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Journal ArticleDOI

Spontaneous generation of pseudoscalar mass in the U(3)×U(3) linear sigma model

30 Apr 1998-Physics Letters B (North-Holland)-Vol. 426, Iss: 1, pp 105-113
TL;DR: In this article, a nonperturbative way to generate chiral symmetry breaking within the linear sigma model for 3 flavors with an interaction term λ Tr [ΣΣ † Σ Σ ] is discussed.
About: This article is published in Physics Letters B.The article was published on 1998-04-30 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Chiral symmetry breaking & Spontaneous symmetry breaking.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the role of light scalar mesons in the three flavor linear sigma model is studied as a {open_quotes}toy model, and the effect of unitarization is shown.
Abstract: The three flavor linear sigma model is studied as a {open_quotes}toy model{close_quotes} for understanding the role of possible light scalar mesons in the {pi}{pi}, {pi}K and {pi}{eta} scattering channels. The approach involves computing the tree level partial wave amplitude for each channel and unitarizing by a simple K-matrix prescription which does not introduce any new parameters. If the renormalizable version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain {pi}{pi} scattering, it is {open_quotes}not quite{close_quotes} right. A reasonable fit can be made if the renormalizability (for the effective Lagrangian) is relaxed while chiral symmetry is maintained. The occurrence of a Ramsauer-Townsend mechanism for the f{sub 0}(980) region naturally emerges. The effect of unitarization is very important and leads to {open_quotes}physical{close_quotes} masses for the scalar nonet all less than about 1 GeV. The a{sub 0}(1450) and K{sub 0}{sup *}(1430) appear to be {open_quotes}outsiders{close_quotes} in this picture and to require additional fields. Comparison is made with a scattering treatment using a more general nonlinear sigma model approach. In addition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructuremore » of the light scalar mesons.« less

105 citations

BookDOI
TL;DR: In this paper, the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group is reported, and a number of appendices are added to review some basic methods and to provide useful details.
Abstract: We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will then review Minimal Walking Technicolor (MWT) and other extensions, such as partially gauged and split technicolor. MWT is a sufficiently general, symmetry wise, model to be considered as a benchmark for any model aiming at breaking the electroweak symmetry dynamically. The unification of the standard model gauge couplings will be revisited within technicolor extensions of the SM. A number of appendices are added to review some basic methods and to provide useful details. In one of the appendices we will show how to gain information on the spectrum of strongly coupled theories relevant for new extensions of the SM by introducing and using alternative large N limits.

94 citations

Journal ArticleDOI
TL;DR: In this article, the chiral Lagrangian is augmented by an isosinglet scalar and the one-loop radiative corrections to the pion mass and decay constant are computed.
Abstract: We augment the chiral Lagrangian by an isosinglet scalar and compute the one-loop radiative corrections to the pion mass and decay constant, as well as the scalar mass. The calculations are carried out for different patterns of chiral symmetry breaking of immediate relevance for phenomenology and lattice investigations. By construction our results encompass several interesting limits, ranging from the dilaton to the linear sigma model.

59 citations


Cites background from "Spontaneous generation of pseudosca..."

  • ...In the linear sigma model limit [65,66] we have S1 1⁄4 2 and S2 1⁄4 1 leading to the same prediction for S3 but the mass and decay constant renormalize differently than in the pseudodilatonic limit....

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Journal ArticleDOI
TL;DR: In this paper, a linear sigma model containing one chiral nonet transforming under the SU(3) invariant limit for two scalar octets and an excited pion octet was studied.
Abstract: We present a detailed study of a linear sigma model containing one chiral nonet transforming under $\mathrm{U}(1{)}_{\mathrm{A}}$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-antidiquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an excited pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.

44 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the dependence on the number of colors of the leading $\ensuremath{\pi}\ensureMath{\pi}$ scattering amplitude in chiral dynamics.
Abstract: We study the dependence on the number of colors of the leading $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude computed from the simple sum of the current algebra and vector meson terms is crossing symmetric and unitary at leading order in a truncated and regularized ${1/N}_{c}$ expansion. The critical number of colors turns out to be ${N}_{c}=6$ and is insensitive to the explicit breaking of chiral symmetry. Below this critical value, an additional state is needed to enforce the unitarity bound; it is a broad one, most likely of a ``four quark'' nature.

32 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a superconductive solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian, and the pions of finite mass are found as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangians which otherwise possesses a certain type of the ∆-ensuremath{gamma{5}$ invariance.
Abstract: Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We find the pions of finite mass as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the ${\ensuremath{\gamma}}_{5}$ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons.

3,923 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown, and they find that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson.
Abstract: We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. The scalar-to-vector mass ratio is computable as a power series in $e$, the electromagnetic coupling constant. We find, to lowest order, $\frac{{m}^{2}(S)}{{m}^{2}(V)}=(\frac{3}{2\ensuremath{\pi}})(\frac{{e}^{2}}{4\ensuremath{\pi}})$. We extend our analysis to non-Abelian gauge theories, and find qualitatively similar results. Our methods are also applicable to theories in which the tree approximation indicates the occurrence of spontaneous symmetry breakdown, but does not give complete information about its character. (This typically occurs when the scalar-meson part of the Lagrangian admits a greater symmetry group than the total Lagrangian.) We indicate how to use our methods in these cases.

3,345 citations

Posted Content
TL;DR: In this article, the renormalization group calculations in Sec. 6.4 are discussed and a scanned version of the original typed manuscript is available at this http://www.latex-transcription.org.
Abstract: Although old, this may be of interest. In particular, I have had inquiries concerning the renormalization group calculations in Sec. 6.4. This is a Latex transcription. A scanned version of the original typed manuscript is available at this http URL .

2,239 citations

Journal ArticleDOI
TL;DR: In this paper, the phase transition restoring chiral symmetry at finite temperatures is considered in a linear σ-sigma model. But the model is not suitable for the case of massless flavors.
Abstract: The phase transition restoring chiral symmetry at finite temperatures is considered in a linear $\ensuremath{\sigma}$ model. For three or more massless flavors, the perturbative $\ensuremath{\epsilon}$ expansion predicts the phase transition is of first order. At high temperatures, the ${\mathrm{U}}_{A}(1)$ symmetry will also be effectively restored.

897 citations