Two mutually-repelling self-avoiding walks: A Monte Carlo study

We consider two self-avoiding walks (SAWs) on a square lattice, beginning simultaneously from two arbitrary nearest neighbours. The walks cross neither themselves nor each other, and grow simultaneously. Using Monte Carlo technique we study the variation, with the length N of the walks, of the average end-to-end distance 〈R_N〉 of each walk and of their average separation 〈S_N〉. We find 〈R_N²〉∞N^2ν, 〈S_N²〉∞N^2λ, where ν ≈ λ ≈ 0.75 for two ordinary SAWs and ν ≈ λ ≈ 0.67 for two growing SAWs in two dimensions. For two directed SAWs, we find 〈R_N∥/⊥²〉 ∞ N^2ν∥/⊥ and 〈S_N∥/⊥² 〉 ∞ N^2λ_∥/⊥, where ν_∥ ≈ 1.00, ν_⊥ ≈ 0.56, λ_∥ ≈ 0.50 and λ_⊥ ≈ 0.59 in two dimensions. We thus find an indirect excluded volume effect on one directed SAW, due to the other.     

Estimate of the mass composition of cosmic rays with E 0 ≤ 1018 eV according to the data from a new muon detector at the Yakutsk EAS array

The lateral distribution function of muons with the threshold E _μ ≈ 0.5secθ GeV (θ is the zenith angle) in extensive air showers with energy E ₀ ≥ 10¹⁷ eV has been examined using a new detector located at a distance of 180 m from the center of the Yakutsk array. This detector has been operating since autumn 2012 and consists of 27 autonomous scintillator counters with an area of 2 m². The experimental data have been compared to the calculations within the QGSJET-01 model with the CORSIKA air shower simulator. Agreement between the experimental data and calculations is achieved for the mixed composition of cosmic rays with the average atomic number satisfying the condition 〈lnA〉 ≈ 2.84 ± 0.08.     

Multihadron production in e+e− collisions up to 3 GeV total C.M. energy

New results on the multihadron production by electron and positron beams colliding with a total energy of up to 3 GeV are reported. Disregarding possible kaon final states, the ratio σ_mh/σ_μμ of the total multihadron cross-section to the point-like cross section for process e⁺e^?→μ⁺μ^? has an average value of 1.58 ± 0.25 in the energy interval 2.6–3.0 GeV. The average charged multiplicity over this energy range is 〈n_c〉 = 2.9 ± 0.3.     

Simulations of inclusive π+p reactions at 16 GeV/c

The influence of inclusive phase space on semi-realistic multiplicity and matrix element assumptions is studied for π⁺p inclusive reactions at 16 GeV/c. It is concluded that a large part of the beam-like leading pion effect is due to charge conservation. The simulated 〈p_⊥〉 is about 60% of that expected from the matrix elements alone.     

Transverse momentum of hadrons produced in ν and ν interactions on an isoscalar target in BEBC

The average transverse momentum squared, 〈p_⊥²〉, of hadrons is studied as a function of W² and of Q² for ν and $\text{ν}$ interactions on an isoscalar target. An increase of 〈p_⊥²〉 with W² is observed for the hadrons emitted forward in the hadronic c.m.s. The p_⊥ dependence of the fragmentation function is found to factorise from the structure function at fixed W, but does not factorise at fixed Q². Unlike the case of forward-going particles, the 〈p_⊥²〉 of hadrons going backward in the c.m.s. shows no strong dependence on W².     

On the intrinsic transverse momentum of partons

Using simple assumptions it is shown that the average transverse momentum of partons is determined by their structure functions. The x-dependence obtained this way agrees well with the experimental data. The size is controlled by the invariant mass of the nucleon core and the behaviour of the structure functions near x = 1. We obtain a lower limit for the intrinsic contribution to 〈k_⊥〉_μμ of ～ 400 MeV.     

Transverse momentum in Drell-Yan processes

We study the transverse momentum distribution of muon pairs from Drell-Yan processes in QCD. In particular the dependence of 〈k_⊥²〉 on Q² is considered. QCD predicts an approximately linear rise of 〈k_⊥²〉 with S or Q² only at fixed τ = Q²/S. The slope as a function of τ is quantitatively studied for P$\text{P}$ and P-nucleus scattering. The most recent data showing a rather flat 〈k_⊥²〉 in Q² at fixed S are found to be consistent with QCD.     

On the particle multiplicity distributions at high energy

An experiment has been performed to study the inclusive photoproduction of π⁰ mesons. Photoproduced π⁰'s were detected in a hodoscope consisting of 14 lead glass Cerenkov counters. To obtain the cross sections at a photon energy of 6 GeV we used the photon-difference method. Data are presented in terms of the Feynman variable $\text{x = q}{}_6{}^1\text{(√s/2)}$ and the trnasverse momentum q⊥. We have measured four q⊥ distributions at x = 0.2, 0.4, 0.6 and 0.8. The results dhow that the π⁰ rate at small values of q⊥ is smaller than the π± rate. The data can be fitted smoothly by a form A exp (?Bq_⊥²) with a value about 3.5 GeV^?2 for the slope parameter B.     

Observation of QCD effects in transverse momenta of e+e− jets

Probability distributions of the total transverse momenta (K⊥) of charged particles produced in hadronic jets in e⁺e^? annihilations have been measured for center of mass energies in the range from 9.2 to 31.6 GeV. A linear increase of the average K_⊥² with Q² is observed. The data are successfully compared with high order QCD predictions (according to a simple q$\text{q}$ picture supplemented by multiple emission of soft gluons). Deviations from this picture at the highest energies and large K_⊥ are then analyzed in terms of hard gluon bremsstrahlung and qualitative agreement is found with first order QCD predictions. Scaling “in the mean” is found to be valid both for jet and single particle transverse momenta.     

Transverse momentum of charged hadrons observed in deep inelastic muon scattering

The transverse momenta of charged hadrons produced in high energy muon-proton scattering have been studied. The average squared transverse momentum 〈p²_⊥〉 shows a strong dependence on z = E_h/v characteristic of intrinsic momentum effects and a significant rise as a function of s = W². The W², q², x and z dependences of the data are compared with the predictions of a perturbative QCD model.     

X-ray determination of the mean-square vibrational amplitudes of atoms in nearly perfect CdS crystals

The mean-square amplitudes of Cd and S atoms in CdS were determined for vibrations parallel as well as perpendicular to the c-axis. The results were obtained by measuring the temperature dependence of X-ray integrated intensities for reflections from both basal and prismatic planes in nearly perfect crystals. The analysis of the experimental data is given in detail. The following results were found for T = 295°K: 〈u²_Cd〉_∥ = 2.85±0.04×10^?18cm², 〈u²_s〉_∥ = 1.94 ± 0.08 × 10^?18cm², 〈u²_Cd〉_⊥= 2.39 ± 0.04 × 10^?18cm² and 〈u²_s〉⊥ = 1.63 ± 0.08 × 10^?18cm². The fact that Cd atoms have a larger vibrational amplitude than the S atoms is briefly discussed.     

Observation of πo mesons with large transverse momentum in high-energy proton-proton collisions

Invariant cross-sections are presented for the inclusive reaction p + p → π^o + anything, Measurements of large transverse momentum π^o's (2.5 GeV/c<p_⊥<9 GeV/c) were made near 90° at the CERN ISR at five centre-of-mass energies (√s = 23.5, 30.6, 44.8, 52.7 and 62.4 GeV. At large p_⊥, the invariant cross-sections are seem to vary with s and p_⊥, in good agreement with a fit of the form Ap_⊥^?nF(p_⊥/√s), with n≈8 and F(p_⊥/√s)≈exp(?26p_⊥/√s).     

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.     

Evidence for planar events and a forward double jet structure in deep inelastic Muon scattering

The final states of charged hadrons produced in 280 GeV μp scattering are analysed with respect to their planarity and jet structure. Distributions of p_⊥² in and p_{⊥ out}² are presented. A two jet structure in the forward hemisphere is observed for events with high p_⊥ tracks are predicted by QCD models.     

Deep inelastic neutrino interactions in the bubble chamber skat at 2–30 GeV

Data on inclusive deep inelastic neutrino interactions at 2–30 GeV are presented. Distributions in x, y and 〈Q²〉 dependence on neutrino energy are compared with quark-parton model predictions. The 〈Q²〉 dependence on energy has the form: 〈Q²〉 = (0.2 ± 0.1) + (0.25 ± 0.02) E_v.     

Contributions from higher twist effects to the quark fragmentation functions in neutrino data

Quark fragmentation functions are studied with ≈3500 charged current events induced in the bubble chamber Gargamelle by neutrinos of the SPS wide band beam, with 〈E_ν〉 ≈ 25 GeV. The Q² and W² regions covered by this experiment are Q² ≈ 0–40 GeV² and W² ≈ 1–100 GeV², the mean values being 〈Q²〉 = 6.5 GeV², 〈W²〉 = 22GeV². A correlation between the variables $\text{z =}\text{E}{}_{\mathrm{\pi }}\text{E}{}_{\mathrm{<mtext>H</mtext>}}$ and $\text{y =}\text{E}{}_{\mathrm{<mtext>H</mtext>}}\text{E}{}_{\mathrm{v}}$ is found in the data in the region Q² = 1–10 GeV², which can be explained in terms of higher twist effects. These effects reproduce the Q² evolution of the non-singlet moments of the fragmentation function without any need for logarithmic terms.     

Spectra of negative particles and photons in collisions of p−W and16O−W at 200 GeV/u

p _⊥ spectra of negative particles were measured for p?W and¹⁶O?W collisions at 200 GeV/u in the rapidity range 0.9<y<1.9. Within the systematic errors of 20% the spectra are identical in the range 0.05<p _⊥<2.0 GeV/c. The p?W and¹⁶O?W spectra exhibit an exponential shape forp _⊥ >250 MeV/c. This is consistent with previous p?A data, but there is a significant excess above this exponential at lowerp _⊥. Photon spectra were measured using a conversion method. Theirp _⊥ distribution agrees in shape with the sum of known hadronic γ-sources.     

Production and decay of quark-gluon strings: inclusive distributions of hadrons in p⊥ and x

The dependence of inclusive cross sections of the production of hadrons $\text{p}\text{p}\text{→ hX}$ on p_⊥ (and also on x and √s) is calculated at high energy in the region of small p_⊥ ? 1–2 GeV. The model of production and decay of quark-gluon strings is used under the simplest assumptions about the k_⊥ dependence of the quark distributions in nucleons ～ exp(?γ₁k²_⊥) and about the form of the string fragmentation function $\text{G}\text{?}{}^{\mathrm{<mtext>h</mtext>}}\text{～}\text{exp}\text{[?γ}{}^{\mathrm{<mtext>h</mtext>}}\text{(}\text{p}{}_{\mathrm{\perp }}\text{? z}\text{k}{}_{\mathrm{\perp }}\text{)}{}^2\text{]}$ where γ₁ and γ^h are some constants. The theory reproduces all existing experimental data and yields the “seagull effect” for the dependence of 〈p_⊥〉 on x. Predictions are given for the p_⊥ dependence of the spectra of π^± mesons produced at high energies at SPS and other future colliders.     

Fluctuations and defects in the spiral state of magnetic superconductors

We want to point out three properties of a magnetic superconductor: (i) The absence of true long-range order in the spiral state leads to the structure functions behaving like (q₆ ? q₀)^η?2 and (q²_⊥)^η?2 for q_⊥=0 and q₆=0, respectively, where q₀ is the preferred momentum. The indices η are measured via Bragg-like neutron scattering. (ii) The state is perforated by line-like defects. (iii) Above some critical temperature the defect lines proliferate, thereby destroying the spiral quasi-order.     

Fission of <Superscript>232</Superscript>Th in a spallation neutron field

The spatial distributions of thorium fission reaction rate in a spallation neutron field of thick lead target bombarded by protons or deuterons with energy between 1.0 and 3.7 GeV were measured. Approximately a linear dependence of the thorium fission rate on the beam energy is observed. The mean fission cross section of ²³²Th 〈σ _f 〉 ≈ 123 mb and it does not depend on energy and type of the beam particles.