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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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.
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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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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