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.
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.
Inclusive e\pmp single and double differential cross sections for neutral and charged current deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of \surds = 319GeV with a total integrated luminosity of 333.7 pb-1 shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative fourmomentum transfer squared, Q2, between 60 and 50 000GeV2, and Bjorken x between 0.0008 and 0.65. The measurements are combined with earlier published unpolarised H1 data to improve statistical precision and used to determine the structure function xF_3^gammaZ. A measurement of the neutral current parity violating structure function F_2^gammaZ is presented for the first time. The polarisation dependence of the charged current total cross section is also measured. The new measurements are well described by a next-to-leading order QCD fit based on all published H1 inclusive cross section data which are used to extract the parton distribution functions of the proton.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 120, 150, 200, 250 and 300 GeV^2.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 400, 500, 650, 800 and 1000 GeV^2.
The Neutral Current Reduced Cross Section for E- P interactions with a beam polarisation of -25.8 % for Q^2 values of 1200, 1500, 2000, 3000 and 5000 GeV^2.
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 values for Compton scattering on the proton were measured at 25 kinematic settings over the range s = 5-11 and -t = 2-7 GeV2 with statistical accuracy of a few percent. The scaling power for the s-dependence of the cross section at fixed center of mass angle was found to be 8.0 +/ 0.2, strongly inconsistent with the prediction of perturbative QCD. The observed cross-section values are in fair agreement with the calculations using the handbag mechanism, in which the external photons couple to a single quark.
Cross section of proton Compton Scattering at centre of mass energy squared of 4.82 GeV.
Cross section of proton Compton Scattering at centre of mass energy squared of 6.79 GeV.
Cross section of proton Compton Scattering at centre of mass energy squared of 8.90 GeV.
Compton scattering from the proton was investigated at s=6.9 (GeV/c)**2 and \t=-4.0 (GeV/c)**2 via polarization transfer from circularly polarized incident photons. The longitudinal and transverse components of the recoil proton polarization were measured. The results are in excellent agreement with a prediction based on a reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton and in disagreement with a prediction of pQCD based on a two-gluon exchange mechanism.
Polarization transfer parameters.
We report on precision measurements of the elastic cross section for electron-proton scattering performed in Hall C at Jefferson Lab. The measurements were made at 28 unique kinematic settings covering a range in momentum transfer of 0.4 $<$ $Q^2$ $<$ 5.5 $(\rm GeV/c)^2$. These measurements represent a significant contribution to the world's cross section data set in the $Q^2$ range where a large discrepancy currently exists between the ratio of electric to magnetic proton form factors extracted from previous cross section measurements and that recently measured via polarization transfer in Hall A at Jefferson Lab.
Measured values of the electron-proton elastic cross section for beam energy 1.148 GeV.
Measured values of the electron-proton elastic cross section for beam energy 1.882 GeV.
Measured values of the electron-proton elastic cross section for beam energy 2.235 GeV.
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.
This final analysis of hadronic and leptonic cross-sections and of leptonic forward-backward asymmetries in e+e- collisions with the OPAL detector makes use of the full LEP1 data sample comprising 161 pb^-1 of integrated luminosity and 4.5 x 10^6 selected Z decays. An interpretation of the data in terms of contributions from pure Z exchange and from Z-gamma interference allows the parameters of the Z resonance to be determined in a model-independent way. Our results are in good agreement with lepton universality and consistent with the vector and axial-vector couplings predicted in the Standard Model. A fit to the complete dataset yields the fundamental Z resonance parameters: mZ = 91.1852 +- 0.0030 GeV, GZ = 2.4948 +- 0.0041 GeV, s0h = 41.501 +- 0.055 nb, Rl = 20.823 +- 0.044, and Afb0l = 0.0145 +- 0.0017. Transforming these parameters gives a measurement of the ratio between the decay width into invisible particles and the width to a single species of charged lepton, Ginv/Gl = 5.942 +- 0.027. Attributing the entire invisible width to neutrino decays and assuming the Standard Model couplings for neutrinos, this translates into a measurement of the effective number of light neutrino species, N_nu = 2.984 +- 0.013. Interpreting the data within the context of the Standard Model allows the mass of the top quark, mt = 162 +29-16 GeV, to be determined through its influence on radiative corrections. Alternatively, utilising the direct external measurement of mt as an additional constraint leads to a measurement of the strong coupling constant and the mass of the Higgs boson: alfa_s(mZ) = 0.127 +- 0.005 and mH = 390 +750-280 GeV.
The cross section for hadron production corrected to the simple kinematic acceptance region defined by SPRIME/S > 0.01. Statistical errors only are shown. Also given is the cross section value corrected for the beam energy spread to correspond to the physical cross section at the central value of SQRT(S).
The cross section for E+ E- production corrected to the simple kinematic acceptance region defined by ABS(COS(THETA(C=E-))) < 0.7 and THETA(C=ACOL) < 10 degrees. Statistical errors only are shown. Also given is the cross section value corrected for the beam energy spread to correspond to the physical cross sectionat the central value of SQRT(S).
The cross section for mu+ mu- production corrected to the simple kinematic acceptance region defined by N = M(P=3_4)**2/S > 0.01. Statistical errors only are shown. Also given is the cross section value corrected for the beam energy spread to correspond to the physical cross section at the central value of SQRT(S).
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