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.

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.

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 Localization of the gauged linear sigma model for KK5-branes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yuki Hiraga ◽  
Yuki Sato
Keyword(s):  
Partition Function ◽  
Sigma Model ◽  
Low Energy ◽  
Target Space ◽  
Linear Sigma Model ◽  
Effective Theory ◽  
Coulomb Branch ◽  
World Sheet ◽  
The World ◽  
Gauged Linear Sigma Model

Abstract We study quantum aspects of the target space of the non-linear sigma model, which is a low-energy effective theory of the gauged linear sigma model (GLSM). As such, we especially compute the exact sphere partition function of the GLSM for KK$5$-branes whose background geometry is a Taub–NUT space, using the supersymmetric localization technique on the Coulomb branch. From the sphere partition function, we distill the world-sheet instanton effects. In particular, we show that, concerning the single-centered Taub–NUT space, instanton contributions exist only if the asymptotic radius of the $S^1$ fiber in the Taub–NUT space is zero.

scholarly journals Inverse mass hierarchy of light scalar mesons driven by anomaly-induced flavor breaking

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Yoshiki Kuroda ◽  
Masayasu Harada ◽  
Shinya Matsuzaki ◽  
Daisuke Jido
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Scalar Meson ◽  
Chiral Symmetry Breaking ◽  
Linear Sigma Model ◽  
Mass Hierarchy ◽  
Scalar Mesons ◽  
Light Scalar ◽  
Symmetry Breaking Term ◽  
Breaking Term

Abstract We propose a novel mechanism to reproduce the observed mass hierarchy for scalar mesons lighter than 1 GeV (called the inverse hierarchy), regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3) flavor-symmetry breaking induced by the U(1) axial anomaly. In particular, the anomaly term including the explicit chiral symmetry breaking plays a significant role in the light scalar meson spectrum. To be concrete, we construct a linear sigma model for scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$, is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ by the strange quark bilinear one, $s\bar{s}$.

scholarly journals DYNAMICAL GENERATION OF THE GAUGED SU(2) LINEAR SIGMA MODEL

1995 ◽  
Vol 10 (03) ◽  
pp. 251-266 ◽  
Author(s):  
R. DELBOURGO ◽  
M. D. SCADRON
Keyword(s):  
Sigma Model ◽  
Decay Constant ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Coupling Constant ◽  
Vector Coupling ◽  
Dynamical Generation ◽  
Meson Coupling ◽  
Quark Level ◽  
The Masses

The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson–quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be mq = fπg, mπ = 0, mσ = 2mq, and we also find that the quark–meson coupling is [Formula: see text], the three-meson coupling is [Formula: see text] and the four-meson coupling is λ = 2g2 = g′/fπ, where fπ ≃ 90 MeV is the pion decay constant and Nc = 3 is the color number. By gauging this model one can generate the couplings to the vector mesons ρ and A1, including the quark–vector coupling constant gρ = 2π, gρππ, gA1ρπ and the masses mρ ~ 700 MeV, [Formula: see text]; of course the vector and axial currents remain conserved throughout.

scholarly journals Finite density $O(3)$ non-linear sigma model and low energy physics

2016 ◽  
Author(s):  
Thomas Kloiber ◽  
Falk Bruckmann ◽  
Christof Gattringer ◽  
Tin Sulejmanpasic
Keyword(s):  
Sigma Model ◽  
Low Energy ◽  
Linear Sigma Model ◽  
Finite Density ◽  
Non Linear ◽  
Energy Physics

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.

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