Pseudo-Goldstone Bosons, Nonlinear Sigma Model, and Chiral Perturbation Theory

2019 ◽  
pp. 632-645
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Chiral Perturbation ◽  
Goldstone Bosons

scholarly journals Chiral Perturbation Theory vs. Linear Sigma Model in A Chiral Imbalance Medium

2019 ◽  
Author(s):  
Alexander Andrianov ◽  
Vladimir Andrianov ◽  
Domenec Espriu
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Decay Constant ◽  
Charged Pion ◽  
Low Energy ◽  
Linear Sigma Model ◽  
Chiral Perturbation ◽  
Energy Constants ◽  
Parity Breaking

We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM) as realizations of low energy QCD for light mesons in a chirally imbalanced medium. The relations between the low-energy constants of the Chiral Lagrangian and the corresponding constants of the Linear Sigma Model are established as well as the expressions for the decay constant of $\pi $-meson in the medium and for the mass of the $a_0$. In the large $N_c$ count taken from QCD the correspondence of ChPT and LSM is remarkably good and give a solid ground for search of chiral imbalance manifestation in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with Local Parity Breaking) is outlined in the charged pion decays inside the fireball.

scholarly journals On the rotator Hamiltonian for the SU (N) × SU (N) sigma model in the delta regime

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
J Balog ◽  
F Niedermayer ◽  
P Weisz
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Two Dimensions ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Casimir Invariant ◽  
The Difference

Abstract We investigate some properties of the standard rotator approximation of the $\mathrm{SU}(N)\times\mathrm{SU}(N)$ sigma-model in the delta regime. In particular, we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next-to-leading order in the limit $\ell=L_t/L\to\infty$. The difference between the results involves terms vanishing like $1/\ell$, plus terms vanishing exponentially with $\ell$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in two dimensions for $N=3$.

scholarly journals MASS AND WIDTH OF THE σ

2007 ◽  
Vol 22 (02n03) ◽  
pp. 257-265 ◽  
Author(s):  
HEINRICH LEUTWYLER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Scattering Amplitude ◽  
Pole Position ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Goldstone Bosons ◽  
Quantum Numbers ◽  
Low Energies ◽  
Work Done

I report on recent work done in collaboration with Irinel Caprini and Gilberto Colangelo1. We observe that the Roy equations lead to a representation of the ππ scattering amplitude that exclusively involves observable quantities, but is valid for complex values of s. At low energies, this representation is dominated by the contributions from the two subtraction constants, which are known to remarkable precision from the low energy theorems of chiral perturbation theory. Evaluating the remaining contributions on the basis of the available data, we demonstrate that the lowest resonance carries the quantum numbers of the vacuum and occurs in the vicinity of the threshold. Although the uncertainties in the data are substantial, the pole position can be calculated quite accurately, because it occurs in the region where the amplitude is dominated by the subtractions. The calculation neatly illustrates the fact that the dynamics of the Goldstone bosons is governed by the symmetries of QCD.

scholarly journals Dilaton chiral perturbation theory and applications

2022 ◽  
Vol 258 ◽  
pp. 08004
Author(s):  
Maarten Golterman ◽  
Yigal Shamir
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Large Mass ◽  
Fermion Mass ◽  
Lattice Data ◽  
Chiral Perturbation ◽  
Goldstone Bosons ◽  
Systematic Expansion ◽  
Light Scalar ◽  
Future Work

We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu–Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

scholarly journals Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium

Particles ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Alexander Andrianov ◽  
Vladimir Andrianov ◽  
Domenec Espriu
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Decay Constant ◽  
Low Energy ◽  
Linear Sigma Model ◽  
Chiral Perturbation ◽  
Large N ◽  
Energy Quantum ◽  
Energy Constants

We compare the chiral perturbation theory (ChPT) and the linear sigma model (LSM) as realizations of low energy quantum chromodynamics (QCD) for light mesons in a chirally-imbalanced medium. The relations between the low-energy constants of the chiral Lagrangian and the corresponding constants of the linear sigma model are established as well as the expressions for the decay constant of π -meson in the medium and for the mass of the a 0 . In the large N c count taken from QCD the correspondence of ChPT and LSM is remarkably good and provides a solid ground for the search of chiral imbalance manifestations in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with local parity breaking) is outlined in the charged pion decays inside the fireball.

scholarly journals Aspects of Chiral Symmetry

1997 ◽  
Vol 06 (02) ◽  
pp. 203-249 ◽  
Author(s):  
Volker Koch
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Nuclear Physics ◽  
Sigma Model ◽  
Heavy Ion ◽  
Nonlinear Sigma Model ◽  
Chiral Perturbation ◽  
Ion Collisions ◽  
Linear And Nonlinear ◽  
Ultrarelativistic Heavy Ion Collisions

This article is an attempt to a pedagogical introduction and review into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.

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