On a Symmetry Property of the Inelastic Scattering Amplitude in the Adiabatic Approximation

1971 ◽  
Vol 49 (8) ◽  
pp. 983-990 ◽  
Author(s):  
H. Sherif
Keyword(s):  
Inelastic Scattering ◽  
Symmetry Property ◽  
Scattering Amplitude ◽  
Arbitrary Spin ◽  
Generalized Polarization ◽  
Interaction Terms ◽  
Symmetry Properties ◽  
Angular Correlation Function ◽  
Nuclear Excited State ◽  
T Matrix

A symmetry property of the exact T matrix for the inelastic scattering of particles with arbitrary spin is derived, in the adiabatic limit, using time reversal invariance properties of the elastic scattering amplitude and neglecting interaction terms that involve spins or velocities of the target nucleons. The symmetry property is used to show the equality of the generalized polarization and asymmetry tensors for inelastic scattering and to derive the symmetry properties, with respect to the adiabatic recoil axis, of the angular correlation function and the circular polarization of the deexcitation gamma rays. It is also shown that the nuclear excited state is aligned along the axis normal to the scattering plane. A brief discussion of the symmetry properties of the adiabatic DWBA amplitude is given. When interaction terms involving spins or velocities of the target nucleons are taken into account, it is shown that the inelastic scattering T matrix can be divided into two parts; one that satisfies the above-mentioned symmetry relation, and a second part which has a different symmetry.

scholarly journals 𝒫𝒯-symmetric quantum field theory on the noncommutative spacetime

2019 ◽  
Vol 35 (05) ◽  
pp. 2050012
Author(s):  
Oleg O. Novikov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitude ◽  
Quantum Field ◽  
Leading Order ◽  
Symmetric Quantum ◽  
Noncommutative Spacetime ◽  
T Matrix ◽  
The One ◽  
New Formula

We consider the [Formula: see text]-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new [Formula: see text]-symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order T-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies that the leading order scattering amplitude preserves the symmetries of the noncommutative geometry if they are not broken in the non-Hermitian formulation.

scholarly journals SINGLE-SPIN ASYMMETRIES IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AND DRELL-YAN PROCESSES

2014 ◽  
Vol 25 ◽  
pp. 1460015
Author(s):  
MATTHEW D. SIEVERT
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Time Reversal ◽  
Complex Phase ◽  
Spin Asymmetries ◽  
Single Spin ◽  
Dependent Part ◽  
Single Spin Asymmetries ◽  
Sign Change ◽  
Symmetry Properties

In this brief article, we summarize our recent work1 regarding the origin of the nucleon Sivers functions within the diquark spectator model in semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process (DY). We demonstrate that the C, P, T symmetry properties of transverse spinors always couple the spin-dependent part of the numerator algebra to the imaginary part of the denominator in the cross section. This complex phase, and its sign change under time reversal, is believed to be responsible for the predicted sign change of the Sivers functions in SIDIS and DY. We study the complex phase generated in both processes by the "color-lensing" mechanism and find that, although the phases appear to be different in structure between SIDIS and DY, they do give rise to the expected sign flip relation at leading twist.

scholarly journals Electron and Positron Scattering by Non-Central Potentials: Matrix Elements and Symmetry Properties in the First Born Approximation

2021 ◽  
Author(s):  
Marcos Barp ◽  
Felipe Arretche
Keyword(s):  
Fourier Transform ◽  
Born Approximation ◽  
Scattering Amplitude ◽  
Point Group ◽  
Computational Effort ◽  
Positron Scattering ◽  
Symmetry Properties ◽  
Linear Molecules ◽  
The Fourier Transform ◽  
Symmetry Relations

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the D∞h point group optimizing the computational effort. Keywords — Positron and electron scattering, Fourier transform of the Gaussian product theorem, McMurchie-Davidson procedure, Obara-Saika procedure, linear molecules .

Cubic interaction terms for arbitrary spin

1983 ◽  
Vol 227 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Anders K.H. Bengtsson ◽  
Ingemar Bengtsson ◽  
Lars Brink
Keyword(s):  
Arbitrary Spin ◽  
Interaction Terms

On the possibility of gluon number fluctuations in diffractive deep inelastic scattering data with impact parameter

2016 ◽  
Vol 31 (33) ◽  
pp. 1650186
Author(s):  
Z. Hu ◽  
W. Xiang ◽  
S. Cai
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Impact Parameter ◽  
Scattering Amplitude ◽  
Global Analysis ◽  
High Energy ◽  
Scattering Data ◽  
Deep Inelastic Scattering Data ◽  
Saturation Exponent ◽  
The Impact

A global analysis of the latest diffractive deep inelastic scattering (DIS) data with gluon number fluctuations and impact parameter is performed. The impact parameter is introduced into the scattering amplitude by saturation scale with a Gaussian b-dependence. The results show that the description of the diffractive DIS data is improved once the gluon number fluctuations and impact parameter are included, with [Formula: see text]/d.o.f = 0.878, [Formula: see text]/d.o.f = 0.928 and [Formula: see text]/d.o.f = 0.897 in different sets of free parameters. Moreover, we find that the impact parameter ([Formula: see text] 0.1) is possibly compressed by the gluon number fluctuations, which leads to the value of saturation exponent returning to [Formula: see text] 0.2. This outcome is compatible with the prediction that the saturation exponent is dominated by the fluctuations at sufficiently high energy, which may indicate the possibility of gluon number fluctuations in diffractive DIS data.

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