Tensor Amplitude Research Articles

The 2D gravity stress tensor and multi-loop amplitudes in string theory

It is shown that the vacuum value of the 2D gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus- n > 1 Riemann surfaces are mapped. Because of the above singularity, one can not construct modular invariant multi-loop amplitudes. The discussed singularity is due to the singularity in the vacuum value of the 2D gravity field that turns out to be on the genus- n > 1 Riemann surfaces.

Phenomenological transition amplitudes for NN-->N Delta at 800 MeV.

A description of pp\ensuremath{\rightarrow}nX inclusive inelastic scattering data for 8 dominated by \ensuremath{\Delta} (3,3) excitation is presented based on a partial wave expansion model for the reaction pp\ensuremath{\rightarrow}n${\mathrm{\ensuremath{\Delta}}}^{++}$. The data selected for analysis include the total reaction cross section, differential cross sections, analyzing powers, polarization transfers, and spin correlation parameters. A semiquantitative fit to the data is achieved and a phenomenological model for the isospin 1 NN\ensuremath{\rightarrow}N\ensuremath{\Delta} transition matrix is presented. The latter quantity is expressed in terms of sixteen parity invariant bilinear combinations of spin operators and accompanying amplitudes. These sixteen amplitudes constitute the first complete phenomenological representation of the NN\ensuremath{\rightarrow}N\ensuremath{\Delta} transition which can be used as input fo r distorted wave Born approximation calculations of nucleon and light ion induced \ensuremath{\Delta} excitation in nuclei. Of the sixteen spin operators ten include rank 2 tensors. The effects of these tensor amplitudes on the inelastic NN\ensuremath{\rightarrow}N\ensuremath{\Delta} observables are substantial.

KARMEN: precision tests of the standard model with neutrinos from muon and pion decay

Neutrinos from pion and muon decay at rest offer unique possibilities for precision tests of the Standard Model at low energies. With typical neutrino interaction rates in this energy domain being only of the order of 10 −42 cm 2 high quality detection methods are required. The spectroscopic quality of neutrino identification in the KARMEN experiment at the pulsed spallation source ISIS allows a high sensitivity search for neutrino oscillations in the appearance channels ν μ → ν ρ and ν μ→ ν ρ . In addition, neutrino spectroscopy is used to look for non-standard (scalar and tensor) amplitudes in weak charged currents, while conservation laws are tested by a search for lepton number violating muon and pion decays allowed in Left - Right symmetric models. We present the results of the KARMEN experiment with regard to tests of the Standard Model obtained from the first three years of data taking.

Spin-dependent interactions and polarization observables in elastic scattering of deuterons at intermediate energies

Deuteron-nucleus spin-dependent interactions are investigated in elastic scattering at intermediate energies. Spin-space tensor amplitudes which characterize spin-dependent interactions are introduced by the invariant-amplitude method so that effects of T R - and T L -type tensor interactions are described separately. Through these amplitudes, numerical calculations based on the folding model clarify that the spin-orbit interactions produce T L -tensor like effects on the scattering amplitude as the higher-order effect and the virtual breakup contribution is only a minor part of this effect in most angles. An additional T L -type tensor interaction, phenomenologically introduced, is found to improve the fit to the experimental data of A yy considerably and A y in less magnitude. The origin of this interaction is discussed. The theoretical prediction is made of which observables enhance the effect of a particular spin-dependent interaction.

Quantum Magnetotransport of a Two-Dimensional Electron Gas Subject to Periodic Electric or Magnetic Modulations

Electrical transport properties of the two-dimensional electron gas are studied in the presence of a perpendicular magnetic field B = Bẑ and of a weak one-dimensional electric (V0 cos (Kx)) or magnetic (B0 = B0 cos (Kx)ẑ) modulation where B0 ≪ B, K = 2π/a, and a is the modulation period. In either case the discrete Landau levels broaden into bands whose width: (1) is proportional to the modulation strength, (2) it oscillates with B, and (3) it gives rise to magnetoresistance oscillations, at low B, that are different in period and temperature dependence from the Shubnikov-de Haas (SdH) ones, at higher B. For equal energy modulation strengths, V0 = heB0/m*, the magnetic bandwidth at the Fermi energy is about one order of magnitude larger than the electric one. The same holds for the oscillation amplitude of the electrical magnetoresistivity tensor. For two-dimensional modulations the energy spectrum has the same structure but with different scales. For weak magnetic fields and equal modulation strengths the gaps in the spectrum can be much larger in the magnetic case thus making easier the observability of the spectrum's fine structure.

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements. >

On the nature of the two low-lying singlet states of anthracene: Vibronic activity in the two-photon excitation spectrum

The two-photon excitation spectrum of anthracene in a n-heptane matrix at 10 K has been measured in the energy region 26 000–32 000 cm−1. Experimental evidence of two-photon band assignment to vibronically induced B1u ×b1u and B2u ×b2u transitions is given. In particular, the two-photon spectrum above ≂28 000 cm−1 shows several vibronic origins built on b2u vibrations and progressions of ag modes on them. The lowest ππ* absorption region (<28 000 cm−1) has, on the contrary, negligible intensity and very weak B1u ×b1u bands are observed. These data can be rationalized in terms of vibronic coupling between electronic states induced by normal coordinates of b1u and b2u symmetry. By means of the Herzberg–Teller theory and displacing the molecule away from equilibrium along the normal coordinate we have calculated the vibronic interaction between electronic states in the orbital following approach. The results based on CNDO/S-CI wave functions show that B2u ×b2u transitions have a larger vibronic activity than the B1u ×b1u transitions. The 1132, 1384, and 1393 cm−1 b2u modes are particularly strong in inducing two-photon intensity through a vibronic coupling mechanism involving essentially the ground and the final 1 1B2u state. The B2u ×b2u two-photon amplitude tensors are not sensitive to the method of calculation. B1u ×b1u tensors have instead a more pronounced dependence on the method used. This is due to the fact that in the two-photon sums most of the intermediate states play an equivalent role in determining the amplitude tensor, in contrast with the B2u ×b2u case. It is important to use a reasonably correct representation of the excited state wave functions. It is shown that more accurate calculations (INDO/S and CNDO/S with increased CI) lead to better agreement of the total vibronic intensity of the 1 1B1u state with experiment and predict the largest activity for the 648 cm−1 b1u mode, as observed in the spectrum.

Vibronic activity in the two-photon spectrum of pyrene

A CNDO/S Cl calculation of the two-photon vibronic activity of some b 1u and b 2u vibrational modes of pyrene is presented. The two-photon amplitude tensor is discussed in terms of vibronic coupling coefficients calculated by means of the orbital-following method. The results are in good agreement with the experimental data taken from a recently observed two-photon spectrum of pyrene in a Shpolskii matrix. The role of the ground-state coupling with the first excited B 1u state has been investigated and is shown to be responsible for most of the vibronically induced two-photon intensity of the spectrum. The calculations also show that the 1310 cm −1 (b 1u; observed ground-state value) mode is associated with the largest vibronic coupling coefficients and the strongest two-photon amplitude tensor and therefore must be correlated with the most intense B 1u X b 1u false origin ≈ 1496 cm −1 from the pure (0-0) line.

On the large-scale dynamics of rapidly rotating convection zones

The fact that the values of the eight basic waves present in turbulent flows in the presence of rotation prohibit a tilt of eddy towards the axis of rotation is incorporated into a formalism for rapidly rotating convection zones. Equations for turbulent velocities are defined in a rotating coordinate system, assuming that gravity and grad delta T act in a radial direction. An expression is derived for the lifetime of a basic wave and then for the average velocity vector. A real convective eddy is formulated and the wave vectors are calculated. The velocity amplitude and the stress tensor amplitude are integrated over the eddy domain. Applied to the solar convective zone, it is found that the convective cells are aligned along the axis of rotation at the poles and at the equator, a model that conflicts with nonrotating mixng length theory predictions.

Phase and energy correcting inelastic contributions in multiple rescattering

In this paper we modify the phase and energy behaviour of conventional weak cut absorption. We parametrize the double-scattering amplitude of the Regge-Gribov scheme to include low- and high-mass inelastic intermediate states. This is done through the introduction of azimuthal correlations between the reggeon and the regular pomeron and reverses the anti-clockwise rotation induced by absorptive cuts. For precision we include Regge-Regge cuts and achieve accurate fits to the vector and tensor amplitude analysis at 6 GeV/c. Polarization and line-reversal symmetry-breaking deficiencies in charge and hypercharge exchange processes are thus remedied at this energy. Cross-over and polarization show a very weak dependence against variations over a wide range of energy. Inelastic and elastic polarization of scattering\(\pi {\mathcal{N}}\) are reconciled for |t|≳αϱ=0. The clockwise rotation included in isoscalar exchange arranges for rising cross-sections without assuming αP(0)>1.

Complete reduction of fermion-antifermion bethe-salpeter equation with static kernel

The Bethe-Salpeter (BS) equation for a spin- 1 2 fermion-antifermion bound system is considered for the case in which the kernel is static and is the fourth component (i.e., three-scalar part) of a vector potential. Relative time (or relative energy) dependence can be eliminated easily. The 16 BS bispinor amplitudes are reexpressed in the usual way in terms of corresponding tensor amplitudes which satisfy 16 coupled integrodifferential equations. If Lorentz-, parity-, and charge-conjugation invariance are used, these equations can be reduced through a sequence of transformations to single eigenvalue equations, involving scalar and three-vector wavefunctions for singlet and triplet states, respectively. The effective Hamiltonians obtained in these equations are correct to all orders in the coupling constant and have a simple structure, consisting in general of a scalar, a spin-orbit, and a tensor part, which are explicitly exhibited. Although the equations could well be used for consideration of a general particleantiparticle system (e.g., quark-antiquark), for the present only positronium with a Coulomb interaction kernel is treated as an illustrative example. There exists a singlettriplet splitting in leading order mα 6 ln α even though no spin-spin forces are directly introduced in the kernel. The splitting is calculated in detail in perturbation theory to order mα 6 ln α and mα 6.

Tensor amplitudes for elastic photon-photon scattering

We have shown that expansions for the fourth-rank vacuum polarization tensor for a virtual four-photon system can be built up in general, in terms of seventeen linearly independent explicitly gauge-invariant polynomial tensors. A special choice of the tensor basis corresponds to the one obtained by Karplus and Neuman. We have also dealt with the real four-photon system. An expression for the tensor amplitude which describes this process has been found in general, in terms of five linearly independent manifestly gauge-invariant polynomial tensors. Both in the case of massive and real photons, we have investigated the kinematical singularities of the scalar amplitudes relative to the chosen tensor bases. For the real case we have also obtained the low-energy limits of the helicity amplitudes in the centre-of-mass system. Finally, we have looked for the effective Lagrangian densities related to the helicity amplitudes in the low-energy region.

Tensor exchange in meson-baryon scattering

Amplitudes for A 2 quantum number exchange in K ±N scattering are determined at p L = 3, 4 and 6 GeV using new K ±N CEX differential cross-section data supplemented by sum rule estimates of polarizations. Amplitudes for ϱ quantum number exchange are calculated from πN scattering by SU(3) octet symmetry. This is justified by K ±N FESR, which furthermore are used to resolve ambiguities in the analysis. Comparison with other reactions involving charge and hyperchange exchange shows reasonable overall consistency between data, SU(3), and the tensor amplitudes. The phase of the A 2 s-channel helicity flip amplitude is well described by a Regge pole term with trajectory displaced downwards relative to that appropriate for the ϱ flip amplitude. This is shown to be the main mechanism contributing to the difference between differential cross sections for the K ±N CEX processes, connected by line reversal. It is suggested that this mechanism may persist at higher energies. The A 2 non-flip amplitude does not have the standard peripheral form.

Strange-meson exchanges in eta and eta-prime productions

In this paper we study strange K*- and K**-meson exchanges using the experimental data of hypercharge exchange reactions K-p -~ ~A and K-p -~ ~'A, and examine the validity of our nonperipheral model developed in the previous paper (1) in which the existence of the nonperipheral, that is central, component is clarified in the imaginary part of the s-channel helicity-nonflip A 2 tensor amplitude, but not in the one of the p vector amplitude. It is interesting to see whether the nonperipheral component exists in the imaginary part of the s-channel helicity-nonflip K** tensor amplitude or not. These two reactions mentioned above receive contributions from both K*- and K**-meson exchanges, but in the former (latter) reaction the K*(K**)-meson exchange contribution dominates over K**(K*)-meson exchange, as is shown below. We construct the mixing of the ~ and ~' in terms of the mixing angle 0 by writing

Shackless on linear absorption models

We examine the fundamental constraints that all Linear Absorption Models must possess, independent of the rescattering amplitude. These constraints are most direct in impact parameter space, where the re-scattering appears simply as a multiplicative factor. It is a crucial test of such models that the ratio of two exchanges — for example vector and tensor exchanges — is completely specified in b-space by the ratio of input Regge pole amplitudes. Amplitude analysis exist for vector π exchange, in π − p→ π O n. Lacking experimental A 2 tensor amplitudes, we use the Linear Absorption Models constraint to calculate A 2 exchange from ϱ input, and compare the results with π − p→ η O n data. Both simplicity and duality assumptions for Regge pole couplings are considered. The results suggest that Linear Absorption Models constraint is not fully consistent with data.

On the Determination of the Phases of Electromagnetic Scattering Amplitudes from Experimental Data

The scattering of electromagnetic waves by systems of unknown charge distribution is considered with the aim of establishing that the phase of the scattered radiation (relative to the incident one) can be computed theoretically from experimentally obtainable data, such as the intensity and the polarization of the scattered wave. By means of the unitarity relation of classical electromagnetic scattering theory, it is demonstrated that, subject to certain restrictions on the magnitude of the scattering data: (i) For an unpolarized incident beam and a spherically symmetric target, knowledge of the differential cross section and the polarization of the scattered radiation is sufficient to determine uniquely the phases of the scattering amplitude tensor. (ii) For a parity-invariant scatterer, and fully circularly or linearly polarized incident beams, knowledge of the differential cross section and the ellipticity of the outgoing radiation is sufficient to completely determine the phases of the scattering amplitude tensor. The scattering data must be available for both the left and the right circularly polarized incoming wave (or for two linearly polarized beams pertaining to the two orthogonal polarizations). (iii) In the above cases it is shown that the phases can be calculated systematically by converging iterative procedures. Conditions for convergence are established, and bounds are provided on the errors associated with the approximants obtained after an arbitrary (but finite) number of iterations. On the basis of result (ii) with the same data assumed to be known, a formal solution to the phase determination problem is given for a general scatterer. However, for this case rigorous results on convergence conditions and error bounds have not been obtained. An outline of the corresponding treatment valid within the framework of the quantum-electrodynamical theory of light scattering is given. To illustrate the proposed methods for phase determination, we apply them to the scattering of light by very simple systems. These include the free electron and an oscillating charge. We conclude by discussing the possibility of applying the above results to obtain solutions of the phase problem in systems of practical interest.

SU(6)WAlgebra and the Commutators of Electric Dipoles at Infinite Momentum

The saturation of the ${\mathrm{SU}(6)}_{W}$ algebra at infinite momentum is discussed. A possible physical interpretation of the tensor generators of ${\mathrm{SU}(6)}_{W}$ in terms of an assumption of partial conservation is critically analyzed. The implied occurrence of singularities in the tensor amplitudes requires a careful definition of a limiting procedure defining the tensor charges. A collinear limiting procedure, which relates the tensor charges to the total magnetic moments, appears as the most convenient one. The matrix elements of the tensor charges are then compared in the infinite-momentum limit with those of the electric dipoles, and the following implications are exhibited: The charge radii of baryons are pure $F$; the $\frac{D}{F}$ ratio of axial charges equals the corresponding ratio for the total baryon magnetic moments; a simple relation exists among the isovector total moment of the nucleon, the axial renormalization constant, and the charge radius of the proton; and an extended form of universality holds for tensor and axial currents. We also discuss the saturation of the unitary symmetric part of the commutators, particularly in connection with the possible occurrence of Schwinger terms.