scholarly journals Comparison of the Linear Sigma Model and Chiral Perturbation Theory for Nucleon Properties

2013 ◽  
Vol 04 (11) ◽  
pp. 1471-1475
Author(s):  
Tarek Sayed Taha Ali
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Chiral Perturbation

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 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 KAON WEAK DECAYS IN CHIRAL THEORIES

1999 ◽  
Vol 14 (19) ◽  
pp. 1273-1285 ◽  
Author(s):  
M. D. SCADRON
Keyword(s):  
Perturbation Theory ◽  
Free Parameter ◽  
Sigma Model ◽  
Axial Current ◽  
Linear Sigma Model ◽  
Pole Model ◽  
Chiral Perturbation ◽  
Weak Decays ◽  
Partial Conservation ◽  
Free Parameters

The ten nonleptonic weak decays K→2π, K→ 3π, KL→2γ, KS→2γ, KL→π02γ, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a KL→π0γγ rate which is 60% shy of the experimental value.

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 REMARK ON PION SCATTERING LENGTHS

2009 ◽  
Vol 24 (28) ◽  
pp. 2285-2289 ◽  
Author(s):  
DEIRDRE BLACK ◽  
AMIR H. FARIBORZ ◽  
RENATA JORA ◽  
NAE WOONG PARK ◽  
JOSEPH SCHECHTER ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Scattering Length ◽  
Linear Sigma Model ◽  
Isotopic Spin ◽  
S Wave ◽  
Tree Amplitude ◽  
Chiral Perturbation ◽  
Pion Scattering ◽  
Scattering Lengths

First it is shown that the tree amplitude for pion–pion scattering in the minimal linear sigma model has an exact expression which is proportional to a geometric series in the quantity [Formula: see text], where mB is the sigma mass which appears in the Lagrangian and is the only a priori unknown parameter in the model. This induces an infinite series for every predicted scattering length in which each term corresponds to a given order in the chiral perturbation theory counting. It is noted that, perhaps surprisingly, the pattern, though not the exact values, of chiral perturbation theory predictions for both the isotopic spin 0 and isotopic spin 2 s-wave pion–pion scattering lengths to orders p2, p4 and p6 seems to agree with this induced pattern. The values of the p8 terms are also given for comparison with a possible future chiral perturbation theory calculation. Further aspects of this approach and future directions are briefly discussed.

scholarly journals The axion-baryon coupling in SU(3) heavy baryon chiral perturbation theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Thomas Vonk ◽  
Feng-Kun Guo ◽  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Heavy Baryon ◽  
Power Counting ◽  
Flavor Symmetry ◽  
Chiral Perturbation ◽  
Third Order ◽  
Stellar Objects ◽  
The Past ◽  
Dense Nuclear Matter

Abstract In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related to the so-called axion window.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

2019 ◽  
Vol 34 (21) ◽  
pp. 1950113
Author(s):  
V. A. Franke ◽  
M. Yu. Malyshev ◽  
S. A. Paston ◽  
E. V. Prokhvatilov ◽  
M. I. Vyazovsky
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Condensate ◽  
Light Front ◽  
Coupling Constants ◽  
Hamiltonian Approach ◽  
Chiral Perturbation ◽  
Dimensional Models ◽  
Villars Regularization ◽  
Ultraviolet Regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

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