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.
The first result of the pp2pp experiment at RHIC on elastic scattering of polarized protons at sqrt{s} = 200 GeV is reported here. The exponential slope parameter b of the diffractive peak of the elastic cross section in the t range 0.010 <= |t| <= 0.019 (GeV/c)^2 was measured to be b = 16.3 +- 1.6 (stat.) +- 0.9 (syst.) (GeV/c)^{-2} .
Measured slope of the elastic cross section.
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.
Quasielastic e-d cross sections have been measured at forward and backward angles. Rosenbluth separations were done to obtain RL and RT at Q2=1.75, 2.50, 3.25, and 4.00 (GeV/c)2. The neutron form factors GEn and GMn have been extracted using a nonrelativistic model. The sensitivity to deuteron wave function, relativistic corrections, and models of the inelastic background are reported. The results for GMn are consistent with the dipole form, while GEn is consistent with zero. Comparisons are made to theoretical models based on vector meson dominance, perturbative QCD, and QCD sum rules, as well as constituent quarks.
Magnetic form factors.
Electric form factors.
The proton elastic electric and magnetic form factors, GEp(Q2) and GMp(Q2), have been separately measured in the range Q2=1.75 to 8.83 (GeV/c)2, more than doubling the Q2 range of previous data. Scaled by the dipole fit, GD(Q2), the results for GMp(Q2)/μpGD(Q2) decrease smoothly from 1.05 to 0.91, while GEp(Q2)/GD(Q2) is consistent with unity. Comparisons are made to QCD sum rule, diquark, constitutent quark, and vector meson dominance models, none of which agree with all of the new data. The ratio Q2F2/F1 approaches a constant value for Q2>3 (GeV/c)2.
Magnetic form factors.
Electric form factors.
We have measured inelastic electron-deuteron, electron-proton, and electron-aluminum cross sections at 10° in the kinematic region between elastic deuteron scattering and the second resonance region at six beam energies between 9.8 and 21 GeV. The elastic electron-neutron cross section was extracted from the quasielastic data at Q2=2.5,4.0,6.0,8.0, and 10.0 (GeV/c)2. The ratio of elastic cross sections σnσp falls with increasing Q2 above 6 (GeV/c)2. The inelastic data are compatible either with y scaling (scattering from a single nucleon) or with ξ scaling (scattering from quarks).
Elastic proton cross sections.
No description provided.
No description provided.
We report measurements of the proton elastic form factors, G E p and G M p , extracted from electron scattering in the range 1⩽ Q 2 ⩽3(GeV/ c ) 2 . The uncertainties are <15% in G E p and <3% in G M p . The values of G E p are larger than indicated by most theoretical parameterizations, The ratio of Pauli and Dirac form factors, Q 2 F 2 p / F 1 p , is lower and demonstrates less Q 2 dependence than most of these parameterizations. Comparisons are made to theoretical models, including those based on perturbative QCD and vector-meson dominance.
No description provided.
No description provided.
No description provided.
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