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.
The spin correlation parameter C NN has been measured for n-p elastic scattering at 181 MeV. A comparison with predictions from various phase shift sets and potential models reveals sizeable deviations from the for the data Paris potential and Saclay phase shifts. For the Paris potential the deviations are directly related to an overprediction of the 3 D 2 phase shift parameter.
Numerical values of data supplied by J. Sowinski.
During 1993 and 1995 LEP was run at 3 energies near the Z$^0$peak in order to give improved measurements of the mass and width of the resonance. During 1994, LEP o
Hadronic cross section measured with the 1993 data. Additional systematic error of 0.10 PCT (efficiencies and backgrounds) and 0.29 PCT (absolute luminosity).
Hadronic cross section measured with the 1994 data. Additional systematic error of 0.11 PCT (efficiencies and backgrounds) and 0.11 PCT (absolute luminosity).
Hadronic cross section measured with the 1995 data. Additional systematic error of 0.10 PCT (efficiencies and backgrounds) and 0.11 PCT (absolute luminosity).
We report on measurements of e+e- annihilation into hadrons and lepton pairs. The data have been collected with the L3 detector at LEP at centre-of-mass energies between 130 and 189 GeV. Using a total integrated luminosity of 243.7 pb^-1, 25864 hadronic and 8573 lepton-pair events are selected for the measurement of cross sections and leptonic forward-backward asymmetries. The results are in good agreement with Standard Model predictions.
Measured cross sections for the hadronic events.
Measured cross sections for the muon-pair events.
Measured cross sections for the tau-pair events.
We report on the measurement of the leptonic and hadronic cross sections and leptonic forward-backward asymmetries at theZ peak with the L3 detector at LEP. The total luminosity of 40.8 pb−1 collected
Results from 1990 data. Additional systematic uncertainty of 0.3 pct.
Results from 1991 data. Additional systematic uncertainty of 0.15 pct.
Results from 1992 data. Additional systematic uncertainty of 0.15 pct.
During the LEP running periods in 1990 and 1991 DELPHI has accumulated approximately 450 000 Z 0 decays into hadrons and charged leptons. The increased event statistics coupled with improved analysis techniques and improved knowledge of the LEP beam energies permit significantly better measurements of the mass and width of the Z 0 resonance. Model independent fits to the cross sections and leptonic forward- backward asymmetries yield the following Z 0 parameters: the mass and total width M Z = 91.187 ± 0.009 GeV, Γ Z = 2.486 ± 0.012 GeV, the hadronicf and leptonic partials widths Γ had = 1.725 ± 0.012 GeV, Γ ℓ = 83.01 ± 0.52 MeV, the invisible width Γ inv = 512 ± 10 MeV, the ratio of hadronic to leptonic partial widths R ℓ = 20.78 ± 0.15, and the Born level hadronic peak cross section σ 0 = 40.90 ± 0.28 nb. Using these results and the value of α s determined from DELPHI data, the number of light neutrino species is determined to be 3.08 ± 0.05. The individual leptonic widths are found to be: Γ e = 82.93 ± 0.70 MeV, Γ μ = 83.20 ± 1.11 MeV and Γ τ = 82.89 ± 1.31 MeV. Using the measured leptonic forward-backward asymmetries and assuming lepton universality, the squared vector and axial-vector couplings of the Z 0 to charged leptons are found to be g V ℓ 2 = (1.47 ± 0.51) × 10 −3 and g A ℓ 2 = 0.2483 ± 0.0016. A full Standard Model fit to the data yields a value of the top mass m t = 115 −82 +52 (expt.) −24 +52 (Higgs) GeV, corresponding to a value of the weak mixing angle sin 2 θ eff lept = 0.2339±0.0015 (expt.) −0.0004 +0.0001 (Higgs). Values are obtained for the variables S and T , or ϵ 1 and ϵ 3 which parameterize electroweak loop effects.
Hadronic cross sections from the 1990 data set. Additional systematic uncertainties come from efficiencies and background of 0.4 pct in addition to the luminosity uncertainty 0.7 pct.
Hadronic cross sections from the 1991 data set. Additional systematic uncertainties come from efficiencies and background of 0.2 pct in addition to the luminosity uncertainty 0.6 pct.
E+ E- cross sections from the 1990 data set for both final state fermions in the polar angle range 44 to 136 degrees and accollinearity < 10 degrees (the s + t data).
We report measurements of the proton form factors GEp and GMp extracted from elastic scattering in the range 1≤Q2≤3 (GeV/c)2 with total uncertainties < 15% in GEp and < 3% in GMp. Comparisons are made to theoretical models, including those based on perturbative QCD, vector-meson dominance, QCD sum rules, and diquark constituents in the proton. The results for GEp are somewhat larger than indicated by most theoretical parametrizations, and the ratios of the Pauli and Dirac form factors Q2(F2pF1p) are lower in value and demonstrate a weaker Q2 dependence than those predictions. A global extraction of the elastic form factors from several experiments in the range 0.1 0.1<Q2<10 (GeV/c)2 is also presented.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
Antiproton-proton elastic scattering was measured at c.m.s. energies √s =546 and 1800 GeV in the range of four-momentum transfer squared 0.025<-t<0.29 GeV2. The data are well described by the exponential form ebt with a slope b=15.28±0.58 (16.98±0.25) GeV−2 at √s =546 (1800) GeV. The elastic scattering cross sections are, respectively, σel=12.87±0.30 and 19.70±0.85 mb.
Final results (systematic errors included).
Final results (systematic errors included).
Statistical errors only. Data supplied by S. Belforte.
The search for an additional heavy gauge boson Z′ is described. The models considered are based on either a superstring-motivated E 6 or on a left-right symmetry and assume a minimal Higgs sector. Cross sections and asymmetries measured with the L3 detector in the vicinity of the Z resonance during the 1990 and 1991 running periods are used to determine limits on the Z-Z′ gauge boson mixing angle and on the Z′ mass. For Z′ masses above the direct limits, we obtain the following allowed ranges of the mixing angle, θ M at the 95% confidence level: −0.004 ⪕ θ M ⪕ 0.015 for the χ model, −0.003 ⪕ θ M ⪕ 0.020 for the ψ model, −0.029 ⪕ θ M ⪕ 0.010 for the η model, −0.002 ⪕ θ M ⪕ 0.020 for the LR model,
Data taken during 1990.
Data taken during 1991.
Data taken during 1990.
Based on 520 000 fermion pairs accumulated during the first three years of data collection by the ALEPH detector at LEP, updated values of the resonance parameters of theZ are determined to beMZ=(91.187±0.009) GeV, ΓZ=(2.501±0.012) GeV, σhad0=(41.60±0.27) nb, andRℓ=20.78±0.13. The corresponding number of light neutrino species isNν=2.97±0.05. The forward-backward asymmetry in lepton-pair decays is used to determine the ratio of vector to axial-vector couplings of leptons:gV2(MZ2)/gA2(MZ2)=0.0052±0.0016. Combining this with ALEPH measurements of theb andc quark asymmetries and τ polarization gives sin2θWeff=0.2326±0.0013. Assuming the minimal Standard Model, and including measurements ofMW/MZ fromp\(\bar p\) colliders and neutrino-nucleon scattering, the mass of the top quark is\(M_{top} = 156 \pm \begin{array}{*{20}c} {22} \\ {25} \\ \end{array} \pm \begin{array}{*{20}c} {17} \\ {22Higgs} \\ \end{array} \) GeV.
Data from 1990 running period.
Data from 1990 running period.
Data from 1990 running period.
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