Finite Width Effects Research Articles

Determination of the Δ++ magnetic dipole moment

Abstract We study the elastic and radiative π+p scattering within a full dynamical model which incorporates the finite width effects of the Δ++. The scattering amplitudes are invariant under contact transformations of the spin 3/2 field and gauge-invariance is fulfilled for the radiative case. The pole parameters of the Δ++ obtained from the elastic cross section are mΔ=(1211.2±0.4) MeV and ΓΔ=(88.2±0.4) MeV. From a fit to the most sensitive observables in radiative π+p scattering, we obtain μΔ=(6.14±0.51)e/2mp for the magnetic dipole moment of the Δ++.

Ground‐based determination of the spectral ultraviolet extraterrestrial solar irradiance: Providing a link between space‐based and ground‐based solar UV measurements

The extraterrestrial solar spectrum between 295 and 355 nm has been determined from direct irradiance measurements made with a Brewer double spectrophotometer, using the Langley method. The measurements in this study consist of 449 half days of data collected during 1998 at Mauna Loa Observatory, Hawaii. The ±2.3% accuracy of this extraterrestrial solar spectrum is obtained by a careful investigation of the instrument calibration and the systematic errors that can arise because of atmospheric and instrument instabilities as well as finite slit width effects and is limited by the uncertainty of the absolute irradiance scale transfer between the standard laboratory and the instrument. A comparison between this extraterrestrial solar spectrum measured from the ground with the mean UARS and ATLAS‐1 spectrum show an agreement better than 3%. The mean ratios are 1.002 for the mean UARS spectrum, 1.003 for the mean ATLAS‐1 spectrum, 1.013 for the SOLSPEC spectrum, and 1.017 for the ATLAS‐3 spectrum.

Finite width effects and gauge cancellations in W- and Z-boson production in the framework of modified perturbation theory

The processes of production and subsequent decay of W- and Z-bosons in $e^+ e^-$ collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such an approach the non-integrable singularities in the phase space, which are intrinsic in the conventional PT, appear as singularities in the coupling constant (with subsequent compensation by the decay factors of unstable particles). In the present paper the systematic investigation of the modified PT is carried out. The results are compared with the results of the conventional approach, based on calculation of the amplitude with Dyson resummation. A solution to the problem of the loss of one-loop PT order in the resonance region is found. On the basis of this solution the proof of gauge cancellations in any order of the modified PT is given. A simple generalization of the fermion-loop scheme is proposed which provides a complete description of W-pair production in next-to-leading order approximation.

The t→ WZb decay in the Standard Model: a critical reanalysis

We compute the t→ WZb decay rate, in the Standard Model, at the leading order in perturbation theory, with special attention to the effects of the finite widths of the W and Z bosons. These effects are extremely important, since the t→ WZb decay occurs near its kinematical threshold. They increase the value of the decay rate by orders of magnitude near threshold or allow it below the nominal threshold. We discuss a procedure to take into account the finite-width effects and compare the results with previous studies of this decay. Within the Standard Model, for a top quark mass in the range between 170 and 180 GeV, we find BR( t→ WZb)≃2×10 −6, which makes the observation at the LHC very difficult if at all possible.

Diffusion and relaxation effects in general stray field NMR experiments.

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.

Finite pion width effects on the rho-meson

We study the influence of the finite damping width of pions on the in-medium properties of the ρ-meson in an interacting meson-gas model at finite temperature. Using vector dominance also implications on the resulting dilepton spectra from the decay of the ρ-meson are presented. A set of coupled Dyson equations with self-energies up to the sunset diagram level is solved self-consistently. Following a Φ-derivable scheme the self-energies are dynamically determined by the self-consistent propagators. Some problems concerning the self-consistent treatment of vector or gauge bosons on the propagator level, in particular, if coupled to currents arising from particles with a sizable damping width, are discussed.

Effect of finite domain-wall width on the domain structures of epitaxial ferroelectric and ferroelastic thin films

A theory of domain (twin) structures, which takes into account the finite width of domain walls, is developed for epitaxial ferroelectric and ferroelastic thin films. The theory is based on the dislocation–disclination modeling of the sources of mechanical stresses in polydomain films. Calculations are performed for an orthorhombic or tetragonal film grown on a dissimilar orthorhombic, tetragonal, or cubic substrate. The case of a laminar 90° domain structure with the walls inclined at 45° to the film/substrate interface (c/a/c/a structure in tetragonal films) is considered. A simple dislocation–disclination model is constructed for the junctions of thick domain walls with the film/substrate interface. Using this model, the stress fields in the film and substrate and the associated elastic energy are evaluated. By minimizing the total energy of the material system at a fixed domain-wall width, the equilibrium geometric parameters of a periodic 90° domain structure are calculated. Then the range of stability of this structure in epitaxial films is determined as a function of the wall width. The mechanical restoring forces, which hinder cooperative translational vibrations of thick 90° walls near their equilibrium positions, are also calculated. On this basis, the domain-wall contributions to the dielectric and piezoelectric responses of prepolarized ferroelectric films are evaluated at different wall widths. Finally, the influence of the film straining by the substrate on the equilibrium domain-wall width is analyzed. An increase of the wall width in an epitaxial thin film relative to that in a bulk crystal is predicted.

Monte Carlo simulations of microstrip lines with random substrate impurity

Monte Carlo simulations of microstrip lines with random substrate impurity are performed. Each realization of current distribution on the microstrip line with substrate impurity is calculated by the hybrid finite element method/multilevel fast multipole algorithm. After taking the ensemble average of all the realizations, the super-resolution estimation of signal parameters via rotational invariance technique algorithm is employed to extract the characteristic parameters of the transmission line from the current distribution. Comparisons of our numerical results and previously published results for the conventional microstrip line with homogeneous substrate confirm the validity, accuracy, and efficiency of our simulation tool. Our Monte Carlo simulations demonstrate that the effect of substrate impurity on the characteristics of a microstrip line can be quite accurately estimated by replacing the inhomogeneous substrate with a homogeneous one whose dielectric constant is the averaged value for different materials weighted by their volume ratios. This simple estimation approach, however, does not apply to the attenuation constant of the line due to the effect of finite substrate width. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 177–187 (2001)

Electroweak physics in six-fermion processes at future colliders

Recent developments in the field of complete electroweak tree-level calculations for six-fermion final states in e + e − collisions are briefly reviewed. Particular attention is given to top-quark and Higgs boson physics, which are items of primary importance at the Next Linear Collider. The relevance of electroweak backgrounds and finite-width effects is discussed, showing the importance of complete calculations for precision studies at the colliders operating in the TeV energy range.

Fast particle destabilization of toroidicity-induced Alfvén eigenmodes in the National Spherical Torus Experiment

Toroidicity-induced Alfvén eigenmode (TAE) stability in the National Spherical Torus Experiment (NSTX) [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)] is analyzed using the improved NOVA-K code [N. N. Gorelenkov, C. Z. Cheng, and G. Y. Fu, Phys. Plasmas 6, 2802 (1999)], which includes finite orbit width and Larmor radius effects and is able to predict the saturation amplitude for the mode using the quasilinear theory. A broad spectrum of unstable global TAEs with different toroidal mode numbers is predicted. Due to the strong poloidal field and the presence of the magnetic well in NSTX, better particle confinement in the presence of TAEs in comparison with tokamaks is illustrated making use of the ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)].

Unstable particles and non-conserved currents: a generalization of the Fermion-Loop scheme

The incorporation of finite-width effects in the theoretical predictions for tree-level processes e+e−→n fermions requires that gauge invariance must not be violated. Among various schemes proposed in the literature, the most satisfactory, from the point of view of field theory is the so-called Fermion-Loop scheme. It consists in the re-summation of the fermionic one-loop corrections to the vector-boson propagators and the inclusion of all remaining fermionic one-loop corrections, in particular those to the Yang–Mills vertices. In the original formulation, the Fermion-Loop scheme requires that vector bosons couple to conserved currents, i.e. that the masses of all external fermions be neglected. There are several examples where fermion masses must be kept to obtain a reliable prediction. The most famous one is the so-called single-W production mechanism, the process e+e−→e−νef1f2 where the outgoing electron is collinear, within a small cone, with the incoming electron. Therefore, me cannot be neglected. Furthermore, among the 20 Feynman diagrams that contribute (for eνeud final states, up to 56 for e+e−νeνe) there are multi-peripheral ones that require a non-vanishing mass also for the other fermions. A generalization of the Fermion-Loop scheme is introduced to account for external, non-conserved, currents. Dyson re-summed transitions are introduced without neglecting the pμpν-terms and including the contributions from the Higgs–Kibble ghosts in the 't Hooft–Feynman gauge. Running vector boson masses are introduced and their relation with the corresponding complex poles are investigated. It is shown that any S-matrix element takes a very simple form when written in terms of these running masses. A special example of Ward identity, the U(1) Ward identity for single-W, is derived in a situation where all currents are non-conserved and where the top quark mass is not neglected inside loops.

Non-conserved currents and gauge-restoring schemes in single W production

We generalize the inclusion of the imaginary parts of the fermionic one-loop corrections for processes with unstable vector bosons to the case of massive external fermions and non conservation of weak currents. We study the effect of initial and final state fermion masses in single Wproduction in connection with the gauge-invariant treatment of the finite-width effects of W and Z bosons, giving numerical comparisons of different gauge-invariance-preserving schemes in the energy range of LEP2 and LC for e − e +→ e − ν ̄ eu d ̄ . We do not find significant differences between the results obtained in the imaginary part fermion loop scheme and in other exactly gauge preserving methods.

Three-dimensional reduced drift kinetic equation for neoclassical transport of helical plasmas in the ultralow collisionality regime

Based on the original five-dimensional drift kinetic equation, a three-dimensional reduced drift kinetic equation has been obtained to describe the neoclassical transport of helical plasmas in the ultralow collisionality regime, where the collision frequency is much lower than the poloidal bounce frequency of the superbanana particles. The reduced drift kinetic equation describes the evolution of the distribution function in terms of three constants of motion as independent variables. This reduced drift kinetic equation is suitable for studying the collisional transport of fast ions in helical magnetic confinement systems, since it includes the effects of finite superbanana width and finite aspect ratio, and it includes the collisional slowing-down and energy-scattering terms in addition to the pitch-angle-scattering term.

Many-body effects in highlyp-type modulation-dopedGaAs/AlxGa1−xAsquantum wells

Many-body effects have been optically investigated for modulation-doped quantum wells at high acceptor densities. The observed band-gap shrinkage, up to $\ensuremath{\approx}20 \mathrm{meV},$ is consistent with calculations based on the Hartree and random-phase approximations including the finite well width effect. A recombination near the Fermi edge with light-hole character is strikingly enhanced at high acceptor densities. An interpretation based on carrier-carrier interaction is proposed. Finally, the exciton is found to be quenched for hole densities higher than $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{12} {\mathrm{cm}}^{\ensuremath{-}2}.$

Gauge invariance and finite width effects in radiative two-pionτlepton decay

The contribution of the ${\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}$ vector meson to the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}\ensuremath{\gamma}$ decay is considered as a potential source for the determination of the magnetic dipole moment of this light vector meson. In order to keep the gauge invariance of the whole decay amplitude, a procedure similar to the fermion-loop scheme for charged gauge bosons is implemented to incorporate the finite width effects of the ${\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}$ vector meson. The absorptive pieces of the one-loop corrections to the propagators and electromagnetic vertices of the ${\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}$ meson and ${W}^{\ifmmode\pm\else\textpm\fi{}}$ gauge boson have identical forms in the limit of massless particles in the loops, suggesting this to be a universal feature of spin-one unstable particles. Model-dependent contributions to the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}\ensuremath{\gamma}$ decay are suppressed by fixing the two-pion invariant mass distribution at the rho meson mass value. The resulting photon energy and angular distribution is relatively sensitive to the effects of the $\ensuremath{\rho}$ magnetic dipole moment.

Effects of finite sample width on transition and flame spread in microgravity

In most microgravity studies of flame spread, the flame is assumed to be two-dimensional, and two-dimensional models are used to aid data interpretation. However, since limited space is available in microgravity facilities, the flames are limited in size. It is important, therefore, to investigate the significance of three-dimensional effects. Three-dimensional and two-dimensional simulations of ignition and subsequent transition to flame spread were performed on a thermally thin cellulosic sample, Ignition occurred by applying a radiant heat flux in a strip across the center of the sample. The sample was bounded by an inert sample holder. Heat loss effects at the interface of the sample and the sample holder were tested by varying the thermal-physical properties of the sample holder. Simulations were also conducted with samples of different widths and with different ambient wind speeds (i.e., different levels of oxygen supply). The width of the sample affected both the duration of the flame transition period and the post-transition flame spread rate. Finite width effects were most significant when the ambient wind was relatively small (limited oxygen supply). In such environments, the velocity due to thermal expansion reduced the net inflow of oxygen enough to significantly affect flame behavior. For a given sample width, the influence of thermal expansion on the net incoming oxygen supply decreased as the ambient wind speed increased. Thus, both the transition and flame spread behavior of the three-dimensional flame (along the centerline) tended to that of the two-dimensional flame with increasing ambient wind speed. Heat losses to the sample holder were found to affect the flame spread rate in the case of the narrowest sample with the slowest ambient wind.

A new f method for neoclassical transport studies

A new f method is presented in detail to solve the drift kinetic equation for the simulation study of neoclassical transport. It is demonstrated that valid results essentially rely on the correct evaluation of the marker density g in the weight calculation. A new weighting scheme is developed without assuming g in the weight equation for advancing particle weights, unlike previous schemes. This scheme employs an additional weight function to directly solve g from its kinetic equation based on the f method itself. Therefore, the severe constraint that the real marker distribution must be consistent with the initially assumed g is relaxed. An improved like-particle collision scheme is also presented. By compensating for momentum, energy and particle losses, the conservations of all three quantities are greatly improved during collisions. With the improvement in both the like-particle collision scheme and the weighting scheme, the f simulation shows a significantly improved performance. The new f method is applied to the study of ion neoclassical transports due to self-collisions, taking the effect of finite orbit width into account. The ion thermal transport near the magnetic axis is shown to be greatly reduced from its conventional neoclassical level, like that of previous f simulations. On the other hand, the direct particle loss from the confinement region may strongly increase the ion thermal transport near the edge. It is found that the ion parallel flow near the axis is also largely reduced due to non-standard orbit topology.

Separation of 2H MAS NMR Spectra by Two-Dimensional Spectroscopy

New methods for optimum separation of 2H MAS NMR spectra are presented. The approach is based on hypercomplex spectroscopy that is useful for sign discrimination and phase separation. A new theoretical formalism is developed for the description of hypercomplex experiments. This exploits the properties of Lie algebras and hypercomplex numbers to obtain a solution to the Liouville–von Neumann equation. The solution is expressed in terms of coherence transfer functions that describe the allowed coherence transfer pathways in the system. The theoretical formalism is essential in order to understand all the features of hypercomplex experiments. The method is applied to the development of two-dimensional quadrupole-resolved 2H MAS NMR spectroscopy. The important features of this technique are discussed and two different versions are presented with widely different characteristics. An improved version of two-dimensional double-quantum 2H MAS NMR spectroscopy is developed. The conditions under which the double-quantum experiment is useful are discussed and its performance is compared with that observed for the quadrupole-resolved experiments. A general method is presented for evaluating the optimum pulse sequence parameters consistent with maximum sensitivity and resolution. This approach improves the performance of the experiments and is essential for any further development of the techniques. The effects of finite pulse width and hypercomplex data processing may lead to both intensity and phase distortions in the spectra. These effects are analyzed and general correction procedures are suggested. The techniques are applied to polycrystalline malonic-acid-2H4 for which the spinning sideband manifolds from the carboxyl and methylene deuterons are separated. The spinning sideband manifolds are simulated to determine the quadrupole parameters. The values are consistent with previous results, indicating that the techniques are both accurate and reliable.

Fast particle finite orbit width and Larmor radius effects on low-n toroidicity induced Alfvén eigenmode excitation

The effects of finite drift orbit width (FOW) and Larmor radius (FLR) of fast particles on the stability of low-n toroidicity-induced Alfvén eigenmodes (TAE) are studied. The formulation is based on the solution of the low frequency gyrokinetic equation (ω≪ωc, where ωc is particle cyclotron frequency). A quadratic form has been derived in terms of invariant variables; energy E, magnetic moment μ, and toroidal angular momentum Pφ. The growth rate of the TAE is computed perturbatively using numerical averaging over the fast particle drift orbit. This new computational capability improves the NOVA-K code [G. Y. Fu, C. Z. Cheng, and K. L. Wong, Phys. Fluids B 5, 4040 (1994)] which included FOW effects in the growth rate calculation based on small radial orbit width approximation. The new NOVA-K version has been benchmarked for different regimes of particle TAE excitation. It is shown that both FOW and FLR effects are typically stabilizing; the TAE growth rate can be reduced by as much as a factor of 2 for tokamak fusion test reactor supershots [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. However, FOW may be destabilizing for the global modes, which are localized at the plasma edge.

Non-local collisional relaxation of neoclassical ions in tokamaks

The reduced drift kinetic equation, expressed in terms of three independent constants of motion, has been obtained to investigate the nonlocal behavior of the neoclassical ion transport in tokamaks. It has been shown that the neoclassical ion transport is determined by the behavior of trapped particles at the turning points, with the effects of finite banana width taken into account.