scholarly journals EVOLUTION OF STRUCTURE FUNCTIONS AND THEIR MOMENTS IN CHIRAL FIELD THEORY

2003 ◽  
Vol 18 (04) ◽  
pp. 593-606
Author(s):  
KAKALI RAY-MAITY ◽  
PADMANABHA DASGUPTA
Keyword(s):  
Field Theory ◽  
Evolution Equations ◽  
Probabilistic Approach ◽  
Perturbation Expansion ◽  
Structure Functions ◽  
Evolution Process ◽  
Effective Theory ◽  
Chiral Field ◽  
Coupling Constant ◽  
Evolution Of Structure

Evolution of structure functions and their moments at low and moderate Q2 is studied in the chiral field theory. Evolution equations based on perturbation expansion in the coupling constant of the effective theory are derived and solved for the moments. The kernels of evolution arising from different processes have been calculated with contributions from direct and cross channels, the interference terms being non-negligible in the kinematic regions under consideration. This is shown to lead to flavor-dependence of the kernels which manifests in observable effects. The invalidity of the probabilistic approach to the evolution process is also pointed out.

An example of a divergent perturbation expansion in field theory

1952 ◽  
Vol 48 (4) ◽  
pp. 625-639 ◽  
Author(s):  
C. A. Hurst
Keyword(s):  
Field Theory ◽  
Lower Bound ◽  
Contact Interaction ◽  
General Problem ◽  
Rest Mass ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Coupling Constant ◽  
Perturbation Expansions ◽  
Irreducible Graphs

AbstractThe convergence of the perturbation expansion for the S-matrix in interaction representation of a three-boson contact interaction is investigated. A lower bound is obtained for the integrals corresponding to irreducible graphs when the total rest mass of the system is insufficient for bare particles to be created. It is shown that in this case the perturbation expansion cannot converge no matter what value the coupling constant has. A discussion is given of the bearing of this result on the general problem of the convergence of perturbation expansions for the S-matrix in renormalized field theories.

Modified propagators in field theory (with application to the anomalous magnetic moment of the nucleon)

1954 ◽  
Vol 223 (1152) ◽  
pp. 112-129 ◽  
Keyword(s):  
Field Theory ◽  
Asymptotic Expansion ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Meson Field ◽  
Coupling Constant ◽  
Zero Coupling ◽  
Better Than

Many attempts have been made to improve upon the perturbation expansion in meson-field theories, one such attempt being the introduction of modified propagators S' F and ∆' F . It is shown in this paper that the introduction of these new propagators (or at least in the form that has been proposed) creates new infinities which cannot be removed by renormalization. These new infinities are due to new complex poles of the modified propagators. A tentative prescription is put forth to get over these new difficulties, but it is still intimately connected with the perturbation expansion. Unfortunately, the prescription does not give an unambiguous answer. A particular S' F is used in the calculation of the anomalous magnetic moment of the nucleon. The results obtained are no better than those of other workers. However, there are many reasons why this may be the case. It is also shown that the subseries which arises in this case leads, at best, to an asymptotic expansion in the coupling constant. The nature of the singularity at zero coupling is found.

scholarly journals PROTON STRUCTURE FUNCTIONS FROM CHIRAL DYNAMICS AND QCD CONSTRAINTS

1998 ◽  
Vol 13 (01) ◽  
pp. 71-82 ◽  
Author(s):  
H. J. WEBER
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Structure Functions ◽  
Chiral Field ◽  
Quark Masses ◽  
Goldstone Bosons ◽  
Proton Structure ◽  
Regge Behavior ◽  
Small X ◽  
Bjorken X

The spin fractions and deep inelastic lepton structure functions of the proton are analyzed based on chiral field theory invloving Goldstone bosons. A detailed comparison with several recent chiral models sheds light on their successful description of the spin fractions of the proton as being due to neglecting quark masses. Initial quark valence distributions at a higher scale than Λ QCD are constructed using quark counting constraints at large Bjorken x→1 and Regge behavior at small x. Reasonable strange quark distributions are then predicted by chiral field theory. The spin fractions also agree with the data.

FLAVOR-ASYMMETRIC SEA QUARK DISTRIBUTION IN A CHIRAL POTENTIAL MODEL

1998 ◽  
Vol 13 (11) ◽  
pp. 1785-1794 ◽  
Author(s):  
KAKALI ROY-MAITY ◽  
PADMANABHA DASGUPTA
Keyword(s):  
Evolution Equations ◽  
Potential Model ◽  
Quark Distribution ◽  
Structure Functions ◽  
Static Properties ◽  
Domain Of Applicability ◽  
Pion Emission ◽  
Additive Contribution ◽  
Evolution Of Structure ◽  
Chiral Potential

Flavor asymmetry of the sea quark distribution which expresses itself in the observed value of the Gottfried sum leads one to consider pion emission as directly contributing to the scale dependence of structure functions. As an example, we study the evolution of structure functions in a chiral potential model which incorporates the pion as the chiral-symmetry-restoring field and which was originally invented to explain the static properties of baryons. Evolution equations for the quark and pion densities are derived in the lowest order at subasymptotic Q2. The kernels of evolution for the effective quark densities turn out to be flavor-dependent and are endowed with properties quite distinct from those possessed by leading log QCD splitting functions. In particular, the commonly used probabilistic treatment of the evolution, which is legitimate in the kinematic region of the perturbative QCD evolution, is seen not to be valid in the domain of applicability of the chiral potential model. The model is shown to lead to nontrivial evolution of the nonsinglet moments in a manner consistent with the observed departure from the Gottfried sum rule in a low Q2 region. For higher Q2, the evolution of the Gottfried sum receives also an additive contribution not envisaged in the earlier works on the phenomenon.

scholarly journals PROTON STRUCTURE FUNCTIONS FROM CHIRAL DYNAMICS AND QCD CONSTRAINTS

1999 ◽  
Vol 14 (19) ◽  
pp. 3005-3027 ◽  
Author(s):  
H. J. WEBER
Keyword(s):  
Field Theory ◽  
Goldstone Boson ◽  
Detailed Comparison ◽  
Structure Functions ◽  
Proton Spin ◽  
Chiral Field ◽  
Pure Spin ◽  
Regge Behavior ◽  
Order Of Magnitude ◽  
Bjorken X

The spin fractions and deep inelastic lepton structure functions of the proton are analyzed using chiral field theory involving Goldstone bosons. A detailed comparison with recent chiral models sheds light on their successful description of the spin fractions of the proton as being due to neglecting helicity nonflip chiral transitions. This approximation is valid for zero mass but not for constituent quarks. Since the chiral spin fraction models with the pure spin-flip approximation reproduce the measured spin fractions of the proton, axialvector constituent-quark-Goldstone boson couplings are found to be inconsistent with the proton spin data. Initial quark valence distributions are then constructed using quark counting constraints at Bjorken x→1 and Regge behavior at x→0. Sea quark distributions predicted by chiral field theory on this basis have the correct order of magnitude and shape. The spin fractions also agree with the data.

Effective Field Theory in Particle Physics and Cosmology

2020 ◽  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Large Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Soft Collinear Effective Theory ◽  
Multiple Length Scales ◽  
Cosmological Observations ◽  
Standard Models

Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.

scholarly journals High-energy operator product expansion at sub-eikonal level

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Operator Product Expansion ◽  
Evolution Equations ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Impact Factors ◽  
Operator Product ◽  
The Impact ◽  
New Distribution

Abstract The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

scholarly journals The Evolutionary Properties on Solitary Solutions of Nonlinear Evolution Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Wenxia Chen ◽  
Danping Ding ◽  
Xiaoyan Deng ◽  
Gang Xu
Keyword(s):  
Soliton Solution ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Evolution Process ◽  
Solution Curve ◽  
Solitary Solutions ◽  
Basic Calculus

The evolution process of four class soliton solutions is investigated by basic calculus theory. For any given x, we describe the special curvature evolution following time t for the curve of soliton solution and also study the fluctuation of solution curve.

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