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.
The polarization of the recoil proton at this energy depends on the interference of the P 33 phase shift with the P 11 and S 11 phase shifts. The measured values indicate the existence of a large P 11 phase shift. The polarization was measured by scattering from carbon blocks in spark chambers using a Vidicon scanner to record the data.
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The parameters D, R, R' and P for pp elastic scattering have been measured in the centre-of-mass angular range 13 degrees to 58 degrees with an accuracy of about +or-0.02 at 209, 324, 379, 425 and 515 MeV. These results are incorporated with earlier data into a phase-shift analysis. Phase-shifts are generally in agreement with the theoretical predictions of the Paris group, although the F-wave spin-orbit combination is rather stronger than predicted. The fitted value for the pi 0pp coupling constant in g02=14.06+or-0.65.
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The absolute normalisation of the polarisation in pp elastic scattering at 24 degrees lab has been determined by means of a double-scattering experiment to an accuracy of +or-1.5% at five energies between 200 and 520 MeV.
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Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 87.2 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 68.4 MeV from the data set 1.
Analyzing power for PI+ P elastic scattering at incidient kinetic energy 57.2 MeV from the data set 1.
Excitation functions of proton-proton elastic scattering cross sections have been measured in narrow steps for projectile momenta pp (energies Tp) from 1100 to 3300MeV/c (500 to 2500 MeV) in the angular range 35°≤Θc.m.≤90° with a detector providing ΔΘc.m.≈1.4° resolution. Measurements have been performed continuously during projectile acceleration in the cooler synchrotron COSY with an internal CH2 fiber target, taking particular care to monitor luminosity as a function of Tp. The advantages of this experimental technique are demonstrated, and the excitation functions obtained are compared to existing cross section data. No evidence for narrow structures was found.
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500 MeV p→+p elastic and quasielastic, and p→+n quasielastic, analyzing powers (Ay) and spin-rotation-depolarization parameters (DSS, DSL, DLS, DLL, DNN) were determined for center-of-momentum angular ranges 6.8°–55.4° (elastic) and 22.4°–55.4° (quasielastic); liquid hydrogen and deuterium targets were used. The p→+p elastic and quasielastic results are in good agreement; both the p→+p and p→+n parameters are well described by current phase shift solutions.
The elastic P P analysing power at 500 MeV incident proton energy. There is an additional overall normalization uncertainty of 1 PCT.
The spin depolarization and spin rotation parameters in 500 MeV P P elastic interactions. Additional normalization uncertainty of 1 PCT (2 PCT for DLL and DLS).
The elastic P P analysing power at 500 MeV incident proton energy. There is an additional overall normalization uncertainty of 1 PCT.
The spin correlation parameter A00NN for 497.5 MeV proton + proton elastic scattering was determined over the center-of-momentum scattering angle region 23.1°–64.9 °. The new A00NN extend to more forward angles than existing A00NN and have significantly smaller statistical errors (±0.01–0.04). The A00NN are qualitatively described by recent phase shift analyses, but a quantitative shape and normalization discrepancy remains in the forward angle region. These new data provide important constraints for nucleon-nucleon spin-dependent amplitudes at forward angles which are used in theoretical models of nucleon-nucleus scattering.
Errors include statistical and systematic uncertainties.
The spin-rotation parameters A and R and the related spin-rotation angle β have been measured for π+p and π−p elastic scattering using protons polarized in the scattering plane. The pion-beam momenta are 427, 471, 547, 625, and 657 MeV/c and the angular range is −0.9≤cosΘc.m.≤0.3. The scattered pion and recoil proton were detected in coincidence, using a scintillator hodoscope for the pions, and the Large Acceptance Spectrometer combined with the JANUS polarimeter for the recoil protons. The results are compared with the four recent πN partial wave analyses (PWA's). Our data show that the major features of these PWA's are correct. The A and R measurements complete our program of pion-nucleon experiments, providing full data sets at three of the above beam momenta. Such sets can be used to test the constraints in the PWA's or to obtain a model-independent set of πN scattering amplitudes.
BETA is the spin-rotation angle.
BETA is the spin-rotation angle.
BETA is the spin-rotation angle.
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