scholarly journals Contribution of QCD condensates to the OPE of Green functions of chiral currents

2019 ◽  
Vol 199 ◽  
pp. 05025
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Perturbation Theory ◽  
Operator Product Expansion ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
Chiral Perturbation ◽  
Unknown Parameters ◽  
Energy Behaviour ◽  
Intrinsic Parity ◽  
Effective Theories

A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.

scholarly journals OPE of Green functions of chiral currents

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Operator Product Expansion ◽  
Chiral Limit ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
High Energy Behavior ◽  
Energy Behavior

Abstract In this paper, we investigate the high-energy behavior of two-point and three-point Green functions of the QCD chiral currents and densities using the framework of the operator product expansion in the chiral limit. In detail, we study the contributions of the quark, gluon, quark-gluon and four-quark condensates to all the relevant non-vanishing three-point correlators.

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.

NEW SCALING VARIABLE FROM LIGHT-CONE PERTURBATION THEORY

1991 ◽  
Vol 06 (03) ◽  
pp. 345-363 ◽  
Author(s):  
BO-QIANG MA ◽  
JI SUN
Keyword(s):  
Perturbation Theory ◽  
Power Law ◽  
Light Cone ◽  
Operator Product Expansion ◽  
Free Field ◽  
Field Operator ◽  
Order Effect ◽  
Operator Product ◽  
Bjorken Scaling ◽  
Twist Effect

We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall “energy” conservation in deep inelastic lepton-nucleon scattering yields a similar new scaling variable xp, which reduces to the Weizmann variable, the Bloom-Gilman variable and the Bjorken variable at some approximations. The xp rescaling is expected to be a good scaling variable, and hence gives strong power-law type corrections to the deviations of Bjorken scaling. An understanding of this xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE is also given, indicating it is likely a higher order effect in the coefficient functions, i.e. it does not belong to the higher twist effect. Therefore this xp rescaling is likely a new effect contributing to the power-law type corrections.

scholarly journals Aspects on Effective Theories and the QCD Transition

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 945
Author(s):  
Angel Gómez Nicola
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Chiral Symmetry ◽  
Current Knowledge ◽  
Chiral Symmetry Restoration ◽  
Chiral Perturbation ◽  
Ward Identities ◽  
Hadron Gas ◽  
Effective Theories

We review recent advances in the understanding of the Quantum Chromodynamics (QCD) transition and its nature, paying special attention to the analysis of chiral symmetry restoration within different approaches based on effective theories. After presenting some of the main aspects of the current knowledge of the phase diagram from the theoretical, experimental and lattice sides, we discuss some recent problems where approaches relying on effective theories have been particularly useful. In particular, the combination of ideas such as Chiral Perturbation Theory, unitarity and Ward Identities allows us to describe successfully several observables of interest. This is particularly relevant for quantities expected to be dominated by the light meson components of the hadron gas such as the scalar and topological susceptibilities. In addition, ward identities and effective Lagrangians provide systematic results regarding chiral and U ( 1 ) A partner degeneration properties which are of great importance for the interplay between those two transitions and the nature of chiral symmetry restoration. Special attention is paid to the connection of this theoretical framework with lattice simulations.

scholarly journals PROSPECTS FOR DISCOVERY OF THE τ- → π-ℓ+ℓ-ντ DECAYS

2014 ◽  
Vol 35 ◽  
pp. 1460460
Author(s):  
PABLO ROIG
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Behavior ◽  
Mass Spectra ◽  
Axial Vector ◽  
Form Factors ◽  
Branching Ratios ◽  
Green Functions ◽  
Vector Resonance ◽  
Chiral Perturbation ◽  
Model Independent

We study the phenomenology of the τ- → π-ντℓ+ℓ- decays (ℓ = e, μ), predicting the respective branching ratios and di-lepton invariant-mass spectra. In addition to the model-independent (QED) contributions, we investigate the structure-dependent (SD) terms, encoding features of the hadronization of QCD currents. The relevant form factors are evaluated by supplementing Chiral Perturbation Theory with the inclusion of the lightest (axial-)vector resonance multiplet as dynamical fields. The Lagrangian couplings are fully predicted requiring the known QCD asymptotic behavior to the relevant Green functions and associated form factors in the limit of an infinite number of colours. As a consequence we predict that the τ- → π-ντe+e- decays should be discovered soon while this is not granted for the ℓ = μ case.

scholarly journals SHORT DISTANCE REPULSION AMONG BARYONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1330012 ◽  
Author(s):  
SINYA AOKI ◽  
JANOS BALOG ◽  
TAKUMI DOI ◽  
TAKASHI INOUE ◽  
PETER WEISZ
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Lattice Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Results ◽  
Wave Functions ◽  
Operator Product ◽  
Distance Behavior

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu–Bethe–Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion (OPE) and a renormalization group (RG) analysis in the perturbation theory (PT) of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

LARGE MASS EXPANSION, OPERATOR PRODUCT EXPANSION, AND R*-OPERATION

1988 ◽  
Vol 03 (04) ◽  
pp. 381-391 ◽  
Author(s):  
V.A. SMIRNOV
Keyword(s):  
Operator Product Expansion ◽  
Arbitrary Order ◽  
Large Mass ◽  
Operator Product ◽  
Light Fields ◽  
Green Functions ◽  
Effective Lagrangian ◽  
Zero Values ◽  
Feynman Amplitudes ◽  
Mass Expansion

An explicit formula for the effective Lagrangian in arbitrary order of the large mass expansion (LME) is derived. It describes the asymptotic expansion of Green functions of light fields when heavy masses tend to infinity and expresses the effective Lagrangian as a sum of the light fields and their derivatives with coefficients which expand in vacuum Feynman amplitudes at zero values of light masses. These coefficients are UV- and IR-finite due to the R*-operation that is a generalisation of the R-operation when IR divergences are involved.

CHIRAL PERTURBATION THEORY AND ANOMALOUS PROCESSES

1993 ◽  
Vol 08 (18) ◽  
pp. 3045-3105 ◽  
Author(s):  
JOHAN BIJNENS
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Constituent Quark ◽  
Constituent Quark Model ◽  
Vector Meson Dominance ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Effective Lagrangian ◽  
Intrinsic Parity ◽  
Energy Processes

The application of chiral perturbation theory to low energy processes of abnormal intrinsic parity (anomalous) is discussed. The full infinite part at next-to-leading order is calculated. Estimates of the finite part of the effective Lagrangian from vector meson dominance and the chiral constituent quark model are obtained. This is then applied to decays of pseudoscalars to photon–photon and photon–three-pseudoscalar couplings.

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