Procedure for Generating Equations in Linear Sigma Model

Fariborz, Amir H.

doi:10.1142/s0217751x11053390

Cited by 8 publications

(6 citation statements)

References 125 publications

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“…Nevertheless, for the purpose of analyzing the mass spectrum and decay channels of isosinglet states, the nonlinear model is reasonably effective. As stated before, in general, various analyses within the nonlinear model in [91][92][93][94][95][96][97][98][99][100][101] have been consistent and complementary to those in the linear model [74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90]. It is noted that under chiral transformation the field ξ defined by U = ξ 2 transforms as…”

Section: Introductionmentioning

confidence: 80%

“…However, for the purpose of exploring the properties of scalar mesons, which are outside the immediate focus of chiral perturbation theory, it is natural to explicitly keep the scalar meson fields in the Lagrangian instead of integrating them out. Two suitable frameworks, that are the foundation of the present study, are the linear sigma model [74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90] as well as the nonlinear chiral Lagrangian models that include scalar fields [91][92][93][94][95][96][97][98][99][100][101]. In such model buildings, the main guiding principles are the well-known chiral symmetry and its breakdown, isospin symmetry (and in relevant processes its breakdown), the U(1) A axial anomaly, and the main assumptions that need to be made are related to modeling the QCD vacuum as well as the potential.…”

Section: Introductionmentioning

confidence: 99%

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Probing the substructure off0(1370)

2015

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Within an effective nonlinear chiral Lagrangian framework the substructure of f0 (1370) is studied. The investigation is conducted in the context of a global picture of scalar mesons in which the importance of the underlying connections among scalar mesons below and above 1 GeV is recognized and implemented. These connections are due to the mixings among various quark-antiquarks, fourquarks and glue components and play a central role in understanding the properties of scalar mesons. Iterative Monte Carlo simulations are first performed on the 14-dimensional parameter space of the model and sets of points in this parameter space (the global sets) that give an overall agreement with all experimental data on mass spectrum, various decay widths and decay ratios of all isosinglet scalar states below 2 GeV are determined. Then within each global set, subsets that give closest agreement for the properties of f0 (1370) are studied. Unlike the properties of other isosinglet states that show a range of variation within each global set, it is found that there is a clear signal for f0(1370) to be predominantly a quark-antiquark state with a substantial ss component, together with small remnants of four-quark and glue components.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Probing the substructure off0(1370)

2015

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“…Moreover, V 0 is an arbitrary function of the independent non derivative SU(3) L ×SU(3) R ×U(1) V (but not necessarily U(1) A ) invariants formed out of M and V SB is a symmetry breaking term. Without knowing details of V 0 and just from chiral symmetry considerations, i.e., using generating equations, it is possible to compute the masses of pseudoscalars and some of the scalar mesons (two-point vertices) and also the three-and four-point vertices [7,67]. However, in such a way, the masses of the lowest lying isoscalars, σ and f 0 (980), and also their mixing angle θ s , the mass of isovector a 0 (980) and consequently the related three-point vertices are not perfectly predicted.…”

Section: Brief Review Of the Single Nonet Linear Sigma Modelmentioning

confidence: 99%

Mixing among lowest-lying scalar mesons and scalar glueball

2018

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Scalar glueball is implemented in single nonet linear sigma model (SNLSM) which basically includes lowest lying scalar and pseudoscalar mesons. Our new version of SNLSM involves mixing among scalar matter fields and glueball field which is enforced by scale symmetry considerations and the associated anomaly. Performing iterative Monte Carlo simulations, it is found that among the three candidates of scalar glueball, i.e., f0(1370), f0(1500) and f0 (1710), only f0 (1500) is predominately a glueball state with the mass prediction of 1.566 ± 0.046 GeV and the other two are predominately quarkonium. The ππ, πK and πη scatterings are reinvestigated in the presence of scalar glueball and it is found that the overall behavior of the real part of the K-matrix unitarized ππ scattering amplitude is more compatible with observed data compared with the case of SNLSM without glueball. We have also presented the predictions of the model for the masses and decay widths of the scalars obtained from the poles of the K-matrix unitarized ππ, πK and πη scattering amplitudes. Moreover the ππ scattering phase shift predicted by our model is compared with the prediction of generalized linear sigma model (GLSM) which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark-antiquark nonet and a four-quark nonet). Despite the fact that at this stage our model lacks the second meson nonet above 1 GeV, its prediction for the ππ scattering phase shift is close to the prediction of GLSM for √ s < 1.1 GeV and in better agreement with experimental data for √ s > 1.1 GeV in comparison with GLSM.

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“…Here we use the same set of parameters to study the η → ηππ decay. In this case the required coupling constants in our "template" equations (1)- (4) are computed from the "generating equations" that express the symmetry of the Lagrangian (7) (a computational algorithm is presented in [90]):…”

Section: Single Nonet Approachmentioning

confidence: 99%

Chiral nonet mixing inη′→ηππdecay

et al. 2014

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Underlying mixing of scalar mesons is studied in η → ηππ decay within a generalized linear sigma model of low-energy QCD which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark-antiquark nonet and a four quark nonet). The model has been previously employed in various investigations of the underlying mixings among scalar mesons below and above 1 GeV (as well as those of their pseudoscalar chiral partners) and has provided a coherent global picture for the physical properties and quark substructure of these states. The potential of the model is defined in terms of two-and four-quark chiral nonets, and based on the number of underlying quark and antiquark lines in each term in the potential, a criterion for limiting the number of terms at each order of calculation (and systematically further improving the results thereafter). At the leading order, which corresponds to neglecting terms in the potential with higher than eight quark and antiquark lines, the free parameters of the model have been previously fixed in detailed global fits to scalar and pseudoscalar experimental mass spectra below and above 1 GeV together with several low-energy parameters. In the present work, the same order of potential with fixed parameters is used to further explore the underlying mixings among scalar mesons in the η → ηππ decay. It is found that the linear sigma model with only a single lowest-lying nonet is not accurate in predicting the decay width, but inclusion of the mixing of this nonet with the next-to-lowest lying nonet, together with the effect of final state interaction of pions, significantly improves this prediction and agrees with experiment up to about 1%. It is also shown that while the prediction of the leading order of the generalized model for the Dalitz parameters is not close to the experiment, the model is able to give a reasonable prediction of the energy dependencies of the normalized decay amplitude squared and that this is expected to improve with further refinement of the complicated underlying mixings. Overall this investigation provides further support for the global picture of scalar mesons: those below 1 GeV are predominantly four-quark states and significantly mix with those above 1 GeV which are closer to the conventional p-wave quark-antiquark states.

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Procedure for Generating Equations in Linear Sigma Model

Cited by 8 publications

References 125 publications

Probing the substructure off0(1370)

Probing the substructure off0(1370)

Mixing among lowest-lying scalar mesons and scalar glueball

Chiral nonet mixing inη′→ηππdecay

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