Charged pion production in 70 GeV/cK + p interactions

Inclusive charged pion production is studied in an exposure of BEBC, filled with hydrogen, to an incidentK ⁺ beam of 70 GeV/c. Total cross sections for pion production and inclusive longitudinal and transverse momentum distributions of π^?'s and of positive particles are presented and compared with data at lower energies. Earlier evidence for scaling in the fragmentation regions is confirmed. The central region π^? cross section increases proportionally top _LAB ^?1/4 ; positive particles show almost no energy dependence atx=0. Particle ratios π⁺/π^? are studied as a function ofx andy ^* and a comparison with 70 GeV/cK ^? p data is made. Analysis of structure functions for (ππ) pairs and of particle production associated with π^± triggers at large |x| in the context of quark/parton models, provides qualitative evidence for the diquark-quark structure of the proton.     

Collapse of vortex lines in hydrodynamics

A new mechanism is proposed for collapse in hydrodynamics associated with the “breaking” of vortex lines. The collapse results in the formation of point singularities of the vorticity field, i.e., a generalized momentum curl. At the point of collapse the vorticity |Ω| increases as ((t ₀ ? t)^?1 and its spatial distribution for t → t ₀ approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l ₁ → (t ₀ ? t)^3/2 whereas in the other two “hard” directions it obeys l ₂ → (t ₀ ? t)^1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ? = ∫|Ω| d r.     

Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|^−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x₀). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Electroproduction of π0-mesons on protons at very low values of |q 2|

The electroproduction of π⁰-mesons on protons has been measured with electrons of 1.7 and 2.1 GeV energy in the region of the nucleon resonances at \(W = \sqrt {(q + p)^2 } = 1,400 - 2,000MeV\) at rather low values of |q ²|=|(e?e′)²|=0.01–0.1 GeV² but at high values of the nucleon recoil |t|=|(p?p′)²|≈0.6–2.2 GeV² corresponding to \(\Theta _\pi ^{cm} \approx 145^ \circ - 180^ \circ\) . Up toW≈1,650 MeV the cross section for π⁰-production with virtual photons of |q ²|≈0.03 GeV² is only slightly smaller than that with real photons. ForW?1,700 MeV the cross section at |q ²|≈0.03 GeV² is on average a factor of 2 smaller than that atq ²=0 but only slightly higher than that at |q ²|≈0.3–1 GeV².     

Topological pomeron andA-universality

The nuclear mass number dependence of inclusive spectra of secondaries with different quantum numbers in the projectile fragmentation region is analysed. We note that in models with topological pomeron, all the particle spectra fall into two main categories. The first one comprises particles which have a common “valence” quark with the projectile, the second one comprises all the other particles built of “sea” quarks. Thus, in the parameterization \(x\frac{{d\sigma }}{{dx}} \propto A^{\alpha (x)} \) the spectra of all “valence” hadrons (p, n, Λ, π^+,0,?,K ⁺, ... in thepA-interaction) atx→1 can be characterized by the single exponent α_υ =α(x?1) which differs slightly from α _s characterizing the spectra of “sea” hadrons ( \(\bar p, \bar \Lambda \) ,K ^?, ... forpA-interactions). This observation is essentially modelindependent and follows only from the topological structure of the pomeron and Gribov's space-time picture of soft hadronic interactions. Deviations from universality due to preasymptotic corrections and coherent particle production processes are estimated.     

Derivation of the Boltzmann equation for a Fermi gas

Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with velocityυ, ¦υ¦=1. In between scatterers the particle moves freely. At a scatterer the particle is either transmitted or reflected, both with probability 1/2. For given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations. If this variable is averaged over the distribution of scatterers, it decays not faster thant ^?3/2.     

Electromagnetic pion radius and dispersion sum rules

A general set of dispersion sum rules is considered for the pion form factor G(t) in the mixed-modulus phase representation. The connection between the distribution of the G(t) complex zeros and the sizes of dispersion integrals along the cut is stated. Under the assumption that G(t) ～ t^α at large t the following restriction on the asymptotic behaviour of G(t) is obtained: |G(t)| ? at^?2 (a>0). Using present experimental data we evaluate the electromagnetic mean squared radius, r_π = 0.71 ± 0.30 fm.     

Random time averaged diffusivities for Lévy walks

We investigate a Lévy walk alternating between velocities ±v ₀ with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic regime where the ensemble averaged mean squared displacement (MSD) at large times is ?x ²? ∝ t ², the latter to enhanced diffusion with ?x ²? ∝ t ^ν, 1 < ν < 2. The correlation function and the time averaged MSD are calculated. In the ballistic case, the deviations of the time averaged MSD from a purely ballistic behavior are shown to be distributed according to a Mittag-Leffler density function. In the enhanced diffusion regime, the fluctuations of the time averages MSD vanish at large times, yet very slowly. In both cases we quantify the discrepancy between the time averaged and ensemble averaged MSDs.     

A simple example of a singular perturbation expansion

For the Hamiltonian?=?? _x ² -αδ(x)+λx ² the bound-(λ>0) and resonance(λ<0) states are discussed. The perturbation expansion of the ground-state? ₀(λ) in powers ofλ is divergent for allλ. The nature of the singularity atλ=0 is investigated and it turns out, that the perturbation series is asymptotic and therefore useful even forλ<0.     

Two-particle production inK + p interactions at 32 GeV/c

Results are presented on two-particle inclusive production inK ⁺ p interactions at 32 GeV/c. We study thex _1,2=x ₁+x ₂ dependence of invariant structure functions of (ππ)-pairs and compare them to single particle inclusive distributions in the fragmentation regions. Distributions of particles observed at Feynmanx ₂ in association with various “trigger” particles or systems atx ₁ in the same hemisphere are dicussed in terms of the reduced variable \(\tilde x_2 = x_2 /(1 - |x_1 |)\) . We further present absolute production rates and production ratios of π⁺'s and π^?'s associated with π^±,K _s ⁰ , Λ, \(\bar \Lambda \) ,K ^*+ (890), (K _s ⁰ π⁺), and (π⁺ π^?)-triggers, and compare them with qualitative predictions of the quark recombination model. Forwardbackward correlations between (K _s ⁰ π^±), (K _s ⁰ ,p), (Λ, π^?), \((\bar \Lambda \pi ^ \pm )\) , and (p, π^?) pairs are also discussed.     

Modelling the voltammetric study of intercalation in a host structure: application to lithium intercalation in RuO2

Intercalation process kinetics have been studied theoretically for the case of potential sweep voltammetry. The influence of the thickness (or the particle radius) of the “host” material and the potential sweep rate has been determined between the limits of thin film diffusion and semi-infinite diffusion for a reversible process. Experimental data have been obtained with the cell: RuO₂/LiClO₄-PEO/Li. The theoretical results have been used to calculate the diffusion coefficient of lithium in the “host” structure RuO₂ at 80°C, giving an approximate value of 1.6 × 10^?11 cm² s^?1     

Study off o (995) resonance in the π0π0 decay channel

A high-statistics study of the π⁰π⁰-system produced in the π^- p→π⁰π⁰ n reaction at 38GeV/c has been carried out at the IHEP accelerator using the GAMS-2000 multiphoton spectrometer. A partial-wave analysis which includesS, D ₀, D_? andD ₊ waves has been performed in the |t|-range up to 1 (GeV/c)². TheS ^*/f ₀(980) resonance is seen as a dip in theS-wave amplitude at small |t|. A distinct peak with a mass of 997±5MeV and a width of 48±10MeV is observed in theS-wave at |t|>0.3 (GeV/c)². The production cross sections are measured.     

On the connection between the macroscopical and microscopical evolution in an exactly soluble hopping model: I. Neutral particles

The hopping rate equation for neutral particles, on an arbitrary periodical lattice, can be solved exactly. It is shown that if one scales the time t and the distances x(t→λ²t, x→λx) then, in the λ→∞ limit, the particle density tends to the solution of the diffusion equation faster than λ^?3. The diffusion coefficient is the same as obtained from both Kubo and Miller-Abrahams theory via the Einstein relation.     

Structure of28Si from the spectroscopy of high-spin states

A search for high-spin states in²⁸Si has been performed byn?y coincidence measurements in the²⁵Mg(α,nγy) reaction atE _α=14 and 15.5 MeV. Spin-parity assignments of the observed levels were obtained fromn?γ angular correlation and lifetime measurements atE _α=14.5 MeV. Theγ-decay of the 9,164 keV level was investigated separately with the²⁷Al(p, γ) reaction at theE _p=2,160 and 2,312 keV resonances. Rotational bands withK ^π=3^? (comprising levels atE _x=6,879, 8,413, 10,188 and 12,204 keV),K ^π =5^? (comprising levels atE _x=9,702, 11,577 and 13,741 keV) andK ^π=0⁺ (comprising levels atE _x=6,691, 7,381, 9,164 and 11,509 keV) were observed. The finding of the latter band supports the idea of coexisting oblate and prolate shapes in²⁸Si. A level at 14,643 keV excitation energy has the properties of theI ^π=8⁺ member of the ground state band. There are additional positive-parity high-spin states which do not fit into rotational bands. All types of positive-parity states are well accounted for by shell model calculations.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

Kinetics of particle coarsening processes

A nonequilibrium statistical mechanical theory for particle coarsening processes is presented. In this theory, the rate of change of a given particle is determined by both a deterministic and a fluctuation terms, and the particle size distribution (PSD) satisfies Fokker-Planck-type equation. We use a time scaling technique and find the PSD scaled by average particle size as well as the power laws of time dependence of some quantities. The asymptotic scaled PSD is independent of initial condition but does depend on the equilibrium volume fraction. We show that the average radius grows att ^1/3 and the density of particles decays ast ^?1.     

Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

Revisiting Cardassian model and cosmic constraint

Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In the non-relativistic limit (x???x,t??t,???0), the boundary conformal algebra changes to boundary Galilean conformal algebra (BGCA). In this work, some aspects of AdS/BCFT in the non-relativistic limit were explored. We constrain correlation functions of Galilean conformal invariant fields with BGCA generators. For a situation with a boundary condition at surface x=0 ( $z=\overline{z}$ ), our result agrees with the non-relativistic limit of the BCFT two-point function. We also introduce the holographic dual of boundary Galilean conformal field theory.