Correlations between neutral and charged pions in multiparticle production

We make a theoretical and phenomenological study of correlations between neutral and charged pions in multiparticle production in the framework of the so-called σ, π, ? and ?-? models. Following the method of Drijard and Pokorski, we express the predictions of various models in terms of the negative multiplicity distribution, which is known experimentally. In particular we compute the average number of $\text{π}{}^0\text{,}\text{n}{}_0\text{(n\_)}$, and the integral of π⁰?π⁰ correlations, f₀²(n_), as a function of the number of negative pions; we study also the total multiplicity distribution P(N) and its first two moments $\text{N}\text{and}\text{D}{}_{\mathrm{<mtext>tot</mtext>}}{}^2$. We show that with the present experimental accuracy neither $\text{n}{}_0\text{(n\_)}$ allow us to discriminate between the different models.     

Uncorrelated-jet-model predictions for the multiplicity distribution of π− mesons produced in high-energy annihilations p¯p → pions

The uncorrelated jet model is used to obtain a grand partition function for the pions produced in the process $\overline{p}p$ → pions. The grand partition function is evaluated asymptotically for large energies. It is used to relate the correlation parameter f₂ = 〈n_?²〉 ? 〈n_?〉² ? 〈n_?〉 to the average multiplicity of negative pions 〈n_?〉. The results are consistent with the presently available experimental data, though data at higher energies are necessary to draw physically interesting conclusions.     

Inclusive particle spectra in p(π+)n interactions at 195 GeV/c

We present results on single-particle inclusive distributions in p(π⁺)n reactions from a Fermilab experiment using the hybrid 30″ bubble chamber and PWC facility. Distributions in rapidity, y, Feynman x and p²_T for π⁺ and π^? are presented and compared with other experiments. The effects of different targets and projectiles (neutrons, protons and pions) on the distributions are demonstrated and discussed in terms of projectile and target fragmentation. The average transverse momentum 〈P_T〉 is studied as a function of x, y and multiplicity.     

Scaling of semi-inclusive events in <Emphasis Type="Italic">pp</Emphasis> interactions

The normalized single-particle semi-inclusive double-differential spectrum of π^t- mesons from pp interactions at 6.6–400 GeV/c and the relative concentration of π⁰ and K _S ⁰ mesons in such events of fixed multiplicity of π^? mesons are completely determined by specifying any feature of this spectrum—for example, 〈y²〉 _n or 〈E〉 _n . Therefore, a two-parameter sample of semi-inclusive events that depends on the energy and the multiplicity reduces to a one-parameter sample.     

On correlations between charged and neutral particles in a cluster model

Correlations between charged and neutral pions at high energies are investigated in the framework of a cluster model in which neutral clusters have a decay distribution determined by isospin conservation and statistical independence. For 〈n₀〉_n? an asymptotic expansion around the mean 〈n_?〉 leading asymptotically to a quadratic form in n_? is derived and compared with data.     

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.     

Charged multiplicity distributions in pd and π+d interactions at 195 GeV/c

Topological inelastic cross-sections and average multiplicities for pd and π⁺d interactions at 195 GeV/c, are obtained from an exposure of the NAL 30″ proportional wire chamber-bubble chamber hybrid system to a positive π⁺/p beam. We find that 〈n_c〉_pn = 7.67 ± 0.25, and 〈n_c〉_π⁺n = 7.56 ± 0.30, yielding a negative multiplicity difference between pn and pp of 0.50 ± 0.14, and that σ_n(pp) is approximattely interleaved between σ_n?1(pn).     

The missing mass squared dependence of the average charged particle multiplicity in the reaction K+p → KoX++ from 5–16 GeV/c

The average charged particle multiplicity, 〈n_ch(M_X²)〉, in the reaction K⁺p→K^oX⁺⁺ is studied as a function of the mass squared, M_X², of the recoil system X and also as a function of the K^o transverse momentum, p_T, at incident momenta of 5.0, 8.2 and 16.0 GeV/c. The complete data samples yield distributions which are not independent of c.m. energy squared, s, They exhibit a linear dependence on log (M_X²_X/M_o²)[M_o²=1 GeV²] with a change in slope occurring for M_X²≈s/2, and do not agree with the corresponding distributions of 〈n_ch〉 as a function of s for K⁺ p inelastic scattering. Sub-samples of the data for which K^o production via beam fragmentation, central production and target fragmentation are expected to be the dominant mechanisms show that, within error, the distribution of 〈n_ch(M_X²)〉 versus M_X² is independent of incident momentum for each sub-sample separately. In particular in the beam fragmentation region the 〈n_ch(M_X²)〉 versus M_X² distribution agrees rather well with that of 〈n_ch〉 versus s for inelastic K⁺p interactions. The latter result agrees with recent results on the reactions pp → pX and π^?p → pX in the NAL energy range. Evidence is presented for the presence of different production mechanisms in these separate regions.     

Multihadronic decays and partial widths of the J/Ψ (3100) resonance produced in e+e− annihilation at adone

The reactions e⁺e^?→ hadrons and e⁺e⁺e^?→e⁺e^? have been studied at the J/gY (3100) resonance). The relative weights of the topological cross sections for fixed charged multiplicity are σ₂=(32±5)%, σ₄=(49±8)%, σ₆=(18±3)%, and σ₈=(1±0.6)%. The average pion multiplicities are 〈n_ch〉=3.8±0.3 and 〈n_{π^o〉=3.1±0.8}. The decay widths are Γ_e=(4.6±0.8) keV, Γ_h=(59±24) keV, and Γ=(68±26) keV.     

Characteristics of π−-meson multiplicity distributions in central collisions of12C and16O with nuclei at a momentum of 4.5 GeV/c per incident nucleon

Multiplicities of π^?-mesons from central collisions of¹²C and¹⁶O(4.5 GeV/c/n momentum) with several target nuclei were studied in a streamer chamber experiment. The parameter η=(〈n _? ² 〉?〈n_?〉²)/〈n_?〉 was determined for several samples of events characterized by different values of Θ _ch — the “vetoangle” for emission of the projectile charged fragments. The value of η is shown to decrease when the projectile mass number increases from 12 to 16 and to decrease significantly when Θ _ch increases from 0° to 4°, whereas it remains nearly constant when Θ _ch increases further to 14°. The results are compared with predictions of some theoretical models.     

Inclusive production of ρ0 in νp charged current interactions

Inclusive ρ⁰ production in neutrino-proton charged-current interactions is studied, using a sample of 7831 events obtained in BEBC filled with hydrogen and exposed to the CERN wideband neutrino beam. An average multiplicity of 0.14±0.02 ρ⁰ per event is found, corresponding to a ratio 〈ρ⁰〉/〈π^?〉=0.13±0.02. The ρ⁰ production characteristics are determined as functions of leptonic variables (W, Q², χ_B) and hadronic variables (χ_F, z, p_t²) and are found to be similar to those determined for hadron- and other lepton-induced reactions.     

A scaling test in π− p semi-inclusive reactions

The scaling properties of the semi-inclusive reactions π^?p → π^?+(n?1) charged + neutrals at 7.5 and 21 GeV/c are analysed. The distributions of the h-functions on the x-variable for π^? particles indicate the presence of a limited scaling. The choosing of a certain value for the reduced charged multiplicity $\text{n}\text{〈n〉}$ is pointed out.     

Charged particle multiplicity distributions for 32 GeV/c K±p and pp interactions and for 50 GeV/c π±p interactions

Topological cross sections are presented for K⁺p, K^?p and $\text{p}\text{p}$ interations at 32 GeV/c and for π⁺p and π^?p interactions at 50 GeV/c observed in the 4.5 m Mirabelle hydrogen bubble chamber at Serpukhov. Parameters characterizing the behaviour of the multiplicity distributions, namely 〈n_c〉, D and f₂ and the normalized moments are given. The dependence of these parameters on the energy and the nature of the beam particle is discussed. The multiplicity distributions obtained cannot be described by a single function in the KNO variables.     

Determination of the fire-ball dimensions from second-order interference between two pions

Positive correlations are observed for pion pairs of equal charge and similar momentum vectors, produced in the reactions πp→p+5π and πp→p + 7π at 4 to 25 GeV/c. The results are consistent with being due to the second-order interference effects expected for pairs of identical bosons and lead to the determination of the average dimension of the “fire-ball’ from which the pions are emitted (〈R〉 = 1.0 ± _?0.2^+0.4 fm). Attempts are made to study the fire-ball shape by selecting pions pair emitted in various polar and azimuthal directions.     

Remarks on the charged multiplicity of hadronic Z0(91) decays

The charged multiplicity distribution of hadronic decays of Z ⁰ from LEP and those of inclusive $e^{+}+e^{-}?ghtarrow h{?erline h} at E_{? cm}=14 {? to} 60 {? GeV}$ at E _cm = 14 to 61 GeV are analyzed using a Poisson-type distribution for photon statistics, due to Scully-Lamb. Its two parameters are expressed in terms of 〈n〉 and f ₂ = 〈n(n ? 1)〉 ? 〈n〉² of the data in order to perform no-free-parameter fits. It is found that f₂ behaves like $E_{? cm}^{a}$ with a = 2.01 ± 0.11, whereas C ₂ = 〈n ²〉/〈n〉² ～ E _cm with ΔC ₂/ΔE _cm = (1.81 ± 0.14)·10^?3.     

Isospin symmetry violating effects and scattering length extraction from kaon decays

The isospin symmetry breaking effects in the charged kaons decays to two or three pions are considered. In semileptonic decay K ^± → π ⁺ π ^?e^± ν (called K _e4) these effects turn out to be crucial for correct extraction of ππ scattering lengths. Taking in account electromagnetic interaction between the pions in the final state and isospin symmetry breaking due to different masses of charged and neutral pions allows to adjust the values of scattering lengths obtained from experimental data on K _e4 decay and predictions of Chiral Perturbation Theory (ChPT). Final state interactions of pions in the decay K ^± → π ^± π ⁰ π ⁰ leading to the anomaly (cusp) in the π ⁰ π ⁰ invariant mass distribution in the vicinity of charged pions’ threshold are discussed and recent results of accounting of the electromagnetic interaction among charged pions leading to π ⁺ π ^? bound states (pioniumatom) just under the charged pions’ threshold are presented.     

Inelastic hadron-nucleus interactions at 20 and 37 GeV/c

The experiment studies charged particle production for π^?, K^?, and $\text{p}$ interactions on nuclei at 20 and 37 GeV/c at the CERN SPS. A non-magnetic detector, consisting of CsI(Tl) scintillation and lucite ?erenkov counters, distinguishes between fast particles, mainly pions, and slow particles, mainly nucleons, with a cut at velocity β ≈ 0.7. Angular distributions, multiplicity distributions and correlations of slow and fast particles were analysed. It is shown that the measurement of the correlations can provide a critical test for different theoretical models of the hadron-nucleus interaction. At the energies studied so far a systematic deviation from KNO scaling is observed. This gives further support to the “standard picture” of the hadron-nucleus interaction and it contrasts with predictions of the coherent-tube model. The regularity observed for the angular distribution of fast secondaries as a function of the number of slow particles can only be explained by combining features predicted by different models.     

π0 Multiplicities in π+;p interactions at 10.5 GeVc

Measurement of the π⁰ multiplicity cross sections are reported for n₀ ? 6, where n⁰ is the number of produced π⁰ particles, and for N ? 8, where N is the number of charged particles. The inclusive π⁰ cross section is 29 ± 3 mb. Values for the correlation parameters, 〈n₀〉 and 〈n₀(n₀ ? 1)〉², are also presented.