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.

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 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.

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.

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 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.

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Alejandro Ayala ◽  
José Luis Hernández ◽  
L. A. Hernández ◽  
Ricardo L. S. Farias ◽  
R. Zamora
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Strong Field ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Field Case
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