Instanton content of finite temperature QCD matter

Chu, M. C.; Schramm, Stefan

doi:10.1103/physrevd.51.4580

Cited by 36 publications

(57 citation statements)

References 30 publications

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“…The final simulations were then performed with an additional temperature dependent factor (1 − tanh( T −Tc ∆T ))/2 inserted in the exponential appearing in eq. (29). From our simulations, we have determined T c ≃ 0.75Λ.…”

Section: The Instanton Ensemble In Qcd At Finite Temperaturementioning

confidence: 93%

Interacting instanton liquid in QCD at zero and finite temperatures

1996

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In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge field and quark induced interactions between instantons we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the groundstate. In the physical case of two light and one intermediate mass flavor the system undergoes a chiral phase transition at T ≃ 140 MeV.We show that the mechanism for this transition is a rearrangement of the instanton liquid, going from a disordered, random, phase at low temperatures to a strongly correlated, molecular, phase at high temperature. We also study the behavior of mesonic susceptibilities near the phase transition.

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Section: The Instanton Ensemble In Qcd At Finite Temperaturementioning

confidence: 93%

Interacting instanton liquid in QCD at zero and finite temperatures

1996

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“…In the language of the semi-classical instanton picture, this behavior can happen if there is a sharp short-distance cut-off in the instanton size parameter ρ so that small instantons do not contribute to the path integral. (See [28,29] for the instanton based models and lattice results suggesting this picture.) If χ t exhibits such a sharp fall off, the estimation of the abundance of the QCD axion in the Universe may be significantly affected.…”

Section: Jhep10(2015)136mentioning

confidence: 99%

Topology in QCD and the axion abundance

Kitano

Yamada

2015

J. High Energ. Phys.

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The temperature dependence of the topological susceptibility in QCD, χ t , essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heatbath algorithm. We obtain an indication that unquenched calculations of χ t encounter the serious problem of autocorrelation already at T ∼ 2 T c or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of χ t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where χ t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.

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“…The main motivation for this development came from lattice studies [12,13,14,15], stimulated by the knowledge of the basic features of the new caloron solutions. These lattice studies aimed at and were successfully identifying structures resembling instantons or calorons in ab-initio Monte Carlo gauge fields, in a similar spirit as earlier instanton (caloron) searches at zero (non-zero) temperature [16,17,18]. All these lattice studies had been and are performed, in order to empirically fix the instanton or caloron content of the simulated fields.…”

Section: Introductionmentioning

confidence: 99%

Improved superposition schemes for approximate multi-caloron configurations

2007

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Two improved superposition schemes for the construction of approximate multi-caloronanticaloron configurations, using exact single (anti)caloron gauge fields as underlying building blocks, are introduced in this paper. The first improvement deals with possible monopole-Dirac string interactions between different calorons with non-trivial holonomy. The second one, based on the ADHM formalism, improves the (anti-)selfduality in the case of small caloron separations. It conforms with Shuryak's well-known ratio-ansatz when applied to instantons. Both superposition techniques provide a higher degree of (anti-)selfduality than the widely used sum-ansatz, which simply adds the (anti)caloron vector potentials in an appropriate gauge. Furthermore, the improved configurations (when discretized onto a lattice) are characterized by a higher stability when they are exposed to lattice cooling techniques.

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Instanton content of finite temperature QCD matter

Cited by 36 publications

References 30 publications

Interacting instanton liquid in QCD at zero and finite temperatures

Interacting instanton liquid in QCD at zero and finite temperatures

Topology in QCD and the axion abundance

Improved superposition schemes for approximate multi-caloron configurations

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