Diffraction and resonance production in exclusive pp interactions at 100 GeV/c

We have investigated the reactions $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{a}\text{?}\text{and}\text{p}\text{p}\text{a}\text{?}\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}\text{at}\text{100}\text{GeV}\text{/c}$. The $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ final state is dominated by diffractive production of a $\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{(}\text{or}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ system which shows a strong tendency to form $\text{Δ}{}^{\mathrm{++}}\text{π}{}^{\mathrm{?}}\text{(}\text{or}\text{Δ}{}^{\mathrm{++}}\text{π}{}^{\mathrm{+}}\text{)}$. The process $\text{p}\text{p}\text{a}\text{?}\text{Δ}{}^{\mathrm{++}}\text{Δ}{}^{\mathrm{++}}$ is also observed in this reaction, indicating an energy dependence of s^?1.5±0.1. The $\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ channel shows less single diffraction, and has a doubly diffractive component consistent with pomeron factorization. Strong Δ⁺⁺(Δ⁺⁺) production is agoain seen, but in contrast to the $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ channel we also observe considerable ?⁰ production.     

Exclusive reactions in pp interactions at 32 GeV/c

The cross sections of several exclusive reactions in $\text{p}\text{p}$ interactions are given. In the channels $\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{p}\text{p}\text{→}\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ which dominate the interactions, the single and double diffractive dissociations are analysed and compared to the results obtained with K^±p interactions at the same energy, pp and $\text{p}\text{p}$ interactions at other energies. The test of factorization at the p → pπ⁺π^? vertex is well verified. The process $\text{p}\text{p}\text{→ Δ}{}^{\mathrm{++}}\text{Δ}{}^{\mathrm{++}}$ is studied and the cross sections of $\text{Δ}{}^{\mathrm{++}}\text{,}\text{Δ}{}^{\mathrm{++}}\text{, ?}{}^0\text{and}\text{f}{}^0$ production are also given.     

Search for non-strange exotic mesons produced via baryon exchange

Negative results on backward production, via baryon exchange, of exotic non-strange mesons are presented. The reactions π^?p→p_forwardX^?and π^?n→ p_forwardX^?? have been studied with a 12 GeV/cπ^? beam in the Omega spectrometer at CERN. No resonant peak in $\text{X}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{,π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ has been seen. The upper limits obtained on cross sections for exotic meson production $\text{X}\text{→}\text{N}\text{N}\text{π,}\text{N}\text{N}\text{π, 4π}$ are lower than the ?^? backward production cross section in the π^?p→p?^? reaction; this result seems to contradict the predictions of the two-component duality model. Compared to already published experiments in the search for exotics produced via baryon exchange, the sensitivity of this experiment is increased by an order of magnitude.     

Study of the Kππ system produced in K−p → KππN reactions at 14.3 GeV/c

We have studied the $\text{K}\text{ππ}$ system in the 14.3 GeV/c reactions K^?p → K^?π⁺π^?p, $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{and}\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{n}$. The data have been obtained from a 500 000 picture exposure of the CERN 2m HBC. The first two final states are dominated by Q-production in the Kππ system; there is also an L-signal at M (Kππ) ～ 1.75 GeV. The reaction cross sections are compared to K^?p data at other energies. We discuss the Kππ mass dependence of the diffractive production slope. Evidence is presented for a Q^?p versus Q⁺p differential cross section cross-over around |t| = 0.17 GeV². A t-channel isospin analysis for the $\text{KN}\text{→}\text{K}\text{1(890)π}\text{N}$ channels in the Q-region shows that the I = 1 exchange amplitude is $\text{? 10\%}$ of the dominant I = 0 exchange amplitude. The Kππ decay distributions indicate a predominant J^P = 1⁺ state in the Q-region, and an important J^P = 2^? contribution in the L-region. We find neither s-channel nor t-channel helicity conservation at the meson vertex in the Q- or L-regions. The Kπ angular correlation moments within the Kππ diffractive system are characteristic of Kπ elastic scattering, suggesting a π-exchange Deck-type production mechanism. There is evidence for a Kf⁰ and κπ contribution (where κ is the J^P(Kπ) = 0⁺ state) to the diffractive Kππ system. A fit to the $\text{K}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{K}{}^0\text{π}{}^{\mathrm{?}}\text{π}{}^0$ Dalitz-plot distributions for the Q-re gion indicates that the ratio of $\text{K}\text{?}\text{to K}{}^1\text{π}$ decay amplitudes decreases with increasing Kππ mass.     

Experimental analysis of pp interactions between 0 and 1.2 GeV/c: Evidence for a pp → 5π effect near 1950 MeV/c2

An experimental analysis of $\text{p}\text{p}$ interactions between the $\text{p}$p threshold (√s = 1878 MeV) and √s = 2 100 MeV leads to clear evidence for an s-channel effect in the reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{at}\text{1949 ± 10}\text{MeV}\text{/c}{}^2\text{(Γ ? 80}\text{MeV}\text{/c}{}^2\text{)}$. A comparison is made with the backward elastic scattering and charge-exchange behaviour. An interpretation in terms of an object strongly coupled to mesonic decay modes, with small or middle-sized elasticity (x ? 0.135_?0.06^+0.13) is given. No significant narrow structure is observed in the backward elastic scattering between 1.9 and 2 GeV. The experimental resolution of √s in this case is 2 MeV.     

The reaction pp→pπ−π+p at 25 and 40 GeV/c

The reaction $\text{p}\text{p}\text{→}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{p}$ has been studied at 25 and 40 GeV/c at the Serpukhov proton synchroton using the CERN-IHEP spectrometer. The differential cross section has been determined as a function of four-momentum transfer to the proton (0.05–0.30 (GeV/c)²) and $\text{p}\text{ππ}$ mass (up to 2.2 and 2.6 GeV/c²). At both energies there is a broad low-mass maximum with an enhancement at 1.6–1.8 GeV/c². The cross section in a given mass band falls rapidly with |t|, with an exponential slope that decreases with increasing mass. In both the background and the 1.7 GeV/c² peak there is a strong $\text{Δ}{}^{\mathrm{??}}\text{π}{}^{\mathrm{+}}$ component. Possible spin-parity (J^P) contributions to it are discussed. Throughout the range 1.5–2.2 GeV there is at least one state of $\text{J ?}\text{3}\text{2}$ and there is interference between states of opposite P, |ΔJ| ? 1. At the peak there is a $\text{J ?}\text{5}\text{2}$ component. There are striking parallels between this reaction and the boson reactions π^?p→π^?π^?π⁺p and K^? → K^?π^?π⁺p.     

Partial-wave analysis of the low-mass (π+π−p) system produced in K−p interactions at 4.2 GeV/c

A partial-wave analysis of the low-mass (π⁺π^?p) system produced in the reaction K^?p → K^?(π⁺π^?p) at 4.2 GeV/c incident momentum is performed in order to study the two (π⁺π^?p) enhancements around 1500 and 1700 MeV. It is found that the low-mass (π⁺π^?p) system can be described using the spin-parity states $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}\text{,}\text{3}\text{2}{}^{\mathrm{?}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ only. In the 1500 MeV region contributions are observed from the $\text{1}\text{2}{}^{\mathrm{+}}$ wave decaying into p? and the $\text{3}\text{2}{}^{\mathrm{?}}$ wave decaying into Δ⁺⁺π^?; in the 1700 MeV region contributions are found from the $\text{1}\text{2}{}^{\mathrm{+}}$ wave decaying into Δ⁺⁺π^?, the $\text{3}\text{2}{}^{\mathrm{?}}$ wave decaying into p?, and the $\text{5}\text{2}{}^{\mathrm{+}}$ wave decaying into p?.     

Determination of and resonance structure in pp → ππ partial waves

We perform a simultaneous analysis of $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{and}\text{p}\text{p}\text{→π}{}^0\text{π}{}^0$ data in the 1–2GeV/c laboratory momentum range. We consider all Barrelet-related π^?π⁺ amplitudes and find the π⁰π⁰ data provide a severe constraint, essentially determining all the partial wave amplitudes aside from a residual PF wave ambiguity. We study the resonant character of the partial waves and compare these with the result of Carter's simplified analysis of just the π^?π⁺ data.     

Experimental analysis of the properties of the five-pion effect observed in pp interactions near 1950 MeV/c2

The properties of the effect observed in the reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{at}\text{1949 ± 10}\text{MeV}\text{/c}{}^2\text{(τ ? 80}\text{MeV}\text{/c}{}^2\text{)}$ are studied. The ω⁰?⁰, A₂⁰π⁺π^? and π⁺π^?π⁺π^?π⁰ (non-resonant) channels are found to be coupled with this object. The assignment I^G = 1^? is established and an analysis of the √s behaviour of the density matrix elements for the final state ω⁰?⁰ clearly favour J^P = 2⁺, 4⁺… Comparisons are made with present theoretical schemes describing this mass region.     

Evidence for two narrow pp resonances at 2020 MeV and 2200 MeV

From the study of the reaction $\text{π}{}^{\mathrm{?}}\text{p→p}{}_{\mathrm{F}}\text{p}\text{p}\text{π}{}^{\mathrm{?}}$ using a fast proton (p_F) trigger device in the CERN Omega spectrometer, we find evidence for two narrow $\text{p}\text{p}$ states produced mainly in association with a Δ° (1232) and a N° (1520). The statistical significance of each peak is greater than 6 standard deviations. Masses and natural widths of these resonances are respectively M = 2020 ± 3 MeV, Λ₁ = 24 ± 12 MeV and M₂ = 2204 ± 5 MeV, Λ₂ = 16_?16⁺²⁰ MeV. Our data are consistent with a small production of the narrow ～ 1935 MeV resonance already reported. Production cross sections for these new $\text{p}\text{p}$ resonances are given.     

Diffractive processes in pp interactions at 5.1 GeV/c

We have investigated the interaction $\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ at 5.1 GeV/c using the prism plot method. In addition to the $\text{Δ}{}^{\mathrm{++}}\text{Δ}{}^{\mathrm{??}}$ final state, we isolate the three particle diffractive dissociation of the proton and antiproton into (pπ⁺π^?) and $\text{(}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ respectively. We estimate this process accounts for 30% of the final state.     

Measurement of the isospin amplitude ∣M012∣ in the reaction γn → ϱ0(pπ−) at 7.5 GeV

The cross-channel isospin amplitude $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ is measured in the single reaction γn → ?⁰(pπ^?) at 7.5 GeV assuming the ?⁰ dominance model. A low-mass enhancement is found for $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}{}^2$ in the range of m(pπ^?) of ～1.2 to ～1.7 GeV. The reaction strongly violates s-channel helicity conservation but is consistent with t-channel helicity conservation. The $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ features are found to be very similar to those obtained in previous analyses of πp → π(Nπ) reactions.     

Investigation of rare non-strange decay modes of the f meson in Π+p interactions at 5GeVc

Rare decay modes of the f meson are studied in the final states Δ⁺⁺π⁺π^?π⁺π^?, Δ⁺⁺π⁺π^?MM and Δ⁺⁺π⁺π^?π⁺π^?MM. The ratio $\text{Γ (f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{π}{}^0\text{)}\text{Γ(f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ is 0.23 ± 0.09 and Γ(f → 4 π) saturates the f inelasticity. A 2 s.d. upper limit of 0.09 is found for the branching ratio $\text{(f → ηη)}\text{(f → 2π)}$.     

Measurement of the polarization parameter for antiproton-proton annihilation into charged pion and kaon pairs between 1.0 and 2.2 GeV/c

The polarization parameter P for the reactions $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ and $\text{p}\text{p}\text{→}\text{K}{}^{\mathrm{?}}\text{K}{}^{\mathrm{+}}$ has been measured over essentially the full angular range at ll laboratory momenta between 1.0 and 2.2. GeV/c, using a proton target polarized perpendicular to the scattering plane. The angles and momenta of both final state particles were determined from wire spark chambers, using the deflection caused by the polarized target magnet. Between 1000 and 5300 π^?π⁺ events, and 140 and 1300 K^?K⁺ events, were measured at each momentum. Differential cross sections for $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ were obtained. These are in excellent agreement with previous results. The polarization parameter for both channels is very close to +1 over much of the angular range. Legendre polynomial fits to the data are presented.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.     

Some three-body final states in K−p reactions at 14.3 GeV/c

We present experimental results on a number of K^?p reactions at 14.3 GeV/c that have three bodies in the final state. The final states are $\text{K}{}^{\mathrm{?}}\text{ω}\text{p}\text{,}\text{K}{}^{\mathrm{?}}\text{π}\text{p}\text{, Λπ}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{, Λ}\text{K}{}^{\mathrm{+}}\text{K}{}^{\mathrm{?}}\text{, Λp}\text{p}\text{,}\text{K}{}^1{}^{\mathrm{?}}\text{ω}\text{p}\text{, Λ(1520)}\text{K}{}^{\mathrm{+}}\text{K}{}^{\mathrm{?}}\text{and}\text{Λ(1520)}\text{p}\text{p}$. Whenever, with one exception explained by the Zweig rule, there is a K^? or a proton in the final state, there is a diffractive-like threshold enhancement in the mass spectrum of the two recoiling particles. These enhancements account for a large fraction of the events in all but the Λπ⁺π^? final state, where they cannot occur, and which is dominated by resonance production. We find evidence for the Q₁(1300) decaying into K^?ω.     

Determining the KS→3π amplitude in pp(OR e+e−)→K0K0

The amplitude ratio 〈3π|T|K_S〉/〈3π|T|K_L〉 can be well determined in e⁺e^? (or low energy $\text{p}\text{p}\text{)→K}{}^{\mathrm{o}}\text{K}{}^{\mathrm{o}}$ from the decay time-distribution when each produced kaon→3π, other unknown parameters of the distribution being obtainable from corresponding observations involving known channels like ππ.     

Two-quasiproton states in 168Er studied by the 169Tm(t, α)168Er reaction

The ${}^{169}\text{Tm}\text{(}\text{t}\text{, α)}{}^{168}\text{Er}$ reaction has been studied using 17 MeV polarized tritons from the Los Alamos National Laboratory tandem Van de Graaff accelerator. The α-spectra were analyzed with a Q3D magnetic spectrometer. The overall energy resolution was typically ~ 15 keV (FHWM) and angular distributions of cross sections and analyzing powers were obtained for levels up to ~ 2.7 MeV. The fact that spins and parities for all levels up to ? 2 MeV were previously known from an extensive series of (n, γ) studies made it possible to determine specific two-quasiproton structures for many bands from the present results. The K^π = 2⁺ γ-vibrational band was found to have a large $\text{3}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ admixture, consistent with the predicted microscopic composition of this phonon, but no $\text{5}\text{2}\text{[413]}{}_{\mathrm{<mtext>p</mtext>}}\text{?}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ component was observed. The K^π = 0₄⁺ band at 1833 keV has ～ 25% of the $\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}\text{?}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ two-quasiproton strength. This is in excellent agreement with the Soloviev model but is inconsistent with the interacting boson model, in which the K^π = 0₄⁺ band is composed almost completely of multiphonon configurations that should not be populated in a single-nucleon transfer reaction. The $\text{K}{}^{\mathrm{\pi }}\text{= 4}{}^{\mathrm{?}}\text{,}\text{7}\text{2}{}^{\mathrm{?}}\text{[523]}{}_{\mathrm{<mtext>p</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ two-quasiproton and the $\text{K}{}^{\mathrm{\pi }}\text{= 4}{}^{\mathrm{?}}\text{,}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}{}_{\mathrm{<mtext>n</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{?}}\text{[521]}{}_{\mathrm{<mtext>n</mtext>}}$ two-quasineutron states are mixed strongly with each other, but the two K^π = 3^? bands composed of antiparallel couplings of the same particles are not. A good qualitative explanation of this mixing pattern is provided in terms of the effective neutron-proton interaction.     

Coherent production of multimeson final states on A ∼ 20 nuclei by K− of 5.5, 10.0, 12.7 GeV

Coherent production of $\text{K}\text{π,}\text{K}\text{2π}\text{and}\text{K}\text{3π}$ final states from A ～ 20 nuclei by K^? beams of 5.5, 10.0 and 12.7 GeV is analyzed. Final states with ? 2π^O are included. Coherent $\text{K}\text{π}$ production occurs (although forbidden via 0⁺ exchange) and is dominated by the $\text{K}$¹ (890). The shape of the t distribution, the alignment of the produced meson and the ratio of the cross section on nuclei to that on hydrogen are consistent with optical model predictions assuming that $\text{K}$¹ (890) are produced on single nucleons by exchange of isoscalar trajectories of natural parity (J^P = 1^?, 2⁺, etc.) and that the $\text{K}$¹ (890) absorption in nuclear matter equals that of the K^?. Coherent $\text{K}\text{ππ}$ production (allowed via 0⁺, 1^?, 2⁺, etc. exchange) is dominated by the Q phenomenon. A Dalitz plot and angular correlation analysis yields values for $\text{K}\text{?/}\text{K}{}^1\text{π}$ fractions, and shows that $\text{J}{}^{\mathrm{P}}\text{= 1}{}^{\mathrm{+}}\text{S-wave}\text{K}{}^1\text{π}$ dominates the coherently produced Q. The helicity of the Q is found to be compatible with 0. The Q^? -nucleaon total cross section is estimated to be 0.98_?0.37⁺⁰²⁴ times the $\text{K}$^? -nucleon total cross section from a comparison of the coherent Q-production cross section with corresponding hydrogen cross sections at 10 and 12.7 GeV. We observe coherent production of $\text{K}$ω. The ration $\text{K}\text{ω/}\text{K}\text{ππ}$ coherently produced in the Q mass region is (4 ± 1)%. Coherent production of $\text{K}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{K}{}^{\mathrm{<mtext>O</mtext>}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{<mtext>O</mtext>}}$ is observed in the L region. Coherent production is not observed in the K4π channels.     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.