# CHIRAL AND UA(1) PHASE TRANSITIONS IN π0, η AND η′ MESONS

21 Jun 2006-Modern Physics Letters A (World Scientific Publishing Company)-Vol. 21, Iss: 19, pp 1529-1539

TL;DR: In this article, the authors generalized the Pisarsky-Wilczek model of studying the UA(1) phase transition in π0, η and η′ system by incorporating the chiral phase transition.

Abstract: We have generalized the Pisarsky–Wilczek model of studying the UA(1) phase transition in π0, η and η′ system by incorporating the chiral phase transition. The mass-squared matrix of the neutral pseudoscalar mesons is revisited explicitly from the chiral effective action which necessitates the mixing among the unmixed states to get the physical states. The derivation of the mass spectra of the neutral pseudoscalar mesons shows that apart from their masses, the mixing angles also become temperature dependent. Based on the dilute instanton gas approximation we show that, the UA(1) phase transition along with the chiral phase transition plays an important role in the process of hadronization of the quark–gluon plasma with the quarks of three flavors.

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TL;DR: In this paper, a detailed quantitative calculation is carried out of the tunneling process described by the Belavin-Polyakov-Schwarz-Tyupkin field configuration, where a certain chiral symmetry is violated as a consequence of the Adler-Bell-Jackiw anomaly.

Abstract: A detailed quantitative calculation is carried out of the tunneling process described by the Belavin-Polyakov-Schwarz-Tyupkin field configuration. A certain chiral symmetry is violated as a consequence of the Adler-Bell-Jackiw anomaly. The collective motions of the pseudoparticle and all contributions from single loops of scalar, spinor, and vector fields are taken into account. The result is an effective interaction Lagrangian for the spinors.

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TL;DR: In this article, the authors present a topological classification of finite-energy, periodic fields and the classical solutions which minimize the action in each topological sector are examined and the effects of instantons can be reliably calculated at sufficiently high temperature.

Abstract: The current understanding of the behavior of quantum chromodynamics at finite temperature is presented. Perturbative methods are used to explore the high-temperature dynamics. At sufficiently high temperatures the plasma of thermal excitations screens all color electric fields and quarks are unconfined. It is believed that the high-temperature theory develops a dynamical mass gap. However in perturbation theory the infrared behavior of magnetic fluctuations is so singular that beyond some order the perturbative expansion breaks down. The topological classification of finite-energy, periodic fields is presented and the classical solutions which minimize the action in each topological sector are examined. These include periodic instantons and magnetic monopoles. At sufficiently high temperature only fields with integral topological charge can contribute to the functional integral. Electric screening completely suppresses the contribution of fields with nonintegral topological charge. Consequently the $\ensuremath{\theta}$ dependence of the free energy at high temperature is dominated by the contribution of instantons. The complete temperature dependence of the instanton density is explicitly computed and large-scale instantons are found to be suppressed. Therefore the effects of instantons may be reliably calculated at sufficiently high temperature. The behavior of the theory in the vicinity of the transition from the high-temperature quark phase to the low-temperature hadronic phase cannot be accurately computed. However, at least in the absence of light quarks, semiclassical techniques and lattice methods may be combined to yield a simple picture of the dynamics valid for both high and low temperature, and to estimate the transition temperature.

1,650 citations

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CERN

^{1}TL;DR: In this paper, the U(1) problem is shown to be consistent with expected θ dependences and anomalous Ward identities, if a modified Kogut-Susskind mechanism is used.

Abstract: Witten's recent proposal that the U(1) problem might be solved in 1/N expanded QCD, is shown to be automatically consistent with expected θ dependences and anomalous Ward identities, if a (modified) Kogut-Susskind mechanism is used. Ward identities are algebraically saturated for large N. A sort of “partial conservation of the U(1) current” is found to hold for the “η” field.

950 citations

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TL;DR: In this article, a variational procedure was used to study finite-density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons, and it was shown that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities.

Abstract: We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons We find that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities, and are therefore unstable This is a precisely defined phenomenon which motivates the basic picture of hadrons assumed in the MIT bag model, with nucleons as droplets of chiral symmetry restored phase At all densities high enough that the chirally symmetric phase fills space, we find that color symmetry is broken by the formation of a 〈 qq 〉 condensate of quark Cooper pairs A plausible ordering scheme leads to a substantial gap in a Lorentz scalar channel involving quarks of two colors, and a much smaller gap in an axial vector channel involving quarks of the third color

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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.

800 citations

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