EFFECTIVE LAGRANGIAN FOR PSEUDOSCALAR MESONS FROM LINEAR SU(3)×SU(3) SIGMA MODEL WITH VECTOR AND AXIAL MESONS

1989 ◽  
Vol 04 (19) ◽  
pp. 1815-1825
Author(s):  
I.V. ANDREEV ◽  
M.M. TSYPIN
Keyword(s):  
Fourth Order ◽  
Pseudoscalar Meson ◽  
Sigma Model ◽  
Scalar Meson ◽  
Linear Sigma Model ◽  
Effective Lagrangian ◽  
Pseudoscalar Mesons ◽  
Meson Octet

The effective Lagrangian for pseudoscalar meson octet including terms up to fourth order in momenta and masses is derived from a linear sigma model with vector and axial mesons. The mass of scalar meson nonet 720±75 MeV ensures a good fit of coefficients in effective Lagrangian with values derived from experiment.

PROCEDURE FOR GENERATING EQUATIONS IN LINEAR SIGMA MODEL

2011 ◽  
Vol 26 (14) ◽  
pp. 2327-2352 ◽  
Author(s):  
AMIR H. FARIBORZ
Keyword(s):  
Scattering Amplitudes ◽  
Sigma Model ◽  
Point Interaction ◽  
Low Energy ◽  
Linear Sigma Model ◽  
Pseudoscalar Mesons ◽  
Decay Widths ◽  
Symmetry Breaking Term ◽  
The Masses ◽  
Breaking Term

A procedure for implementation of the generating equations in the linear sigma model of low energy QCD is presented. For any explicit symmetry breaking term, this procedure computes the masses of scalar and pseudoscalar mesons as well as various three-point and four-point interaction vertices that are needed in calculation of different decay widths and scattering amplitudes.

CHIRAL SYMMETRY RESTORATION IN THE LINEAR SIGMA MODEL

1992 ◽  
Vol 03 (05) ◽  
pp. 993-1009 ◽  
Author(s):  
H. MEYER-ORTMANNS ◽  
H.-J. PIRNER ◽  
A. PATKÓS
Keyword(s):  
Chiral Symmetry ◽  
Sigma Model ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Gradual Change ◽  
Chiral Symmetry Restoration ◽  
Meson Octet ◽  
First Order Transition ◽  
Experimental Values

We report on results about the mass sensitivity of chiral symmetry restoration in the linear sigma model. For masses of the pseudoscalar meson octet which are close to the experimental values, we observed only a gradual change in the order parameters, when the temperature was changed. To estimate the size of the first order transition region around the chiral limit, we have varied the mass input for the tree level parametrization in several ways. The point with realistic meson masses turned out to lie well inside the crossover region.

scholarly journals Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950034
Author(s):  
Amir H. Fariborz ◽  
Renata Jora ◽  
Maria Lyukova
Keyword(s):  
Numerical Simulation ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Pseudoscalar Mesons ◽  
Singlet States ◽  
Scalar Octet ◽  
Light Scalar ◽  
The Masses

Within the framework of the generalized linear sigma model with glueballs recently proposed,[Formula: see text] we study the schematic spectroscopy of scalar and pseudoscalar mesons in the SU(3) flavor limit and explore their quark and glue contents. In this framework, for both scalars and pseudoscalars, the two octet physical states are admixtures of quark–antiquark and four-quark components, and the three singlet states contain quark–antiquark, four-quark and glue components. We identify the two scalar octets with [Formula: see text] and [Formula: see text] and the two pseudoscalar octets with [Formula: see text] and [Formula: see text]. We show that, as expected, the light pseudoscalar octet is made dominantly of quark–antiquarks whereas the light scalar octet has a reversed substructure with a dominant four-quark component. The case of singlets is more complex due to surplus of states up to around 2 GeV. We consider all 35 permutations for identifying the three pseudoscalar singlets of our model with three of the seven experimental candidates. Our numerical simulation unambiguously identifies the lightest and the heaviest pseudoscalar singlets with [Formula: see text] and [Formula: see text], respectively, and favors the identification of the middle singlet with either [Formula: see text] or [Formula: see text] (or, to a lesser extent, with [Formula: see text]) and thereby allows a probe of their substructures. We then estimate the quark and glue components and find that the three pseudoscalar singlets (from lightest to heaviest) are mainly of quark–antiquark, four-quark and glue substructure, while the corresponding three scalar singlets (from lightest to heaviest) are of four-quark, quark–antiquark and glue contents. The masses of pure pseudoscalar and scalar glueballs are estimated around 2.0 and 1.6 GeV, respectively.

scholarly journals A LINEAR SIGMA MODEL WITH THREE FLAVORS AND VECTOR AND AXIAL-VECTOR MESONS

2011 ◽  
Vol 26 (03n04) ◽  
pp. 607-609 ◽  
Author(s):  
DENIS PARGANLIJA ◽  
FRANCESCO GIACOSA ◽  
DIRK H. RISCHKE ◽  
PÉTER KOVÁCS ◽  
GYŐRGY WOLF
Keyword(s):  
Degrees Of Freedom ◽  
Sigma Model ◽  
Scalar Meson ◽  
Axial Vector ◽  
Linear Sigma Model ◽  
Vector Mesons ◽  
Preliminary Results

We outline the extension of the globally chirally invariant Nf = 2 linear sigma model with vector and axial-vector degrees of freedom to Nf = 3. We present preliminary results concerning the scalar meson masses.

scholarly journals Two-body decay widths of lowest lying and next-to-lowest lying scalar and pseudoscalar mesons in generalized linear sigma model

2015 ◽  
Vol 30 (22) ◽  
pp. 1550134 ◽  
Author(s):  
S. Mohammad Zebarjad ◽  
Soodeh Zarepour
Keyword(s):  
Energy Region ◽  
Sigma Model ◽  
Low Energy ◽  
Experimental Results ◽  
Linear Sigma Model ◽  
Pseudoscalar Mesons ◽  
Decay Widths

Two-body decay widths of lowest lying and next-to-lowest lying scalar and pseudoscalar mesons are studied in generalized linear sigma model (GLSM) of low-energy QCD. This model which considers mixing between “two-quark” and “four-quark” chiral nonets has been employed to investigate various decays and scatterings in low-energy region of QCD. In this paper, [Formula: see text] and [Formula: see text] are obtained and it is shown that two-body decay widths of lowest lying mesons are well predicted by this model while for the next-to-lowest lying mesons, only some of the decay widths agree with the experimental results. We have compared the predicted decay widths in GLSM with the results obtained in single nonet linear sigma model (SNLSM) to indicate that chiral nonet mixing greatly improves the predictions of SNLSM for decay widths.

Quarkonia-Glueball Structure of the Ground Pseudoscalar Mesons

2003 ◽  
Vol 18 (19) ◽  
pp. 3335-3346 ◽  
Author(s):  
De-Min Li ◽  
Bing Ma ◽  
Hong Yu
Keyword(s):  
Symmetry Breaking ◽  
Pseudoscalar Meson ◽  
Scalar Meson ◽  
Radiative Decays ◽  
Flavor Symmetry ◽  
Average Data ◽  
Two Photon ◽  
Pseudoscalar Mesons ◽  
Pseudo Scalar ◽  
Glueball State

Considering corrections due to SU(3) flavor symmetry breaking, non-ideal ω - ϕ mixing, double OZI and electromagnetic amplitudes of J/ψ decays into a vector and a pseudo-scalar meson, and three-gluon-annihilation amplitudes of radiative decays of J/ψ into a pseudoscalar meson, we investigate two-photon decays of pseudoscalar mesons, radiative decays between pseudoscalar and vector mesons, decays of J/ψ into a vector and a pseudoscalar meson, and radiative decays of J/ψ into a pseudoscalar meson. The quarkonia-glueball structure of η, η′ and η(1440) is phenomenologically deduced from the fit to the updated world average data concerning the above mentioned decays. We find that η (η′) contains about 48.7%, 47.6%, 3.7% (32.9%, 48.8%, 18.3%) non-strange quarkonium, strange quarkonium and glueball components, respectively, and that η(1410) is mainly a glueball state (about 78% glueball component), mixed with 18.5% non-strange quarkonium and 3.5% strange quarkonium. We predict that Br (J/ψ→γη) : Br (J/ψ→γη′) : Br (J/ψ→γη(1410)) = 1.0:5.2:8.0, which can be tested at BEPC/BES with 50 million J/ψ events.

scholarly journals QUARK MASS RATIOS AND MASS SPLIT OF π0-π±INChPTWITH THE DIFFERENCE OF QUARK CONDENSATES CONSIDERED

2008 ◽  
Vol 23 (22) ◽  
pp. 3493-3507
Author(s):  
XIAOYA LI ◽  
BIN WANG ◽  
XIAOZHAO CHEN ◽  
XIAOFU LÜ
Keyword(s):  
Chiral Symmetry ◽  
Pseudoscalar Meson ◽  
Quark Mass ◽  
Quark Condensate ◽  
Breaking Effect ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Pseudoscalar Mesons ◽  
Mass Ratios ◽  
The Difference

The chiral effective Lagrangian for pseudoscalar meson nonet including eight Goldstone bosons and a SU (3) singlet η0is constructed with the breaking effect of chiral symmetry in both quark condensate and quark mass differences taken into account. The [Formula: see text] mixing is discussed. By solving the mass equations of pseudoscalar mesons, the quark mass ratios are obtained and the quark condensate ratios are constrained in ranges. The mass split of π0-π±is discussed.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

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