scholarly journals Remark on the Kinematics of the One-Photon Production in Electron–Proton Scattering

1997 ◽  
Vol 12 (21) ◽  
pp. 1553-1559
Author(s):  
Wei Lu
Keyword(s):  
Phase Space ◽  
Deeply Virtual Compton Scattering ◽  
Quark Distribution ◽  
Photon Production ◽  
Distribution Functions ◽  
Proton Scattering ◽  
Diquark Model ◽  
Space Factor ◽  
The Cross ◽  
The One

We clarify some misleading mistakes in the literature about the phase space for the one-photon production in electron–proton scattering and present the correct overall phase space factor in the cross-section formula. Our conclusion is that the earlier diquark model predictions for the cross-sections of the one-photon production in electron–proton scattering are unreliable. Furthermore, we specify the phase space boundaries. In relation to the recent proposal to measure the off-diagonal quark distribution functions in the deeply virtual Compton scattering off the proton, we point out that the kinematics strongly disfavors such experiments.

scholarly journals Structure Functions of Hadrons in the QCD Effective Theory

1997 ◽  
Vol 50 (1) ◽  
pp. 139
Author(s):  
Takayuki Shigetani ◽  
Katsuhiko Suzuki ◽  
Hiroshi Toki
Keyword(s):  
Quark Distribution ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Low Energy ◽  
Effective Theory ◽  
Spin Distribution ◽  
Diquark Model ◽  
Model Calculations ◽  
Diquark Correlation

We study the structure functions of hadrons with the low energy effective theory of QCD. We try to clarify a link between the low energy effective theory, where non-perturbative dynamics is essential, and the high energy deep inelastic scattering experiment. We calculate the leading twist matrix elements of the structure function at the low energy model scale within the effective theory. Calculated structure functions are taken to the high momentum scale with the help of the perturbative QCD, and compared with the experimental data. Through a comparison of the model calculations with the experiment, we discuss how the non-perturbative dynamics of the effective theory is reflected in the deep inelastic phenomena. We first evaluate the structure functions of the pseudoscalar mesons using the NJL model. The resulting structure functions show reasonable agreement with experiments. We then study the quark distribution functions of the nucleon using a covariant quark–diquark model. We calculate three leading twist distribution functions, the spin-independent f1(x), the longitudinal spin distribution g1(x), and the chiral-odd transversity spin distribution h1(x). The results for f1(x) and g1(x) turn out to be consistent with available experiments because of the strong spin-0 diquark correlation.

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

scholarly journals Covariant phase space and soft factorization in non-Abelian gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Temple He ◽  
Prahar Mitra
Keyword(s):  
Phase Space ◽  
Ward Identity ◽  
Gauge Theories ◽  
Minkowski Spacetime ◽  
Soft Gluon ◽  
Careful Study ◽  
Abelian Gauge ◽  
Gauge Sector ◽  
Vacuum States ◽  
The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

scholarly journals Detection and Localization for Multiple Stationary Human Targets Based on Cross-Correlation of Dual-Station SFCW Radars

2019 ◽  
Vol 11 (12) ◽  
pp. 1428 ◽  
Author(s):  
Yong Jia ◽  
Yong Guo ◽  
Chao Yan ◽  
Haoxuan Sheng ◽  
Guolong Cui ◽  
...  
Keyword(s):  
Cross Correlation ◽  
Continuous Wave ◽  
Coefficient Matrix ◽  
Constant False Alarm Rate ◽  
Localization Algorithm ◽  
Cfar Detection ◽  
Stepped Frequency ◽  
The Cross ◽  
The One ◽  
Detection And Localization

This paper demonstrates the feasibility of detection and localization of multiple stationary human targets based on cross-correlation of the dual-station stepped-frequency continuous-wave (SFCW) radars. Firstly, a cross-correlation operation is performed on the preprocessed pulse signals of two SFCW radars at different locations to obtain the correlation coefficient matrix. Then, the constant false alarm rate (CFAR) detection is applied to extract the ranges between each target and the two radars, respectively, from the correlation matrix. Finally, the locations of human targets is calculated with the triangulation localization algorithm. This cross-correlation operation mainly brings about two advantages. On the one hand, the cross-correlation explores the correlation feature of target respiratory signals, which can effectively detect all targets with different signal intensities, avoiding the missed detection of weak targets. On the other hand, the pairing of two ranges between each target and two radars is implemented simultaneously with the cross-correlation. Experimental results verify the effectiveness of this algorithm.

BESSEL-WEIGHTED ASYMMETRIES AND TRANSVERSE SPIN EFFECTS

2012 ◽  
Vol 20 ◽  
pp. 168-176
Author(s):  
LEONARD GAMBERG
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Parton Distribution ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Transverse Spin ◽  
High Transverse Momentum ◽  
Transverse Momentum Dependent ◽  
Fragmentation Functions ◽  
The Cross

We consider the cross section for semi-inclusive deep inelastic scattering in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

scholarly journals The Spin Structure of the Nucleon

2016 ◽  
Vol 40 ◽  
pp. 1660001
Author(s):  
Xiangdong Ji ◽  
Yong Zhao
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Proton Spin ◽  
Effective Theory ◽  
Large Momentum ◽  
Theory Approach ◽  
The One ◽  
The Relationship

We justify the physical meaning of the spin and orbital angular momentum of free partons in the infinite momentum frame, and discuss the relationship between the Jaffe-Manohar and Ji’s sum rules for proton spin. The parton orbital angular momentum in the Jaffe-Manohar sum rule can be measured through twist-three GPD’s in hard scattering processes such as deeply virtual Compton scattering. Furthermore, we propose that the paton orbital angular momentum as well as the gluon helicity can be calculated in lattice QCD through a large momentum effective theory approach, and provide all the one-loop matching conditions for the proton spin content in perturbative QCD.

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