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 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.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The total elastic cross section and the observed elastic cross section within the fiducial volume.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. In a special run with high-$\beta^{\star}$ beam optics, an integrated luminosity of 80 $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $|t|$ range from 0.01 GeV$^2$ to 0.1 GeV$^2$ to extrapolate to $|t|\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $$\sigma_{\mathrm{tot}}(pp\rightarrow X) = 95.35 \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb},$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $|t|\rightarrow 0$. In addition, the slope of the elastic cross section at small $|t|$ is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The Optical Point dsigma/(elastic)/dt(t-->0), the total elastic cross section and the observed elastic cross section within the fiducial volume. The first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
K−−p interactions in the Columbia-BNL 30-in. hydrogen bubble chamber were studied at nine momenta from 594 to 820 MeVc. The results for elastic-scattering and zero-prong-plus-V0 events are presented here. Differential cross sections are given for the K−p, K¯0n, and Λπ0 final states. A fit to the K¯N channels was obtained which shows the effects of a 32− resonance at 1701 MeV. This energy is appreciably displaced from the peak in the inelastic cross section.
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We present a measurement of the elastic differential cross section $d\sigma(p\bar{p}\rightarrow p\bar{p})/dt$ as a function of the four-momentum-transfer squared t. The data sample corresponds to an integrated luminosity of $\approx 31 nb^{-1}$ collected with the D0 detector using dedicated Tevatron $p\bar{p} $ Collider operating conditions at sqrt(s) = 1.96 TeV and covers the range $0.26 <|t|< 1.2 GeV^2$. For $|t|<0.6 GeV^2$, d\sigma/dt is described by an exponential function of the form $Ae^{-b|t|}$ with a slope parameter $ b = 16.86 \pm 0.10(stat) \pm 0.20(syst) GeV^{-2}$. A change in slope is observed at $|t| \approx 0.6 GeV^2$, followed by a more gradual |t| dependence with increasing values of |t|.
The $d\sigma$/$dt$ differential cross section. The statistical and systematic uncertainties are added in quadrature.
Cross-section and angular distributions for hadronic and lepton-pair final states in e+e- collisions at centre-of-mass energies between 189 GeV and 209 GeV, measured with the OPAL detector at LEP, are presented and compared with the predictions of the Standard Model. The measurements are used to determine the electromagnetic coupling constant alphaem at LEP2 energies. In addition, the results are used together with OPAL measurements at 91-183 GeV within the S-matrix formalism to determine the gamma-Z interference term and to make an almost model-independent measurement of the Z mass. Limits on extensions to the Standard Model described by effective four-fermion contact interactions or the addition of a heavy Z boson are also presented.
CM energy values.
Measured cross section for QUARK QUARKBAR (HADRON) production. The data are corrected to no interference between initial and final state radiation.
Measured cross section for MU+ MU- production. The data are corrected to no interference between initial and final state radiation.
We present direct measurements of the $Z~0$-lepton coupling asymmetry parameters, $A_e$, $A_\mu$, and $A_\tau$, based on a data sample of 12,063 leptonic $Z~0$ decays collected by the SLD detector. The $Z$ bosons are produced in collisions of beams of polarized $e~-$ with unpolarized $e~+$ at the SLAC Linear Collider. The couplings are extracted from the measurement of the left-right and forward-backward asymmetries for each lepton species. The results are: $A_e=0.152 \pm 0.012 {(stat)} \pm 0.001 {(syst)}$, $A_\mu=0.102 \pm 0.034 \pm 0.002$, and $A_\tau=0.195 \pm 0.034 \pm 0.003$.
No description provided.
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.
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