We have measured the differential cross section for pp and p̄p elastic scattering at √ s = 31, 53 and 62 GeV in the interval 0.05 < | t | < 0.85 GeV 2 at the CERN ISR using the Split Field Magnet detector. At 53 and 62 GeV, for 0.17 < | t | < 0.85 GeV 2 both pp and p̄p data show simple exponential behaviour in t ; at √ s = 31 GeV the data for 0.05 < | t | < 0.85 GeV 2 are consistent with a change in slope near | t | = 0.15 GeV 2 .
ERRORS CONTAIN BOTH STATISTICAL AND T-DEPENDENT SYSYEMATIC ERRORS.
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LOCAL SLOPE PARAMETERS BASED ON QUADRATIC EXPONENTIAL FIT.
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.
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 single-pion production reactions $pp\to d\pi^+$, $pp\to np\pi^+$ and $pp\to pp\pi^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus all pion production channels were recorded with 1-4 overconstraints. The total and differential cross sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the $pp\pi^0$ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular we observe very large anisotropies for the $\pi^0$ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with $\pi^0$ $s$- and $d$-partial waves and emphasizing the important role of $\pi^0$ d-waves.
Total cross section measurements.. Errors are mainly systematic.
Measured angular distribution for elastic P P scattering in the CM system normalised to the data in the SAID database (Arndt et al. PR C62,034005(2000). This measurement is made to determine the luminosity.
The measured pion angular distribution in the CM system in the reaction P P --> DEUT PI+.
The differential cross sections for the elastic scattering of π+, π−, K+, K−, p, and p¯ on protons have been measured in the t interval -0.04 to -0.75 GeV2 at five momenta: 50, 70, 100, 140, and 175 GeV/c. The t distributions have been parametrized by the quadratic exponential form dσdt=Aexp(B|t|+C|t|2) and the energy dependence has been described in terms of a single-pole Regge model. The pp and K+p diffraction peaks are found to shrink with α′∼0.20 and ∼0.15 GeV−2, respectively. The p¯p diffraction peak is antishrinking while π±p and K−p are relatively energy-independent. Total elastic cross sections are calculated by integrating the differential cross sections. The rapid decline in σel observed at low energies has stopped and all six reactions approach relatively constant values of σel. The ratio of σelσtot approaches a constant value for all six reactions by 100 GeV, consistent with the predictions of the geometric-scaling hypothesis. This ratio is ∼0.18 for pp and p¯p, and ∼0.12-0.14 for π±p and K±p. A crossover is observed between K+p and K−p scattering at |t|∼0.19 GeV2, and between pp and p¯p at |t|∼0.11 GeV2. Inversion of the cross sections into impact-parameter space shows that protons are quite transparent to mesons even in head-on collisions. The probability for a meson to pass through a proton head-on without interaction inelastically is ∼20% while it is only ∼6% for an incident proton or antiproton. Finally, the results are compared with various quark-model predictions.
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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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At the LHC energy of $\sqrt s = 7\,{\mathrm { TeV}}$ , under various beam and background conditions, luminosities, and Roman Pot positions, TOTEM has measured the differential cross-section for proton-proton elastic scattering as a function of the four-momentum transfer squared t. The results of the different analyses are in excellent agreement demonstrating no sizeable dependence on the beam conditions. Due to the very close approach of the Roman Pot detectors to the beam center (≈5σ(beam)) in a dedicated run with β* = 90 m, |t|-values down to 5·10(−)(3) GeV(2) were reached. The exponential slope of the differential elastic cross-section in this newly explored |t|-region remained unchanged and thus an exponential fit with only one constant B = (19.9 ± 0.3) GeV(−)(2) over the large |t|-range from 0.005 to 0.2 GeV(2) describes the differential distribution well. The high precision of the measurement and the large fit range lead to an error on the slope parameter B which is remarkably small compared to previous experiments. It allows a precise extrapolation over the non-visible cross-section (only 9%) to t = 0. With the luminosity from CMS, the elastic cross-section was determined to be (25.4 ± 1.1) mb, and using in addition the optical theorem, the total pp cross-section was derived to be (98.6 ± 2.2) mb. For model comparisons the t-distributions are tabulated including the large |t|-range of the previous measurement (TOTEM Collaboration (Antchev G. et al), EPL, 95 (2011) 41001).
The measured differential elastic cross section.
The measured differential elastic cross section in the high |T| region. where it originally appeared as a plot, but was not tabulated.
The fitted slope parameter for the elastic cross section fitted over 4 |T| ranges.
We report a study of 20 exclusive reactions measured at the AGS at 5.9 GeV/c incident momentum, 90° center of mass. This experiment confirms the strong quark flow dependence of two-body hadron-hadron scattering at large angle. At 9.9 GeV/c an upper limit had been set for the ratio of cross sections for (p¯p→p¯p)(pp→pp) at 90° c.m., with the ratio less than 4%. The present experiment was performed at lower energy to gain sensitivity, but was still within the fixed angle scaling region. A ratio R(p¯ppp)≈140 was measured at 5.9 GeV/c, 90° c.m. in comparison to a ratio near 1.7 for small angle scattering. In addition, many other reactions were measured, often for the first time at 90° c.m. in the scaling region, using beams of π±, K±, p, and p¯ on a hydrogen target. There are similar large differences in cross sections for other reactions: R(K−p→π+Σ−K−p→π−Σ+)≈112, for example. The relative magnitudes of the different cross sections are consistent with the dominance of quark interchange in these 90° reactions, and indicate that pure gluon exchange and quark-antiquark annihilation diagrams are much less important. The angular dependence of several elastic cross sections and the energy dependence at a fixed angle of many of the reactions are also presented.
Cross sections at 90 degrees in the centre-of-mass.
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The charged-particle multiplicity distribution in 205−GeVc proton-proton interactions is presented. In addition, the total diffractive contributions to each charged multiplicity are estimated assuming a factorizable Pomeron.
THE TOTAL CROSS SECTION NORMALIZATION COMES FROM THIS AND OTHER EXPERIMENTS.
Measurements of the total cross section have been performed at the ISR with c.m. energies between 23.5 GeV and 62.5 GeV. Two independent experimental methods have been applied, a measurement of total interaction rate and of small angle elastic scattering. Both experiments give consistent results showing that the total cross section increases by (11.8±1.5) % over the ISR energy range. This experiment has also measured the slope of the forward diffraction peak in elastic scattering at small momentum transfer. The elastic cross section shows the same relative rise as the total cross section, and the ratio λ of elastic to total cross section approaches a constant value of λ =0.178±0.003.
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TOTAL CROSS SECTION FROM (INTERACTION RATE)/(LUMINOSITY). SYSTEMATIC ERROR <0.8 PCT.
TOTAL CROSS SECTION FROM APPLYING THE OPTICAL THEOREM TO SMALL ANGLE ELASTIC SCATTERING EXTRAPOLATED TO T=0.
Interactions initiated by 3-Bev protons of the Brookhaven Cosmotron were studied by photoemulsion technique. With appropriate criteria, 115 events are attributed to interactions of the incident beam protons with hydrogen nuclei (∼55%) and with bound protons of other nuclei (∼45%). A detailed analysis allowed the subdivision of the 115 events in categories, according to the number of π mesons (N>~0) produced in the collision. The ratio of elastic scattering to the total number of events was estimated to be σelσtotal=0.20−0.07+0.04. The observed cross section for pure elastic scattering is σel=8.9±1.0 mb. The percentages of single, double, triple, and quadruple π-meson production are respectively: 34−20+22; 35.6−23+20; 9.6−4+6; ∼1.0+3.5. Among the 20 most probable cases of single π-meson production—the estimated ratio of π+ to π0 is σπ+σπ0=5.3−1.4+0.3. The experimental results are not in agreement with the Fermi statistical-model theory (in particular the lower limit for the experimental ratio of triple to single production is given by σ3σ1>∼110 in contrast with the predicted ratio σ3σ1=167) but are not inconsistent with the Peaslee excited-state-model theory.
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Measurements of proton-proton elastic scattering at angles around 6 mrad have been made at centre-of-mass energies of 23, 31, 45 and 53 GeV using the CERN Intersecting Storage Rings. The absolute scale of the cross-section was established by determination of the effective density of the colliding beans in their overlap region. Proton-proton total cross sections were deduced by extrapolation of the elastic differential cross-section to the forward direction and by application of the optical theorem. The results indicate that over the energy range studied the proton-proton total cross-section increases from about 39 to about 43 mb.
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NEW VALUES OF ELASTIC SLOPE USING APPARATUS DESCRIBED IN U. AMALDI ET AL., PL 43B, 231 (1973).
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The total cross sections σT of p, p¯, π±, and K± on hydrogen and deuterium have been measured between 6 and 22 GeVc at intervals of 2GeVc to an accuracy greater than previously reported. The method utilized was a conventional good-geometry transmission experiment with scintillation counters subtending various solid angles at targets of liquid H2 and D2. With the increase in statistical accuracy of the data, it was found that a previously adopted procedure of linearly extrapolating to zero solid angle the partial cross sections measured at finite solid angles was not a sufficiently accurate procedure from which to deduce σT. The particle-neutron cross sections are derived by applying the Glauber screening correction to the difference between the particle-deuteron and particle-proton cross sections. The cross sections σT(π+d) and σT(π−d) are equal at all measured momenta, which confirms the validity of charge symmetry up to 20GeVc. Results are presented showing the variation of cross sections with momentum; evidence is presented for a small but significant decrease in σT(pp) [and σT(pn)] in the momentum region above 12GeVc.
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The Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.
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Measurements of π±p, K±p, pp, and p¯p elastic scattering are presented for incident momenta of 3, 3.65, 5, and 6 GeVc and momentum transfers typically 0.03 to 1.8 GeV2. The angle and momentum of the scattered particle were measured with the Argonne Effective Mass Spectrometer for 300 000 events, yielding 930 cross-section values with an uncertainty in absolute normalization of ±4%. Only the K+ and proton data show any significant change in slope of the forward diffraction peak with incident momentum. The particle-antiparticle crossover positions are consistent with no energy dependence, average values being 0.14 ± 0.03, 0.190 ± 0.006, and 0.162 ± 0.004 GeV2 for π' s, K' s, and protons, respectively; these errors reflect both statistics and the ±1.5% uncertainty in particle-antiparticle relative normalization. Differences between particle and antiparticle cross sections isolate interference terms between amplitudes of opposite C parity in the t channel; these differences indicate that the imaginary part of the odd-C nonflip-helicity amplitude has a J0(r(−t)12) structure for −t<0.8 GeV2, as predicted by strong absorption models. The cross-section differences for K± and proton-antiproton are in qualitative agreement with the predictions of ω universality, the agreement improving with increasing energy. The corresponding quark-model predictions relating the π± and K± differences failed by more than a factor of 2. We have combined our π± cross sections with other data to better determine the πN amplitudes in a model-independent way; results of this analysis are presented.
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Measurements are reported of the difference ΔσL between proton-proton total cross sections for parallel and antiparallel spin states and of the parameter CLL for proton-proton elastic scattering near 90°, for thirteen energies between 300 and 800 MeV. The ΔσL results agree well with previous ANL ZGS and SIN data, but disagree with recent results from TRIUMF. Attempts to understand the cause of the discrepancy have been unsuccessful, but possible sources are discussed. The ΔσL and CLL results have been used with other experimental data to extract quantities which depend only on spin-singlet, coupled spin-triplet, and spin-triplet partial waves. Structure is found in these quantities, which appears to be associated with the resonantlike D21 and F33 partial waves. Additional similar structure is also found, which may be due either to the P03 partial wave or the (P23,F23) partial-wave pair.
ERROR IS STATISTICAL ONLY (ERROR IN BRACKETS IS STATISTICAL WITH THE ENERGY DEPENDENT UNCERTAINTIES FOLDED IN).
ERRORS ARE STATISTICAL ONLY. THERE IS ADDITION OF 2.0 AND 2.1 PCT SYSTEMATICS.
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We have measured the differential cross section for small angle p−p scattering from 25 to 200 GeV incident energy and in the momentum transfer range 0.015<|t|<0.080 (GeVc)2. We find that the slope of the forward diffraction peak, b(s), increases with energy and can be fitted by the form b(s)=b0+2α′ lns, where b0=8.3±1.3 and α′=0.28±0.13 (GeVc)−2. Such dependence is compatible with the data existing both at higher and lower energies. We have also obtained the energy dependence of the p−p total cross section in the energy range from 48 to 196 GeV. Within our errors which are ± 1.1 mb the total cross section remains constant.
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THE TOTAL CROSS SECTION IS NORMALIZED TO 38.5 +- 0.1 MB AT 48 GEV. IT HAS BEEN DERIVED USING THE OPTICAL THEOREM FROM THE EXTRAPOLATED FORWARD ELASTIC CROSS SECTION AND WITH ALPHA = -0.09.
In an exposure of the 30-in. hydrogen bubble chamber to a 303−GeVc proton beam, 2245 interactions have been observed. The measured total cross section is 39.0±1.0 mb and the average charged particle multiplicity 〈nch〉=8.86±0.16.
TOPOLOGICAL CROSS SECTIONS.
Proton-proton elastic scattering has been measured at the CERN Intersecting Storage Rings in the four-momentum transfer range 0.001 ⩽… t …⩽ 0.015 GeV 2 at centre-of-mass energies of 23 and 31 GeV. The detection of Coulomb scattering and of its interference with nuclear scattering leads to the determination of the real part of the nuclear amplitude and of the total proton-proton cross section by the optical theorem.
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We have measured π+p, π−p, and pp elastic scattering at an incident-beam momentum of 200 GeV/c in the region of −t, four-momentum transfer squared, from 0.021 to 0.665 (GeV/c)2. The data allow an investigation of the t dependence of the logarithmic forward slope parameter b≡(ddt)(lndσdt). In addition to standard parametrization, we use functional forms suggested by the additive quark model to fit the measured dσdt distributions. Within the context of this model we estimate the size of the clothed quark in the pion and proton. Limits on the elastic-scattering amplitude derived from unitarity bounds are checked, and no violations are observed.
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Elastic scattering of hadrons on protons has been measured at momenta of 50, 100, and 200 GeV/c. The meson-proton scattering is found to be independent of momentum and meson type for −t>0.8 (GeV/c)2. The momentum dependence of the pp dip at −t=1.4 (GeV/c)2 was investigated. Slope parameters are given.
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In a 35 000-picture exposure of the 30-in. hydrogen bubble chamber to a 300-GeV/c proton beam at the Fermi National Accelerator Laboratory, 10054 interactions have been observed. The measured total cross section is $40.68 \pm 0.55$ mb, the elastic cross section is $7.89 \pm 0.52$ mb, and the average charged-particle multiplicity for inelastic events is $8.S0 \pm 0.12$.
QUOTED ERRORS INCLUDE EFFECTS OF CORRECTIONS.
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