scholarly journals Chiral Perturbation Theory at NNNLO

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1262
Author(s):  
Nils Hermansson-Truedsson
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Chiral Perturbation Theory ◽  
Pion Mass ◽  
Effective Field ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Effective Lagrangian ◽  
Low Energies

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum p2, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.

scholarly journals SPIN POLARIZABILITY OF THE NUCLEON IN THE EFFECTIVE FIELD THEORY OF HEAVY BARYON

2006 ◽  
Vol 21 (19n20) ◽  
pp. 3947-3966
Author(s):  
K. B. VIJAYA KUMAR ◽  
YONG-LIANG MA ◽  
YUE-LIANG WU
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Chiral Perturbation Theory ◽  
Heavy Baryon ◽  
Effective Field ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Spin Polarizability ◽  
Large Correction

We have constructed a heavy baryon effective field theory with photon as an external field in accordance with the symmetry requirements similar to the heavy quark effective field theory. By treating the heavy baryon and antibaryon equally on the same footing in the effective field theory, we have calculated the spin polarizabilities γi, i = 1,…,4 of the nucleon at third order and at fourth-order of the spin-dependent Compton scattering. At leading order (LO), our results agree with the corresponding results of the heavy baryon chiral perturbation theory, at the next-to-leading order (NLO) the results show a large correction to the ones in the heavy baryon chiral perturbation theory due to baryon–antibaryon coupling terms. The low-energy theorem is satisfied both at LO and at NLO. The contributions arising from the heavy baryon–antibaryon vertex were found to be significant and the results of the polarizabilities obtained from our theory is much closer to the experimental data.

πNN SYSTEM AT LOW ENERGY

2011 ◽  
Vol 26 (03n04) ◽  
pp. 586-588 ◽  
Author(s):  
VADIM BARU
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Chiral Perturbation Theory ◽  
High Accuracy ◽  
Effective Field ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Recent Developments

With the advent of chiral perturbation theory, the low-energy effective field theory of QCD, high accuracy calculations for hadronic reactions have become possible. We review the recent developments in the reaction NN → NNπ in chiral EFT.

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.

scholarly journals The role of isospin filtering reactions in the S = −1 sector

2019 ◽  
Vol 199 ◽  
pp. 03008
Author(s):  
A. Feijoo ◽  
V.K. Magas ◽  
A. Ramos
Keyword(s):  
Perturbation Theory ◽  
High Spin ◽  
Chiral Perturbation Theory ◽  
Low Energy ◽  
Scattering Data ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Effective Lagrangian ◽  
Energy Constants

The present study reveals interesting constraining effects of isospin filtering reactions on the low energy constants present in meson-baryon chiral effective Lagrangian, particularly, on the next-to-leading order constants. Our model has been developed within the framework of Unitarized Chiral Perturbation Theory and has been fitted to two-body scattering data in the sector of S = −1. In addition, the model was further elaborated by means of the inclusion of high-spin hyperonic resonances.

scholarly journals Recent results of the pion-nucleon scattering and the widths of the delta and Roper resonances in BChPT

2019 ◽  
Vol 199 ◽  
pp. 01005
Author(s):  
J. Gegelia
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Degrees Of Freedom ◽  
Effective Field ◽  
Chiral Perturbation ◽  
Nucleon Scattering ◽  
Delta Resonances ◽  
Pion Nucleon ◽  
Dynamical Degrees

Recent calculations of the pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit delta resonances are presented. Two-loop results of the widths of the Δ and Roper resonances are discussed in the framework of an effective field theory with nucleons, pions and the Roper and delta resonances as dynamical degrees of freedom.

scholarly journals THE ROLE OF THE Δ(1232)-RESONANCE IN COVARIANT BARYON CHIRAL PERTURBATION THEORY

2014 ◽  
Vol 26 ◽  
pp. 1460088
Author(s):  
J. M. ALARCÓN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Scattering Data ◽  
Theory Approach ◽  
Chiral Perturbation ◽  
Chiral Effective Field Theory ◽  
Dynamical Degree

We stress, on theoretical and phenomenological grounds, the importance of the Δ(1232)-resonance in a chiral effective field theory approach to the study of πN scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from πN scattering data.

scholarly journals BARYON CHIRAL PERTURBATION THEORY IN MANIFESTLY LORENTZ-INVARIANT FORM

2006 ◽  
Vol 21 (04) ◽  
pp. 881-884 ◽  
Author(s):  
STEFAN SCHERER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Effective Field ◽  
Renormalization Scheme ◽  
Perturbative Expansion ◽  
Power Counting ◽  
Counting Method ◽  
Chiral Perturbation ◽  
Effective Lagrangian ◽  
Expansion Scheme

A successful effective field theory program requires besides the most general effective Lagrangian a perturbative expansion scheme for observables in terms of a consistent power counting method. We discuss a renormalization scheme for manifestly Lorentz-invariant baryon chiral perturbation theory generating a simple and consistent power counting for renormalized diagrams. The approach may be used in an iterative procedure to renormalize higher-order loop diagrams and also allows for implementing a consistent power counting when vector mesons are explicitly included.

scholarly journals On the three-particle analog of the Lellouch-Lüscher formula

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Müller ◽  
Akaki Rusetsky
Keyword(s):  
Field Theory ◽  
Finite Volume ◽  
Effective Field Theory ◽  
Effective Field ◽  
Infinite Volume ◽  
Leading Order ◽  
Particle Decay ◽  
Particle Decays

Abstract Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

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