In a special run of the LHC with $\beta^\star = 2.5~$km, proton-proton elastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t = 2.5 \cdot 10^{-4}~$GeV$^{2}$ to $-t = 0.46~$GeV$^{2}$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t \rightarrow 0$. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the $t$-dependence. The results for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*} \sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \; \; \; \rho = \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The rho-parameter, i.e. the ratio of the real to imaginary part of the elastic scattering amplitude extrapolated to t=0. The systematic uncertainty includes experimental and theoretical uncerainties.
The nuclear slope parameter B from a fit of the form exp(-Bt-Ct^2-Dt^3). The systematic uncertainty includes experimental and theoretical uncerainties.
High-precision measurements by the ATLAS Collaboration are presented of inclusive $W^+\to\ell^+\nu$, $W^-\to\ell^-\bar{\nu}$ and $Z/\gamma^*\to\ell\ell$ ($\ell=e,\mu$) Drell-Yan production cross sections at the LHC. The data were collected in proton-proton collisions at $\sqrt{s} = 7$ TeV with an integrated luminosity of 4.6 fb$^{-1}$. Differential $W^+$ and $W^-$ cross sections are measured in a lepton pseudorapidity range $|\eta_{\ell}| = 2.5$. Differential $Z/\gamma^*$ cross sections are measured as a function of the absolute dilepton rapidity, for $|y_{\ell\ell}| < 3.6$, for three intervals of dilepton mass, $m_{\ell\ell}$, extending from 46 to 150 GeV. The integrated and differential electron- and muon-channel cross sections are combined and compared to theoretical predictions using recent sets of parton distribution functions. The data, together with the final inclusive $e^{\pm}p$ scattering cross-section data from H1 and ZEUS, are interpreted in a next-to-next-to-leading-order QCD analysis, and a new set of parton distribution functions, ATLAS-epWZ16, is obtained. The ratio of strange-to-light sea-quark densities in the proton is determined more accurately than in previous determinations based on collider data only, and is established to be close to unity in the sensitivity range of the data. A new measurement of the CKM matrix element $|V_{cs}|$ is also provided.
Fiducial cross sections times branching ratios for $W^+$, $W^-$, central and forward $Z/\gamma^*$ ($m_{ee} = 66-116$ GeV) production in the electron decay channels. The fiducial regions used for the measurement are those defined for the combined fiducial regions, except that the central electron pseudorapidity is restricted to be $|\eta|<2.47$ and excludes $1.37<|\eta|<1.52$, and the forward electron pseudorapidity excludes the region $3.16<|\eta|<3.35$. The uncertainties denote the statistical (stat), the systematic (syst) and the luminosity (lumi) uncertainties.
Fiducial cross sections times branching ratios for $W^+$, $W^-$ and $Z/\gamma^*$ ($m_{\mu\mu} = 66-116$ GeV) production in the muon decay channels. The fiducial regions used for the measurement are those defined for the combined fiducial regions, except that the muon pseudorapidity is restricted to be $|\eta|<2.4$. The uncertainties denote the statistical (stat), the systematic (syst) and the luminosity (lumi) uncertainties.
Integrated fiducial cross sections times leptonic branching ratios in the electron and muon channels and their combination with statistical and systematic uncertainties, for $W^+$, $W^-$, their sum and the $Z/\gamma^*$ process measured at $\sqrt{s}=7$ TeV. The $Z/\gamma^*$ cross section is defined for the dilepton mass window $m_{\ell\ell} = 66 - 116$ GeV. The common fiducial regions are defined in Section 2.3. The uncertainties denote the statistical (stat), the experimental systematic (syst), and the luminosity (lumi) contributions.
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