Polarization Matrix Elements Research Articles

Contribution of Discrete and Continuum Wave Functions in the Ground State Polarizability of Hydrogen

We analytically derive a discrete radial Green function for a hydrogenic system in terms of associated Leguerre polynomials. We investigate the polarizability of the ground-state hydrogen using the so-called length gauge approximation of electrodynamics. The polarizability is the sum of the polarization matrix elements for the negative and the positive frequency values. We estimate the contribution of discrete wavefunctions to the static ground state polarizability. We found that the contribution of continuum states dominates over that of discrete states to the polarizability by an order of magnitude.

NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC

Measuring the polarization of electroweak bosons at the LHC allows for important tests of the electroweak-symmetry-breaking mechanism that is realized in nature. Therefore, precise Standard Model predictions are needed for the production of polarized bosons in the presence of realistic kinematic selections. We formulate a method for the calculation of polarized cross-sections at NLO that relies on the pole approximation and the separation of polarized matrix elements at the amplitude level. In this framework, we compute NLO-accurate cross-sections for the production of two polarized Z bosons at the LHC, including for the first time NLO EW corrections and combining them with NLO QCD corrections and contributions from the gluon-induced process.

Automated predictions from polarized matrix elements

The anticipated experimental resolution and data cache of the High Luminosity Large Hadron Collider will enable precision investigations of polarization in multiboson processes. This includes, for the first time, vector boson scattering. To facilitate such studies, we report the automation of polarized matrix element computations in the publicly available Monte Carlo tool suite, MadGraph5_aMC@NLO. This enables scattering and decay simulations involving helicity-polarized asymptotic or intermediate states, preserving both spin-correlation and off-shell effects. As demonstrations of the method, we investigate the leading order production and decay of polarized weak gauge bosons in the process ppto {jjW}_{lambda}^{+}{W}_{lambda prime}^{-} , with helicity eigenstates (λ, λ′) defined in various reference frames. We consider the Standard Model at both mathcal{O} (α4) and mathcal{O} (α2 {alpha}_s^2 ) as well as a benchmark composite Higgs scenario. We report good agreement with polarization studies based on the On-Shell Projection (OSP) technique. Future capabilities are discussed.

Study of single-spin asymmetries with polarized target at the SPASCHARM experiment at U70 accelerator

A new experiment SPASCHARM for systematic study of polarization phenomena in inclusive and exclusive hadronic reactions is currently under commissioning at IHEP. The universal experimental setup will detect dozens of various resonances and stable particles produced in collisions of unpolarized beams with the polarized target, and at the next stage, using polarized beams. At the first stage with polarized target, the final states composed of light quarks (u, d, s) will be reconstructed. Hyperon polarization and spin density matrix elements of the vector mesons will be measured along with the single-spin asymmetries. The 2π-acceptance in azimuth, which is extremely useful for reduction of systematic errors in measurements of spin observables, will be implemented in the experiment. The solid angle acceptance of the setup, Δθ≈250 mrad vertically and 350 mrad horizontally in the beam fragmentation region, covers a wide range of kinematic variables pT and xF. This provides the opportunity for separating dependences on these two variables which is usually not possible in the setups with a small solid angle acceptance. Unlike some previous polarization experiments, the SPASCHARM will be able to simultaneously accumulate and record data on the both, charged and neutral particle production.

Systematic Study of Spin Effects at SPASCHARM Experiment at 70-GeV Accelerator in Protvino

A new experiment SPASCHARM for systematic study of polarization phenomena in the inclusive and exclusive hadronic reactions in the energy range of IHEP accelerator U-70 (12–50[Formula: see text]GeV) is currently under development. The universal experimental setup will detect dozens of various resonances and stable particles produced in collisions of unpolarized beams with the polarized target, and at the next stage, using polarized proton and antiproton beams. At the beginning, the final states consisting of light quarks ([Formula: see text], [Formula: see text], [Formula: see text]) will be reconstructed, and later on the charmonium states will be studied. Measurements are planned for a variety of beams: [Formula: see text], antiprotons. Hyperon polarization and spin density matrix elements of the vector mesons will be measured along with the single-spin asymmetry (SSA). The 2[Formula: see text]-acceptance in azimuth, which is extremely useful for reduction of systematic errors in measurements of spin observables, will be implemented in the experiment. The solid angle acceptance of the setup, [Formula: see text] mrad vertically and 350 mrad horizontally in the beam fragmentation region, covers a wide range of kinematic variables [Formula: see text] and [Formula: see text]. This provides the opportunity for separating dependences on these two variables which is usually not possible in the setups with a small solid angle acceptance. Unlike some previous polarization experiments, the SPASCHARM will be able to simultaneously accumulate and record data on the both, charged and neutral particle production.

Optical polarization characteristics of m-plane GaN/AlGaN quantum well structures grown on m-plane SiC substrate

Abstract Optical polarization characteristics of m-plane GaN/AlGaN QW structures grown on m-plane SiC substrate were theoretically investigated using the multiband effective-mass theory. The QW structure grown on SiC substrate shows much larger in-plane optical polarization than that grown on GaN substrate. This is attributed to the fact that the QW structure grown on SiC substrate has larger y ′ -polarized optical emission and smaller x ′ -polarized optical emission than the QW structure grown on GaN substrate. Also, the magnitude of the optical polarization is found to depend on the carrier density and decrease gradually with increasing carrier density. This can be explained by the fact that, with increasing k ∥ , the x ′ -polarized matrix element increases while the y ′ -polarized matrix element rapidly decreases.

Polarization characteristics of 480–680 nm (1 1 [formula omitted] 2) InGaN/GaN quantum well structures with strain relaxation effects

The polarization characteristics as a function of the In composition for semipolar (112¯2) InGaN/GaN quantum well (QW) structures with strain relaxation effects are investigated by using the multiband effective-mass theory. We assumed that the strain relaxation ratio ∊y′y′0-∊y′y′/∊y′y′0 is linearly proportional to the difference in the lattice constants between the well and the substrate. The energy spacing between the first two subbands increases with increasing In composition, and the average hole effective mass of the first subband is reduced for a QW structure with a larger In composition. The [1¯1¯23] x′-polarized matrix elements are shown to be much larger than the [11¯00] y′-polarized matrix elements. As a result, the x′-polarized light emission is shown to be dominant and a weak function of the In composition. On the other hand, the light emission for y′-polarizations rapidly decreases with increasing In composition, mainly due to a decrease in the matrix elements. Thus, the absolute value of the polarization ratio rapidly increases with increasing transition wavelength.

Optical polarization characteristics of m-plane InGaN/GaN quantum well structures and comparison with experiment

The optical polarization characteristics of the light emission in non-polar m-plane InGaN/GaN quantum well (QW) structures were theoretically investigated using the multiband effective-mass theory. The optical anisotropy of m-plane QW structure is ranging from 0.65 at 440 nm to 0.83 at 560 nm at the sheet carrier density of N2D=15×1012 cm−2 and is found to decrease gradually with increasing carrier density, which is in good agreement with the experimental result. The decrease in the optical anisotropy can be explained by the fact that the y′-polarized matrix element decreases with increasing k‖ while the x′-polarized matrix element gradually increases. Also, the decreasing rate of the QW structure with a smaller In composition is shown to be greater than that of the QW structure with a larger In composition.

Bond detectors for molecular dynamics simulations, Part I: Hydrogen bonds

Charge sensitivity analysis in AMBER force-field resolution has been used in quest for detectors of hydrogen bonds (HBs). The process of HB formation was investigated on ab initio classical trajectories (B3LYP/6-31G*) of different nucleobase pairs. Several charge sensitivities, namely: electronegativity, hardness, Fukui function (FF), and polarization matrix, were analyzed. The global and constrained equilibria were considered. It was demonstrated that FF indices and polarization matrix elements are good detectors of HB formation.

Perturbative role in the inelastic electron scattering from 29Si

Inelastic electron scattering form factors away from the closed sd -shell are investigated. This investigation covers the low-lying states in 29Si , which is considered according to the many-particle configuration mixing shell model as the 16O core, plus thirteen nucleons distributed over the entire sd -shell orbits. The investigation concentrates on the perturbative role of the core, which is called core polarization effects, on the inelastic electron scattering form factors. Core polarization effects are taken into consideration through the excitation of nucleons from 1s and 1p core orbits, and also from the 2s -1d valence orbits into higher shells, with 2ℏω excitations. Core polarization matrix elements are calculated with the M3Y effective interaction. For the sd -shell model space, a new Hamiltonian, based on a renormalized G -matrix, USDB, is used. All calculations are performed without adjusting any parameters.

Light scattering from spheres

For some applications, it has been assumed that scattering from an object placed near a highly reflecting substrate such as aluminum can be approximated by the scattering from that object placed near a perfectly conducting substrate. We examine this approximation by comparing the calculated scattering from dielectric spheres resting on plane substrates that are perfectly conducting and composed of aluminum. Examination of the Mueller polarization matrix elements shows appreciable differences between these two scattering systems. The differences, however, become small at scattering angles where the intensities are relatively large.

Multiple photon Monte Carlo simulation for polarized Mo-slashller scattering with Yennie-Fraustchi-Suura exponentiation at high energies.

We present the theoretical basis and sample Monte Carlo data for the YFS exponentiated O~a! calculation of polarized Moiller scattering at c.m.s. energies large compared to 2 me . Both longitudinal and transverse polarizations are discussed. Possible applications to Moiller polarimetry at the SLD are thus illustrated. @S0556-2821~96!05713-X# ization utilizes the polarization dependence of the Moiller scattering cross section for polarized electrons in the SLC beam on a stationary polarized foil of known polarization- so-called Moiller polarimetry. While this method of measure- ment is not the primary method of measuring the SLC e 2 polarization, it is used @4# as an important cross check on the more accurate Compton polarimetry employed by the SLD Collaboration in their high precision ALR studies. Accord- ingly, radiative corrections to polarized Moiller scattering at the below 1% precision level are now of some interest. In this paper, we present the first results on the Yennis- Fraustchi-Suura ~YFS !@ 5 #exponentiated exact O~a! Monte Carlo approach @6# to these corrections in analogy with the results on the crossed Bhabha process presented in @7,8#, for example. Specifically, we extend the BHLUMI 1.xx Monte Carlo event generator in Ref. @7# to the crossed reaction of interest here. The extension involves introducing a new polarized matrix element into BHLUMI which is exact to O~a! for arbi- trarily polarized incoming e 2 beams. To this end, we follow the work of Ref. @9# for polarized Bhabha scattering and obtain the required exact O~a! matrix elements by crossing transformations on the virtual and soft corrections in this latter reference. For the corresponding O~a! hard brems- strahlung matrix element for Moiller scattering, we find it convenient to calculate it directly. These exact O~a! results are then combined with our standard YFS Monte Carlo methods as they pertain to Moiller scattering ~the respective YFS form factors are obtained via crossing from those al- ready in BHLUMI 1.xx! to yield the first ever realistic multiple photon Monte Carlo event generator for Moiller scattering with arbitrary initial beam polarizations. We call this new event generator BMOLLR. In what follows, we first review the relevant aspects of BHLUMI 1.xx insofar as our crossing transformations to the Moiller process are concerned. This is done in the next sec- tion. In Sec. III, we present the respective crossed virtual and soft corrections derived from Ref. @9#. In Sec. IV, we calcu- late the desired hard bremsstrahlung correction. In Sec. V, we combine our results to create BMOLLR and we present sample Monte Carlo data to illustrate the corresponding mul- tiple photon corrections. Comparisons with earlier analytic work in Refs. @10-12# as well as with recent SLD results @3# are also discussed in this section. Section VI contains some summary remarks.

Polarization instability of ring lasers

We give a theoretical analysis of the stability of single-frequency operation of travelling-wave ring lasers in which the active medium consists of randomly oriented, identical two-level molecules having linearly or circularly polarized matrix elements of the dipole moment on signal transition. The generation of stable lasing is shown to be strongly dependent on the mutual polarization states of the generated wave and the dipole moment, and in case of an isotropic laser, generation of the field with polarization collinear to the dipole moment is unstable.

Design and performance of a 215 GHz pulsed radar system

A high-power 215-GHz pulsed radar system developed for remote-sensing applications is described that is capable of making backscatter measurements from terrain targets at ranges of several kilometers under normal atmospheric conditions. By using separate transmit and receive antennas, the amplitudes of the polarization matrix elements may be measured conveniently. A dedicated data acquisition system was developed allowing up to 15 range gates to be sampled at 100-ns intervals. Instrument stability of +or-1.0 dB yields accurate scattering measurements of a variety of terrestrial targets. System performance and calibration, together with measurements of snow backscatter coefficients made during early 1987, are discussed. >

Energy-dependent β-γ circular polarization and nuclear matrix elements in 84Rb

The energy-dependent β-γ circular polarization correlation P γ was measured to restrict the possible nuclear matrix-element solutions which can be used to describe the 2 −–2 + positron transition in 84Rb. The analysis shows that there may be a significant contribution from all six matrix elements. The matrix-element analysis indicates that A 3 is much smaller than A 1 in P γ .

General relations between photoproduction of pions and vector meson production by πN collision based on the photon-vector-meson analogy model

The relations among differential cross section, polarization and helicity density matrix elements in γN → πN and πN → VN processes are given for the photon-vector-meson analogy model. For example, the differential cross sections of γN → πN processes are given in terms of density matrix elements and differential cross sections of πN → ϱN processes, and the relations fit the experimental data fairly well.