Radiative corrections to the lepton current in unpolarized elastic lp-interaction for fixed $$Q^2$$ and scattering angle

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

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Scattering-angle dependence of signal/background ratio of inner-shell electron excitation loss in EELS

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075701 ◽

1983 ◽

Vol 41 ◽

pp. 390-391

Author(s):

T. Oikawa ◽

M. Inoue ◽

T. Honda ◽

Y. Kokubo

Keyword(s):

Energy Loss ◽

Electron Excitation ◽

Heavy Elements ◽

Background Intensity ◽

Light Elements ◽

Energy Analyzer ◽

High Background ◽

Scattering Angle ◽

Angle Dependence ◽

Shell Electron

EELS allows us to make analysis of light elements such as hydrogen to heavy elements of microareas on the specimen. In energy loss spectra, however, elemental signals ride on a high background; therefore, the signal/background (S/B) ratio is very low in EELS. A technique which collects the center beam axial-symmetrically in the scattering angle is generally used to obtain high total intensity. However, the technique collects high background intensity together with elemental signals; therefore, the technique does not improve the S/B ratio. This report presents the experimental results of the S/B ratio measured as a function of the scattering angle and shows the possibility of the S/B ratio being improved in the high scattering angle range.Energy loss spectra have been measured using a JEM-200CX TEM with an energy analyzer ASEA3 at 200 kV.Fig.l shows a typical K-shell electron excitation edge riding on background in an energy loss spectrum.

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Analytic integration of contrast transfer functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010010617x ◽

1988 ◽

Vol 46 ◽

pp. 822-823

Author(s):

Peter Rez

Keyword(s):

Wave Function ◽

Transfer Function ◽

Transfer Functions ◽

Spherical Aberration ◽

Continuous Distribution ◽

Objective Lens ◽

Direction Parallel ◽

Scattering Angle ◽

Analytic Integration ◽

Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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Radiative Corrections for e+e- Collisions

10.1007/978-3-642-74925-4 ◽

1989 ◽

Keyword(s):

Radiative Corrections

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Presentations from LoopFest V: Radiative Corrections For The International Linear Collider: Multi-Loops And Multi-Legs, 19-21 June 2006, SLAC, Menlo Park, California

10.2172/894926 ◽

2006 ◽

Author(s):

L Dixon

Keyword(s):

Linear Collider ◽

International Linear Collider ◽

Radiative Corrections

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Quantities Directly Measurable by Scattering

10.1093/oso/9780199670871.003.0003 ◽

2018 ◽

Author(s):

Eaton E. Lattman ◽

Thomas D. Grant ◽

Edward H. Snell

Keyword(s):

Molecular Weight ◽

Particle Shape ◽

Particle Surface ◽

Scattering Data ◽

Radius Of Gyration ◽

Particle Volume ◽

Particle Surface Area ◽

Scattering Angle ◽

Particle Dimension ◽

Maximum Particle

In this chapter we note that solution scattering data can be divided into four regions. At zero scattering angle, the scattering provides information on molecular weight of the particle in solution. Beyond that, the scattering is influenced by the radius of gyration. As the scattering angle increases, the scattering is influenced by the particle shape, and finally by the interface with the particle and the solution. There are a number of important invariants that can be calculated directly from the data including molecular mass, radius of gyration, Porod invariant, particle volume, maximum particle dimension, particle surface area, correlation length, and volume of correlation. The meaning of these is described in turn along with their mathematical derivations.

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