Diffraction dissociation of neutrons in the reaction dp → pppπ− at 25 GeV/c

We observe the reaction dp → p_spec (pπ^?)p in a bubble chamber exposure at 25 GeV/c incident deuteron momentum. The (pπ^?) system with invariant mass below 2.0 GeV is interpreted as neutron diffraction dissociation. The (pπ^?) mass spectra show little if any direct evidence of N¹ production. The decay angular distributions and the momentum transfer distributions of the (pπ^?) system suggest a smooth increase in contributions from higher partial waves $\text{(J ?}\text{3}\text{2}\text{)}$ with increased mass or momentum transfer. A simple partial-wave analysis shows a P₁₁ contribution below 1.3 GeV for small ?t′ and a dominant D₁₃ contribution elsewhere. Both the P₁₁ and D₁₃ amplitudes peak far below the N¹(1470) and N¹(1520) resonances. We also find evidence for the charge-exchange reaction np → p(pπ^?). In this process the (pπ^?) system shows evidence for Δ^o(1236) and N¹(1520) production.     

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.     

Fluctuations with a 1/f α spectrum in nonequilibrium phase transitions in a spatially distributed system

Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ～ f ^?α and S(k) ～ k ^?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ～ τ^?β) and size (P(s) ～ s^?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2).     

Monte Carlo simulation of film growth in a phase separating binary alloy model

Using a kinetic Monte Carlo method, we simulate binary film (A_0.5B_0.5/A) growth on an L×L square lattice with the focus on the domain growth behaviour. We compute the average domain area, A(t), as a measure of domain size. For a sufficiently large system, we find that A(t) grows with a power law in time with A(t)∼t^2/3 after the initial transient time. This implies that the dynamic exponent for domain growth with non-conserved order parameter is z=3, a value which was theoretically predicted for the conserved order parameter case. Further analysis reveals that such a power-law behaviour emerges because the order parameter is approximately conserved after the early stage of growth.     

An asymptotically free Reggeon field theory

Renormalization group techniques are used to examine Reggeon field theories with derivative triple Pomeranchuk interactions in accord with the decoupling theorems. The simplest asymptotically free “weak coupling” solution has total cross sections which behave as σ_tot^AB(s) ∽ g_Ag_B?c/log s +…, and the triple Pomeranchuk vertex has a nonsense wrong signature zero asymptotically ～(t?t₁?t₂). Another “strong coupling” solution reproduces the results of Migdal, Polyakov, Ter-Martirosyan, Abarbanel and Bronzan to lowest order in the ?-expansion.     

Classical Motion in Force Fields with Short Range Correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy 〈p ²(t)〉/2 and mean-squared displacement 〈q ²(t)〉 is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, 〈p ²(t)〉～t ^2/5 independently of the details of the potential and of the space dimension. The stochastically accelerated particle motion is then superballistic in one dimension, with 〈q ²(t)〉～t ^12/5, and ballistic in higher dimensions, with 〈q ²(t)〉～t ². These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: 〈p ²(t)〉～t ^2/3 and 〈q ²(t)〉～t ^8/3 in all dimensions d≥1.     

Non-normal tracer diffusion from stirring by swimming microorganisms

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ??(??) with long time behaviour ??(??) ?? ?? ^?1??? and a step size distribution p(??x) ?? (??x)^?2??? . The experimentally observed behaviour that ??x ²?? ?? t is obtained for a one-parameter family of exponents with ?? = 2??. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.      

An analysis of the new pion form factor data

A form factor F(t) for the pion is constructed which is compatible with analyticity and the data in the space-like and time-like region. For the mean square pion radius 〈r²〉 = (0.46_?0.08^+0.06) fm² is obtained. Typical errors of the extrapolated F(t) are given (e.g. F(t =?8 GeV²/c²) = 0.07_?0.10^+0.04). Assuming F(t) ≈ β/(?t)^α at the end of the space-like data region we obtain β = 0.31, α = 0.81 for t in GeV²/c² together with the error contours of (α, β). No conclusive answer on the existence of zeroes of F(t) can be given.     

Possible parametrization of parton distributions incorporating singular smallx behaviour implied by QCD and its phenomenological implications for HERA

The gluon and quark distributions of the nucleon are evaluated using the Altarelli-Parisi equations with the input distributions atQ ₀ ² =5 GeV² for seaquarks and gluons modified by the factor (ax ^?0.5+b). The new parametrization is constrained to satisfy the momentum sum rule and after backward evolution (fromQ ₀ ² =5 GeV² toQ ²=1 GeV²) it is also constrained to give approximately 1/x behaviour of the sea-quark and gluon distributions in the limited region of smallx (10^?3<x<10^?2 or so). The theoretical predictions relevant for HERA for structure functionsF ₂(x, Q ²) andF _L (x, Q ²) in the region of very smallx(10^?4<x<10^?2) and largeQ ² and for the cross-sectionσ(γ^* p→ΨX) are presented. Distributions of heavy quarks (c,b,t) are also discussed.     

K1-Dominance of the Ke3 form factor and Sirlin's relation

We discuss the precise momentum dependence of the K_e3 form factor f₊(t) by studying some of the recent experimental results on K⁰_L → π^± e^? ν decays. The parametrization of f₊(t) based on the assumption of K¹-dominance can considerably improve the agreement of Sirlin's relation with existing data.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

Principles of generalized spin-echo spectroscopy

The concept is proposed for determining the total dynamic scattering function of an object under study, representing a sum of odd and even parts measured by the generalized neutron spin-echo method in the form of the signals S _odd(q, t) ～ ΣS(ω, q)sin(ωt)dω and S_even(q, t) ～ ΣS(ω,q)cos(ωt)dω as functions of the momentum q transferred to the neutron and the time t corresponding to the frequency ω and the transferred energy ?ω. The principle of the generalized spin echo and the results of mathematical modeling are confirmed in experiments on inelastic scattering on magnetic fluids and polymer solutions. The developed method makes it possible to study the features of the dynamics of atomic and molecular systems, e.g., to analyze soft vibrational spectra of nanoparticle ensembles against the background of intense relaxation processes, which is inaccessible for classical spin-echo spectrometry.     

Exact solution of a meiman problem with an application to the pionic contribution to the muon magnetic moment

An exact solution is obtained tp the follpwing problem: given a form factor F(t) analytic in the cut t plane, to find a lower bpund to a weighted ontegral over |F(t)|² over the cut in the presence of space-like data and also time-like data on both the modulus and the phase of F(t). The solution is used to obtain a lower bound on the pionic contribution to the muon magnetic moment (a_μ(ππ)). We obtain a_μ(ππ) ≥ 41.8 × 10^?9.     

Limit behavior of saturated approximations of nonlinear Schrödinger equation

We consider the solutionu _?(t) of the saturated nonlinear Schrödinger equation (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} u + \varepsilon \left| u \right|^{q - 1} uandu(0,.) = \varphi (.)$$ where \(N \geqslant 2,\varepsilon > 0,1 + 4/N< q< (N + 2)/(N - 2),u:\mathbb{R} \times \mathbb{R}^N \to \mathbb{C},\varphi \) , ? is a radially symmetric function inH ¹(R ^N ). We assume that the solution of the limit equation is not globally defined in time. There is aT>0 such that \(\mathop {\lim }\limits_{t \to T} \left\| {u(t)} \right\|_{H^1 } = + \infty \) , whereu(t) is solution of (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} uandu(0,.) = \varphi (.)$$ For ?>0 fixed,u _?(t) is defined for all time. We are interested in the limit behavior as ?→0 ofu _?(t) fort≥T. In the case where there is no loss of mass inu _? at infinity in a sense to be made precise, we describe the behavior ofu _? as ? goes to zero and we derive an existence result for a solution of (1) after the blow-up timeT in a certain sense. Nonlinear Schrödinger equation with supercritical exponents are also considered.     

The correlation function for a quantum oscillator in a low-temperature heat bath

The momentum autocorrelation function c(t) for a quantum oscillator coupled with harmonic forces to a heat bath of oscillators is calculated at low temperatures. It is found that c(t) contains two distinct terms: one, the zero-point contribution c₀(t), is temperature independent, and the other, c₁(t), does depend on temperature. We concentrate our attention on the low-temperature case. An expression for c₁(t) is obtained, which is valid for arbitrary strenghts of the coupling and for arbitrary times. It is shown that c₁(t) is governed by the low-frequency behaviour of F(λ) = A²(λ)ϱ(λ), where ϱ(λ) is the density of normal modes and A(λ) is the central-oscillator component of the λth normal mode; other details of the problem are irrelevant. It is found that c₁(t) decays in time as an inverse-power law, with a relaxation time t_q ≈ ħ/kT.     

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n _h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n _h (A, t) = 2c _h /(A + λ _h t)², demonstrating the validity of dynamical scaling in this system. Here $ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-0em} 8}\pi \sqrt 3 $ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ _h is a material parameter. The distribution of domain areas, n _d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ _h t. Identical forms are obtained for coarsening from a critical initial state, but with c _h replaced by c _h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c _h . By applying a ‘mean-field’ type of approximation we obtain the form n _d (A, t) ? 2c _d [λ _d (t+t ₀)] ^τ?2/[A+λ _d (t+t ₀)] ^τ , where t ₀ is a microscopic timescale and τ = 187/91 ? 2.055, for a disordered initial state, and a similar result for a critical initial state but with c _d → c _d /2 and τ → τ _c = 379/187 ? 2.027. We also find that c _d = c _h + O(c _h ² ) and λ _d = λ _h (1 + O(c _h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.     

Multiplicity distributions and double scattering effects in π−d interactions at 205 GeV

Multiplicity distributions of charged secondaries, σ_N(π^?d) are obtained. The effective multiplicities σ_N(π^?n) and σ_N(π^?p) are extracted using the measured spectator momentum. The probability of double scattering P_N is found to be independent of multiplicity.     

Inclusive production of Σ±(1385) in pp interactions at 12 and 24 GeV/c

The inclusive production of Σ^±(1385) is studied in pp interactions at 12 and 24 GeV/c. In this energy range, the inclusive cross sections for Σ⁺(1385) and Σ^?(1385) rise from 0.20 ± 0.03 mb to 0.28 ± 0.03 mb and from 0.07 ± 0.02 mb to 0.12 ± 0.02 mb. The decays of Σ^±(1385) account for ～20% of all observed Λ hyperons. The p_T² distributions are compatible with an exponential decrease and the slopes are in agreement with a common value of B ～ 3 (GeV/c)^?2. The longitudinal spectra are significantly different: Σ^?(1385) is mainly produced in the central region, whereas proton fragmentation contributes strongly to Σ⁺(1385) production.