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.
Data on coherent elastic and inelastic deuteron-proton scattering are presented. The measurements were made at the CERN ISR with a single arm spectrometer, at s = 2800 GeV 2 and momentum transfer squared (− t ) in the range 0.15 to 0.42 GeV 2 . The data are compared with elastic and inelastic diffractive proton-proton scattering data taken with the same apparatus at the same s and t values. The t dependence of the elastic dp → dp differential cross section is compared to simple predictions based on Glauber theory. The differential cross sections for pp → pX and dp → dX are also compared for M X 2 → 280 GeV 2 , where M X denotes the mass of system X recoiling against the measured proton and deuteron.
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The properties of the diffractive peak observed in the mass spectra of systems recoiling against observed high-momentum protons emerging from pp collisions at the CERN ISR have been investigated. The cross sections in this peak have been found to have a steep t dependence which flattens out as | t | increases. The high mass side of the peak varies approximately as 1/ M 2 (where M is the missing mass of the recoiling system) and scales well in terms of the variable M 2 / s . The position of the maximum has been observed to move to lower values of M 2 / s as the kinematic boundary of this variable decreases with increasing s . The measured cross sections, integrated up to M 2 / s =0.05, rise by (15±5)% over the s range 549 to 1464 GeV 2 .
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Results are reported concerning the charged-particle multiplicity distribution obtained in an exposure of the high-resolution hydrogen bubble chamber LEBC to a beam of 800 GeV protons at the Fermilab MPS. This is the first time that such data have been available at this energy. The distribution of the number n ch of charged particles produced in inelastic interactions obeys KNO-scaling. The average multiplicity is 〈 n ch 〉 = 10.26±0.15. For n ch ⩾8 the data can be well fitted to a negative binomial. The difference between the overall experimental multiplicity distribution and that resulting from the latter fit is in agreement with the contribution expected from diffractive processes.
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The angular and energy distributions of pions produced by 650-MeV protons and pion-nucleon correlations were studied using a liquid hydrogen bubble chamber. The present investigation indicates that the experimental angular distributions of neutral and charged pions are consis- tent with the assumption of isotopic spin conservation. The contributions of rrN subsystem states with isospin T 11'N = 7' 2 and % are measured; the contribution of the latter is 72 ± 3%.
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A 14-in. liquid-hydrogen-filled bubble chamber in a 17.5-kG magnetic field was exposed to a beam of negative pions produced by the Cosmotron at Brookhaven National Laboratory. About 26 000 pictures were taken and examined for the following final states: (1) elastic scattering (π−p); (2) π+ production (π−π+n); (3) π0 production (π−π0p); (4) neutrals. Values for the cross sections for these processes are σ(elastic)=17.56±0.43 mb, σ(π+)=7.14±0.23 mb, σ(π0)=4.65±0.17 mb. The elastic-scattering angular dependence in the c.m. system is fitted by a power-series expansion in cosθ and gives the following coefficients: a0=0.27±0.02, a1=1.48±0.11, a2=3.86±0.22, a3=−0.29±0.53, a4=−0.65±0.28, a5=1.69±0.52 (units: mb/sr). Cross sections for multiple-pion production were also measured: σ(π−π+π0n)=0.33±0.04 mb, σ(π−π+π−p)=0.08±0.02 mb. The total neutral cross section was σ(neutrals)=11.78±0.43 mb; the total charged events cross section was σ(charged)=29.76±0.69 mb; and the total cross section was σ(total)=41.54±0.82 mb. For single-pion production events, two-body mass distributions and angular distributions were compared with the predictions of the Olsson-Yodh isobar model.
Axis error includes +- 0.0/0.0 contribution (?////STATISTICAL YIELD DOMINATES).
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Elastic scattering, single-pion and deuteron production have been investigated. The cross-section for elastic scattering is σelastic = (13.5±0.3) mb. The angular distribution has been fitted to dσ/d|t|=(dσ/d|t|)0 e −bt in the region of low values oft. The best fit givesb=(6.7±0.5) (GeV/c)−2 and (dσ/d|t|)0=(91±5) mb(GeV/c)−2. The cross-sections for ppπ0, pnπ+ reactions are respectively (2.6±0.3) mb and (9.7±0.4) mb. These reactions are dominated by the (3/2, 3/2) nucleonpion isobar production and by forward backward collimation of the nucleons. The production rates for the isobars ++1238 , +1238 , +1500 have been estimated, taking into account the experimental peripheral behaviour of the interaction. In the pnπ+ reaction they are (50±2)%; (10±3)%; (4±3)%. In the ppπ+ reaction the production of ++1238 is estimated to be (45±10)%. The dπ+ and dπ+π+π- reaction cross-sections are respectively (0.03±0.01) mb, and (0.04±0.01) mb.
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Invariant single-particle cross sections for pion and proton production in π ± p interactions at 8 and 16 GeV/ c are presented in terms of integrated distributions as functions of x , reduced rapidity ζ and p ⊥ 2 , and also in terms of double differential cross sections E d 2 σ /(d x d p ⊥ 2 ) and d ζ d p ⊥ 2 ). A comparison of π ± and π − induced reactions is made and the energy dependence is discussed. It is shown that the single-particle structure function cannot be factorized in its dependece on transverse and longitudinal momentum. For the beam-unlike pion, there is an indication for factorizability in terms of rapidity and transverse momentum in a small central region.
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