Momentum dependence of the spectral functions in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>linear sigma model at finite temperature

Hidaka, Yoshimasa; Morimatsu, Osamu; Nishikawa, Tetsuo

doi:10.1103/physrevd.67.056004

Cited by 17 publications

(20 citation statements)

References 14 publications

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“…7 Comparison of pion (ρ π ) and sigma meson (ρ σ ) spectral functions for parameter sets corresponding to two different pion masses poles on the real axis. One expects a zero on the unphysical sheet, however, as illustrated in [16,31]. Except for a significantly lower sigma mass in our calculations, the zero-temperature spectral functions are in qualitative agreement with perturbation theory results [16][17][18][19].…”

Section: Methodssupporting

confidence: 78%

“…The analysis of the O(N ) scalar model, which is frequently used as a chiral effective model for QCD (N = 4), has a long history. Spectral functions in O(N ) models have been calculated, for example, in optimized perturbation theory [16][17][18][19] by taking into account the σ → π + π process. The critical exponents have been evaluated in [17].…”

Section: Introductionmentioning

confidence: 99%

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Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

et al. 2014

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In the framework of the functional renormalization group we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N ) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.

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Section: Methodssupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

et al. 2014

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“…The inverse propagator, D −1 σ (k), is analytic on the complex plane except for the real axis and has branch cuts for |ω| > 2m 0π and |ω| > 2m 0σ at one loop level. Accordingly, we perform the analytic continuation of D −1 σ following [9,10] to locate the relevant poles. Through different cuts one goes to different Riemann sheets on which different analytic continuations are defined.…”

mentioning

confidence: 99%

Two-pion bound state in the sigma channel at finite temperature

et al. 2004

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We study how we can understand the change of the spectral function and the pole location of the correlation function for sigma at finite temperature, which were previously obtained in the linear sigma model with a resummation technique called optimized perturbation theory. There are two relevant poles in the sigma channel. One pole is the original sigma pole which shows up as a broad peak at zero temperature and becomes lighter as the temperature increases. The behavior is understood from the decreasing of the sigma condensate, which is consistent with the Brown-Rho scaling. The other pole changes from a virtual state to a bound state of ππ as the temperature increases which causes the enhancement at the ππ threshold. The behavior is understood as the emergence of the ππ bound state due to the enhancement of the ππ attraction by the induced emission in medium. The latter pole, not the former, eventually degenerates with pion above the critical temperature of the chiral transition. This means that the observable "σ" changes from the former to the latter pole, which can be interpreted as the level crossing of σ and ππ at finite temperature. Restoration of chiral symmetry at finite temperature is an interesting topic in hadron physics and recently discussed in connection with deconfinement transition [1, 2, 3] as well as mixed chiral condensate in lattice simulation [4]. Even below the critical temperature T c , drastic change of the meson spectrum is expected as a precursor for the restoration of chiral symmetry [5], and actually strong enhancement of σ spectrum near the ππ threshold was reported [6]. This spectrum enhancement is naturally understood based on the partial restoration of chiral symmetry as follows; As temperature increases, σ diminishes its mass while π becomes heavier because their masses degenerate above T c . This demands that the mass of σ coincides with twice that of π at certain temperature and the phase space of the decay σ → ππ is squeezed. This squeeze causes the spectrum enhancement. In view of the above we analyzed complex poles of the propagator and elucidated that two poles are dominant on the σ spectrum [7]. One of these poles corresponds to the broad bump at T = 0 and the other pole causes the threshold enhancement.In this paper we study how the behavior of these poles is understood. We show that the behavior of the pole, which causes the threshold enhancement, is understood as the emergence of the ππ bound state due to the enhancement of the ππ attraction by the induced emission in medium.Let us briefly review the results of [7], in which we calculated the spectral function and pole locations using the O(4) linear sigma model with a resummation technique called the optimized perturbation theory (OPT) [6,8]. The lagrangian of the O(4) linear sigma model is as follows:with φ α = (φ 0 , π). In order to describe the spontaneously broken chiral symmetry at low temperature (T ), µ 2 must be negative. Then, the field φ 0 has a nonvanishing expectation value ξ, which makes us decompose the f...

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“…The dispersion relations of the excitations of the finite temperature system may be computed using the propagator (two-time) formalism, either with real-times (SchwingerKeldysh) formalism [42] or with imaginary-times (Matsubara) formalism with subsequent analytic continuation [43]. Although such calculations have been performed by various authors [35,44,45] numerical results have been presented focusing on the time-like region of the spectral functions. We study with our kinetic theory the entire range of the (ω, k) plane including the space-like excitations of the system.…”

Section: Dispersion Relation Of the Excitations Near Equilibriummentioning

confidence: 99%

Quantized meson fields in and out of equilibrium. I: Kinetics of meson condensate and quasi-particle excitations

Matsui¹,

Matsuo²

2008

Nuclear Physics A

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We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freeze-out stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg equation of motion for a single component real scalar quantum field taking the mean field approximation for the non-linear interaction. The mesonic mean field obeys the classical non-linear Klein-Gordon equation with a modification due to the coupling to mesonic quasi-particle excitations which are expressed in terms of the Wigner functions of the quantum fluctuations of the meson field, namely the statistical average of the bilinear forms of the meson creation and annihilation operators. In the long wavelength limit, the equations of motion of the diagonal components of the Wigner functions take a form of Vlasov equation with a particle source and sink which arises due to the non-vanishing off-diagonal components of the Wigner function expressing coherent pair-creation and pair-annihilation process in the presence of non-uniform condensate. We show that in the static homogeneous system, these kinetic equations reduce to the well-known gap equation in the Hartree approximation, and hence they may be considered as a generalization of the Hartree approximation method to non-equilibrium systems. As an application of these kinetic equations, we compute the dispersion relations of the collective mesonic excitations in the system near equilibrium.

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Momentum dependence of the spectral functions in theO(4)linear sigma model at finite temperature

Cited by 17 publications

References 14 publications

Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

Two-pion bound state in the sigma channel at finite temperature

Quantized meson fields in and out of equilibrium. I: Kinetics of meson condensate and quasi-particle excitations

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