Chiral perturbation theory: An effective field theory

2008 ◽  
Vol 61 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Barry R. Holstein
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Chiral Perturbation Theory ◽  
Effective Field ◽  
Chiral Perturbation

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.

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 Perturbative QCD at High Temperature

1997 ◽  
Vol 12 (08) ◽  
pp. 1431-1464 ◽  
Author(s):  
Agustin Nieto
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Perturbation Theory ◽  
High Temperature ◽  
Perturbative Qcd ◽  
Effective Field Theory ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Effective Field ◽  
Recent Developments

Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for ϕ4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g5 and the calculation of the g6 term is outlined. Implications for the application of perturbative QCD to the quark–gluon plasma are also discussed.

scholarly journals Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Alexandre Salas-Bernárdez ◽  
Felipe Llanes-Estrada ◽  
Juan Escudero-Pedrosa ◽  
José Antonio Oller
Keyword(s):  
Perturbation Theory ◽  
Partial Wave ◽  
Chiral Perturbation Theory ◽  
A Priori ◽  
Resonance Region ◽  
New Physics ◽  
Effective Field ◽  
Chiral Perturbation ◽  
Inverse Amplitude Method ◽  
Inverse Amplitude

Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting particles remains small, as they do not respect exact elastic unitarity. This limits their predictive power towards new physics at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory techniques have been devised to extend the reach of the EFT to regimes where partial waves are saturating unitarity, but their uncertainties have hitherto not been addressed thoroughly. Here we take one of the best known of them, the Inverse Amplitude Method (IAM), and carefully following its derivation, we quantify the uncertainty introduced at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT applications. We find that the relative theoretical uncertainty of the IAM at the mass of the first resonance encountered in a partial-wave is of the same order in the counting as the starting uncertainty of the EFT at near-threshold energies, so that its unitarized extension should a priori be expected to be reasonably successful. This is so provided a check for zeroes of the partial wave amplitude is carried out and, if they appear near the resonance region, we show how to modify adequately the IAM to take them into account.

Effective Field Theory of Large-Scale Structure

2020 ◽  
pp. 415-478
Author(s):  
Tobias Baldauf
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Effective Field Theory ◽  
Random Fields ◽  
Large Scale ◽  
Large Scale Structure ◽  
Gaussian Random Fields ◽  
Effective Field ◽  
Scale Structure ◽  
Linear Perturbation Theory

The lectures featured in this chapter review the observables relevant to the large-scale structure (LSS) of our Universe. The chapter introduces an effective field theory (EFT) that allows us to analytically describe the growth of fluctuations into the non-linear era, with uncertainties better controlled than in classical linear perturbation theory. Topics covered in the chapter include random fields in three-dimensional space, Fourier space conventions, the shape of the matter power spectrum, Gaussian random fields, estimators and cosmic variance, dynamics in the Newtonian regime, a perturbative solution of the fluid equations, the EFT approach, the Lagrangian perturbation theory, biased tracers, and redshift space distortions.

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