The final result is:

$\displaystyle\mbox{$m_{t}^{\mathrm{pole}}$}=173.2\pm 0.9\pm 0.8\pm
1.2\,\text{Ge\kern-1.00006ptV},$

where the three uncertainties arise from data statistics, experimental
systematic effects, and uncertainties in the theoretical predictions. This
result is in excellent agreement with other determinations of
$m_{t}^{\mathrm{pole}}$ from inclusive and differential cross-sections, and
traditional measurements based on reconstruction of the top quark decay
products.

## 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; SRNSF,
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; 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. [140].

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The ATLAS Collaboration

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88}}$, B. Abbott${}^{\textrm{\scriptsize 115}}$, O.
Abdinov${}^{\textrm{\scriptsize 12}}$,∗, B. Abeloos${}^{\textrm{\scriptsize
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Acharya${}^{\textrm{\scriptsize 167a,167b}}$,a, S.
Adachi${}^{\textrm{\scriptsize 157}}$, L. Adamczyk${}^{\textrm{\scriptsize
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Arslan${}^{\textrm{\scriptsize 23}}$, A. Artamonov${}^{\textrm{\scriptsize
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Artz${}^{\textrm{\scriptsize 86}}$, S. Asai${}^{\textrm{\scriptsize 157}}$, N.
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Axen${}^{\textrm{\scriptsize 16}}$, M.K. Ayoub${}^{\textrm{\scriptsize 35a}}$,
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Bagnaia${}^{\textrm{\scriptsize 134a,134b}}$, M.
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Bauce${}^{\textrm{\scriptsize 134a,134b}}$, F. Bauer${}^{\textrm{\scriptsize
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Bellerive${}^{\textrm{\scriptsize 31}}$, M. Bellomo${}^{\textrm{\scriptsize
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155}}$,∗, D. Benchekroun${}^{\textrm{\scriptsize 137a}}$, M.
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89}}$, G. Bernardi${}^{\textrm{\scriptsize 83}}$, C.
Bernius${}^{\textrm{\scriptsize 145}}$, F.U.
Bernlochner${}^{\textrm{\scriptsize 23}}$, T. Berry${}^{\textrm{\scriptsize
80}}$, P. Berta${}^{\textrm{\scriptsize 86}}$, C.
Bertella${}^{\textrm{\scriptsize 35a}}$, G. Bertoli${}^{\textrm{\scriptsize
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Bessner${}^{\textrm{\scriptsize 45}}$, N. Besson${}^{\textrm{\scriptsize
138}}$, A. Bethani${}^{\textrm{\scriptsize 87}}$, S.
Bethke${}^{\textrm{\scriptsize 103}}$, A. Betti${}^{\textrm{\scriptsize 23}}$,
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17}}$, R. Bielski${}^{\textrm{\scriptsize 87}}$, K.
Bierwagen${}^{\textrm{\scriptsize 86}}$, N.V. Biesuz${}^{\textrm{\scriptsize
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Billoud${}^{\textrm{\scriptsize 97}}$, H. Bilokon${}^{\textrm{\scriptsize
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Bingul${}^{\textrm{\scriptsize 20b}}$, C. Bini${}^{\textrm{\scriptsize
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47}}$, D.M. Bjergaard${}^{\textrm{\scriptsize 48}}$, J.E.
Black${}^{\textrm{\scriptsize 145}}$, K.M. Black${}^{\textrm{\scriptsize
24}}$, R.E. Blair${}^{\textrm{\scriptsize 6}}$, T.
Blazek${}^{\textrm{\scriptsize 146a}}$, I. Bloch${}^{\textrm{\scriptsize
45}}$, C. Blocker${}^{\textrm{\scriptsize 25}}$, A.
Blue${}^{\textrm{\scriptsize 56}}$, U. Blumenschein${}^{\textrm{\scriptsize
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Bobrovnikov${}^{\textrm{\scriptsize 111}}$,c, S.S.
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48}}$, C. Bock${}^{\textrm{\scriptsize 102}}$, M.
Boehler${}^{\textrm{\scriptsize 51}}$, D. Boerner${}^{\textrm{\scriptsize
178}}$, D. Bogavac${}^{\textrm{\scriptsize 102}}$, A.G.
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148a}}$, V. Boisvert${}^{\textrm{\scriptsize 80}}$, P.
Bokan${}^{\textrm{\scriptsize 168}}$,i, T. Bold${}^{\textrm{\scriptsize
41a}}$, A.S. Boldyrev${}^{\textrm{\scriptsize 101}}$, A.E.
Bolz${}^{\textrm{\scriptsize 60b}}$, M. Bomben${}^{\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}}$, D.
Boscherini${}^{\textrm{\scriptsize 22a}}$, M. Bosman${}^{\textrm{\scriptsize
13}}$, J.D. Bossio Sola${}^{\textrm{\scriptsize 29}}$, J.
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Thacker${}^{\textrm{\scriptsize 75}}$, D. Boumediene${}^{\textrm{\scriptsize
37}}$, C. Bourdarios${}^{\textrm{\scriptsize 119}}$, S.K.
Boutle${}^{\textrm{\scriptsize 56}}$, A. Boveia${}^{\textrm{\scriptsize
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Boyko${}^{\textrm{\scriptsize 68}}$, A.J. Bozson${}^{\textrm{\scriptsize
80}}$, J. Bracinik${}^{\textrm{\scriptsize 19}}$, A.
Brandt${}^{\textrm{\scriptsize 8}}$, G. Brandt${}^{\textrm{\scriptsize 57}}$,
O. Brandt${}^{\textrm{\scriptsize 60a}}$, F. Braren${}^{\textrm{\scriptsize
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Brau${}^{\textrm{\scriptsize 89}}$, J.E. Brau${}^{\textrm{\scriptsize 118}}$,
W.D. Breaden Madden${}^{\textrm{\scriptsize 56}}$, K.
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Bressler${}^{\textrm{\scriptsize 175}}$, D.L. Briglin${}^{\textrm{\scriptsize
19}}$, T.M. Bristow${}^{\textrm{\scriptsize 49}}$, D.
Britton${}^{\textrm{\scriptsize 56}}$, D. Britzger${}^{\textrm{\scriptsize
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Canale${}^{\textrm{\scriptsize 106a,106b}}$, M. Cano
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Cardillo${}^{\textrm{\scriptsize 51}}$, I. Carli${}^{\textrm{\scriptsize
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Carlino${}^{\textrm{\scriptsize 106a}}$, B.T. Carlson${}^{\textrm{\scriptsize
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Catmore${}^{\textrm{\scriptsize 121}}$, A. Cattai${}^{\textrm{\scriptsize
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Chau${}^{\textrm{\scriptsize 31}}$, C.A. Chavez
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Chen${}^{\textrm{\scriptsize 35c}}$,m, Y. Chen${}^{\textrm{\scriptsize 70}}$,
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Chiarelli${}^{\textrm{\scriptsize 126a,126b}}$, G.
Chiodini${}^{\textrm{\scriptsize 76a}}$, A.S. Chisholm${}^{\textrm{\scriptsize
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Chomont${}^{\textrm{\scriptsize 37}}$, S. Chouridou${}^{\textrm{\scriptsize
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Christodoulou${}^{\textrm{\scriptsize 81}}$, M.C. Chu${}^{\textrm{\scriptsize
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Chuinard${}^{\textrm{\scriptsize 90}}$, J.J.
Chwastowski${}^{\textrm{\scriptsize 42}}$, L. Chytka${}^{\textrm{\scriptsize
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Cinca${}^{\textrm{\scriptsize 46}}$, V. Cindro${}^{\textrm{\scriptsize 78}}$,
I.A. Cioara${}^{\textrm{\scriptsize 23}}$, A. Ciocio${}^{\textrm{\scriptsize
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Clark${}^{\textrm{\scriptsize 52}}$, B.L. Clark${}^{\textrm{\scriptsize 59}}$,
M.R. Clark${}^{\textrm{\scriptsize 38}}$, P.J. Clark${}^{\textrm{\scriptsize
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Clement${}^{\textrm{\scriptsize 148a,148b}}$, Y.
Coadou${}^{\textrm{\scriptsize 88}}$, M. Cobal${}^{\textrm{\scriptsize
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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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Coniavitis${}^{\textrm{\scriptsize 51}}$, S.H. Connell${}^{\textrm{\scriptsize
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Constantinescu${}^{\textrm{\scriptsize 28b}}$, G.
Conti${}^{\textrm{\scriptsize 32}}$, F. Conventi${}^{\textrm{\scriptsize
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Corradi${}^{\textrm{\scriptsize 134a,134b}}$, F.
Corriveau${}^{\textrm{\scriptsize 90}}$,o, A. Cortes-
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Creager${}^{\textrm{\scriptsize 124}}$, G. Cree${}^{\textrm{\scriptsize 31}}$,
S. Crépé-Renaudin${}^{\textrm{\scriptsize 58}}$, F.
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Croft${}^{\textrm{\scriptsize 112}}$, G. Crosetti${}^{\textrm{\scriptsize
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Cukierman${}^{\textrm{\scriptsize 145}}$, J. Cummings${}^{\textrm{\scriptsize
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Cúth${}^{\textrm{\scriptsize 86}}$, S. Czekierda${}^{\textrm{\scriptsize
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D’Onofrio${}^{\textrm{\scriptsize 77}}$, M.J. Da Cunha Sargedas De
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87}}$, W. Dabrowski${}^{\textrm{\scriptsize 41a}}$, T.
Dado${}^{\textrm{\scriptsize 146a}}$, T. Dai${}^{\textrm{\scriptsize 92}}$, O.
Dale${}^{\textrm{\scriptsize 15}}$, F. Dallaire${}^{\textrm{\scriptsize 97}}$,
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Daneri${}^{\textrm{\scriptsize 29}}$, N.P. Dang${}^{\textrm{\scriptsize
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Dann${}^{\textrm{\scriptsize 87}}$, M. Danninger${}^{\textrm{\scriptsize
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Dao${}^{\textrm{\scriptsize 150}}$, G. Darbo${}^{\textrm{\scriptsize 53a}}$,
S. Darmora${}^{\textrm{\scriptsize 8}}$, J. Dassoulas${}^{\textrm{\scriptsize
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Daubney${}^{\textrm{\scriptsize 45}}$, W. Davey${}^{\textrm{\scriptsize 23}}$,
C. David${}^{\textrm{\scriptsize 45}}$, T. Davidek${}^{\textrm{\scriptsize
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Davison${}^{\textrm{\scriptsize 81}}$, E. Dawe${}^{\textrm{\scriptsize 91}}$,
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R. de Asmundis${}^{\textrm{\scriptsize 106a}}$, A. De
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Groot${}^{\textrm{\scriptsize 108}}$, P. de Jong${}^{\textrm{\scriptsize
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Lorenzi${}^{\textrm{\scriptsize 67}}$, A. De Maria${}^{\textrm{\scriptsize
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Salvo${}^{\textrm{\scriptsize 134a}}$, U. De Sanctis${}^{\textrm{\scriptsize
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Dedovich${}^{\textrm{\scriptsize 68}}$, N. Dehghanian${}^{\textrm{\scriptsize
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Deliot${}^{\textrm{\scriptsize 138}}$, C.M. Delitzsch${}^{\textrm{\scriptsize
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Volpe${}^{\textrm{\scriptsize 52}}$, M. Delmastro${}^{\textrm{\scriptsize
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Delsart${}^{\textrm{\scriptsize 58}}$, D.A. DeMarco${}^{\textrm{\scriptsize
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Denysiuk${}^{\textrm{\scriptsize 138}}$, D. Derendarz${}^{\textrm{\scriptsize
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Derue${}^{\textrm{\scriptsize 83}}$, P. Dervan${}^{\textrm{\scriptsize 77}}$,
K. Desch${}^{\textrm{\scriptsize 23}}$, C. Deterre${}^{\textrm{\scriptsize
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Devesa${}^{\textrm{\scriptsize 29}}$, P.O. Deviveiros${}^{\textrm{\scriptsize
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Dhaliwal${}^{\textrm{\scriptsize 25}}$, F.A. Di Bello${}^{\textrm{\scriptsize
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Ciaccio${}^{\textrm{\scriptsize 5}}$, W.K. Di Clemente${}^{\textrm{\scriptsize
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Girolamo${}^{\textrm{\scriptsize 32}}$, B. Di Girolamo${}^{\textrm{\scriptsize
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Nardo${}^{\textrm{\scriptsize 32}}$, K.F. Di Petrillo${}^{\textrm{\scriptsize
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Sipio${}^{\textrm{\scriptsize 161}}$, D. Di Valentino${}^{\textrm{\scriptsize
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Diamond${}^{\textrm{\scriptsize 161}}$, F.A. Dias${}^{\textrm{\scriptsize
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Diehl${}^{\textrm{\scriptsize 92}}$, J. Dietrich${}^{\textrm{\scriptsize
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Dimitrievska${}^{\textrm{\scriptsize 14}}$, J.
Dingfelder${}^{\textrm{\scriptsize 23}}$, P. Dita${}^{\textrm{\scriptsize
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Dittus${}^{\textrm{\scriptsize 32}}$, F. Djama${}^{\textrm{\scriptsize 88}}$,
T. Djobava${}^{\textrm{\scriptsize 54b}}$, J.I.
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Dolejsi${}^{\textrm{\scriptsize 131}}$, Z. Dolezal${}^{\textrm{\scriptsize
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Donati${}^{\textrm{\scriptsize 126a,126b}}$, P.
Dondero${}^{\textrm{\scriptsize 123a,123b}}$, J.
Donini${}^{\textrm{\scriptsize 37}}$, J. Dopke${}^{\textrm{\scriptsize 133}}$,
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Drechsler${}^{\textrm{\scriptsize 57}}$, M. Dris${}^{\textrm{\scriptsize
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Duchovni${}^{\textrm{\scriptsize 175}}$, G. Duckeck${}^{\textrm{\scriptsize
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Duperrin${}^{\textrm{\scriptsize 88}}$, H. Duran
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Duschinger${}^{\textrm{\scriptsize 47}}$, B. Dutta${}^{\textrm{\scriptsize
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Ecker${}^{\textrm{\scriptsize 103}}$, R.C. Edgar${}^{\textrm{\scriptsize
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Eigen${}^{\textrm{\scriptsize 15}}$, K. Einsweiler${}^{\textrm{\scriptsize
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Ellert${}^{\textrm{\scriptsize 168}}$, S. Elles${}^{\textrm{\scriptsize 5}}$,
F. Ellinghaus${}^{\textrm{\scriptsize 178}}$, A.A.
Elliot${}^{\textrm{\scriptsize 172}}$, N. Ellis${}^{\textrm{\scriptsize 32}}$,
J. Elmsheuser${}^{\textrm{\scriptsize 27}}$, M. Elsing${}^{\textrm{\scriptsize
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Enari${}^{\textrm{\scriptsize 157}}$, J.S. Ennis${}^{\textrm{\scriptsize
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Erdmann${}^{\textrm{\scriptsize 46}}$, A. Ereditato${}^{\textrm{\scriptsize
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Errede${}^{\textrm{\scriptsize 169}}$, M. Escalier${}^{\textrm{\scriptsize
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Esposito${}^{\textrm{\scriptsize 50}}$, O. Estrada
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Evans${}^{\textrm{\scriptsize 64}}$, A. Ezhilov${}^{\textrm{\scriptsize
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Fabbri${}^{\textrm{\scriptsize 22a,22b}}$, L. Fabbri${}^{\textrm{\scriptsize
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Facini${}^{\textrm{\scriptsize 81}}$, R.M.
Fakhrutdinov${}^{\textrm{\scriptsize 132}}$, S.
Falciano${}^{\textrm{\scriptsize 134a}}$, R.J. Falla${}^{\textrm{\scriptsize
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Fang${}^{\textrm{\scriptsize 35a}}$, M. Fanti${}^{\textrm{\scriptsize
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Farilla${}^{\textrm{\scriptsize 136a}}$, C. Farina${}^{\textrm{\scriptsize
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Farooque${}^{\textrm{\scriptsize 93}}$, S. Farrell${}^{\textrm{\scriptsize
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Farthouat${}^{\textrm{\scriptsize 32}}$, F. Fassi${}^{\textrm{\scriptsize
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Fassouliotis${}^{\textrm{\scriptsize 9}}$, M. Faucci
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Fayard${}^{\textrm{\scriptsize 119}}$, O.L. Fedin${}^{\textrm{\scriptsize
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Feigl${}^{\textrm{\scriptsize 121}}$, L. Feligioni${}^{\textrm{\scriptsize
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Feng${}^{\textrm{\scriptsize 32}}$, M.J. Fenton${}^{\textrm{\scriptsize 56}}$,
A.B. Fenyuk${}^{\textrm{\scriptsize 132}}$, L.
Feremenga${}^{\textrm{\scriptsize 8}}$, P. Fernandez
Martinez${}^{\textrm{\scriptsize 170}}$, J. Ferrando${}^{\textrm{\scriptsize
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Ferrari${}^{\textrm{\scriptsize 109}}$, R. Ferrari${}^{\textrm{\scriptsize
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Ferrer${}^{\textrm{\scriptsize 170}}$, D. Ferrere${}^{\textrm{\scriptsize
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Fiedler${}^{\textrm{\scriptsize 86}}$, A. Filipčič${}^{\textrm{\scriptsize
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Filthaut${}^{\textrm{\scriptsize 108}}$, M. Fincke-
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Fiorini${}^{\textrm{\scriptsize 170}}$, A. Fischer${}^{\textrm{\scriptsize
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Fischer${}^{\textrm{\scriptsize 178}}$, W.C. Fisher${}^{\textrm{\scriptsize
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Fleck${}^{\textrm{\scriptsize 143}}$, P. Fleischmann${}^{\textrm{\scriptsize
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Flick${}^{\textrm{\scriptsize 178}}$, B.M. Flierl${}^{\textrm{\scriptsize
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Flowerdew${}^{\textrm{\scriptsize 103}}$, G.T.
Forcolin${}^{\textrm{\scriptsize 87}}$, A. Formica${}^{\textrm{\scriptsize
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Forti${}^{\textrm{\scriptsize 87}}$, A.G. Foster${}^{\textrm{\scriptsize
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Fox${}^{\textrm{\scriptsize 75}}$, S. Fracchia${}^{\textrm{\scriptsize 141}}$,
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Franchini${}^{\textrm{\scriptsize 22a,22b}}$, S.
Franchino${}^{\textrm{\scriptsize 60a}}$, D. Francis${}^{\textrm{\scriptsize
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Franklin${}^{\textrm{\scriptsize 59}}$, M. Frate${}^{\textrm{\scriptsize
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Freeborn${}^{\textrm{\scriptsize 81}}$, S.M. Fressard-
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Frost${}^{\textrm{\scriptsize 122}}$, C. Fukunaga${}^{\textrm{\scriptsize
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Fuster${}^{\textrm{\scriptsize 170}}$, O. Gabizon${}^{\textrm{\scriptsize
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Gabrielli${}^{\textrm{\scriptsize 16}}$, G.P. Gach${}^{\textrm{\scriptsize
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Gadomski${}^{\textrm{\scriptsize 80}}$, G. Gagliardi${}^{\textrm{\scriptsize
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Galea${}^{\textrm{\scriptsize 108}}$, B. Galhardo${}^{\textrm{\scriptsize
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Gallop${}^{\textrm{\scriptsize 133}}$, P. Gallus${}^{\textrm{\scriptsize
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Gan${}^{\textrm{\scriptsize 113}}$, S. Ganguly${}^{\textrm{\scriptsize 37}}$,
Y. Gao${}^{\textrm{\scriptsize 77}}$, Y.S. Gao${}^{\textrm{\scriptsize
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García${}^{\textrm{\scriptsize 170}}$, J.E. García
Navarro${}^{\textrm{\scriptsize 170}}$, J.A. García
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Garonne${}^{\textrm{\scriptsize 121}}$, A. Gascon
Bravo${}^{\textrm{\scriptsize 45}}$, K. Gasnikova${}^{\textrm{\scriptsize
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Gaudiello${}^{\textrm{\scriptsize 53a,53b}}$, G.
Gaudio${}^{\textrm{\scriptsize 123a}}$, I.L.
Gavrilenko${}^{\textrm{\scriptsize 98}}$, C. Gay${}^{\textrm{\scriptsize
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Gazis${}^{\textrm{\scriptsize 10}}$, C.N.P. Gee${}^{\textrm{\scriptsize
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Geisen${}^{\textrm{\scriptsize 86}}$, M.P. Geisler${}^{\textrm{\scriptsize
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Gemme${}^{\textrm{\scriptsize 53a}}$, M.H. Genest${}^{\textrm{\scriptsize
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Gentile${}^{\textrm{\scriptsize 134a,134b}}$, C.
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Geßner${}^{\textrm{\scriptsize 46}}$, S. Ghasemi${}^{\textrm{\scriptsize
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Gillberg${}^{\textrm{\scriptsize 31}}$, G. Gilles${}^{\textrm{\scriptsize
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Giugliarelli${}^{\textrm{\scriptsize 167a,167c}}$, D.
Giugni${}^{\textrm{\scriptsize 94a}}$, F. Giuli${}^{\textrm{\scriptsize
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Giulini${}^{\textrm{\scriptsize 60b}}$, B.K. Gjelsten${}^{\textrm{\scriptsize
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Gkialas${}^{\textrm{\scriptsize 9}}$,s, E.L.
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Glaysher${}^{\textrm{\scriptsize 45}}$, A. Glazov${}^{\textrm{\scriptsize
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Godlewski${}^{\textrm{\scriptsize 42}}$, S. Goldfarb${}^{\textrm{\scriptsize
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Gongadze${}^{\textrm{\scriptsize 68}}$, J.L. Gonski${}^{\textrm{\scriptsize
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Gorini${}^{\textrm{\scriptsize 76a,76b}}$, A. Gorišek${}^{\textrm{\scriptsize
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Grefe${}^{\textrm{\scriptsize 23}}$, K. Gregersen${}^{\textrm{\scriptsize
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Grillo${}^{\textrm{\scriptsize 139}}$, K. Grimm${}^{\textrm{\scriptsize 75}}$,
S. Grinstein${}^{\textrm{\scriptsize 13}}$,v, Ph. Gris${}^{\textrm{\scriptsize
37}}$, J.-F. Grivaz${}^{\textrm{\scriptsize 119}}$, S.
Groh${}^{\textrm{\scriptsize 86}}$, E. Gross${}^{\textrm{\scriptsize 175}}$,
J. Grosse-Knetter${}^{\textrm{\scriptsize 57}}$, G.C.
Grossi${}^{\textrm{\scriptsize 82}}$, Z.J. Grout${}^{\textrm{\scriptsize
81}}$, A. Grummer${}^{\textrm{\scriptsize 107}}$, L.
Guan${}^{\textrm{\scriptsize 92}}$, W. Guan${}^{\textrm{\scriptsize 176}}$, J.
Guenther${}^{\textrm{\scriptsize 32}}$, F. Guescini${}^{\textrm{\scriptsize
163a}}$, D. Guest${}^{\textrm{\scriptsize 166}}$, O.
Gueta${}^{\textrm{\scriptsize 155}}$, B. Gui${}^{\textrm{\scriptsize 113}}$,
E. Guido${}^{\textrm{\scriptsize 53a,53b}}$, T.
Guillemin${}^{\textrm{\scriptsize 5}}$, S. Guindon${}^{\textrm{\scriptsize
32}}$, U. Gul${}^{\textrm{\scriptsize 56}}$, C.
Gumpert${}^{\textrm{\scriptsize 32}}$, J. Guo${}^{\textrm{\scriptsize 36c}}$,
W. Guo${}^{\textrm{\scriptsize 92}}$, Y. Guo${}^{\textrm{\scriptsize 36a}}$,w,
R. Gupta${}^{\textrm{\scriptsize 43}}$, S. Gurbuz${}^{\textrm{\scriptsize
20a}}$, G. Gustavino${}^{\textrm{\scriptsize 115}}$, B.J.
Gutelman${}^{\textrm{\scriptsize 154}}$, P. Gutierrez${}^{\textrm{\scriptsize
115}}$, N.G. Gutierrez Ortiz${}^{\textrm{\scriptsize 81}}$, C.
Gutschow${}^{\textrm{\scriptsize 81}}$, C. Guyot${}^{\textrm{\scriptsize
138}}$, M.P. Guzik${}^{\textrm{\scriptsize 41a}}$, C.
Gwenlan${}^{\textrm{\scriptsize 122}}$, C.B. Gwilliam${}^{\textrm{\scriptsize
77}}$, A. Haas${}^{\textrm{\scriptsize 112}}$, C.
Haber${}^{\textrm{\scriptsize 16}}$, H.K. Hadavand${}^{\textrm{\scriptsize
8}}$, N. Haddad${}^{\textrm{\scriptsize 137e}}$, A.
Hadef${}^{\textrm{\scriptsize 88}}$, S. Hageböck${}^{\textrm{\scriptsize
23}}$, M. Hagihara${}^{\textrm{\scriptsize 164}}$, H.
Hakobyan${}^{\textrm{\scriptsize 180}}$,∗, M. Haleem${}^{\textrm{\scriptsize
45}}$, J. Haley${}^{\textrm{\scriptsize 116}}$, G.
Halladjian${}^{\textrm{\scriptsize 93}}$, G.D.
Hallewell${}^{\textrm{\scriptsize 88}}$, K. Hamacher${}^{\textrm{\scriptsize
178}}$, P. Hamal${}^{\textrm{\scriptsize 117}}$, K.
Hamano${}^{\textrm{\scriptsize 172}}$, A. Hamilton${}^{\textrm{\scriptsize
147a}}$, G.N. Hamity${}^{\textrm{\scriptsize 141}}$, P.G.
Hamnett${}^{\textrm{\scriptsize 45}}$, L. Han${}^{\textrm{\scriptsize 36a}}$,
S. Han${}^{\textrm{\scriptsize 35a,35d}}$, K. Hanagaki${}^{\textrm{\scriptsize
69}}$,x, K. Hanawa${}^{\textrm{\scriptsize 157}}$, M.