We measured dσdt for p↑+p↑→p+p from P⊥2=4.50 to 5.09 (GeV/c)2 at 11.75 GeV/c. We used a 59%-polarized proton beam and a 71%-polarized proton target with both spins oriented perpendicular to the scattering plane. In these large-P⊥2 hard-scattering events, spin effects are very large and the ratio (dσdt)↑↑:(dσdt)↑↓ grows rapidly with increasing P⊥2, reaching a value of 4 at 90° (c.m.). Thus, hard elastic scattering, which is presumably due to the direct scattering of the protons' constituents, may only occur when the two incident protons' spins are parallel.
THE ERRORS INCLUDE STATISTICAL AND SYSTEMATIC ERRORS ADDED IN QUADRATURE. THE PARALLEL/ANTIPARALLEL SPIN CROSS SECTION RATIO IS (1+CNN)/(1-CNN).
Exclusive photoproduction of $\rho^0(770)$ mesons is studied using the H1 detector at the $ep$ collider HERA. A sample of about 900000 events is used to measure single- and double-differential cross sections for the reaction $\gamma p \to \pi^{+}\pi^{-}Y$. Reactions where the proton stays intact (${m_Y{=}m_p}$) are statistically separated from those where the proton dissociates to a low-mass hadronic system ($m_p{<}m_Y{<}10$ GeV). The double-differential cross sections are measured as a function of the invariant mass $m_{\pi\pi}$ of the decay pions and the squared $4$-momentum transfer $t$ at the proton vertex. The measurements are presented in various bins of the photon-proton collision energy $W_{\gamma p}$. The phase space restrictions are $0.5 < m_{\pi\pi} < 2.2$ GeV, ${\vert t\vert < 1.5}$ GeV${}^2$, and ${20 < W_{\gamma p} < 80}$ GeV. Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are described by analytic functions. Parametrising the $m_{\pi\pi}$ dependence with resonant and non-resonant contributions added at the amplitude level leads to a measurement of the $\rho^{0}(770)$ meson mass and width at $m_\rho = 770.8\ {}^{+2.6}_{-2.7}$ (tot) MeV and $\Gamma_\rho = 151.3\ {}^{+2.7}_{-3.6}$ (tot) MeV, respectively. The model is used to extract the $\rho^0(770)$ contribution to the $\pi^{+}\pi^{-}$ cross sections and measure it as a function of $t$ and $W_{\gamma p}$. In a Regge asymptotic limit in which one Regge trajectory $\alpha(t)$ dominates, the intercept $\alpha(t{=}0) = 1.0654\ {}^{+0.0098}_{-0.0067}$ (tot) and the slope $\alpha^\prime(t{=}0) = 0.233\ {}^{+0.067 }_{-0.074 }$ (tot) GeV${}^{-2}$ of the $t$ dependence are extracted for the case $m_Y{=}m_p$.
Elastic ($m_Y=m_p$) and proton-dissociative ($1<m_Y<10$ GeV) $\pi^{+}\pi^{-}$ photoproduction off protons, differential in the dipion mass. The tabulated cross sections are $\gamma p$ cross sections but can be converted to $ep$ cross sections using the effective photon flux $\Phi_{\gamma/e}$.
Elastic ($m_Y=m_p$) and proton-dissociative ($1<m_Y<10$ GeV) $\pi^{+}\pi^{-}$ photoproduction off protons, differential in the dipion mass --- statistical correlations coefficients $\rho_{ij}$ only. Only one half of the (symmetric) matrix is stored. Bins are identified by their global bin number.
Fit of elastic ($m_Y=m_p$) and proton-dissociative ($1<m_Y<10$ GeV) $\pi^{+}\pi^{-}$ photoproduction cross section off protons with a Soeding-inspired analytic function including $\rho$ and $\omega$ meson resonant contributions as well as a continuum background which interfere at the amplitude level. Parameters with subscript "el" and "pd" correspond to elastic and proton-dissociative cross sections, respectively.
Based on 150 000 photographs taken at the ZGS with the 30 inch deuterium-filled chamber we present an analysis of the elastic p d scattering reaction. Due to unrecoreded small deuteron recoils we were only able to measure the elastic cross section in the four-momentum region | t | > 0.03 (GeV/ c ) 2 . Extrapolation towards small | t | by two different methods gave us two compatible estimates of the total elastic cross section. The differential cross section was analyzed by means of the Glauber formalism both with and without the effects due to the D-wave part of the deuteron wave function. The differential cross sections of np at 5.4 GeV/ c and pn deduced from our data were compared and exhibit a crossover phenomenon.
CALCULATED USING TOTAL ELASTIC SIG(-T > 0.03 GEV**2) = 7.2 +- 0.4. THE SMALL ANGLE SCATTERING APPROXIMATION HOLDS: D(SIG)/DOMEGA(RF=LAB) = (P**2/PI)*D(SIG)/DT.
INTEGRATED CROSS SECTION USING EITHER EXPONENTIAL EXTRAPOLATION OR GLAUBER MODEL FIT FOR -T < 0.03 GEV**2.
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.
Antiproton-proton and proton-proton small-angle elastic scattering was measured for centre-of-mass energies s =30.6, 52.8 and 62.3 GeV at the CERN Intersectung Storage Rings. In addition, proton-proton elastic scattering was measured at s =23.5 GeV . Using the optical theorem, total cross sections are obtained with an accuracy of about 0.5% for proton-proton scattering and about 1% for antiproton-proton scattering. The measurement of the interference of the Coulomb scattering and the hadronic scattering permits a determination of the ratio of the real-to-imaginary part of the forward hadronic scattering amplitude. Also presented are measurements of the hadronic slope parameter.
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Antiproton-proton and proton-proton small-angle elastic scattering have been measured for centre-of-mass energies √ s = 30.7 and 62.5 GeV at the CERN Intersecting Storage Rings (ISR). Antiproton-proton and proton-proton total cross sections are obtained using the optical theorem. The measurement of the Coulomb scattering and its interference with the nuclear scattering allows a determination of the ratio of the real-to-imaginary part of the forward nuclear scattering amplitude. Also presented are measurements for the nuclear slope parameter at √ s = 62.5 GeV. Our new results reinforce the conclusions drawn recently from our measurements at √ s = 52.8 GeV. In particular, the pp̄ total cross section is rising at ISR energies and should continue to rise well beyond these energies.
DATA REQUESTED FROM AUTHORS.
RESULTS OF FITS.
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The cross section for the diffractive deep-inelastic scattering process $ep \to e X p$ is measured, with the leading final state proton detected in the H1 Forward Proton Spectrometer. The data analysed cover the range \xpom <0.1 in fractional proton longitudinal momentum loss, 0.08 < |t| < 0.5 GeV^{-2} in squared four-momentum transfer at the proton vertex, 2 < Q^2 < 50 GeV^2 in photon virtuality and 0.004 < \beta = x / \xpom < 1, where x is the Bjorken scaling variable. For $\xpom \lapprox 10^{-2}$, the differential cross section has a dependence of approximately ${\rm d} \sigma / {\rm d} t \propto e^{6 t}$, independently of \xpom, \beta and Q^2 within uncertainties. The cross section is also measured triple differentially in \xpom, \beta and Q^2. The \xpom dependence is interpreted in terms of an effective pomeron trajectory with intercept $\alpha_{\pom}(0)=1.114 \pm 0.018 ({\rm stat.}) \pm 0.012 ({\rm syst.}) ^{+0.040}_{-0.020} ({\rm model})$ and a sub-leading exchange. The data are in good agreement with an H1 measurement for which the event selection is based on a large gap in the rapidity distribution of the final state hadrons, after accounting for proton dissociation contributions in the latter. Within uncertainties, the dependence of the cross section on x and Q^2 can thus be factorised from the dependences on all studied variables which characterise the proton vertex, for both the pomeron and the sub-leading exchange.
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A study of 205-GeV/c π−p interactions has been made with a 48 800-picture exposure in the bare Fermilab 30-inch hydrogen bubble chamber. The average number of charged particles produced per inelastic interaction is 7.99±0.06. The elastic cross section is 3.18±0.13 mb and the total cross section is 24.19±0.44 mb. The inclusive cross sections for neutral-particle production are: σ(γ)=171.3±15.3 mb, σ(KS0)=3.64±0.61 mb (x<0.3), σ(Λ)=1.71±0.34 mb (x<0.3), and σ(Λ¯)=0.59±0.23 mb (x<0.1). The average number of π0's produced per inelastic collision is consistent with a linear rise with the number of charged particles, and about equal to the number of produced π− or π+. The average number of K0's, Λ's, and Λ¯'s is consistent with very little dependence on the number of charged particles. General characteristics of neutral-particle production are presented and compared with other experiments. For each topology the produced neutral energy is ∼13 of the incident energy.
THE ERRORS INCLUDE THOSE DUE TO VARIOUS CORRECTIONS.
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The np elastic differential cross section has been measured for incident neutron momenta 100–400 GeV/ c in the | t | range 6 · 10 −6 − 5 · 10 −1 (GeV/ c ) 2 . The np data of this experiment provide a first direct measurement of the hadronic amplitude for | t | < 10 −2 (GeV/ c ) 2 , which is consistent with the extrapolations from higher | t | values. Our data for | t | < 10 −4 (GeV/ c ) 2 are consistent with a rise which can be attributed to Schwinger scattering, caused by the interaction of the neutron magnetic moment with the proton.
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The K − p differential and total elastic cross-sections have been measured at 14.25 GeV/ c . The results have been compared with various Regge models.
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