SMP-18-005

SMP-18-005

# Determination of the strong coupling constant $\alpS(m_{\PZ})$ from
measurements of inclusive and $\PZ$ boson production cross sections in proton-
proton collisions at $\sqrt{s}=7$ and $8\TeV$

###### Abstract

Twelve measurements of inclusive cross sections of and boson production,
performed in proton-proton collisions at centre-of-mass energies of 7 and 8,
are compared with perturbative quantum chromodynamics calculations at next-to-
next-to-leading order (NNLO) accuracy obtained with the CT14, HERAPDF2.0,
MMHT14, and NNPDF3.0 parton distribution functions (PDFs). Data and theory
agree well for all PDF sets, taking into account the experimental and
theoretical uncertainties. A novel procedure is employed to extract the strong
coupling constant at the pole mass from a detailed comparison of all the
experimental fiducial cross sections to the corresponding NNLO theoretical
predictions, yielding $\alpS(m_{\PZ})=0.1163^{+0.0024}_{-0.0031}$ (CT14),
$0.1072^{+0.0043}_{-0.0040}$ (HERAPDF2.0), $0.1186\pm 0.0025$ (MMHT14), and
$0.1147\pm 0.0023$ (NNPDF3.0). Using the results obtained with the CT14 and
MMHT14 PDFs, which yield the most robust and stable $\alpha_{S}(m_{\PZ})$
extractions, a value $\alpha_{S}(m_{\PZ})=0.1175^{+0.0025}_{-0.0028}$ is
determined.

##  0.1 Introduction

In the chiral limit of zero quark masses, the $\alpS$ coupling is the only
free parameter of quantum chromodynamics (QCD), the theory of the strong
interaction between quarks and gluons. Because of its logarithmic decrease
with energy (asymptotic freedom), $\alpS$ is commonly given at a reference
scale, often taken at the pole mass. Its current value,
$\alpS(m_{\PZ})=0.1181\pm 0.0011$, is known with a $\pm$0.9% uncertainty,
making it the least precisely known of all interaction couplings in nature
[1]. The precision of the strong coupling value plays an important role in all
theoretical calculations of perturbative QCD (pQCD) processes involving
partons, and currently leads to 3–7% uncertainties in key Higgs boson
processes, such as the cross sections for gluon-gluon fusion ($\Pg\Pg\to\PH$)
and associated production with a top quark pair ($\ttbar\PH$), as well as the
$\PH\to\bbbar,\ccbar,\Pg\Pg$ partial decay widths [2]. As one of the
fundamental parameters of the standard model (SM), the uncertainties of the
QCD coupling value also dominate the propagated parametric uncertainties in
the theoretical calculations of the top quark mass [3], as well as of
electroweak (EW) precision observables [4]. Last but not least, $\alpS$ also
impacts physics approaching the Planck scale, either through the EW vacuum
stability [5], or in searches of new coloured sectors that may modify its
running towards the grand unification scale [6, 7].

The current $\alpS(m_{\PZ})$ world-average value is derived from a combination
of six subclasses of (mostly) independent observables measured at various
energy scales, which are compared with pQCD calculations at next-to-next-to-
leading order (NNLO), or beyond, accuracy [1]. The only hadron collider
observable so far that provides a constraint on $\alpS$ at this level of
theoretical accuracy is the total $\ttbar$ cross section [8, 9, 10]. One of
the paths towards improvement of our knowledge of the QCD coupling is the
inclusion into the world average of new independent observables sensitive to
$\alpS$ that are experimentally and theoretically known with high precision
[11, 12]. Charged- and neutral-current Drell–Yan processes in their leptonic
decay modes, $\Pp\Pp\to\PWpm\to\ell^{\pm}\Pgn_{\ell}$ and
$\Pp\Pp\to\PZ\to\ell^{+}\ell^{-}$ with $\ell^{\pm}=\Pepm,\PGmpm$, are the most
accurately known processes currently accessible in proton-proton ($\Pp\Pp$)
collisions at the CERN LHC. Experimentally, the uncertainties in the inclusive
= , production cross sections measured by the CMS experiment are between 3 and
5%; these are dominated by the integrated luminosity uncertainty, whereas the
statistical uncertainties are at the subpercent level (Table 0.2) [13, 14]. On
the theoretical side, the corresponding cross sections are known at NNLO pQCD
accuracy [15], with about 1–4% parton distribution function (PDF), and
0.3–1.3% scale uncertainties [16]. Electroweak corrections, which lead to a
few percent reduction of the pure-pQCD and boson production cross sections,
are known at next-to-leading order (NLO) accuracy [17].

Theoretical calculations [18] indicate that about one fourth of the total
production cross sections at LHC energies come from partonic processes beyond
the Born level, and thereby depend on the QCD coupling value. By calculating
the production cross sections at NNLO for varying $\alpS(m_{\PZ})$ values, and
by comparing the theoretical predictions to experimental data, one can
therefore derive a value of the strong coupling constant at the pole,
independent of other current extractions [19]. By combining such a result with
those derived from other methods, the overall uncertainty in the
$\alpS(m_{\PZ})$ world average can eventually be reduced. The use of inclusive
, boson cross sections to extract the QCD coupling is presented here for the
first time. This method is similar to the one used to extract $\alpS$ from the
inclusive $\ttbar$ cross sections at hadron colliders [8, 9, 10], except that
the underlying physical process is quite different. Whereas $\sigma(\ttbar)$
depends on $\alpS$ already at leading order (LO), albeit with $\approx$5%
theoretical and experimental uncertainties, $\sigma(\PV)$ is more precisely
known experimentally and theoretically, although at the Born level its
underlying partonic processes are purely EW with a dependence on $\alpS$ that
comes only through higher-order pQCD corrections (at LO, the $\sigma(\PV)$
cross sections also depend on $\alpS$ via the PDFs).

The paper is organised as follows. The experimental setup used in the twelve
CMS original measurements is summarised in Section 0.2. In Section 0.3, the
theoretical tools used to perform the calculations are outlined. In Section
0.4, the experimental and theoretical cross sections with associated
uncertainties, are compared. In Section 0.5, the method to extract
$\alpS(m_{\PZ})$ from the data-to-theory comparison for each measurement is
described, as well as the approach to combine all $\alpS(m_{\PZ})$ estimates
into a single value per PDF set that properly takes into account the
experimental and theoretical uncertainties and their correlations. The final
$\alpS(m_{\PZ})$ values derived are presented and discussed in Section 0.6.
The work is summarised in Section 0.7.

##  0.2 The CMS detector

The results presented here are based on a phenomenological study of and boson
fiducial cross sections measured by the CMS experiment in $\Pp\Pp$ collisions
at centre-of-mass (c.m.) energies of $\sqrt{s}=7$ and 8with integrated
luminosities of 38.0 and 18.2, respectively [13, 14]. The experimental and
theoretical EW boson production cross sections quoted in the whole paper are
to be understood as multiplied by their associated leptonic branching
fractions, but for simplicity are referred to as “cross sections” hereafter.
The final states of interest are those with decay charged leptons (electrons
or muons) passing the acceptance criteria listed in Table 0.2.

The central feature of the CMS apparatus is a superconducting solenoid, of 6m
internal diameter, providing a magnetic field of 3.8T. Within the field volume
are a silicon pixel and strip tracker, a crystal electromagnetic calorimeter
(ECAL), and a brass and scintillator hadron calorimeter. Electrons with
$\pt>25\GeV$ are identified as clusters of energy deposits in the ECAL matched
to tracks measured with the silicon tracker. The ECAL fiducial region is
defined by $\abs{\eta}<1.44$ (barrel) or $1.57<\abs{\eta}<2.5$ (endcap), where
$\eta$ is the pseudorapidity of the energy cluster. Muons are measured in gas-
ionisation detectors embedded in the steel flux-return yoke of the magnet.
Muons with $\pt>20$ or 25and $\abs{\eta}<2.1$ are selected in the analyses.
Details of the CMS detector and its performance can be found elsewhere [20].

Summary of the twelve and boson production cross sections, along with their
individual (and total, added in quadrature) uncertainties, measured with the
indicated fiducial selection criteria on the transverse momentum
($\pt^{\ell}$) and pseudorapidity ($\eta^{\ell}$), in the electron
($\PWpm_{\Pe}$, $\PZ_{\Pe}$) and muon ($\PWpm_{\PGm}$, $\PZ_{\PGm}$) final
states, in $\Pp\Pp$ collisions at $\sqrt{s}=7$ and 8 [13, 14].  Measurement
Fiducial cross section $\Pp\Pp$ at $\sqrt{s}=7\TeV$ [13] $\PW^{+}_{\Pe}$,
$\pt^{\Pe}>25\GeV$, $\abs{\eta^{\Pe}}<2.5$ $3404\pm 12\stat\pm 67{\syst}\pm
136\lum\unit{pb}=3404\pm 152\unit{pb}$ $\PW^{-}_{\Pe}$, $\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<2.5$ $2284\pm 10\stat\pm 43{\syst}\pm
91\lum\unit{pb}=2284\pm 101\unit{pb}$ $\PZ_{\Pe}$, $\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<2.5$, $60<m_{\PZ}<120\GeV$ $452\pm 5\stat\pm 10{\syst}\pm
18\lum\unit{pb}=452\pm 21\unit{pb}$ $\PW^{+}_{\PGm}$, $\pt^{\PGm}>25\GeV$,
$\abs{\eta^{\PGm}}<2.1$ $2815\pm 9\stat\pm 42{\syst}\pm
113\lum\unit{pb}=2815\pm 121\unit{pb}$ $\PW^{-}_{\PGm}$, $\pt^{\PGm}>25\GeV$,
$\abs{\eta^{\PGm}}<2.1$ $1921\pm 8\stat\pm 27{\syst}\pm
77\lum\unit{pb}=1921\pm 82\unit{pb}$ $\PZ_{\PGm}$, $\pt^{\PGm}>20\GeV$,
$\abs{\eta^{\PGm}}<2.1$, $60<m_{\PZ}<120\GeV$ $396\pm 3\stat\pm 7{\syst}\pm
16\lum\unit{pb}=396\pm 18\unit{pb}$ $\Pp\Pp$ at $\sqrt{s}=8\TeV$ [14]
$\PW^{+}_{\Pe}$, $\pt^{\Pe}>25\GeV$, $\abs{\eta^{\Pe}}<1.44$,
$1.57<\abs{\eta^{\Pe}}<2.5$ $3540\pm 20\stat\pm 110{\syst}\pm
90\lum\unit{pb}=3540\pm 140\unit{pb}$ $\PW^{-}_{\Pe}$, $\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<1.44$, $1.57<\abs{\eta^{\Pe}}<2.5$ $2390\pm 10\stat\pm
60{\syst}\pm 60\lum\unit{pb}=2390\pm 90\unit{pb}$ $\PZ_{\Pe}$,
$\pt^{\Pe}>25\GeV$, $\abs{\eta^{\Pe}}<1.44$, $1.57<\abs{\eta^{\Pe}}<2.5$,
$60<m_{\PZ}<120\GeV$ $450\pm 10\stat\pm 10{\syst}\pm 10\lum\unit{pb}=450\pm
20\unit{pb}$ $\PW^{+}_{\PGm}$, $\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$
$3100\pm 10\stat\pm 40{\syst}\pm 80\lum\unit{pb}=3100\pm 90\unit{pb}$
$\PW^{-}_{\PGm}$, $\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$ $2240\pm
10\stat\pm 20{\syst}\pm 60\lum\unit{pb}=2240\pm 60\unit{pb}$ $\PZ_{\PGm}$,
$\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$, $60<m_{\PZ}<120\GeV$ $400\pm
10\stat\pm 10{\syst}\pm 10\lum\unit{pb}=400\pm 20\unit{pb}$

##  0.3 Theoretical calculations

According to the pQCD factorisation theorem [21], the cross section for the
production of a heavy elementary particle in $\Pp\Pp$ collisions can be
calculated through the convolution of matrix elements for the relevant parton-
parton subprocesses, computed at a given order in the $\alpS$ expansion
evaluated at a renormalisation scale $\PGm_{\textsc{r}}$, and a universal
nonperturbative part describing the parton density at the factorisation energy
scale $\PGm_{\textsc{f}}$ and parton fractional momentum $x_{i}$ in the
proton. The production cross section of an EW boson can be written

$\sigma(\Pp\Pp\to\PV+\text{X})=\int\int\rd x_{1}\rd
x_{2}\,f_{1}(x_{1},\PGm_{\textsc{f}})f_{2}(x_{2},\PGm_{\textsc{f}})\,\left[\hat{\sigma}_{\textsc{lo}}+\hat{\sigma}_{\textsc{nlo}}(\alpS(\PGm_{\textsc{r}}))+\hat{\sigma}_{\textsc{nnlo}}(\alpS(\PGm_{\textsc{r}}))+\cdots\right],$

where the functions $f_{i}$ represent the PDFs of each proton, determined from
experimental data, and the expression in brackets is the perturbative
expansion of the underlying partonic cross sections $\hat{\sigma}$. At hadron
colliders, the LO production of and bosons involves the annihilation of a
quark-antiquark pair of the same ($\qqbar\to\PZ+\text{X}$) or different
($\qqbar^{\prime}\to\PW+\text{X}$) flavour. At NLO, the Born terms are
supplemented with initial-state real gluon emission, virtual gluon exchange,
and contributions from gluon-quark and gluon-antiquark scattering processes.
At NNLO, additional gluon radiation and virtual exchanges further contribute
to the total cross section [15, 18]. Although at LO the partonic cross
sections are independent of $\alpS$, the vertices of the higher-order terms
introduce a dependence on $\alpS$ that enables the determination of the QCD
coupling by comparing high-precision theoretical calculations to the
experimental data. The size of such higher-order corrections [19], encoded in
the so-called $K$-factor, amounts to
$K=\sigma_{\textsc{nnlo}}/\sigma_{\textsc{lo}}\approx 1.25$–1.37 as derived
with v.8.0 [16] for the and cross sections measured at 7 and 8in the CMS
fiducial acceptance, and indicates that EW boson production is indeed
sensitive to $\alpS(m_{\PZ})$ at NNLO accuracy.

In this work, the NNLO cross sections are computed with the code interfaced
with lhapdf v.6.1.6 [22] to access four different PDFs: CT14 [23], HERAPDF2.0
[24], MMHT14 [25], and NNPDF3.0 [26]. All these PDFs use as the default
central set the one with the QCD coupling constant fixed to
$\alpS(m_{\PZ})=0.118$ in their global fits of the data, but also provide a
variety of alternative sets with their corresponding central values derived
for different fixed values of $\alpS(m_{\PZ})$. We note, however, that when
the QCD coupling constant is left free in their NNLO PDF fits, the following
values are preferred by the different PDF sets: $\alpS(m_{\PZ})$ = 0.115
(CT14) [23], 0.108 (HERAPDF2.0) [24], and 0.1172 (MMHT2014) [25]. The
HERAPDF2.0 set is obtained from fits to HERA deep inelastic scattering (DIS)
data only. The CT14, MMHT14, and NNPDF3.0 global fits have been obtained
including DIS, fixed target, and LHC measurements. These latter PDF sets
incorporate one or two or differential CMS distributions at 7 [13] in their
global fits, but did not use any of the twelve absolute inclusive EW boson
cross sections listed in Table 0.2, and therefore the corresponding values of
$\alpS$ extracted here are truly independent of the data contributing to the
extraction of PDF sets themselves. The so-called $G_{\PGm}$ electroweak
scheme, where the input parameters are $m_{\PW}$, $m_{\PZ}$, and
$G_{\text{F}}$, is used in all the predictions. The leptonic and branching
fractions are obtained in from the theoretical leptonic width (computed at LO
in electroweak accuracy) normalized to the total and widths experimentally
measured [1]. All numerical results have been obtained using the latest SM
parameters for particle masses, widths, and couplings [1]. For simplicity, the
default value of the charm quark mass in and NNPDF3.0,
$m_{\text{\cPqc}}=1.275\GeV$, is used for all the calculations—rather than the
preferred values of the other PDF sets: $m_{\text{\cPqc}}=1.3\GeV$ (CT14),
$1.43\GeV$ (HERAPDF2.0), $1.4\GeV$ (MMHT14)—because the computed cross
sections vary only by a few per mille, within the numerical uncertainty.

The default renormalisation and factorisation scales are set to the
corresponding EW boson mass for each process,
$\PGm=\PGm_{\textsc{f}}=\PGm_{\textsc{r}}=m_{\PW},m_{\PZ}$. For all PDF sets,
we computed the NNLO cross sections at various $\alpS(m_{\PZ})$ values over
the range [0.115–0.121]. For NNPDF3.0, the available values are
$\alpS(m_{\PZ})=0.115$, 0.117, 0.118, 0.119, and 0.121; and for the other PDF
sets they are $\alpS(m_{\PZ})=0.115$, 0.116, 0.117, 0.118, 0.119, 0.120, and
0.121. Technically, the central sets selected via lhapdf for this study are:
CT14nnlo_as_0$iii$ (for $iii=115$–121), HERAPDF20_NNLO_ALPHAS_$iii$ (for
$iii=115$–121), MMHT2014nnlo_asmzlargerange (with
$\alpS(m_{\PZ})=0.115,...,0.121$ grids), and NNPDF30_nnlo_as_0$iii$ (with
$iii=115$–121). For the PDF uncertainties, only NNPDF3.0 provides independent
replicas for each $\alpS(m_{\PZ})$ set, which we use in our calculations and
uncertainties propagation, whereas the rest of PDFs use the same eigenvalues
corresponding to the set determined with $\alpS(m_{\PZ})=0.118$. Calculations
are carried out implementing the fiducial selection criteria for the final-
state charged leptons corresponding to each of the six different measurements
($\PW^{+}_{\Pe}$, $\PW^{-}_{\Pe}$, $\PZ_{\Pe}$, $\PW^{+}_{\PGm}$,
$\PW^{-}_{\PGm}$, $\PZ_{\PGm}$) at $\sqrt{s}=7$ and 8listed in Table 0.2,
thereby providing altogether twelve theoretical cross sections per PDF that
can be used to individually extract $\alpS(m_{\PZ})$.

The PDF uncertainties of the theoretical fiducial cross sections are obtained
by taking into account the different eigenvector sets, or replicas, that come
with each of the PDFs. We use the “official” prescriptions of each PDF set to
compute their associated uncertainties. More specifically, the PDF
uncertainties are calculated from the cross sections obtained with the central
PDF member ($\sigma_{0}$) and with the rest of eigenvalues or replicas
($\sigma_{i}$) as follows:

  * •

For CT14, the uncertainty eigenvectors are considered in pairs from the
$i=1$–56 PDF members. The largest positive and negative differences from each
pair are summed quadratically to obtain the corresponding positive and
negative PDF uncertainties:

$\Delta\sigma_{\pm}=\sqrt{\sum_{j=1}^{28}\max\left(\pm(\sigma_{2j-1}-\sigma_{0}),\,\pm(\sigma_{2j}-\sigma_{0}),\,0\right)^{2}}.$

The CT14 PDF set results in asymmetric uncertainties interpreted as a 90%
confidence level interval. To convert those to one standard deviation, as for
the rest of PDF sets, they are divided by a factor of
$\sqrt{2}\erf^{-1}(0.9)\approx 1.645$.

  * •

For HERAPDF2.0, a first asymmetric uncertainty is derived from the so-called
’EIG’ (experimental uncertainties) PDF members, and a second one from the
$i=1$–10 ’VAR’ (variation) members, as for CT14. A third asymmetric
uncertainty is taken from the $i=11$–13 VAR members, as the maximum positive
and negative differences $\Delta\sigma_{i}$ with respect to $\sigma_{0}$.
Finally, all positive and negative uncertainties are separately added
quadratically to get the final uncertainties.

  * •

For MMHT14, uncertainties are obtained from its corresponding 50 eigenvalues
as done for CT14.

  * •

For NNPDF3.0, the average cross section $\hat{\sigma}$ from replica members
$i=1$–100 is calculated first, and the associated standard deviation,
$\sqrt{\sum_{i=1}^{100}(\sigma_{i}-\hat{\sigma})^{2}/99}$, is taken as the
symmetric PDF uncertainty.

To determine the scale uncertainty associated with missing corrections beyond
the NNLO accuracy, the cross sections are recalculated for each PDF and
measurement using factorisation and renormalisation scales varied within
factors of two, such that the ratio of the two scales is not less than 0.5 or
more than 2. This gives seven combinations:
$(\PGm_{\textsc{f}},\PGm_{\textsc{r}})$,
$(\PGm_{\textsc{f}}/2,\PGm_{\textsc{r}}/2)$,
$(\PGm_{\textsc{f}}/2,\PGm_{\textsc{r}})$,
$(\PGm_{\textsc{f}},\PGm_{\textsc{r}}/2)$,
$(2\PGm_{\textsc{f}},\PGm_{\textsc{r}})$,
$(\PGm_{\textsc{f}},2\PGm_{\textsc{r}})$,
$(2\PGm_{\textsc{f}},2\PGm_{\textsc{r}})$. The largest and smallest cross
sections of the seven combinations are determined, and the scale uncertainty
is taken as half the difference of the extremal values. The scale variation
uncertainties amount to 0.5–1% of the theoretical cross sections.

Since does not include EW corrections, arising from additional , , and/or
photons exchanged and/or radiated in the partonic process, those are computed
separately. For this purpose, the mcsanc v.1.01 code [17] is used. For
$\Pe^{\pm}$ final states, we follow the “calorimetric” prescription, proposed
in theoretical and boson production cross section benchmarking studies at the
LHC [27], and recombine any radiated photon with the $\Pe^{\pm}$ if their
relative distance in the pseudorapidity-azimuth plane is $\Delta
R=\sqrt{(\eta^{\Pe}-\eta^{\gamma})^{2}+(\phi^{\Pe}-\phi^{\gamma})^{2}}<0.1$.
For $\PGm^{\pm}$ final states, we use directly the “bare” mcsanc cross
section. We run mcsanc at NLO with EW corrections on and off, and compute the
corresponding multiplicative factor
$K_{\textsc{EW}}=\sigma(\textsc{nlo,ew}\,\text{on})/\sigma(\textsc{nlo,ew}\,\text{off})$,
which is used to correct the pQCD results. The EW corrections, in the range of
1–4%, are all negative, they reduce the overall cross section with respect to
the pure pQCD result. Since the EW corrections are small, their associated
uncertainties are neglected hereafter because they would propagate into the
final computed and cross section at a few per mille level, below the numerical
uncertainty of the calculation. Subtracting the EW corrections, rather than
applying them multiplicatively via a $K_{\textsc{EW}}$ factor as done here,
gives consistent results within the (neglected) per mille uncertainties. For
simplicity, in the mcsanc calculations, the electron pseudorapidity range
$1.44<\abs{\eta}<1.57$ (excluded in the actual measurements) is also included,
since we are interested in the relative correction, this small range (present
in both the numerator and denominator of the correcting factor) does not
affect the $K_{\textsc{EW}}$ ratio. The roles of photon-induced contributions
and of mixed QCD$\oplus$QED NLO corrections to Drell–Yan processes in $\Pp\Pp$
collisions have been computed in Refs. [28] and [29], respectively. The impact
of such corrections to the inclusive and cross sections is at a few per mille
level, and also neglected here.

All the relevant sources of uncertainties in the and boson cross sections are
summarised in Table 0.3. The largest experimental and theoretical
uncertainties come from the integrated luminosity and PDF knowledge,
respectively. Each calculated cross section has a numerical accuracy, as
reported by , in the range of 0.2–0.6%. Such an uncertainty is commensurate
with the typical differences encountered when computing NNLO and boson cross
sections with different pQCD codes that implement higher-order virtual-real
corrections with various methods [27].

Summary of the typical experimental and theoretical uncertainties in the and
boson production cross sections, and their degree of correlation (details are
provided in Section 0.5.3).  Uncertainties Degree of correlation Experimental:
Integrated luminosity 2–4% fully correlated at a given c.m. energy Systematic
1–3% partially correlated Statistical 0.5–2% uncorrelated Theoretical: PDF
1–4% partially correlated within each PDF set Theoretical scale 0.3–1.3%
partially correlated statistical numerical 0.2–0.6% uncorrelated

##  0.4 EW boson fiducial cross sections: data versus theory

All the experimental and theoretical fiducial cross sections for , , and
production in $\Pp\Pp$ collisions are given in Tables 0.4 and 0.4 for 7 and 8,
respectively. For each measurement, the fiducial cross section definition and
the experimental result are listed along with their uncertainties from the
different sources listed in Table 0.3. The theoretical predictions computed
with all four PDF sets for their preferred default $\alpS(m_{\PZ})=0.118$
value are listed including their associated PDF, $\alpS$ (obtained, as
described in Section 0.5.2, from the cross section change when
$\alpS(m_{\PZ})$ is modified by $\pm 0.001$), and scale uncertainties. For
each system, the NLO mcsanc EW correction factors (absolute and relative) are
also listed. For the results at $\sqrt{s}=8\TeV$, the theoretical result
obtained with the alternative NNLO pQCD calculator [30], using the MSTW2008
PDF set [31] as provided in the original Ref. [14], is also listed to show the
very similar theoretical predictions expected with an alternative NNLO code
and a pre-LHC PDF set.

Experimental and theoretical fiducial cross sections for and production in
$\Pp\Pp$ collisions at $\sqrt{s}=7\TeV$, with the uncertainty sources listed
in Table 0.3. The NNLO pQCD results are obtained with for
$\alpS(m_{\PZ})=0.118$ using the CT14, HERAPDF2.0, MMHT14, and NNPDF3.0 PDF
sets. (The quoted $\alpS$ uncertainties are derived from the cross section
changes when $\alpS(m_{\cPZ})$ is modified by $\pm 0.001$). The NLO EW
corrections are computed with mcsanc .  System Fiducial cross section
$\Pp\Pp\to\PWp(\Pe^{+}\Pgn)+\text{X}$, $\sqrt{s}$ = 7($\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<2.5$) Measurement [13] $3404\pm 12\stat\pm 67{\syst}\pm
136\lum\unit{pb}$ (NNLO, CT14) $3361\,^{+93}_{-94}{\,\text{(PDF)}}\pm
30{\,(\alpS)}\pm 49\,\text{(scale)}\pm 18\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$3574\,^{+63}_{-94}{\,\text{(PDF)}}\pm 19{\,(\alpS)}\pm 33\,\text{(scale)}\pm
23\stat\unit{pb}$ (NNLO, MMHT14) $3407\,^{+92}_{-74}{\,\text{(PDF)}}\pm
37{\,(\alpS)}\pm 31\,\text{(scale)}\pm 18\stat\unit{pb}$ (NNLO, NNPDF3.0)
$3345\pm 70{\,\text{(PDF)}}\pm 32{\,(\alpS)}\pm 29\,\text{(scale)}\pm
18\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-36\unit{pb}\;(-1.1\%)$ $\Pp\Pp\to\PWm(\Pe^{-}\Pagn)+\text{X}$, $\sqrt{s}$ =
7($\pt^{\Pe}>25\GeV$, $\abs{\eta^{\Pe}}<2.5$) Measurement [13] $2284\pm
10\stat\pm 43{\syst}\pm 91\lum\unit{pb}$ (NNLO, CT14)
$2235\,^{+66}_{-57}{\,\text{(PDF)}}\pm 19{\,(\alpS)}\pm 19\,\text{(scale)}\pm
7\stat\unit{pb}$ (NNLO, HERAPDF2.0) $2319\,^{+21}_{-51}{\,\text{(PDF)}}\pm
8{\,(\alpS)}\pm 19\,\text{(scale)}\pm 7\stat\unit{pb}$ (NNLO, MMHT14)
$2248\,^{+28}_{-62}{\,\text{(PDF)}}\pm 23{\,(\alpS)}\pm 17\,\text{(scale)}\pm
7\stat\unit{pb}$ (NNLO, NNPDF3.0) $2192\pm 47{\,\text{(PDF)}}\pm
16{\,(\alpS)}\pm 16\,\text{(scale)}\pm 7\stat\unit{pb}$ mcsanc (NLO EW
correction, NNPDF3.0) $-24\unit{pb}\;(-1.1\%)$
$\Pp\Pp\to\PZ(\Pe^{+}\Pe^{-})+\text{X}$, $\sqrt{s}$ = 7($\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<2.5$, $60<m_{\PZ}<120\GeV$) Measurement [13] $452\pm
5\stat\pm 10{\syst}\pm 18\lum\unit{pb}$ (NNLO, CT14)
$430\,^{+11}_{-13}{\,\text{(PDF)}}\pm 4{\,(\alpS)}\pm 2\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, HERAPDF2.0) $444\,^{+4}_{-12}{\,\text{(PDF)}}\pm
2{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$ (NNLO, MMHT14)
$433\,^{+6}_{-10}{\,\text{(PDF)}}\pm 5{\,(\alpS)}\pm 3\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, NNPDF3.0) $421\pm 9{\,\text{(PDF)}}\pm 3{\,(\alpS)}\pm
2\,\text{(scale)}\pm 1\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-12\unit{pb}\;(-2.6\%)$ $\Pp\Pp\to\PWp(\PGm^{+}\nu)+\text{X}$, $\sqrt{s}$ =
7($\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$) Measurement [13] $2815\pm
9\stat\pm 42{\syst}\pm 113\lum\unit{pb}$ (NNLO, CT14)
$2827\,^{+65}_{-110}{\,\text{(PDF)}}\pm 29{\,(\alpS)}\pm 21\,\text{(scale)}\pm
13\stat\unit{pb}$ (NNLO, HERAPDF2.0) $2976\,^{+42}_{-118}{\,\text{(PDF)}}\pm
16{\,(\alpS)}\pm 37\,\text{(scale)}\pm 15\stat\unit{pb}$ (NNLO, MMHT14)
$2833\,^{+63}_{-90}{\,\text{(PDF)}}\pm 29{\,(\alpS)}\pm 17\,\text{(scale)}\pm
16\stat\unit{pb}$ (NNLO, NNPDF3.0) $2806\pm 62{\,\text{(PDF)}}\pm
26{\,(\alpS)}\pm 29\,\text{(scale)}\pm 15\stat\unit{pb}$ mcsanc (NLO EW
correction, NNPDF3.0) $-64\unit{pb}\;(-2.2\%)$
$\Pp\Pp\to\PWm(\PGm^{-}\Pagn)+\text{X}$, $\sqrt{s}$ = 7($\pt^{\PGm}>25\GeV$,
$\abs{\eta^{\PGm}}<2.1$) Measurement [13] $1921\pm 8\stat\pm 27{\syst}\pm
77\lum\unit{pb}$ (NNLO, CT14) $1915\,^{+43}_{-68}{\,\text{(PDF)}}\pm
19{\,(\alpS)}\pm 16\,\text{(scale)}\pm 6\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$1976\,^{+33}_{-29}{\,\text{(PDF)}}\pm 8{\,(\alpS)}\pm 19\,\text{(scale)}\pm
6\stat\unit{pb}$ (NNLO, MMHT14) $1937\,^{+33}_{-41}{\,\text{(PDF)}}\pm
20{\,(\alpS)}\pm 17\,\text{(scale)}\pm 6\stat\unit{pb}$ (NNLO, NNPDF3.0)
$1877\pm 40{\,\text{(PDF)}}\pm 13{\,(\alpS)}\pm 17\,\text{(scale)}\pm
6\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0) $-42\unit{pb}\;(-2.2\%)$
$\Pp\Pp\to\PZ(\PGm^{+}\PGm^{-})+\text{X}$, $\sqrt{s}$ = 7($\pt^{\PGm}>20\GeV$,
$\abs{\eta^{\PGm}}<2.1$, $60<m_{\PZ}<120\GeV$) Measurement [13] $396\pm
3\stat\pm 7{\syst}\pm 16\lum\unit{pb}$ (NNLO, CT14)
$380\,^{+7}_{-16}{\,\text{(PDF)}}\pm 3{\,(\alpS)}\pm 2\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, HERAPDF2.0) $392\,^{+6}_{-6}{\,\text{(PDF)}}\pm
2{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$ (NNLO, MMHT14)
$382\,^{+11}_{-4}{\,\text{(PDF)}}\pm 4{\,(\alpS)}\pm 2\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, NNPDF3.0) $373\pm 8{\,\text{(PDF)}}\pm 3{\,(\alpS)}\pm
2\,\text{(scale)}\pm 1\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-14\unit{pb}\;(-3.9\%)$

Experimental and theoretical fiducial cross sections for and production in
$\Pp\Pp$ collisions at $\sqrt{s}=8\TeV$, with the uncertainty sources listed
in Table 0.3. The NNLO pQCD results are obtained with for
$\alpS(m_{\PZ})=0.118$ using the CT14, HERAPDF2.0, MMHT14, and NNPDF3.0 PDF
sets, as well as with using the MSTW2008 PDF. (The quoted $\alpS$
uncertainties are derived from the cross section changes when
$\alpS(m_{\cPZ})$ is modified by $\pm 0.001$). The NLO EW corrections are
computed with mcsanc .  System Fiducial cross section
$\Pp\Pp\to\PWp(\Pe^{+}\nu)+\text{X}$, $\sqrt{s}$ = 8($\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<1.44$, $1.57<\abs{\eta^{\Pe}}<2.5$) Measurement [14]
$3540\pm 20\stat\pm 110{\syst}\pm 90\lum\unit{pb}$ (NNLO, MSTW2008) [14]
$3450\pm 120\unit{pb}$ (NNLO, CT14) $3522\,^{+113}_{-123}{\,\text{(PDF)}}\pm
23{\,(\alpS)}\pm 35\,\text{(scale)}\pm 21\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$3721\,^{+127}_{-97}{\,\text{(PDF)}}\pm 13{\,(\alpS)}\pm 48\,\text{(scale)}\pm
22\stat\unit{pb}$ (NNLO, MMHT14) $3581\,^{+61}_{-137}{\,\text{(PDF)}}\pm
36{\,(\alpS)}\pm 38\,\text{(scale)}\pm 20\stat\unit{pb}$ (NNLO, NNPDF3.0)
$3515\pm 75{\,\text{(PDF)}}\pm 34{\,(\alpS)}\pm 42\,\text{(scale)}\pm
20\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-45\unit{pb}\;(-1.2\%)$ $\Pp\Pp\to\PWm(\Pe^{-}\Pagn)+\text{X}$, $\sqrt{s}$ =
8($\pt^{\Pe}>25\GeV$, $\abs{\eta^{\Pe}}<1.44$, $1.57<\abs{\eta^{\Pe}}<2.5$)
Measurement [14] $2390\pm 10\stat\pm 60{\syst}\pm 60\lum\unit{pb}$ (NNLO,
MSTW2008) [14] $2380\pm 90\unit{pb}$ (NNLO, CT14)
$2426\,^{+69}_{-61}{\,\text{(PDF)}}\pm 24{\,(\alpS)}\pm 14\,\text{(scale)}\pm
8\stat\unit{pb}$ (NNLO, HERAPDF2.0) $2513\,^{+51}_{-44}{\,\text{(PDF)}}\pm
11{\,(\alpS)}\pm 21\,\text{(scale)}\pm 10\stat\unit{pb}$ (NNLO, MMHT14)
$2445\,^{+40}_{-67}{\,\text{(PDF)}}\pm 28{\,(\alpS)}\pm 26\,\text{(scale)}\pm
8\stat\unit{pb}$ (NNLO, NNPDF3.0) $2375\pm 51{\,\text{(PDF)}}\pm
17{\,(\alpS)}\pm 14\,\text{(scale)}\pm 8\stat\unit{pb}$ mcsanc (NLO EW
correction, NNPDF3.0) $-30\unit{pb}\;(-1.2\%)$
$\Pp\Pp\to\PZ(\Pe^{+}\Pe^{-})+\text{X}$, $\sqrt{s}$ = 8($\pt^{\Pe}>25\GeV$,
$\abs{\eta^{\Pe}}<1.44$, $1.57<\abs{\eta^{\Pe}}<2.5$, $60<m_{\PZ}<120\GeV$)
Measurement [14] $450\pm 10\stat\pm 10{\syst}\pm 10\lum\unit{pb}$ (NNLO,
MSTW2008) [14] $450\pm 20\unit{pb}$ (NNLO, CT14)
$437\,^{+11}_{-15}{\,\text{(PDF)}}\pm 4{\,(\alpS)}\pm 2\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, HERAPDF2.0) $451\,^{+7}_{-11}{\,\text{(PDF)}}\pm
2{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$ (NNLO, MMHT14)
$441\,^{+11}_{-6}{\,\text{(PDF)}}\pm 5{\,(\alpS)}\pm 3\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, NNPDF3.0) $429\pm 9{\,\text{(PDF)}}\pm 3{\,(\alpS)}\pm
2\,\text{(scale)}\pm 1\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-13\unit{pb}\;(-2.7\%)$ $\Pp\Pp\to\PWp(\PGm^{+}\nu)+\text{X}$, $\sqrt{s}$ =
8($\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$) Measurement [14] $3100\pm
10\stat\pm 40{\syst}\pm 80\lum\unit{pb}$ (NNLO, MSTW2008) [14] $3140\pm
110\unit{pb}$ (NNLO, CT14) $3108\,^{+94}_{-87}{\,\text{(PDF)}}\pm
25{\,(\alpS)}\pm 34\,\text{(scale)}\pm 19\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$3309\,^{+20}_{-153}{\,\text{(PDF)}}\pm 18{\,(\alpS)}\pm 34\,\text{(scale)}\pm
17\stat\unit{pb}$ (NNLO, MMHT14) $3148\,^{+67}_{-95}{\,\text{(PDF)}}\pm
33{\,(\alpS)}\pm 29\,\text{(scale)}\pm 15\stat\unit{pb}$ (NNLO, NNPDF3.0)
$3095\pm 69{\,\text{(PDF)}}\pm 30{\,(\alpS)}\pm 21\,\text{(scale)}\pm
18\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0)
$-77\unit{pb}\;(-2.4\%)$ $\Pp\Pp\to\PWm(\PGm^{-}\Pagn)+\text{X}$, $\sqrt{s}$ =
8($\pt^{\PGm}>25\GeV$, $\abs{\eta^{\PGm}}<2.1$) Measurement [14] $2240\pm
10\stat\pm 20{\syst}\pm 60\lum\unit{pb}$ (NNLO, MSTW2008) [14] $2220\pm
80\unit{pb}$ (NNLO, CT14) $2187\,^{+74}_{-56}{\,\text{(PDF)}}\pm
19{\,(\alpS)}\pm 14\,\text{(scale)}\pm 6\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$2274\,^{+40}_{-20}{\,\text{(PDF)}}\pm 10{\,(\alpS)}\pm 17\,\text{(scale)}\pm
7\stat\unit{pb}$ (NNLO, MMHT14) $2200\,^{+42}_{-36}{\,\text{(PDF)}}\pm
23{\,(\alpS)}\pm 20\,\text{(scale)}\pm 7\stat\unit{pb}$ (NNLO, NNPDF3.0)
$2148\pm 48{\,\text{(PDF)}}\pm 16{\,(\alpS)}\pm 17\,\text{(scale)}\pm
7\stat\unit{pb}$ mcsanc (NLO EW correction, NNPDF3.0) $-47\unit{pb}\;(-2.1\%)$
$\Pp\Pp\to\PZ(\PGm^{+}\PGm^{-})+\text{X}$, $\sqrt{s}$ = 8($\pt^{\PGm}>25\GeV$,
$\abs{\eta^{\PGm}}<2.1$, $60<m_{\PZ}<120\GeV$) Measurement [14] $400\pm
10\stat\pm 10{\syst}\pm 10\lum\unit{pb}$ (NNLO, MSTW2008) [14] $400\pm
10\unit{pb}$ (NNLO, CT14) $389\,^{+12}_{-12}{\,\text{(PDF)}}\pm
3{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$ (NNLO, HERAPDF2.0)
$401\,^{+6}_{-8}{\,\text{(PDF)}}\pm 2{\,(\alpS)}\pm 2\,\text{(scale)}\pm
1\stat\unit{pb}$ (NNLO, MMHT14) $391\,^{+11}_{-3}{\,\text{(PDF)}}\pm
4{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$ (NNLO, NNPDF3.0) $381\pm
8{\,\text{(PDF)}}\pm 3{\,(\alpS)}\pm 2\,\text{(scale)}\pm 1\stat\unit{pb}$
mcsanc (NLO EW correction, NNPDF3.0) $-16\unit{pb}\;(-3.9\%)$

For each of the twelve experimental and boson cross section measurements
listed in Table 0.2, we have computed their corresponding theoretical NNLO
pQCD predictions using the four PDF sets and five to seven different values of
$\alpS(m_{\PZ})$. It is important to stress again that, for each QCD coupling
constant, we use the specific PDF sets that are associated with that
particular $\alpS(m_{\PZ})$ value. We calculated the NLO EW corrections using
NNPDF3.0 and $\alpS(m_{\PZ})=0.118$. By comparing the whole set of theoretical
calculations to the experimental data, a preferred value of the QCD coupling
constant can be derived for each PDF set as explained in the next section.
Figures 1–2 show the fiducial cross sections as a function of
$\alpS(m_{\PZ})$, with the experimental values indicated by the horizontal
black line with the inner grey band showing the integrated luminosity
uncertainty, and the outer darker band showing the total experimental
uncertainties added in quadrature. The filled ellipses represent the contours
of the joint probability density functions (Jpdfs) of the theoretical and
experimental results, with a width representing a two-dimensional one standard
deviation obtained from the product of the probability densities of the
experimental and theoretical results for each PDF, as described in the next
section. For any fixed value of $\alpS(m_{\PZ})$, a hierarchy of , theoretical
cross sections is apparent with HERAPDF2.0 predictions tending to be
systematically above the data, and the NNPDF3.0 ones below the latter. In
between the results of these two PDF sets, the cross sections derived with
MMHT14 tend to be above those with CT14, although they are often very similar
and overlap most of the time. Alternatively, the results of Figs. 1–2 indicate
that, in order to reproduce the experimental cross sections, HERAPDF2.0
(NNPDF3.0) tends in general to prefer a smaller (larger) value of
$\alpS(m_{\PZ})$ than other PDFs, and that the predictions from CT14 and
MMHT14 tend to be less scattered over the $\alpS(m_{\PZ})$ axis than those
from HERAPDF2.0 and NNPDF3.0. The HERAPDF2.0 (MMHT14) filled ellipses have the
smallest (largest) relative slope as a function of $\alpS(m_{\PZ})$. A larger
slope is advantageous for extracting the strong coupling constant, because
this means that the underlying $\alpS(m_{\PZ})$ value in the calculations has
a larger impact on the computed cross sections, also leading to a lower
propagated uncertainty in the $\alpS(m_{\PZ})$ value derived by comparing the
theoretical prediction to the experimental value.

Figure 1: Experimental fiducial cross section for the production of
$\PW^{+}_{\Pe}$ (upper left) and $\PW^{+}_{\PGm}$ (upper right),
$\PW^{-}_{\Pe}$ (middle left) and $\PW^{-}_{\PGm}$ (middle right), and
$\PZ_{\Pe}$ (lower left) and $\PZ_{\PGm}$ (lower right) in $\Pp\Pp$ collisions
at $\sqrt{s}=7\TeV$ compared to the corresponding joint probability density
functions (elliptical contours, see text) obtained with four different PDFs as
a function of $\alpS(m_{\PZ})$ and $\sigma$. The experimental measurements are
plotted as a horizontal black line with the inner grey band indicating the
integrated luminosity uncertainty, and the outer darker band showing all
experimental uncertainties added in quadrature. The filled ellipses are
obtained from the product of the probability distributions of the experimental
and theoretical results for each PDF, and represent the two-dimensional one
standard deviation. The points where the filled ellipses cross the vertical
dashed line at $\alpS(m_{\PZ})=0.118$ indicate the most likely cross section
interval that would be obtained using the baseline QCD coupling constant value
of all PDF sets.

Figure 2: Same as Fig. 1 for the production of $\PW^{+}_{\Pe}$ (upper left)
and $\PW^{+}_{\PGm}$ (upper right), $\PW^{-}_{\Pe}$ (middle left) and
$\PW^{-}_{\PGm}$ (middle right), and $\PZ_{\Pe}$ (lower left) and $\PZ_{\PGm}$
(lower right) in $\Pp\Pp$ collisions at $\sqrt{s}=8\TeV$ .

Overall, the theoretical predictions computed using the world-average value of
the QCD coupling constant (vertical dashed line in Figs. 1–2) agree well with
the experimental values within the uncertainties. The level of data-theory
agreement can be quantified with a goodness-of-fit test,
$\chi^{2}=\xi_{i}(M^{-1})_{ij}\xi_{j}$, where $M$ is the covariance matrix
taking all the uncertainties and their correlations into account, as explained
in Section 0.5.3, and $\xi_{i}=\sigma_{i,\text{th}}-\sigma_{i,\text{exp}}$ is
the difference between theoretical and experimental cross sections for each
PDF set. In the $\chi^{2}$ calculation, the asymmetric uncertainties of the
CT14, HERAPDF2.0, and MMHT14 PDF sets are symmetrised to the largest of the
two values and also separately to the smallest of the two values. The results
are listed in Table 0.4.

Overall goodness-of-fit per number of degrees of freedom, $\chi^{2}$/ndf,
among the twelve experimental measurements of and boson production cross
sections and the corresponding theoretical calculations obtained with the four
different PDF sets for their default $\alpS(m_{\PZ})=0.118$ value. The first
(second) row is obtained symmetrising the PDF uncertainties of the cross
sections obtained with the CT14, HERAPDF2.0, and MMHT14 sets to the largest
(smallest) of their respective values.  CT14 HERAPDF2.0 MMHT14 NNPDF3.0
$\chi^{2}/$ndf (symmetrised to the largest PDF uncertainty value) 12.0/11
11.0/11 9.0/11 31.7/11 $\chi^{2}/$ndf (symmetrised to the smallest PDF
uncertainty value) 15.2/11 28.3/11 13.9/11 31.7/11

##  0.5 Extraction of the QCD coupling constant

###  0.5.1 Extraction of $\alpS(m_{\PZ})$ for each single and cross section
measurement

The dependence of the theoretical cross sections on the QCD coupling constant
$\alpS(m_{\PZ})$, shown in Figs. 1–2, is fitted through a linear
$\chi^{2}$-minimisation procedure over $\alpS(m_{\PZ})\in[0.115,0.121]$, to
extract the slope $k$. Over the considered $\alpS(m_{\PZ})$ range, the
empirical linear fit describes well the observed $\alpS$-dependence of the
theoretical cross section for all PDF sets. The value of $\alpS(m_{\PZ})$
preferred by each individual measurement is determined by the crossing point
of the fitted linear theoretical curve with the experimental horizontal line.
The resulting $\alpS(m_{\PZ})$ values are listed in Table 0.5.1. For each
theoretical point used in the fit, the uncertainty in the cross section is
given by the quadratic sum of its associated PDF, scale, and numerical
uncertainties. In order to exploit the dependence of $\sigma_{\text{th}}(\PV)$
on $\alpS$ to quantitatively derive the latter, a joint probability density
function is constructed for each PDF prediction, as explained next. When the
theoretical cross section value has positive and negative uncertainties
$\delta_{\text{+-}}$, the experimental cross section is $\sigma_{\text{exp}}$
with uncertainty $\delta_{\text{exp}}$, the slope of the fit is $k$, and the
fitted QCD coupling constant is $\alpS(m_{\PZ})$, then the Jpdf as a function
of $\sigma$ and $\alpS$ is proportional to

$\exp\left\\{-\frac{1}{2}\left[\left(\frac{\sigma-\sigma_{\text{exp}}}{\delta_{\text{exp}}}\right)^{2}+\left(\frac{\sigma-\sigma_{\text{exp}}-k(\alpS-\alpS(m_{\PZ}))}{\delta_{\text{+-}}}\right)^{2}\right]\right\\}.$
(1)

The sign of $(\sigma-\sigma_{\text{exp}}-k(\alpS-\alpS(m_{\PZ})))$ determines
which of the $\delta_{\text{+-}}$ is used. For symmetric uncertainties the
Jpdfs have elliptical contours, but for asymmetric ones they are two filled
ellipses combined together. This procedure is repeated for all the twelve
different measurements and for all four PDF sets, and plotted as the filled
ellipses shown in Figs. 1–2, where each coloured area corresponds to one two-
dimensional (in $\sigma$ and $\alpS(m_{\PZ})$) standard deviation.

Extracted $\alpS(m_{\PZ})$ values from the different data-theory and boson
production cross section comparisons for each PDF set, with associated
uncertainties from different experimental (statistical, integrated luminosity,
and systematic) and theoretical (PDF, scale, and numerical) sources.  Cross
section PDF $\alpS(m_{\PZ})$ (total) $\delta_{\alpS}\stat$
$\delta_{\alpS}\lum$ $\delta_{\alpS}\syst$ $\delta_{\alpS}$(PDF)
$\delta_{\alpS}$(scale) $\delta_{\alpS}\,(\text{num})$ $\PW^{+}_{\Pe}$ (7)
CT14 0.1193 ${}^{+0.0062}_{-0.0062}$ 0.0004 0.0046 0.0022
${}^{+0.0031}_{-0.0032}$ 0.0017 0.0006 HERAPDF2.0 0.1108
${}^{+0.0090}_{-0.0097}$ 0.0006 0.0072 0.0035 ${}^{+0.0033}_{-0.0050}$ 0.0017
0.0012 MMHT14 0.1179 ${}^{+0.0049}_{-0.0047}$ 0.0003 0.0037 0.0018
${}^{+0.0025}_{-0.0020}$ 0.0008 0.0005 NNPDF3.0 0.1200
${}^{+0.0054}_{-0.0054}$ 0.0004 0.0043 0.0021 ${}^{+0.0022}_{-0.0022}$ 0.0009
0.0006 $\PW^{-}_{\Pe}$ (7) CT14 0.1208 ${}^{+0.0064}_{-0.0061}$ 0.0005 0.0047
0.0022 ${}^{+0.0034}_{-0.0030}$ 0.001 0.0004 HERAPDF2.0 0.1152
${}^{+0.0136}_{-0.0149}$ 0.0013 0.0118 0.0056 ${}^{+0.0027}_{-0.0066}$ 0.0025
0.0009 MMHT14 0.1195 ${}^{+0.0047}_{-0.0053}$ 0.0004 0.0040 0.0019
${}^{+0.0012}_{-0.0027}$ 0.0007 0.0003 NNPDF3.0 0.1239
${}^{+0.0073}_{-0.0073}$ 0.0007 0.0060 0.0028 ${}^{+0.0029}_{-0.0029}$ 0.0011
0.0005 $\PZ_{\Pe}$ (7) CT14 0.1247 ${}^{+0.0068}_{-0.0070}$ 0.0014 0.0051
0.0028 ${}^{+0.0031}_{-0.0036}$ 0.0004 0.0003 HERAPDF2.0 0.1226
${}^{+0.0106}_{-0.0121}$ 0.0025 0.0088 0.0049 ${}^{+0.0018}_{-0.0061}$ 0.0007
0.0005 MMHT14 0.1222 ${}^{+0.0047}_{-0.0050}$ 0.0011 0.0038 0.0021
${}^{+0.0012}_{-0.0022}$ 0.0006 0.0002 NNPDF3.0 0.1279
${}^{+0.0074}_{-0.0074}$ 0.0016 0.0058 0.0032 ${}^{+0.0027}_{-0.0027}$ 0.0007
0.0003 $\PW^{+}_{\PGm}$ (7) CT14 0.1178 ${}^{+0.0049}_{-0.0058}$ 0.0003 0.0040
0.0015 ${}^{+0.0023}_{-0.0039}$ 0.0007 0.0005 HERAPDF2.0 0.1085
${}^{+0.0083}_{-0.0108}$ 0.0006 0.0070 0.0026 ${}^{+0.0026}_{-0.0073}$ 0.0023
0.0009 MMHT14 0.1170 ${}^{+0.0048}_{-0.0053}$ 0.0003 0.0039 0.0015
${}^{+0.0022}_{-0.0031}$ 0.0006 0.0006 NNPDF3.0 0.1185
${}^{+0.0054}_{-0.0054}$ 0.0003 0.0044 0.0016 ${}^{+0.0022}_{-0.0022}$ 0.0011
0.0006 $\PW^{-}_{\PGm}$ (7) CT14 0.1186 ${}^{+0.0050}_{-0.0057}$ 0.0004 0.0041
0.0014 ${}^{+0.0023}_{-0.0036}$ 0.0009 0.0003 HERAPDF2.0 0.1109
${}^{+0.0111}_{-0.0109}$ 0.001 0.0094 0.0033 ${}^{+0.0040}_{-0.0035}$ 0.0023
0.0008 MMHT14 0.1177 ${}^{+0.0046}_{-0.0047}$ 0.0004 0.0039 0.0014
${}^{+0.0017}_{-0.0021}$ 0.0009 0.0003 NNPDF3.0 0.1212
${}^{+0.0070}_{-0.0070}$ 0.0006 0.0058 0.0020 ${}^{+0.0029}_{-0.0029}$ 0.0013
0.0004 $\PZ_{\PGm}$ (7) CT14 0.1232 ${}^{+0.0062}_{-0.0077}$ 0.001 0.0051
0.0022 ${}^{+0.0023}_{-0.0051}$ 0.0005 0.0003 HERAPDF2.0 0.1200
${}^{+0.0108}_{-0.0108}$ 0.0017 0.0092 0.0040 ${}^{+0.0034}_{-0.0034}$ 0.0012
0.0005 MMHT14 0.1213 ${}^{+0.0051}_{-0.0045}$ 0.0007 0.0039 0.0017
${}^{+0.0027}_{-0.001}$ 0.0005 0.0002 NNPDF3.0 0.1261 ${}^{+0.0070}_{-0.0070}$
0.0011 0.0057 0.0025 ${}^{+0.0028}_{-0.0028}$ 0.0007 0.0003 $\PW^{+}_{\Pe}$
(8) CT14 0.1181 ${}^{+0.0081}_{-0.0083}$ 0.0009 0.0039 0.0047
${}^{+0.0049}_{-0.0053}$ 0.0015 0.0009 HERAPDF2.0 0.1030
${}^{+0.0154}_{-0.0140}$ 0.0015 0.0070 0.0085 ${}^{+0.0099}_{-0.0075}$ 0.0037
0.0017 MMHT14 0.1172 ${}^{+0.0045}_{-0.0057}$ 0.0006 0.0025 0.0031
${}^{+0.0017}_{-0.0039}$ 0.0011 0.0006 NNPDF3.0 0.1188
${}^{+0.0049}_{-0.0049}$ 0.0006 0.0027 0.0032 ${}^{+0.0022}_{-0.0022}$ 0.0012
0.0006 $\PW^{-}_{\Pe}$ (8) CT14 0.1169 ${}^{+0.0046}_{-0.0044}$ 0.0004 0.0025
0.0025 ${}^{+0.0029}_{-0.0025}$ 0.0006 0.0003 HERAPDF2.0 0.1066
${}^{+0.0098}_{-0.0094}$ 0.001 0.0057 0.0057 ${}^{+0.0049}_{-0.0042}$ 0.0020
0.0009 MMHT14 0.1163 ${}^{+0.0036}_{-0.0041}$ 0.0004 0.0022 0.0022
${}^{+0.0014}_{-0.0025}$ 0.001 0.0003 NNPDF3.0 0.1187 ${}^{+0.0059}_{-0.0059}$
0.0006 0.0035 0.0035 ${}^{+0.0029}_{-0.0029}$ 0.0008 0.0005 $\PZ_{\Pe}$ (8)
CT14 0.1216 ${}^{+0.0056}_{-0.0062}$ 0.0027 0.0027 0.0027
${}^{+0.0029}_{-0.0040}$ 0.0007 0.0003 HERAPDF2.0 0.1173
${}^{+0.0084}_{-0.0093}$ 0.0045 0.0045 0.0045 ${}^{+0.0031}_{-0.0051}$ 0.0009
0.0005 MMHT14 0.1201 ${}^{+0.0044}_{-0.0039}$ 0.0021 0.0021 0.0021
${}^{+0.0023}_{-0.0013}$ 0.0006 0.0002 NNPDF3.0 0.1245
${}^{+0.0060}_{-0.0060}$ 0.0031 0.0031 0.0031 ${}^{+0.0027}_{-0.0027}$ 0.0006
0.0003 $\PW^{+}_{\PGm}$ (8) CT14 0.1173 ${}^{+0.0055}_{-0.0053}$ 0.0004 0.0032
0.0016 ${}^{+0.0038}_{-0.0035}$ 0.0014 0.0008 HERAPDF2.0 0.1076
${}^{+0.0055}_{-0.0101}$ 0.0006 0.0045 0.0022 ${}^{+0.0011}_{-0.0085}$ 0.0019
0.0009 MMHT14 0.1168 ${}^{+0.0035}_{-0.0041}$ 0.0003 0.0024 0.0012
${}^{+0.0020}_{-0.0029}$ 0.0009 0.0005 NNPDF3.0 0.1182
${}^{+0.0038}_{-0.0038}$ 0.0003 0.0027 0.0013 ${}^{+0.0022}_{-0.0022}$ 0.0007
0.0006 $\PW^{-}_{\PGm}$ (8) CT14 0.1209 ${}^{+0.0053}_{-0.0046}$ 0.0005 0.0032
0.0011 ${}^{+0.0039}_{-0.0030}$ 0.0008 0.0003 HERAPDF2.0 0.1147
${}^{+0.0081}_{-0.0072}$ 0.0010 0.0062 0.0021 ${}^{+0.0041}_{-0.0021}$ 0.0018
0.0007 MMHT14 0.1195 ${}^{+0.0035}_{-0.0034}$ 0.0004 0.0026 0.0009
${}^{+0.0019}_{-0.0016}$ 0.0009 0.0003 NNPDF3.0 0.1238
${}^{+0.0052}_{-0.0052}$ 0.0006 0.0039 0.0013 ${}^{+0.0029}_{-0.0029}$ 0.0011
0.0004 $\PZ_{\PGm}$ (8) CT14 0.1220 ${}^{+0.0067}_{-0.0069}$ 0.0032 0.0032
0.0032 ${}^{+0.0037}_{-0.0040}$ 0.0006 0.0003 HERAPDF2.0 0.1170
${}^{+0.0112}_{-0.0116}$ 0.0060 0.0060 0.0060 ${}^{+0.0036}_{-0.0048}$ 0.0013
0.0006 MMHT14 0.1202 ${}^{+0.0050}_{-0.0043}$ 0.0024 0.0024 0.0024
${}^{+0.0027}_{-0.0007}$ 0.0005 0.0002 NNPDF3.0 0.1244
${}^{+0.0066}_{-0.0066}$ 0.0034 0.0034 0.0034 ${}^{+0.0028}_{-0.0028}$ 0.0006
0.0003

###  0.5.2 Propagation of $\alpS(m_{\PZ})$ uncertainties

Appropriate propagation of the separated experimental and theoretical
uncertainties into each value of $\alpS(m_{\PZ})$ obtained from each
particular and measurement, is crucial to combine all estimates taking into
account their correlations, and extract a single final $\alpS(m_{\PZ})$
result. The method employed to determine the individual sources of
uncertainties associated with a given $\alpS(m_{\PZ})$ value is similar to
that used in Refs. [8, 9] for the $\alpS(m_{\PZ})$ extraction from inclusive
$\ttbar$ cross sections. In summary, each source of uncertainty $\delta\sigma$
propagates into a corresponding $\alpS(m_{\PZ})$ uncertainty through
$\delta\sigma/k$, where $k$ is the slope of the fit of the theoretical cross
section versus $\alpS(m_{\PZ})$. The validity of such a simple propagation of
uncertainties can be demonstrated calculating first a theoretical uncertainty
distribution by adding up quadratically the PDF, scale, and numerical
uncertainties assuming Gaussian distributions (for the asymmetric PDF
uncertainties, only the largest of the positive and negative uncertainties are
used). Then, a Jpdf can be derived from the product of the theoretical and
experimental distributions $f_{\text{th}}(\sigma|\alpS(m_{\PZ}))$ and
$f_{\text{exp}}(\sigma)$. Integration over $\sigma$ gives the marginalised
posterior

$P(\alpS)=\int
f_{\text{exp}}(\sigma)\,f_{\text{th}}(\sigma|\alpS)\,\rd\sigma.$

The expected value of the theoretical probability distribution changes
linearly according to the fitted first-order polynomial, but all the
theoretical and experimental uncertainties remain the same for all
$\alpS(m_{\PZ})$ values. Since all the uncertainties have Gaussian
distributions and the marginalisation is, in essence, a convolution, the
resulting $\alpS(m_{\PZ})$ posterior will be also Gaussian, with the impact of
each cross section uncertainty adding quadratically to the $\alpS(m_{\PZ})$
uncertainty. More specifically, each cross section uncertainty source
$\delta\sigma$ will result in a propagated $\alpS(m_{\PZ})$ uncertainty in
$\delta\sigma/k$ size, where $k$ is the slope of the linear fit to theoretical
calculations. In this demonstration, we symmetrised the PDF uncertainties for
simplicity, but the $\delta\sigma/k$ prescription will be also used hereafter
for the case of asymmetric uncertainties. All the extracted $\alpS(m_{\PZ})$
values, along with the uncertainty breakdowns from every source, for each
system and PDF set are given in Table 0.5.1. The results from the MMHT14 PDF
feature the extracted $\alpS(m_{\PZ})$ values with the lowest overall
uncertainty, in some cases as low as 3%.

###  0.5.3 Combination of all individual $\alpS(m_{\PZ})$ values

From the twelve $\alpS(m_{\PZ})$ extractions per PDF set listed in Table
0.5.1, we can determine a single $\alpS(m_{\PZ})$ value by appropriately
combining them taking into account their uncorrelated, partially-, and fully-
correlated experimental and theoretical uncertainties. For this, the program
convino v1.2 [32] is employed, which uses a $\chi^{2}$ minimisation to
determine the best estimate. In the current analysis, the Neyman $\chi^{2}$
code option is always used. As an independent cross-check, we confirm that,
for symmetric uncertainties, the results are identical to those obtained with
the BLUE method [33]. The following correlation coefficients are used:

  * •

The integrated luminosity uncertainty is fully correlated for all
$\alpS(m_{\PZ})$ results obtained at the same $\sqrt{s}$, but fully
uncorrelated between the two different c.m. energies.

  * •

The experimental systematic uncertainty is partially correlated. Since the
exact correlation values impact the final result, a dedicated study of the
correlations is carried out in Section 0.5.3.

  * •

The experimental statistical uncertainty is fully uncorrelated among
$\alpS(m_{\PZ})$ extractions.

  * •

The PDF uncertainty is partially correlated for the $\alpS(m_{\PZ})$ values
extracted with the same PDF set, as discussed in detail in Section 0.5.3.

  * •

The scale uncertainty is partially correlated, as explained in Section 0.5.3.

  * •

The theoretical numerical uncertainty is fully uncorrelated among
$\alpS(m_{\PZ})$ extractions.

By properly implementing all the uncertainties and their correlations in
convino, we can derive a single final combined $\alpS(m_{\PZ})$ value and
associated uncertainties for each PDF set.

#### Correlations among the experimental systematic uncertainties

For all the experimental measurements of the cross sections, the size of their
systematic uncertainties of each type are listed in Table 0.5.3. The absolute
uncertainties are given in the same proportions as in Table 0.5.3, but
rescaled such that they add up quadratically to the total experimental
systematic uncertainty listed in Tables 0.4 and 0.4.

Breakdown of the experimental systematic uncertainties (in percent) for each
of the and boson production cross section measurements at 7 and 8 [13, 14].
Measurement $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$
$\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ 7 Lepton reconstruction and identification 1.5
1.5 1.8 0.9 0.9 Muon trigger inefficiency 0.5 0.5 0.5 Energy scale and
resolution 0.5 0.6 0.12 0.19 0.25 0.35 Missing $\pt$ scale and resolution 0.3
0.3 0.2 0.2 Background subtraction and modelling 0.3 0.5 0.14 0.4 0.5 0.28 8
Lepton reconstruction and identification 2.8 2.5 2.8 1.0 0.9 1.1 Energy scale
and resolution 0.4 0.7 0.0 0.3 0.3 0.0 Missing $\pt$ scale and resolution 0.8
0.7 0.5 0.5 Background subtraction and modelling 0.2 0.3 0.4 0.2 0.1 0.4

The detailed correlations between the different uncertainty sources of Table
0.5.3 are listed in Tables .8 to .8 of the Appendix. By using the experimental
systematic uncertainty breakdown and the correlations between the
uncertainties, the total correlations between the experimental uncertainty
sources can be calculated using the formula

$\rho_{ij}=\frac{\sum_{k}\rho_{k,ij}\,\delta\sigma_{k,i}\,\delta\sigma_{k,j}}{\sqrt{\sum_{k}\delta\sigma_{k,i}^{2}}\,\sqrt{\sum_{k}\delta\sigma_{k,j}^{2}}},$
(2)

where the subscript $k$ labels the uncertainty (background subtraction), and
$i$, $j$ denote the associated measurement ($\PW^{+}_{\Pe}$ at 7). The
calculated total correlations among experimental systematic uncertainties are
given in Table .8 of the Appendix. Many of the propagated experimental
uncertainties appear strongly correlated. To give an idea of the correlations
among $\alpS(m_{\PZ})$ estimates taking into account all the uncertainty
sources, both experimental and theoretical, an example correlation matrix for
the NNPDF3.0 set is given in Table .8 of the Appendix. One can see that many
of the $\alpS(m_{\PZ})$ values derived within a given PDF set are strongly
correlated, especially across the same $\sqrt{s}$.

#### Correlations among PDF and scale uncertainties

In the theoretical cross section calculations, the PDF uncertainties are in
the range of a few percent, scale uncertainty up to one percent, and numerical
uncertainty around half a percent (Tables 0.4 and 0.4). The numerical
uncertainty cannot be neglected because differences with respect to the
prediction computed with the central eigenvalue/replica members are used to
calculate the PDF uncertainties. The cross sections for the central PDF
members have intrinsic numerical fluctuations that impact the PDF uncertainty
magnitude, asymmetry, and also the correlations among theoretical
uncertainties. To take this into account, a Pearson correlation coefficient is
calculated for each pair of measurements and for each PDF set using the cross
sections from all the PDF members that were used in calculating the PDF
uncertainty. Similarly for the scale uncertainties, for each pair of
measurements the Pearson correlation coefficient is calculated using the
results obtained from varying the theoretical scales. The correlations are
mostly in the 0.8–0.9, 0.4–0.7, 0.2–0.6, and 0.9–1.0 ranges for CT14,
HERAPDF2.0, MMHT14, and NNPDF3.0, respectively. The scale correlations are
around 0.6–0.9. When combining the $\alpS(m_{\PZ})$ estimates, the specific
correlation coefficient calculated for every specific pair of estimates is
used.

##  0.6 Results and discussion

Figure 3 shows the individual results (error bars) and the final combined
$\alpS(m_{\PZ})$ value (coloured areas) obtained per PDF, as explained in the
previous section. The width of the coloured areas in the plot indicates the
size of the total propagated uncertainty in the final $\alpS(m_{\PZ})$ derived
for each PDF set. Table 0.6 lists the final $\alpS(m_{\PZ})$ values determined
for each PDF set through the combination of the twelve individual extractions.
The total uncertainties amount to 2.0% for MMHT14 and NNPDF3.0, 2.3% for CT14,
and $\approx$4% for HERAPDF2.0. The total $\alpS(m_{\PZ})$ uncertainties
derived for NNPDF3.0 are symmetric by construction, and are also symmetric at
the end for MMHT14 within the accuracy given. Small asymmetries remain for the
final CT14 and HERAPDF2.0 results. The dominant source of experimental
uncertainty is the integrated luminosity, whereas on the theoretical side it
is the knowledge of the parton densities. The last column of Table 0.6 lists
the goodness-of-fit per degree of freedom ($\chi^{2}$/ndf) of the final single
combined result compared to the twelve individual $\alpS(m_{\PZ})$
extractions.

Figure 3: Individual $\alpS(m_{\PZ})$ values extracted from each measured and
boson production cross section (bars), and final $\alpS(m_{\PZ})$ values
obtained combining the twelve individual determinations (vertical coloured
areas), for each PDF set.

Strong coupling constant $\alpS(m_{\PZ})$ values extracted per PDF set by
combining all the individual results obtained for each and boson production
cross section measurements (Table 0.5.1), listed along with their total and
individual uncertainties. The last column tabulates the goodness-of-fit per
degree of freedom $\chi^{2}$/ndf of the final single combined result compared
to the twelve individual $\alpS(m_{\PZ})$ extractions.  PDF $\alpS(m_{\PZ})$
$\delta\stat$ $\delta\lum$ $\delta\syst$ $\delta$(PDF) $\delta$(scale)
$\delta(\text{num})$ $\chi^{2}$/ndf CT14 $0.1163^{+0.0024}_{-0.0031}$ 0.0007
0.0013 0.0010 ${}^{+0.0016}_{-0.0022}$ 0.0009 0.0006 13.3/11 HERAPDF2.0
$0.1072^{+0.0043}_{-0.0040}$ 0.0012 0.0027 0.0012 ${}^{+0.0027}_{-0.0020}$
0.0012 0.0009 14.2/11 MMHT14 $0.1186\pm 0.0025$ 0.0003 0.0018 0.0009 0.0013
0.0007 0.0002 10.2/11 NNPDF3.0 $0.1147\pm 0.0023$ 0.0009 0.0008 0.0007 0.0014
0.0006 0.0010 29.2/11

The $\alpS(m_{\PZ})$ results obtained with HERAPDF2.0 and NNPDF3.0 show
various differences with respect to those derived with the CT14 and MMHT14
sets. First, the QCD coupling constant derived with HERAPDF2.0,
$\alpS(m_{\PZ})=0.1072^{+0.0043}_{-0.0040}$, is between 1.7 and 2.7 standard
deviations smaller than the rest of extractions (Fig. 4 left). Although as
discussed later, in the context of the cross-checks described in Table 0.6,
such a disagreement is reduced when symmetrising the HERAPDF2.0 uncertainties
to their maximum values. As discussed before, since the HERAPDF2.0 cross
sections for $\alpS(m_{\PZ})=0.118$ tend to overpredict the measured and boson
production cross sections (Figs. 1–2), a data-theory agreement can only be
obtained for a value of $\alpS$ that is reduced compared to its default value.
For all global PDF fits extracted with different $\alpS$ values as input,
there exists a generic anticorrelation between the values of $\alpS(Q^{2})$
and the parton densities evaluated at $(x,Q^{2}$), particularly, for the gluon
and in turn (through perturbative evolution) for the sea quarks. It is thereby
important to analyze in more detail the differences between the PDF sets for
each flavour. For this purpose, a comparison study of parton densities and
parton luminosities has been carried out with apfel v2.7.1 [34]. This study
indicates that the HERAPDF2.0 -quark densities (and the overall quark-
antiquark luminosities) are enhanced by about 5% compared to the rest of PDFs
in the $(x,Q^{2})$ region of relevance for EW boson production. This fact
increases the weight of the LO contributions to the theoretical and boson
production cross sections, and thereby pushes down the cross section
contributions from higher-order pQCD diagrams that are sensitive to
$\alpS(m_{\PZ})$. The effective result is a comparatively reduced
$\alpS(m_{\PZ})$ value. The level of agreement between the twelve individual
and the total $\alpS(m_{\PZ})$ extractions turns out to be good for this PDF
set ($\chi^{2}/\mathrm{ndf}\approx 1$ in Table 0.6), because of the relatively
wide span of $\alpS$ values derived and their associated large uncertainties
(Fig. 3). Since HERAPDF2.0 uses DIS data alone, and therefore lacks the extra
constraints on the PDFs provided by the LHC data, we conclude that one would
need an updated refit of these parton densities to an extended set of
experimental data, including LHC results, before relying on the QCD coupling
constant derived following the procedure described here.

The features of the $\alpS(m_{\PZ})$ results obtained with NNPDF3.0 show the
opposite behaviour to those observed for the HERAPDF2.0 set. The and boson
production cross sections computed with this PDF tend to underpredict the
experimental measurements (Figs. 1–2), and yield an overall bad data-theory
agreement ($\chi^{2}/\mathrm{ndf}\approx 3$ in Table 0.4), for the baseline
$\alpS(m_{\PZ})=0.118$ coupling constant. A reproduction of the individual
measurements by theory can thus be achieved only for an $\alpS(m_{\PZ})$ value
that is enlarged compared to the default value for this PDF set. Thus, many of
the individual $\alpS(m_{\PZ})$ extractions obtained with NNPDF3.0 have values
relatively larger than those obtained for other PDFs. However, the final
combined NNPDF3.0 value appears shifted down to $\alpS(m_{\PZ})=0.1147\pm
0.0023$ (Table 0.6), falling outside of the region around
$\alpS(m_{\PZ})\approx 0.120$ defined by most of the individual estimates
(Table 0.5.1), and, consequently, the final level of agreement of the combined
and single extractions is poor ($\chi^{2}/\mathrm{ndf}\approx 3$ in Table
0.6). Such a seemingly counterintuitive behaviour is due to the presence of
strong correlations among individual extractions for a fixed value of
$\alpS(m_{\PZ})$, and the fact that the lowest $\alpS(m_{\PZ})$ values derived
have smaller uncertainties than the rest, thereby pulling down the final
average. The effect of a combined result lying outside of the range of the
input values caused by, large underlying nonlinearities among individual
estimates, is called “Peelle’s pertinent puzzle” [35]. The absence of
parametrisation bias in this neural-network PDF results in parton densities
that can be less well constrained (have larger uncertainties) than the rest of
PDFs in some regions of phase space. The same apfel v2.7.1 study mentioned
above indicates that the NNPDF3.0 quark-antiquark luminosities tend to be
somewhat less precise than those from the other PDF sets in the relevant
$(x,Q^{2})$ range for and production. A larger span of replicas results in
nontrivial correlations among PDF uncertainties that push the final
$\alpS(m_{\PZ})$ value off the individual extractions for each single
measurement. In any case, the latest version released (v3.1) of the NNPDF
global fit [36] shows much better agreement of the theoretical EW boson cross
sections with the LHC data for the central $\alpS(m_{\PZ})=0.118$ value.
However, this latter NNPDF3.1 set cannot be directly employed to independently
extract $\alpS(m_{\PZ})$ from the CMS measurements through the approach
discussed here, as this updated global fit does include already the absolute
normalisation of a fraction of the and cross sections used in this work.

The final $\alpS(m_{\PZ})$ extractions are plotted in Fig. 4 (left)—with
(asymmetric, where needed) parabolas constructed so as to have a minimum at
each final central $\alpS(m_{\PZ})$ result and (one standard deviation)
uncertainties matching those listed in Table 0.6—compared with the current
world average of $\alpS(m_{\PZ})=0.1181\pm 0.0011$ (orange band).

Figure 4: Final $\alpS(m_{\PZ})$ values extracted for the CT14, HERAPDF2.0,
MMHT14, and NNPDF3.0 PDF sets (left), and combined $\alpS(m_{\PZ})$ extraction
from the CT14 and MMHT14 PDFs (right), compared to the current world average
(vertical orange band). The asymmetric parabolas are constructed to have a
minimum at the combined value and are fitted to go through $\Delta\chi^{2}=1$
(horizontal black lines) at the one std. deviation uncertainties quoted in
Table 0.6.

To analyse the robustness and stability of the final $\alpS(m_{\PZ})$
extractions to the underlying data sets, their uncertainties, and
correlations, we repeat the convino combination varying several ingredients,
as explained next. First, $\alpS(m_{\PZ})$ values are extracted using
separately the measurements at $\sqrt{s}=7$ and 8alone, as shown in the top
rows of Table 0.6. This separation of data sets yields final $\alpS(m_{\PZ})$
values mostly consistent with those derived from the combined ones listed in
Table 0.6, with the largest deviations from the original results being those
from the 7NNPDF3.0 and 8HERAPDF2.0 extractions, with 1.0 and 0.85 standard
deviations, respectively. Although the CMS luminosity studies confirm that
these uncertainties are fully uncorrelated between 7 and 8, we have checked
the impact of relaxing such an assumption by assuming a 0.5 correlation factor
between them. Such a correlation factor results in a change of the final
$\alpS(m_{\PZ})$ by at most one-third of the current total uncertainty.
Another cross-check is carried out by symmetrising the PDF uncertainties to
their maximum value of the two (this does not apply to NNPDF3.0, because its
uncertainties are symmetric by construction). The corresponding results are
given in the left bottom half of Table 0.6. Changing from asymmetric to
symmetric PDF uncertainties causes the HERAPDF2.0 combined value to increase
by 1.1 standard deviation, whereas all other PDF results are consistent with
the default $\alpS(m_{\PZ})$ extractions. Such a large sensitivity to changes
in the PDF uncertainty confirms the relative lack of robustness of the
$\alpS(m_{\PZ})$ values derived for HERAPDF2.0 in our analysis, because the
asymmetries of the PDF uncertainties can be significantly affected by random
numerical errors. To further test the sensitivity of the $\alpS(m_{\PZ})$
extraction to the assumptions made on the underlying and cross section
uncertainties and their correlations, the original analysis is repeated by
adding an uncorrelated 1% numerical uncertainty to all theoretical cross
sections. Such a value accounts for possible overlooked small uncorrelated
uncertainties, coming from the use of different codes for the theoretical pQCD
and/or EW calculations [27]. The impact of such a change is not significant in
the final results, as observed by comparing the numbers in Table 0.6 and those
in the bottom-right columns of Table 0.6. Further similar tests and cross-
checks have been carried out in a recent $\alpS(m_{\PZ})$ extraction that
exploits all the LHC electroweak boson data [37] with the same approach used
here, which confirm these conclusions. All these systematic tests indicate
that HERAPDF2.0 and NNPDF3.0 have larger variations when changing the
ingredients of the combination, but for CT14 and MMHT14 the final
$\alpS(m_{\PZ})$ values extracted are reasonably robust within the quoted
uncertainties.

Sensitivity of the final $\alpS(m_{\PZ})$ extractions per PDF set to various
data, uncertainties, and correlation assumptions. Top rows: Extractions of
$\alpS(m_{\PZ})$ using only the 7 and 8measurements separately. Bottom rows:
Extractions of $\alpS(m_{\PZ})$ when symmetrising the asymmetric PDF
uncertainties by taking the maximum of the negative and positive values
(left), and when adding a 1% uncorrelated uncertainty to all cross sections
(right).  PDF $\alpS(m_{\PZ})$ [7data] $\alpS(m_{\PZ})$ [8data] CT14
$0.1158^{+0.0048}_{-0.0052}$ $0.1174^{+0.0041}_{-0.0037}$ HERAPDF2.0
$0.1075\pm 0.0060$ $0.1038^{+0.0107}_{-0.0073}$ MMHT14
$0.1192^{+0.0071}_{-0.0059}$ $0.1184\pm 0.0029$ NNPDF3.0 $0.1123\pm 0.0032$
$0.1148\pm 0.0031$ PDF $\alpS(m_{\PZ})$ [symm. PDF uncert.] $\alpS(m_{\PZ})$
[$+1\%$ uncorr. uncert.] CT14 $0.1148\pm 0.0034$ $0.1169^{+0.0027}_{-0.0034}$
HERAPDF2.0 $0.1119\pm 0.0056$ $0.1089\pm 0.0045$ MMHT14 $0.1185\pm 0.0028$
$0.1186\pm 0.0026$ NNPDF3.0 $0.1147\pm 0.0023$ $0.1155\pm 0.0029$

Among PDFs, the results obtained using MMHT14 and CT14 feature the largest
sensitivity to $\alpS$ variations, they show a larger $k$ slope, Eq. (1),
compared to those obtained with HERAPDF2.0 and NNPDF3.0 (Figs. 1–2). Since the
uncertainty in the $\alpS(m_{\PZ})$ value derived from HERAPDF2.0 is the
largest (up to twice as large as some of the other extractions), because of
the absence of constraining LHC input data in this HERA-only PDF fit, and
since the final NNPDF3.0 result has a larger tension between the combined and
individual extractions from each single measurement (Table 0.6), we consider
the values extracted with CT14, $\alpS(m_{\PZ})=0.1163^{+0.0024}_{-0.0031}$,
and MMHT14, $\alpS(m_{\PZ})=0.1186\pm 0.0025$, as the most reliable in this
analysis. Providing a single final $\alpS(m_{\PZ})$ value from this study is
not obvious because, in general, there is no unique way to derive a final best
estimate of $\alpS$ based on the results obtained from different PDF sets. An
unbiased approach for combining results from different PDFs, in line with the
PDG practice [1] as well as with the procedure employed to produce the PDF4LHC
combined PDF set [38], is to average them without applying any further
weighting. The same approach was followed also in the similar combination of
QCD coupling constant values obtained from the inclusive $\ttbar$ cross
sections [9]. By taking the straight average of the mean values and of the
uncertainties of the individual CT14 and MMHT14 combinations, we obtain a
final value of the QCD coupling constant at the pole mass,
$\alpS(m_{\PZ})=0.1175^{+0.0025}_{-0.0028}$, with a total (symmetrised)
uncertainty of 2.3%. Such a result compares very well with the
$\alpS(m_{\PZ})=0.1177^{+0.0034}_{-0.0036}$ value, with an uncertainty of
$\approx$3%, extracted from the theoretical analysis of top pair cross section
data [9]. The right plot of Fig. 4 shows the $\alpS(m_{\PZ})$ parabola
extracted combining the CT14 and MMHT14 results. This final extraction is
fully consistent with the PDG world average (orange band), and has an overall
uncertainty similar to that of other recent determinations at this level of
(NNLO) theoretical accuracy, such as those from EW precision fits [39], and
$\ttbar$ cross sections [8, 9, 10].

##  0.7 Summary

We have used twelve measurements of the inclusive fiducial and production
cross sections in proton-proton collisions ($\Pp\Pp$) at $\sqrt{s}=7$ and 8,
carried out in the electron and muon decay channels by the CMS experiment, to
extract the value of the strong coupling constant at the pole mass,
$\alpS(m_{\PZ})$. The procedure is based on a detailed comparison of the
measured electroweak boson cross sections to theoretical calculations computed
at next-to-next-to-leading-order accuracy with the CT14, HERAPDF2.0, MMHT14,
and NNPDF3.0 parton distribution function (PDF) sets. The overall data-theory
agreement is good within the experimental and theoretical uncertainties. A
$\chi^{2}$-minimisation procedure has been employed to combine all twelve
individual $\alpS$ extractions per PDF set, properly taking into account all
individual sources of experimental and theoretical uncertainties, and their
correlations. The following combined values are extracted for the four
different PDFs: $\alpS(m_{\PZ})=0.1163^{+0.0024}_{-0.0031}$ (CT14),
$0.1072^{+0.0043}_{-0.0040}$ (HERAPDF2.0), $0.1186\pm 0.0025$ (MMHT14), and
$0.1147\pm 0.0023$ (NNPDF3.0). The largest propagated uncertainties are
associated with the experimental integrated luminosity and theoretical intra-
PDF uncertainties. Among the four extractions, the cross section calculated
with the CT14 and MMHT14 sets appear as the most sensitive to the underlying
$\alpS$ value and, at the same time, the derived $\alpS(m_{\PZ})$ values are
the most robust and stable with respect to variations in the data and
theoretical cross sections, their uncertainties, and correlations. The result
derived combining the CT14 and MMHT14 extractions,
$\alpS(m_{\PZ})=0.1175^{+0.0025}_{-0.0028}$, has a 2.3% uncertainty that is
comparable to that previously obtained in a similar analysis of the inclusive
$\ttbar$ cross sections in $\Pp\Pp$ collisions at the LHC. This extracted
value is fully compatible with the current $\alpS(m_{\PZ})$ world average.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centres and personnel of the Worldwide LHC Computing Grid for
delivering so effectively the computing infrastructure essential to our
analyses. Finally, we acknowledge the enduring support for the construction
and operation of the LHC and the CMS detector provided by the following
funding agencies: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq,
CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST,
and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF
(Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); Academy
of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG,
and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM
(Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES
(Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT,
LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC
(Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom,
RAS, RFBR, and NRC KI (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER
(Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST
(Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK
(Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie programme and the
European Research Council and Horizon 2020 Grant, contract Nos. 675440,
752730, and 765710 (European Union); the Leventis Foundation; the A.P. Sloan
Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science
Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et
dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door
Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium)
under the “Excellence of Science – EOS” – be.h project n. 30820817; the
Beijing Municipal Science & Technology Commission, No. Z181100004218003; the
Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the
Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy –
EXC 2121 “Quantum Universe” – 390833306; the Lendület (“Momentum”) Programme
and the János Bolyai Research Scholarship of the Hungarian Academy of
Sciences, the New National Excellence Program ÚNKP, the NKFIA research grants
123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary);
the Council of Science and Industrial Research, India; the HOMING PLUS
programme of the Foundation for Polish Science, cofinanced from European
Union, Regional Development Fund, the Mobility Plus programme of the Ministry
of Science and Higher Education, the National Science Center (Poland),
contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543,
2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406;
the National Priorities Research Program by Qatar National Research Fund; the
Ministry of Science and Education, grant no. 3.2989.2017 (Russia); the
Programa Estatal de Fomento de la Investigación Científica y Técnica de
Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa
del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by
EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral
Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its
2nd Century Project Advancement Project (Thailand); the Nvidia Corporation;
the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

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##  .8 Correlation matrices of the experimental measurements

Relevant correlation matrices of the experimental systematic uncertainties in
the measurements of and boson production cross sections, and in their
associated extractions of $\alpS(m_{\PZ})$, are listed in Tables .8–.8 and
.8–.8, respectively.

Experimental systematic uncertainties: Lepton reconstruction and
identification correlation matrix.  7 8 $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$
$\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$
$\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$
$\PW^{+}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 $\PW^{-}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0
0 7 $\PZ_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1 0 0 0
1 1 1 $\PW^{-}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1 0 0 0
1 1 1 $\PW^{+}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 $\PW^{-}_{\Pe}$ 1 1 1 0 0 0 1 1
1 0 0 0 8 $\PZ_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1
0 0 0 1 1 1 $\PW^{-}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1
0 0 0 1 1 1

Experimental systematic uncertainties: Muon trigger inefficiency correlation
matrix [40].  7 8 $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$
$\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$
$\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ 0 0 0 0 0 0 0 0
0 0 0 0 $\PW^{-}_{\Pe}$ 0 0 0 0 0 0 0 0 0 0 0 0 7 $\PZ_{\Pe}$ 0 0 0 0 0 0 0 0
0 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PW^{-}_{\PGm}$ 0 0 0 1
1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PW^{+}_{\Pe}$ 0 0 0 0 0
0 0 0 0 0 0 0 $\PW^{-}_{\Pe}$ 0 0 0 0 0 0 0 0 0 0 0 0 8 $\PZ_{\Pe}$ 0 0 0 0 0
0 0 0 0 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PW^{-}_{\PGm}$ 0
0 0 1 1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1

Experimental systematic uncertainties: Energy and momentum scale and
resolution correlation matrix.  7 8 $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$
$\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$
$\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$
$\PW^{+}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 $\PW^{-}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0
0 7 $\PZ_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1 0 0 0
1 1 1 $\PW^{-}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1 0 0 0
1 1 1 $\PW^{+}_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 $\PW^{-}_{\Pe}$ 1 1 1 0 0 0 1 1
1 0 0 0 8 $\PZ_{\Pe}$ 1 1 1 0 0 0 1 1 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 0 0 0 1 1 1
0 0 0 1 1 1 $\PW^{-}_{\PGm}$ 0 0 0 1 1 1 0 0 0 1 1 1 $\PZ_{\PGm}$ 0 0 0 1 1 1
0 0 0 1 1 1

Experimental systematic uncertainties: Missing $\pt$ scale and resolution
correlation matrix.  7 8 $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$
$\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$
$\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ 1 1
0 1 1 0 1 1 0 1 1 0 $\PW^{-}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1 0 7 $\PZ_{\Pe}$ 0 0
1 0 0 0 0 0 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0
$\PW^{-}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PZ_{\PGm}$ 0 0 0 0 0 1 0 0 1 0 0 1
$\PW^{+}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PW^{-}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1
0 8 $\PZ_{\Pe}$ 0 0 1 0 0 0 0 0 1 0 0 0 TeV $\PW^{+}_{\PGm}$ 1 1 0 1 1 0 1 1 0
1 1 0 $\PW^{-}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PZ_{\PGm}$ 0 0 0 0 0 1 0 0 0
0 0 1

Experimental systematic uncertainties: Background subtraction and modelling
correlation matrix.  7 8 $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$
$\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$
$\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ 1 1
0 1 1 0 1 1 0 1 1 0 $\PW^{-}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1 0 7 $\PZ_{\Pe}$ 0 0
1 0 0 1 0 0 1 0 0 1 TeV $\PW^{+}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0
$\PW^{-}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PZ_{\PGm}$ 0 0 1 0 0 1 0 0 1 0 0 1
$\PW^{+}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PW^{-}_{\Pe}$ 1 1 0 1 1 0 1 1 0 1 1
0 8 $\PZ_{\Pe}$ 0 0 1 0 0 1 0 0 1 0 0 1 TeV $\PW^{+}_{\PGm}$ 1 1 0 1 1 0 1 1 0
1 1 0 $\PW^{-}_{\PGm}$ 1 1 0 1 1 0 1 1 0 1 1 0 $\PZ_{\PGm}$ 0 0 1 0 0 1 0 0 1
0 0 1

Total experimental systematic uncertainties correlations among
$\alpS(m_{\PZ})$ values extracted from all individual measurements at 7 and 8
[13, 14] of the and boson production cross sections.  7 8 $\PW^{+}_{\Pe}$
$\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$ $\PZ_{\PGm}$
$\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$
$\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ 1.000 0.992 0.932 0.097 0.108 0.000 0.974 0.993
0.907 0.109 0.102 0.000 $\PW^{-}_{\Pe}$ 0.992 1.000 0.892 0.133 0.152 0.000
0.945 0.975 0.865 0.124 0.108 0.000 7 $\PZ_{\Pe}$ 0.932 0.892 1.000 0.000
0.000 0.032 0.954 0.936 0.996 0.000 0.000 0.026 TeV $\PW^{+}_{\PGm}$ 0.097
0.133 0.000 1.000 0.996 0.414 0.072 0.084 0.000 0.850 0.821 0.743
$\PW^{-}_{\PGm}$ 0.108 0.152 0.000 0.996 1.000 0.423 0.074 0.090 0.000 0.842
0.809 0.712 $\PZ_{\PGm}$ 0.000 0.000 0.032 0.414 0.423 1.000 0.000 0.000 0.059
0.133 0.145 0.143 $\PW^{+}_{\Pe}$ 0.974 0.945 0.954 0.072 0.074 0.000 1.000
0.991 0.941 0.127 0.132 0.000 $\PW^{-}_{\Pe}$ 0.993 0.975 0.936 0.084 0.090
0.000 0.991 1.000 0.915 0.129 0.130 0.000 8 $\PZ_{\Pe}$ 0.907 0.865 0.996
0.000 0.000 0.059 0.941 0.915 1.000 0.000 0.000 0.048 TeV $\PW^{+}_{\PGm}$
0.109 0.124 0.000 0.850 0.842 0.133 0.127 0.129 0.000 1.000 0.996 0.800
$\PW^{-}_{\PGm}$ 0.102 0.108 0.000 0.821 0.809 0.145 0.132 0.130 0.000 0.996
1.000 0.785 $\PZ_{\PGm}$ 0.000 0.000 0.026 0.743 0.712 0.143 0.000 0.000 0.048
0.800 0.785 1.000

Total experimental and theoretical correlations between all the
$\alpS(m_{\PZ})$ values extracted from all measurements at 7 and 8 [13, 14] of
and boson production cross sections, obtained using the NNPDF3.0 PDF set.  7 8
$\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$ $\PW^{-}_{\PGm}$
$\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ $\PW^{-}_{\Pe}$ $\PZ_{\Pe}$ $\PW^{+}_{\PGm}$
$\PW^{-}_{\PGm}$ $\PZ_{\PGm}$ $\PW^{+}_{\Pe}$ 1.000 0.976 0.933 0.857 0.856
0.818 0.426 0.444 0.360 0.243 0.243 0.161 $\PW^{-}_{\Pe}$ 0.976 1.000 0.938
0.871 0.880 0.835 0.417 0.435 0.353 0.248 0.254 0.168 7 $\PZ_{\Pe}$ 0.933
0.938 1.000 0.797 0.817 0.803 0.443 0.430 0.392 0.210 0.210 0.167 TeV
$\PW^{+}_{\PGm}$ 0.857 0.871 0.797 1.000 0.967 0.893 0.200 0.236 0.189 0.343
0.322 0.289 $\PW^{-}_{\PGm}$ 0.856 0.880 0.817 0.967 1.000 0.908 0.222 0.239
0.198 0.339 0.328 0.292 $\PZ_{\PGm}$ 0.818 0.835 0.803 0.893 0.908 1.000 0.177
0.201 0.195 0.242 0.246 0.199 $\PW^{+}_{\Pe}$ 0.426 0.417 0.443 0.200 0.222
0.177 1.000 0.940 0.794 0.664 0.685 0.467 $\PW^{-}_{\Pe}$ 0.444 0.435 0.430
0.236 0.239 0.201 0.940 1.000 0.816 0.730 0.761 0.520 8 $\PZ_{\Pe}$ 0.360
0.353 0.392 0.189 0.198 0.195 0.794 0.816 1.000 0.612 0.643 0.472 TeV
$\PW^{+}_{\PGm}$ 0.243 0.248 0.210 0.343 0.339 0.242 0.664 0.730 0.612 1.000
0.934 0.740 $\PW^{-}_{\PGm}$ 0.243 0.254 0.210 0.322 0.328 0.246 0.685 0.761
0.643 0.934 1.000 0.729 $\PZ_{\PGm}$ 0.161 0.168 0.167 0.289 0.292 0.199 0.467
0.520 0.472 0.740 0.729 1.000

##  .9 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan${}^{\textrm{\textdagger}}$, A. Tumasyan Institut für
Hochenergiephysik, Wien, Austria
W. Adam, F. Ambrogi, T. Bergauer, M. Dragicevic, J. Erö, A. Escalante Del
Valle, M. Flechl, R. Frühwirth1, M. Jeitler1, N. Krammer, I. Krätschmer, D.
Liko, T. Madlener, I. Mikulec, N. Rad, J. Schieck1, R. Schöfbeck, M. Spanring,
W. Waltenberger, C.-E. Wulz1, M. Zarucki Institute for Nuclear Problems,
Minsk, Belarus
V. Drugakov, V. Mossolov, J. Suarez Gonzalez Universiteit Antwerpen,
Antwerpen, Belgium
M.R. Darwish, E.A. De Wolf, D. Di Croce, X. Janssen, A. Lelek, M. Pieters, H.
Rejeb Sfar, H. Van Haevermaet, P. Van Mechelen, S. Van Putte, N. Van Remortel
Vrije Universiteit Brussel, Brussel, Belgium
F. Blekman, E.S. Bols, S.S. Chhibra, J. D’Hondt, J. De Clercq, D. Lontkovskyi,
S. Lowette, I. Marchesini, S. Moortgat, Q. Python, S. Tavernier, W. Van
Doninck, P. Van Mulders Université Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, B. Clerbaux, G. De Lentdecker, H. Delannoy, B. Dorney, L.
Favart, A. Grebenyuk, A.K. Kalsi, L. Moureaux, A. Popov, N. Postiau, E.
Starling, L. Thomas, C. Vander Velde, P. Vanlaer, D. Vannerom Ghent
University, Ghent, Belgium
T. Cornelis, D. Dobur, I. Khvastunov2, M. Niedziela, C. Roskas, K. Skovpen, M.
Tytgat, W. Verbeke, B. Vermassen, M. Vit Université Catholique de Louvain,
Louvain-la-Neuve, Belgium
O. Bondu, G. Bruno, C. Caputo, P. David, C. Delaere, M. Delcourt, A.
Giammanco, V. Lemaitre, J. Prisciandaro, A. Saggio, M. Vidal Marono, P.
Vischia, J. Zobec Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro,
Brazil
G.A. Alves, G. Correia Silva, C. Hensel, A. Moraes Universidade do Estado do
Rio de Janeiro, Rio de Janeiro, Brazil
E. Belchior Batista Das Chagas, W. Carvalho, J. Chinellato3, E. Coelho, E.M.
Da Costa, G.G. Da Silveira4, D. De Jesus Damiao, C. De Oliveira Martins, S.
Fonseca De Souza, L.M. Huertas Guativa, H. Malbouisson, J. Martins5, D. Matos
Figueiredo, M. Medina Jaime6, M. Melo De Almeida, C. Mora Herrera, L. Mundim,
H. Nogima, W.L. Prado Da Silva, P. Rebello Teles, L.J. Sanchez Rosas, A.
Santoro, A. Sznajder, M. Thiel, E.J. Tonelli Manganote3, F. Torres Da Silva De
Araujo, A. Vilela Pereira Universidade Estadual Paulista a, Universidade
Federal do ABC b, São Paulo, Brazil
C.A. Bernardesa, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M. Gregoresb,
D.S. Lemos, P.G. Mercadanteb, S.F. Novaesa, SandraS. Padulaa Institute for
Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia,
Bulgaria
A. Aleksandrov, G. Antchev, R. Hadjiiska, P. Iaydjiev, M. Misheva, M. Rodozov,
M. Shopova, G. Sultanov University of Sofia, Sofia, Bulgaria
M. Bonchev, A. Dimitrov, T. Ivanov, L. Litov, B. Pavlov, P. Petkov, A. Petrov
Beihang University, Beijing, China
W. Fang7, X. Gao7, L. Yuan Department of Physics, Tsinghua University,
Beijing, China
M. Ahmad, Z. Hu, Y. Wang Institute of High Energy Physics, Beijing, China
G.M. Chen8, H.S. Chen8, M. Chen, C.H. Jiang, D. Leggat, H. Liao, Z. Liu, A.
Spiezia, J. Tao, E. Yazgan, H. Zhang, S. Zhang8, J. Zhao State Key Laboratory
of Nuclear Physics and Technology, Peking University, Beijing, China
A. Agapitos, Y. Ban, G. Chen, A. Levin, J. Li, L. Li, Q. Li, Y. Mao, S.J.
Qian, D. Wang, Q. Wang Zhejiang University, Hangzhou, China
M. Xiao Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C. Florez, C.F. González Hernández, M.A. Segura Delgado
Universidad de Antioquia, Medellin, Colombia
J. Mejia Guisao, J.D. Ruiz Alvarez, C.A. Salazar González, N. Vanegas Arbelaez
University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia
D. Giljanović, N. Godinovic, D. Lelas, I. Puljak, T. Sculac University of
Split, Faculty of Science, Split, Croatia
Z. Antunovic, M. Kovac Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, K. Kadija, B. Mesic, M. Roguljic, A. Starodumov9,
T. Susa University of Cyprus, Nicosia, Cyprus
M.W. Ather, A. Attikis, E. Erodotou, A. Ioannou, M. Kolosova, S. Konstantinou,
G. Mavromanolakis, J. Mousa, C. Nicolaou, F. Ptochos, P.A. Razis, H.
Rykaczewski, H. Saka, D. Tsiakkouri Charles University, Prague, Czech Republic
M. Finger10, M. Finger Jr.10, A. Kveton, J. Tomsa Escuela Politecnica
Nacional, Quito, Ecuador
E. Ayala Universidad San Francisco de Quito, Quito, Ecuador
E. Carrera Jarrin Academy of Scientific Research and Technology of the Arab
Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
Y. Assran11,12, S. Elgammal12 National Institute of Chemical Physics and
Biophysics, Tallinn, Estonia
S. Bhowmik, A. Carvalho Antunes De Oliveira, R.K. Dewanjee, K. Ehataht, M.
Kadastik, A. Poldaru, M. Raidal, C. Veelken Department of Physics, University
of Helsinki, Helsinki, Finland
P. Eerola, L. Forthomme, H. Kirschenmann, K. Osterberg, M. Voutilainen
Helsinki Institute of Physics, Helsinki, Finland
F. Garcia, J. Havukainen, J.K. Heikkilä, V. Karimäki, M.S. Kim, R. Kinnunen,
T. Lampén, K. Lassila-Perini, S. Laurila, S. Lehti, T. Lindén, H. Siikonen, E.
Tuominen, J. Tuominiemi Lappeenranta University of Technology, Lappeenranta,
Finland
P. Luukka, T. Tuuva IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
M. Besancon, F. Couderc, M. Dejardin, D. Denegri, B. Fabbro, J.L. Faure, F.
Ferri, S. Ganjour, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry,
C. Leloup, B. Lenzi, E. Locci, J. Malcles, J. Rander, A. Rosowsky, M.Ö. Sahin,
A. Savoy-Navarro13, M. Titov, G.B. Yu Laboratoire Leprince-Ringuet,
CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris
S. Ahuja, C. Amendola, F. Beaudette, P. Busson, C. Charlot, B. Diab, G.
Falmagne, R. Granier de Cassagnac, I. Kucher, A. Lobanov, C. Martin Perez, M.
Nguyen, C. Ochando, P. Paganini, J. Rembser, R. Salerno, J.B. Sauvan, Y.
Sirois, A. Zabi, A. Zghiche Université de Strasbourg, CNRS, IPHC UMR 7178,
Strasbourg, France
J.-L. Agram14, J. Andrea, D. Bloch, G. Bourgatte, J.-M. Brom, E.C. Chabert, C.
Collard, E. Conte14, J.-C. Fontaine14, D. Gelé, U. Goerlach, C. Grimault, M.
Jansová, A.-C. Le Bihan, N. Tonon, P. Van Hove Centre de Calcul de l’Institut
National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3,
Villeurbanne, France
S. Gadrat Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3,
Institut de Physique Nucléaire de Lyon, Villeurbanne, France
S. Beauceron, C. Bernet, G. Boudoul, C. Camen, A. Carle, N. Chanon, R.
Chierici, D. Contardo, P. Depasse, H. El Mamouni, J. Fay, S. Gascon, M.
Gouzevitch, B. Ille, Sa. Jain, I.B. Laktineh, H. Lattaud, A. Lesauvage, M.
Lethuillier, L. Mirabito, S. Perries, V. Sordini, L. Torterotot, G. Touquet,
M. Vander Donckt, S. Viret Georgian Technical University, Tbilisi, Georgia
G. Adamov Tbilisi State University, Tbilisi, Georgia
Z. Tsamalaidze10 RWTH Aachen University, I. Physikalisches Institut, Aachen,
Germany
C. Autermann, L. Feld, K. Klein, M. Lipinski, D. Meuser, A. Pauls, M. Preuten,
M.P. Rauch, J. Schulz, M. Teroerde RWTH Aachen University, III. Physikalisches
Institut A, Aachen, Germany
M. Erdmann, B. Fischer, S. Ghosh, T. Hebbeker, K. Hoepfner, H. Keller, L.
Mastrolorenzo, M. Merschmeyer, A. Meyer, P. Millet, G. Mocellin, S. Mondal, S.
Mukherjee, D. Noll, A. Novak, T. Pook, A. Pozdnyakov, T. Quast, M. Radziej, Y.
Rath, H. Reithler, J. Roemer, A. Schmidt, S.C. Schuler, A. Sharma, S.
Wiedenbeck, S. Zaleski RWTH Aachen University, III. Physikalisches Institut B,
Aachen, Germany
G. Flügge, W. Haj Ahmad15, O. Hlushchenko, T. Kress, T. Müller, A. Nowack, C.
Pistone, O. Pooth, D. Roy, H. Sert, A. Stahl16 Deutsches Elektronen-
Synchrotron, Hamburg, Germany
M. Aldaya Martin, P. Asmuss, I. Babounikau, H. Bakhshiansohi, K. Beernaert, O.
Behnke, A. Bermúdez Martínez, A.A. Bin Anuar, K. Borras17, V. Botta, A.
Campbell, A. Cardini, P. Connor, S. Consuegra Rodríguez, C. Contreras-Campana,
V. Danilov, A. De Wit, M.M. Defranchis, C. Diez Pardos, D. Domínguez Damiani,
G. Eckerlin, D. Eckstein, T. Eichhorn, A. Elwood, E. Eren, E. Gallo18, A.
Geiser, A. Grohsjean, M. Guthoff, M. Haranko, A. Harb, A. Jafari, N.Z.
Jomhari, H. Jung, A. Kasem17, M. Kasemann, H. Kaveh, J. Keaveney, C.
Kleinwort, J. Knolle, D. Krücker, W. Lange, T. Lenz, J. Lidrych, W. Lohmann19,
R. Mankel, I.-A. Melzer-Pellmann, A.B. Meyer, M. Meyer, M. Missiroli, J.
Mnich, A. Mussgiller, V. Myronenko, D. Pérez Adán, S.K. Pflitsch, D. Pitzl, A.
Raspereza, A. Saibel, M. Savitskyi, V. Scheurer, P. Schütze, C.
Schwanenberger, R. Shevchenko, A. Singh, R.E. Sosa Ricardo, H. Tholen, O.
Turkot, A. Vagnerini, M. Van De Klundert, R. Walsh, Y. Wen, K. Wichmann, C.
Wissing, O. Zenaiev, R. Zlebcik University of Hamburg, Hamburg, Germany
R. Aggleton, S. Bein, L. Benato, A. Benecke, T. Dreyer, A. Ebrahimi, F.
Feindt, A. Fröhlich, C. Garbers, E. Garutti, D. Gonzalez, P. Gunnellini, J.
Haller, A. Hinzmann, A. Karavdina, G. Kasieczka, R. Klanner, R. Kogler, N.
Kovalchuk, S. Kurz, V. Kutzner, J. Lange, T. Lange, A. Malara, J. Multhaup,
C.E.N. Niemeyer, A. Reimers, O. Rieger, P. Schleper, S. Schumann, J. Schwandt,
J. Sonneveld, H. Stadie, G. Steinbrück, B. Vormwald, I. Zoi Karlsruher
Institut fuer Technologie, Karlsruhe, Germany
M. Akbiyik, M. Baselga, S. Baur, T. Berger, E. Butz, R. Caspart, T. Chwalek,
W. De Boer, A. Dierlamm, K. El Morabit, N. Faltermann, M. Giffels, A.
Gottmann, F. Hartmann16, C. Heidecker, U. Husemann, S. Kudella, S. Maier, S.
Mitra, M.U. Mozer, D. Müller, Th. Müller, M. Musich, A. Nürnberg, G. Quast, K.
Rabbertz, D. Schäfer, M. Schröder, I. Shvetsov, H.J. Simonis, R. Ulrich, M.
Wassmer, M. Weber, C. Wöhrmann, R. Wolf, S. Wozniewski Institute of Nuclear
and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Anagnostou, P. Asenov, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas,
G. Paspalaki National and Kapodistrian University of Athens, Athens, Greece
M. Diamantopoulou, G. Karathanasis, P. Kontaxakis, A. Manousakis-katsikakis,
A. Panagiotou, I. Papavergou, N. Saoulidou, A. Stakia, K. Theofilatos, K.
Vellidis, E. Vourliotis National Technical University of Athens, Athens,
Greece
G. Bakas, K. Kousouris, I. Papakrivopoulos, G. Tsipolitis, A. Zacharopoulou
University of Ioánnina, Ioánnina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, S. Mallios, K.
Manitara, N. Manthos, I. Papadopoulos, J. Strologas, F.A. Triantis, D.
Tsitsonis MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
M. Bartók20, R. Chudasama, M. Csanad, P. Major, K. Mandal, A. Mehta, G.
Pasztor, O. Surányi, G.I. Veres Wigner Research Centre for Physics, Budapest,
Hungary
G. Bencze, C. Hajdu, D. Horvath21, F. Sikler, V. Veszpremi, G.
Vesztergombi${}^{\textrm{\textdagger}}$ Institute of Nuclear Research ATOMKI,
Debrecen, Hungary
N. Beni, S. Czellar, J. Karancsi20, J. Molnar, Z. Szillasi Institute of
Physics, University of Debrecen, Debrecen, Hungary
P. Raics, D. Teyssier, Z.L. Trocsanyi, B. Ujvari Eszterhazy Karoly University,
Karoly Robert Campus, Gyongyos, Hungary
T. Csorgo, W.J. Metzger, F. Nemes, T. Novak Indian Institute of Science
(IISc), Bangalore, India
S. Choudhury, J.R. Komaragiri, P.C. Tiwari National Institute of Science
Education and Research, HBNI, Bhubaneswar, India
S. Bahinipati23, C. Kar, G. Kole, P. Mal, V.K. Muraleedharan Nair Bindhu, A.
Nayak24, D.K. Sahoo23, S.K. Swain Panjab University, Chandigarh, India
S. Bansal, S.B. Beri, V. Bhatnagar, S. Chauhan, N. Dhingra25, R. Gupta, A.
Kaur, M. Kaur, S. Kaur, P. Kumari, M. Lohan, M. Meena, K. Sandeep, S. Sharma,
J.B. Singh, A.K. Virdi University of Delhi, Delhi, India
A. Bhardwaj, B.C. Choudhary, R.B. Garg, M. Gola, S. Keshri, Ashok Kumar, M.
Naimuddin, P. Priyanka, K. Ranjan, Aashaq Shah, R. Sharma Saha Institute of
Nuclear Physics, HBNI, Kolkata, India
R. Bhardwaj26, M. Bharti26, R. Bhattacharya, S. Bhattacharya, U. Bhawandeep26,
D. Bhowmik, S. Dutta, S. Ghosh, B. Gomber27, M. Maity28, K. Mondal, S. Nandan,
A. Purohit, P.K. Rout, G. Saha, S. Sarkar, T. Sarkar28, M. Sharan, B. Singh26,
S. Thakur26 Indian Institute of Technology Madras, Madras, India
P.K. Behera, S.C. Behera, P. Kalbhor, A. Muhammad, P.R. Pujahari, A. Sharma,
A.K. Sikdar Bhabha Atomic Research Centre, Mumbai, India
D. Dutta, V. Jha, D.K. Mishra, P.K. Netrakanti, L.M. Pant, P. Shukla Tata
Institute of Fundamental Research-A, Mumbai, India
T. Aziz, M.A. Bhat, S. Dugad, G.B. Mohanty, N. Sur, RavindraKumar Verma Tata
Institute of Fundamental Research-B, Mumbai, India
S. Banerjee, S. Bhattacharya, S. Chatterjee, P. Das, M. Guchait, S. Karmakar,
S. Kumar, G. Majumder, K. Mazumdar, N. Sahoo, S. Sawant Indian Institute of
Science Education and Research (IISER), Pune, India
S. Dube, B. Kansal, A. Kapoor, K. Kothekar, S. Pandey, A. Rane, A. Rastogi, S.
Sharma Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
S. Chenarani, S.M. Etesami, M. Khakzad, M. Mohammadi Najafabadi, M. Naseri, F.
Rezaei Hosseinabadi University College Dublin, Dublin, Ireland
M. Felcini, M. Grunewald INFN Sezione di Bari a, Università di Bari b,
Politecnico di Bari c, Bari, Italy
M. Abbresciaa,b, R. Alya,b,29, C. Calabriaa,b, A. Colaleoa, D. Creanzaa,c, L.
Cristellaa,b, N. De Filippisa,c, M. De Palmaa,b, A. Di Florioa,b, W.
Elmetenaweea,b, L. Fiorea, A. Gelmia,b, G. Iasellia,c, M. Incea,b, S.
Lezkia,b, G. Maggia,c, M. Maggia, J.A. Merlina, G. Minielloa,b, S. Mya,b, S.
Nuzzoa,b, A. Pompilia,b, G. Pugliesea,c, R. Radognaa, A. Ranieria, G.
Selvaggia,b, L. Silvestrisa, F.M. Simonea,b, R. Vendittia, P. Verwilligena
INFN Sezione di Bologna a, Università di Bologna b, Bologna, Italy
G. Abbiendia, C. Battilanaa,b, D. Bonacorsia,b, L. Borgonovia,b, S. Braibant-
Giacomellia,b, R. Campaninia,b, P. Capiluppia,b, A. Castroa,b, F.R. Cavalloa,
C. Cioccaa, G. Codispotia,b, M. Cuffiania,b, G.M. Dallavallea, F. Fabbria, A.
Fanfania,b, E. Fontanesia,b, P. Giacomellia, C. Grandia, L. Guiduccia,b, F.
Iemmia,b, S. Lo Meoa,30, S. Marcellinia, G. Masettia, F.L. Navarriaa,b, A.
Perrottaa, F. Primaveraa,b, A.M. Rossia,b, T. Rovellia,b, G.P. Sirolia,b, N.
Tosia INFN Sezione di Catania a, Università di Catania b, Catania, Italy
S. Albergoa,b,31, S. Costaa,b, A. Di Mattiaa, R. Potenzaa,b, A. Tricomia,b,31,
C. Tuvea,b INFN Sezione di Firenze a, Università di Firenze b, Firenze, Italy
G. Barbaglia, A. Cassese, R. Ceccarelli, V. Ciullia,b, C. Civininia, R.
D’Alessandroa,b, F. Fioria,c, E. Focardia,b, G. Latinoa,b, P. Lenzia,b, M.
Meschinia, S. Paolettia, G. Sguazzonia, L. Viliania INFN Laboratori Nazionali
di Frascati, Frascati, Italy
L. Benussi, S. Bianco, D. Piccolo INFN Sezione di Genova a, Università di
Genova b, Genova, Italy
M. Bozzoa,b, F. Ferroa, R. Mulargiaa,b, E. Robuttia, S. Tosia,b INFN Sezione
di Milano-Bicocca a, Università di Milano-Bicocca b, Milano, Italy
A. Benagliaa, A. Beschia,b, F. Brivioa,b, V. Cirioloa,b,16, M.E. Dinardoa,b,
P. Dinia, S. Gennaia, A. Ghezzia,b, P. Govonia,b, L. Guzzia,b, M. Malbertia,
S. Malvezzia, D. Menascea, F. Montia,b, L. Moronia, M. Paganonia,b, D.
Pedrinia, S. Ragazzia,b, T. Tabarelli de Fatisa,b, D. Valsecchia,b, D.
Zuoloa,b INFN Sezione di Napoli a, Università di Napoli ’Federico II’ b,
Napoli, Italy, Università della Basilicata c, Potenza, Italy, Università G.
Marconi d, Roma, Italy
S. Buontempoa, N. Cavalloa,c, A. De Iorioa,b, A. Di Crescenzoa,b, F.
Fabozzia,c, F. Fiengaa, G. Galatia, A.O.M. Iorioa,b, L. Layera,b, L. Listaa,b,
S. Meolaa,d,16, P. Paoluccia,16, B. Rossia, C. Sciaccaa,b, E. Voevodinaa,b
INFN Sezione di Padova a, Università di Padova b, Padova, Italy, Università di
Trento c, Trento, Italy
P. Azzia, N. Bacchettaa, D. Biselloa,b, A. Bolettia,b, A. Bragagnoloa,b, R.
Carlina,b, P. Checchiaa, P. De Castro Manzanoa, T. Dorigoa, U. Dossellia, F.
Gasparinia,b, U. Gasparinia,b, A. Gozzelinoa, S.Y. Hoha,b, M. Margonia,b, A.T.
Meneguzzoa,b, J. Pazzinia,b, M. Presillab, P. Ronchesea,b, R. Rossina,b, F.
Simonettoa,b, A. Tikoa, M. Tosia,b, M. Zanettia,b, P. Zottoa,b, A.
Zucchettaa,b, G. Zumerlea,b INFN Sezione di Pavia a, Università di Pavia b,
Pavia, Italy
A. Braghieria, D. Fiorinaa,b, P. Montagnaa,b, S.P. Rattia,b, V. Rea, M.
Ressegottia,b, C. Riccardia,b, P. Salvinia, I. Vaia, P. Vituloa,b INFN Sezione
di Perugia a, Università di Perugia b, Perugia, Italy
M. Biasinia,b, G.M. Bileia, D. Ciangottinia,b, L. Fanòa,b, P. Laricciaa,b, R.
Leonardia,b, E. Manonia, G. Mantovania,b, V. Mariania,b, M. Menichellia, A.
Rossia,b, A. Santocchiaa,b, D. Spigaa INFN Sezione di Pisa a, Università di
Pisa b, Scuola Normale Superiore di Pisa c, Pisa, Italy
K. Androsova, P. Azzurria, G. Bagliesia, V. Bertacchia,c, L. Bianchinia, T.
Boccalia, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa, S. Donatoa, L.
Gianninia,c, A. Giassia, M.T. Grippoa, F. Ligabuea,c, E. Mancaa,c, G.
Mandorlia,c, A. Messineoa,b, F. Pallaa, A. Rizzia,b, G. Rolandi32, S. Roy
Chowdhury, A. Scribanoa, P. Spagnoloa, R. Tenchinia, G. Tonellia,b, N. Turini,
A. Venturia, P.G. Verdinia INFN Sezione di Roma a, Sapienza Università di Roma
b, Rome, Italy
F. Cavallaria, M. Cipriania,b, D. Del Rea,b, E. Di Marcoa, M. Diemoza, E.
Longoa,b, P. Meridiania, G. Organtinia,b, F. Pandolfia, R. Paramattia,b, C.
Quarantaa,b, S. Rahatloua,b, C. Rovellia, F. Santanastasioa,b, L. Soffia,b
INFN Sezione di Torino a, Università di Torino b, Torino, Italy, Università
del Piemonte Orientale c, Novara, Italy
N. Amapanea,b, R. Arcidiaconoa,c, S. Argiroa,b, M. Arneodoa,c, N. Bartosika,
R. Bellana,b, A. Bellora, C. Biinoa, A. Cappatia,b, N. Cartigliaa, S.
Comettia, M. Costaa,b, R. Covarellia,b, N. Demariaa, B. Kiania,b, F. Legger,
C. Mariottia, S. Masellia, E. Migliorea,b, V. Monacoa,b, E. Monteila,b, M.
Montenoa, M.M. Obertinoa,b, G. Ortonaa,b, L. Pachera,b, N. Pastronea, M.
Pelliccionia, G.L. Pinna Angionia,b, A. Romeroa,b, M. Ruspaa,c, R.
Salvaticoa,b, V. Solaa, A. Solanoa,b, D. Soldia,b, A. Staianoa, D. Trocinoa,b
INFN Sezione di Trieste a, Università di Trieste b, Trieste, Italy
S. Belfortea, V. Candelisea,b, M. Casarsaa, F. Cossuttia, A. Da Rolda,b, G.
Della Riccaa,b, F. Vazzolera,b, A. Zanettia Kyungpook National University,
Daegu, Korea
B. Kim, D.H. Kim, G.N. Kim, J. Lee, S.W. Lee, C.S. Moon, Y.D. Oh, S.I. Pak, S.
Sekmen, D.C. Son, Y.C. Yang Chonnam National University, Institute for
Universe and Elementary Particles, Kwangju, Korea
H. Kim, D.H. Moon, G. Oh Hanyang University, Seoul, Korea
B. Francois, T.J. Kim, J. Park Korea University, Seoul, Korea
S. Cho, S. Choi, Y. Go, S. Ha, B. Hong, K. Lee, K.S. Lee, J. Lim, J. Park,
S.K. Park, Y. Roh, J. Yoo Kyung Hee University, Department of Physics
J. Goh Sejong University, Seoul, Korea
H.S. Kim Seoul National University, Seoul, Korea
J. Almond, J.H. Bhyun, J. Choi, S. Jeon, J. Kim, J.S. Kim, H. Lee, K. Lee, S.
Lee, K. Nam, M. Oh, S.B. Oh, B.C. Radburn-Smith, U.K. Yang, H.D. Yoo, I. Yoon
University of Seoul, Seoul, Korea
D. Jeon, J.H. Kim, J.S.H. Lee, I.C. Park, I.J Watson Sungkyunkwan University,
Suwon, Korea
Y. Choi, C. Hwang, Y. Jeong, J. Lee, Y. Lee, I. Yu Riga Technical University,
Riga, Latvia
V. Veckalns33 Vilnius University, Vilnius, Lithuania
V. Dudenas, A. Juodagalvis, A. Rinkevicius, G. Tamulaitis, J. Vaitkus National
Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
F. Mohamad Idris34, W.A.T. Wan Abdullah, M.N. Yusli, Z. Zolkapli Universidad
de Sonora (UNISON), Hermosillo, Mexico
J.F. Benitez, A. Castaneda Hernandez, J.A. Murillo Quijada, L. Valencia Palomo
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
H. Castilla-Valdez, E. De La Cruz-Burelo, I. Heredia-De La Cruz35, R. Lopez-
Fernandez, A. Sanchez-Hernandez Universidad Iberoamericana, Mexico City,
Mexico
S. Carrillo Moreno, C. Oropeza Barrera, M. Ramirez-Garcia, F. Vazquez Valencia
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
J. Eysermans, I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada Universidad
Autónoma de San Luis Potosí, San Luis Potosí, Mexico
A. Morelos Pineda University of Montenegro, Podgorica, Montenegro
J. Mijuskovic2, N. Raicevic University of Auckland, Auckland, New Zealand
D. Krofcheck University of Canterbury, Christchurch, New Zealand
S. Bheesette, P.H. Butler, P. Lujan National Centre for Physics, Quaid-I-Azam
University, Islamabad, Pakistan
A. Ahmad, M. Ahmad, M.I.M. Awan, Q. Hassan, H.R. Hoorani, W.A. Khan, M.A.
Shah, M. Shoaib, M. Waqas AGH University of Science and Technology Faculty of
Computer Science, Electronics and Telecommunications, Krakow, Poland
V. Avati, L. Grzanka, M. Malawski National Centre for Nuclear Research,
Swierk, Poland
H. Bialkowska, M. Bluj, B. Boimska, M. Górski, M. Kazana, M. Szleper, P.
Zalewski Institute of Experimental Physics, Faculty of Physics, University of
Warsaw, Warsaw, Poland
K. Bunkowski, A. Byszuk36, K. Doroba, A. Kalinowski, M. Konecki, J.
Krolikowski, M. Olszewski, M. Walczak Laboratório de Instrumentação e Física
Experimental de Partículas, Lisboa, Portugal
M. Araujo, P. Bargassa, D. Bastos, A. Di Francesco, P. Faccioli, B. Galinhas,
M. Gallinaro, J. Hollar, N. Leonardo, T. Niknejad, J. Seixas, K. Shchelina, G.
Strong, O. Toldaiev, J. Varela Joint Institute for Nuclear Research, Dubna,
Russia
S. Afanasiev, P. Bunin, M. Gavrilenko, I. Golutvin, I. Gorbunov, A. Kamenev,
V. Karjavine, A. Lanev, A. Malakhov, V. Matveev37,38, P. Moisenz, V. Palichik,
V. Perelygin, M. Savina, S. Shmatov, S. Shulha, N. Skatchkov, V. Smirnov, N.
Voytishin, A. Zarubin Petersburg Nuclear Physics Institute, Gatchina (St.
Petersburg), Russia
L. Chtchipounov, V. Golovtcov, Y. Ivanov, V. Kim39, E. Kuznetsova40, P.
Levchenko, V. Murzin, V. Oreshkin, I. Smirnov, D. Sosnov, V. Sulimov, L.
Uvarov, A. Vorobyev Institute for Nuclear Research, Moscow, Russia
Yu. Andreev, A. Dermenev, S. Gninenko, N. Golubev, A. Karneyeu, M. Kirsanov,
N. Krasnikov, A. Pashenkov, D. Tlisov, A. Toropin Institute for Theoretical
and Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’,
Moscow, Russia
V. Epshteyn, V. Gavrilov, N. Lychkovskaya, A. Nikitenko41, V. Popov, I.
Pozdnyakov, G. Safronov, A. Spiridonov, A. Stepennov, M. Toms, E. Vlasov, A.
Zhokin Moscow Institute of Physics and Technology, Moscow, Russia
T. Aushev National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
P. Parygin, D. Philippov, E. Popova, V. Rusinov, E. Zhemchugov P.N. Lebedev
Physical Institute, Moscow, Russia
V. Andreev, M. Azarkin, I. Dremin, M. Kirakosyan, A. Terkulov Skobeltsyn
Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow,
Russia
A. Belyaev, E. Boos, M. Dubinin42, L. Dudko, A. Ershov, A. Gribushin, V.
Klyukhin, O. Kodolova, I. Lokhtin, S. Obraztsov, S. Petrushanko, V. Savrin, A.
Snigirev Novosibirsk State University (NSU), Novosibirsk, Russia
A. Barnyakov43, V. Blinov43, T. Dimova43, L. Kardapoltsev43, Y. Skovpen43
Institute for High Energy Physics of National Research Centre ‘Kurchatov
Institute’, Protvino, Russia
I. Azhgirey, I. Bayshev, S. Bitioukov, V. Kachanov, D. Konstantinov, P.
Mandrik, V. Petrov, R. Ryutin, S. Slabospitskii, A. Sobol, S. Troshin, N.
Tyurin, A. Uzunian, A. Volkov National Research Tomsk Polytechnic University,
Tomsk, Russia
A. Babaev, A. Iuzhakov, V. Okhotnikov Tomsk State University, Tomsk, Russia
V. Borchsh, V. Ivanchenko, E. Tcherniaev University of Belgrade: Faculty of
Physics and VINCA Institute of Nuclear Sciences
P. Adzic44, P. Cirkovic, M. Dordevic, P. Milenovic, J. Milosevic, M.
Stojanovic Centro de Investigaciones Energéticas Medioambientales y
Tecnológicas (CIEMAT), Madrid, Spain
M. Aguilar-Benitez, J. Alcaraz Maestre, A. Álvarez Fernández, I. Bachiller, M.
Barrio Luna, CristinaF. Bedoya, J.A. Brochero Cifuentes, C.A. Carrillo
Montoya, M. Cepeda, M. Cerrada, N. Colino, B. De La Cruz, A. Delgado Peris,
J.P. Fernández Ramos, J. Flix, M.C. Fouz, O. Gonzalez Lopez, S. Goy Lopez,
J.M. Hernandez, M.I. Josa, D. Moran, Á. Navarro Tobar, A. Pérez-Calero
Yzquierdo, J. Puerta Pelayo, I. Redondo, L. Romero, S. Sánchez Navas, M.S.
Soares, A. Triossi, C. Willmott Universidad Autónoma de Madrid, Madrid, Spain
C. Albajar, J.F. de Trocóniz, R. Reyes-Almanza Universidad de Oviedo,
Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias
(ICTEA), Oviedo, Spain
B. Alvarez Gonzalez, J. Cuevas, C. Erice, J. Fernandez Menendez, S. Folgueras,
I. Gonzalez Caballero, J.R. González Fernández, E. Palencia Cortezon, C. Ramón
Álvarez, V. Rodríguez Bouza, S. Sanchez Cruz Instituto de Física de Cantabria
(IFCA), CSIC-Universidad de Cantabria, Santander, Spain
I.J. Cabrillo, A. Calderon, B. Chazin Quero, J. Duarte Campderros, M.
Fernandez, P.J. Fernández Manteca, A. García Alonso, G. Gomez, C. Martinez
Rivero, P. Martinez Ruiz del Arbol, F. Matorras, J. Piedra Gomez, C. Prieels,
F. Ricci-Tam, T. Rodrigo, A. Ruiz-Jimeno, L. Russo45, L. Scodellaro, I. Vila,
J.M. Vizan Garcia University of Colombo, Colombo, Sri Lanka
K. Malagalage University of Ruhuna, Department of Physics, Matara, Sri Lanka
W.G.D. Dharmaratna, N. Wickramage CERN, European Organization for Nuclear
Research, Geneva, Switzerland
D. Abbaneo, B. Akgun, E. Auffray, G. Auzinger, J. Baechler, P. Baillon, A.H.
Ball, D. Barney, J. Bendavid, M. Bianco, A. Bocci, P. Bortignon, E. Bossini,
E. Brondolin, T. Camporesi, A. Caratelli, G. Cerminara, E. Chapon, G.
Cucciati, D. d’Enterria, A. Dabrowski, N. Daci, V. Daponte, A. David, O.
Davignon, A. De Roeck, M. Deile, R. Di Maria, M. Dobson, M. Dünser, N. Dupont,
A. Elliott-Peisert, N. Emriskova, F. Fallavollita46, D. Fasanella, S.
Fiorendi, G. Franzoni, J. Fulcher, W. Funk, S. Giani, D. Gigi, K. Gill, F.
Glege, L. Gouskos, M. Gruchala, M. Guilbaud, D. Gulhan, J. Hegeman, C.
Heidegger, Y. Iiyama, V. Innocente, T. James, P. Janot, O. Karacheban19, J.
Kaspar, J. Kieseler, M. Krammer1, N. Kratochwil, C. Lange, P. Lecoq, C.
Lourenço, L. Malgeri, M. Mannelli, A. Massironi, F. Meijers, S. Mersi, E.
Meschi, F. Moortgat, M. Mulders, J. Ngadiuba, J. Niedziela, S. Nourbakhsh, S.
Orfanelli, L. Orsini, F. Pantaleo16, L. Pape, E. Perez, M. Peruzzi, A.
Petrilli, G. Petrucciani, A. Pfeiffer, M. Pierini, F.M. Pitters, D. Rabady, A.
Racz, M. Rieger, M. Rovere, H. Sakulin, J. Salfeld-Nebgen, S. Scarfi, C.
Schäfer, C. Schwick, M. Selvaggi, A. Sharma, P. Silva, W. Snoeys, P.
Sphicas47, J. Steggemann, S. Summers, V.R. Tavolaro, D. Treille, A. Tsirou,
G.P. Van Onsem, A. Vartak, M. Verzetti, W. Xiao, W.D. Zeuner Paul Scherrer
Institut, Villigen, Switzerland
L. Caminada48, K. Deiters, W. Erdmann, R. Horisberger, Q. Ingram, H.C.
Kaestli, D. Kotlinski, U. Langenegger, T. Rohe ETH Zurich - Institute for
Particle Physics and Astrophysics (IPA), Zurich, Switzerland
M. Backhaus, P. Berger, N. Chernyavskaya, G. Dissertori, M. Dittmar, M.
Donegà, C. Dorfer, T.A. Gómez Espinosa, C. Grab, D. Hits, W. Lustermann, R.A.
Manzoni, M.T. Meinhard, F. Micheli, P. Musella, F. Nessi-Tedaldi, F. Pauss, G.
Perrin, L. Perrozzi, S. Pigazzini, M.G. Ratti, M. Reichmann, C. Reissel, T.
Reitenspiess, B. Ristic, D. Ruini, D.A. Sanz Becerra, M. Schönenberger, L.
Shchutska, M.L. Vesterbacka Olsson, R. Wallny, D.H. Zhu Universität Zürich,
Zurich, Switzerland
T.K. Aarrestad, C. Amsler49, C. Botta, D. Brzhechko, M.F. Canelli, A. De Cosa,
R. Del Burgo, B. Kilminster, S. Leontsinis, V.M. Mikuni, I. Neutelings, G.
Rauco, P. Robmann, K. Schweiger, Y. Takahashi, S. Wertz National Central
University, Chung-Li, Taiwan
C.M. Kuo, W. Lin, A. Roy, S.S. Yu National Taiwan University (NTU), Taipei,
Taiwan
P. Chang, Y. Chao, K.F. Chen, P.H. Chen, W.-S. Hou, Y.y. Li, R.-S. Lu, E.
Paganis, A. Psallidas, A. Steen Chulalongkorn University, Faculty of Science,
Department of Physics, Bangkok, Thailand
B. Asavapibhop, C. Asawatangtrakuldee, N. Srimanobhas, N. Suwonjandee Çukurova
University, Physics Department, Science and Art Faculty, Adana, Turkey
A. Bat, F. Boran, A. Celik50, S. Damarseckin51, Z.S. Demiroglu, F. Dolek, C.
Dozen52, I. Dumanoglu, G. Gokbulut, EmineGurpinar Guler53, Y. Guler, I. Hos54,
C. Isik, E.E. Kangal55, O. Kara, A. Kayis Topaksu, U. Kiminsu, G. Onengut, K.
Ozdemir56, S. Ozturk57, A.E. Simsek, U.G. Tok, S. Turkcapar, I.S. Zorbakir, C.
Zorbilmez Middle East Technical University, Physics Department, Ankara, Turkey
B. Isildak58, G. Karapinar59, M. Yalvac Bogazici University, Istanbul, Turkey
I.O. Atakisi, E. Gülmez, M. Kaya60, O. Kaya61, Ö. Özçelik, S. Tekten, E.A.
Yetkin62 Istanbul Technical University, Istanbul, Turkey
A. Cakir, K. Cankocak63, Y. Komurcu, S. Sen64 Istanbul University, Istanbul,
Turkey
S. Cerci65, B. Kaynak, S. Ozkorucuklu, D. Sunar Cerci65 Institute for
Scintillation Materials of National Academy of Science of Ukraine, Kharkov,
Ukraine
B. Grynyov National Scientific Center, Kharkov Institute of Physics and
Technology, Kharkov, Ukraine
L. Levchuk University of Bristol, Bristol, United Kingdom
E. Bhal, S. Bologna, J.J. Brooke, D. Burns66, E. Clement, D. Cussans, H.
Flacher, J. Goldstein, G.P. Heath, H.F. Heath, L. Kreczko, B. Krikler, S.
Paramesvaran, T. Sakuma, S. Seif El Nasr-Storey, V.J. Smith, J. Taylor, A.
Titterton Rutherford Appleton Laboratory, Didcot, United Kingdom
K.W. Bell, A. Belyaev67, C. Brew, R.M. Brown, D.J.A. Cockerill, J.A. Coughlan,
K. Harder, S. Harper, J. Linacre, K. Manolopoulos, D.M. Newbold, E. Olaiya, D.
Petyt, T. Reis, T. Schuh, C.H. Shepherd-Themistocleous, A. Thea, I.R. Tomalin,
T. Williams Imperial College, London, United Kingdom
R. Bainbridge, P. Bloch, S. Bonomally, J. Borg, S. Breeze, O. Buchmuller, A.
Bundock, GurpreetSingh CHAHAL68, D. Colling, P. Dauncey, G. Davies, M. Della
Negra, P. Everaerts, G. Hall, G. Iles, M. Komm, L. Lyons, A.-M. Magnan, S.
Malik, A. Martelli, V. Milosevic, A. Morton, J. Nash69, V. Palladino, M.
Pesaresi, D.M. Raymond, A. Richards, A. Rose, E. Scott, C. Seez, A.
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Wardle, D. Winterbottom, A.G. Zecchinelli, S.C. Zenz Brunel University,
Uxbridge, United Kingdom
J.E. Cole, P.R. Hobson, A. Khan, P. Kyberd, C.K. Mackay, I.D. Reid, L.
Teodorescu, S. Zahid Baylor University, Waco, USA
A. Brinkerhoff, K. Call, B. Caraway, J. Dittmann, K. Hatakeyama, C. Madrid, B.
McMaster, N. Pastika, C. Smith Catholic University of America, Washington, DC,
USA
R. Bartek, A. Dominguez, R. Uniyal, A.M. Vargas Hernandez The University of
Alabama, Tuscaloosa, USA
A. Buccilli, S.I. Cooper, S.V. Gleyzer, C. Henderson, P. Rumerio, C. West
Boston University, Boston, USA
A. Albert, D. Arcaro, Z. Demiragli, D. Gastler, C. Richardson, J. Rohlf, D.
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Providence, USA
G. Benelli, B. Burkle, X. Coubez17, D. Cutts, Y.t. Duh, M. Hadley, U. Heintz,
J.M. Hogan70, K.H.M. Kwok, E. Laird, G. Landsberg, K.T. Lau, J. Lee, M.
Narain, S. Sagir71, R. Syarif, E. Usai, W.Y. Wong, D. Yu, W. Zhang University
of California, Davis, Davis, USA
R. Band, C. Brainerd, R. Breedon, M. Calderon De La Barca Sanchez, M. Chertok,
J. Conway, R. Conway, P.T. Cox, R. Erbacher, C. Flores, G. Funk, F. Jensen, W.
Ko${}^{\textrm{\textdagger}}$, O. Kukral, R. Lander, M. Mulhearn, D. Pellett,
J. Pilot, M. Shi, D. Taylor, K. Tos, M. Tripathi, Z. Wang, F. Zhang University
of California, Los Angeles, USA
M. Bachtis, C. Bravo, R. Cousins, A. Dasgupta, A. Florent, J. Hauser, M.
Ignatenko, N. Mccoll, W.A. Nash, S. Regnard, D. Saltzberg, C. Schnaible, B.
Stone, V. Valuev University of California, Riverside, Riverside, USA
K. Burt, Y. Chen, R. Clare, J.W. Gary, S.M.A. Ghiasi Shirazi, G. Hanson, G.
Karapostoli, O.R. Long, N. Manganelli, M. Olmedo Negrete, M.I. Paneva, W. Si,
S. Wimpenny, B.R. Yates, Y. Zhang University of California, San Diego, La
Jolla, USA
J.G. Branson, P. Chang, S. Cittolin, S. Cooperstein, N. Deelen, M. Derdzinski,
J. Duarte, R. Gerosa, D. Gilbert, B. Hashemi, D. Klein, V. Krutelyov, J.
Letts, M. Masciovecchio, S. May, S. Padhi, M. Pieri, V. Sharma, M. Tadel, F.
Würthwein, A. Yagil, G. Zevi Della Porta University of California, Santa
Barbara - Department of Physics, Santa Barbara, USA
N. Amin, R. Bhandari, C. Campagnari, M. Citron, V. Dutta, J. Incandela, B.
Marsh, H. Mei, A. Ovcharova, H. Qu, J. Richman, U. Sarica, D. Stuart, S. Wang
California Institute of Technology, Pasadena, USA
D. Anderson, A. Bornheim, O. Cerri, I. Dutta, J.M. Lawhorn, N. Lu, J. Mao,
H.B. Newman, T.Q. Nguyen, J. Pata, M. Spiropulu, J.R. Vlimant, S. Xie, Z.
Zhang, R.Y. Zhu Carnegie Mellon University, Pittsburgh, USA
M.B. Andrews, T. Ferguson, T. Mudholkar, M. Paulini, M. Sun, I. Vorobiev, M.
Weinberg University of Colorado Boulder, Boulder, USA
J.P. Cumalat, W.T. Ford, E. MacDonald, T. Mulholland, R. Patel, A. Perloff, K.
Stenson, K.A. Ulmer, S.R. Wagner Cornell University, Ithaca, USA
J. Alexander, Y. Cheng, J. Chu, A. Datta, A. Frankenthal, K. Mcdermott, J.R.
Patterson, D. Quach, A. Ryd, S.M. Tan, Z. Tao, J. Thom, P. Wittich, M. Zientek
Fermi National Accelerator Laboratory, Batavia, USA
S. Abdullin, M. Albrow, M. Alyari, G. Apollinari, A. Apresyan, A. Apyan, S.
Banerjee, L.A.T. Bauerdick, A. Beretvas, D. Berry, J. Berryhill, P.C. Bhat, K.
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D. Mason, P. McBride, P. Merkel, S. Mrenna, S. Nahn, V. O’Dell, V.
Papadimitriou, K. Pedro, C. Pena42, F. Ravera, A. Reinsvold Hall, L. Ristori,
B. Schneider, E. Sexton-Kennedy, N. Smith, A. Soha, W.J. Spalding, L. Spiegel,
S. Stoynev, J. Strait, L. Taylor, S. Tkaczyk, N.V. Tran, L. Uplegger, E.W.
Vaandering, C. Vernieri, R. Vidal, M. Wang, H.A. Weber, A. Woodard University
of Florida, Gainesville, USA
D. Acosta, P. Avery, D. Bourilkov, L. Cadamuro, V. Cherepanov, F. Errico, R.D.
Field, D. Guerrero, B.M. Joshi, M. Kim, J. Konigsberg, A. Korytov, K.H. Lo, K.
Matchev, N. Menendez, G. Mitselmakher, D. Rosenzweig, K. Shi, J. Wang, S.
Wang, X. Zuo Florida International University, Miami, USA
Y.R. Joshi Florida State University, Tallahassee, USA
T. Adams, A. Askew, S. Hagopian, V. Hagopian, K.F. Johnson, R. Khurana, T.
Kolberg, G. Martinez, T. Perry, H. Prosper, C. Schiber, R. Yohay, J. Zhang
Florida Institute of Technology, Melbourne, USA
M.M. Baarmand, M. Hohlmann, D. Noonan, M. Rahmani, M. Saunders, F. Yumiceva
University of Illinois at Chicago (UIC), Chicago, USA
M.R. Adams, L. Apanasevich, R.R. Betts, R. Cavanaugh, X. Chen, S. Dittmer, O.
Evdokimov, C.E. Gerber, D.A. Hangal, D.J. Hofman, V. Kumar, C. Mills, T. Roy,
M.B. Tonjes, N. Varelas, J. Viinikainen, H. Wang, X. Wang, Z. Wu The
University of Iowa, Iowa City, USA
M. Alhusseini, B. Bilki53, K. Dilsiz72, S. Durgut, R.P. Gandrajula, M.
Haytmyradov, V. Khristenko, O.K. Köseyan, J.-P. Merlo, A. Mestvirishvili73, A.
Moeller, J. Nachtman, H. Ogul74, Y. Onel, F. Ozok75, A. Penzo, C. Snyder, E.
Tiras, J. Wetzel, K. Yi76 Johns Hopkins University, Baltimore, USA
B. Blumenfeld, A. Cocoros, N. Eminizer, A.V. Gritsan, W.T. Hung, S. Kyriacou,
P. Maksimovic, J. Roskes, M. Swartz, T.Á. Vámi The University of Kansas,
Lawrence, USA
C. Baldenegro Barrera, P. Baringer, A. Bean, S. Boren, A. Bylinkin, T.
Isidori, S. Khalil, J. King, G. Krintiras, A. Kropivnitskaya, C. Lindsey, D.
Majumder, W. Mcbrayer, N. Minafra, M. Murray, C. Rogan, C. Royon, S. Sanders,
E. Schmitz, J.D. Tapia Takaki, Q. Wang, J. Williams, G. Wilson Kansas State
University, Manhattan, USA
S. Duric, A. Ivanov, K. Kaadze, D. Kim, Y. Maravin, D.R. Mendis, T. Mitchell,
A. Modak, A. Mohammadi Lawrence Livermore National Laboratory, Livermore, USA
F. Rebassoo, D. Wright University of Maryland, College Park, USA
A. Baden, O. Baron, A. Belloni, S.C. Eno, Y. Feng, N.J. Hadley, S. Jabeen,
G.Y. Jeng, R.G. Kellogg, A.C. Mignerey, S. Nabili, M. Seidel, Y.H. Shin, A.
Skuja, S.C. Tonwar, L. Wang, K. Wong Massachusetts Institute of Technology,
Cambridge, USA
D. Abercrombie, B. Allen, R. Bi, S. Brandt, W. Busza, I.A. Cali, M. D’Alfonso,
G. Gomez Ceballos, M. Goncharov, P. Harris, D. Hsu, M. Hu, M. Klute, D.
Kovalskyi, Y.-J. Lee, P.D. Luckey, B. Maier, A.C. Marini, C. Mcginn, C.
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Shi, G.S.F. Stephans, K. Sumorok, K. Tatar, D. Velicanu, J. Wang, T.W. Wang,
B. Wyslouch University of Minnesota, Minneapolis, USA
R.M. Chatterjee, A. Evans, S. Guts${}^{\textrm{\textdagger}}$, P. Hansen, J.
Hiltbrand, Sh. Jain, Y. Kubota, Z. Lesko, J. Mans, M. Revering, R. Rusack, R.
Saradhy, N. Schroeder, N. Strobbe, M.A. Wadud University of Mississippi,
Oxford, USA
J.G. Acosta, S. Oliveros University of Nebraska-Lincoln, Lincoln, USA
K. Bloom, S. Chauhan, D.R. Claes, C. Fangmeier, L. Finco, F. Golf, R.
Kamalieddin, I. Kravchenko, J.E. Siado, G.R. Snow${}^{\textrm{\textdagger}}$,
B. Stieger, W. Tabb State University of New York at Buffalo, Buffalo, USA
G. Agarwal, C. Harrington, I. Iashvili, A. Kharchilava, C. McLean, D. Nguyen,
A. Parker, J. Pekkanen, S. Rappoccio, B. Roozbahani Northeastern University,
Boston, USA