The triangle diagram at finite temperature

Contreras, Caterina; Loewe, M.

doi:10.1007/bf01555887

Cited by 22 publications

(22 citation statements)

References 18 publications

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Section: Introductioncontrasting

confidence: 79%

“…π 0 → 2γ the observation in [1,2] is: "In a hot, chirally symmmetric phase, π 0 doesn't go into 2γ, but π 0 σ does"! This statement indeed contradicts results which have been obtained previously [7,8].In [1,2] the effective anomalous couplings for π 0 → 2γ (π 0 σ → 2γ) are found in the framework of the constituent quark model [4,9] by calculating the contribution from the Feynman one-loop triangle (box) diagrams at temperature T = 0 and at nonzero, high T , respectively.In this note we attempt a different approach in order to confirm Pisarski's interesting result. As in [1,2] we start from the linear sigma model with constituent quarks interacting with bosons [10,11].…”

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confidence: 81%

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Anomalous processes in effective chiral theories at high temperatures

1996

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We discuss chiral theories of constituent quarks interacting with bosons at high temperatures. In the chirally symmetric phase we demonstrate by applying functional methods the presence of effective anomalous couplings for e.g. πσ → γγ, γ → πππσ, KK → πππσ, etc., as they have recently been discussed by Pisarski. I. INTRODUCTIONIn recent papers [1,2] Pisarski pointed out that although the chiral (abelian as well as nonabelian) anomaly [3,4] in terms of fundamental fields is temperature independent [5,6] the manifestation of the anomaly, however, in terms of effective fields changes with temperature. When considering e.g. π 0 → 2γ the observation in [1,2] is: "In a hot, chirally symmmetric phase, π 0 doesn't go into 2γ, but π 0 σ does"! This statement indeed contradicts results which have been obtained previously [7,8].In [1,2] the effective anomalous couplings for π 0 → 2γ (π 0 σ → 2γ) are found in the framework of the constituent quark model [4,9] by calculating the contribution from the Feynman one-loop triangle (box) diagrams at temperature T = 0 and at nonzero, high T , respectively.In this note we attempt a different approach in order to confirm Pisarski's interesting result. As in [1,2] we start from the linear sigma model with constituent quarks interacting with bosons [10,11]. In order to include the effect of the axial anomaly on the bosons we transform the basis of right-and left-handed quarks following ref. [12], but in the situation of the chirally symmetric phase at high T [13]. At T = 0 and in the spontaneously broken phase this procedure allows a direct calculation of the Wess-Zumino-Witten action [14] for the Goldstone bosons, after applying functional methods for the evaluation of the fermion determinant in connection with path integrals [15].In Sec. II we define the effective lagrangian and describe the way of performing the chirally symmetric limit at high temperature. Sec. III is devoted to the zeta-regularization used to evaluate the fermion determinant in the symmetric case. In Secs. IV and V we discuss the effective anomalous low-energy electromagnetic and hadronic couplings as a result of the chiral anomaly at high T . II. EFFECTIVE CHIRAL LAGRANGIANSWe consider the SU (2) L SU (2) R lagrangian for N C coloured right-and left-handed quarks parametrized in the linear form ("Σ-basis"),with the SU (2) matrix Σ = σ + i τ · π, where we closely follow the notation used in [10]. In the following the explicit form of the boson lagrangian L boson is not needed [10,11]. Although in the strictly symmetric phase the constituent quark mass m has to vanish, we nevertheless introduce explicitly a breaking termWe treat m as an explicit regularization parameter, which is finally removed in the symmetric phase by performing the limit m → 0. However, we do not break the chiral symmetry spontaneously by the standard redefinition of the scalar field σ. * Supported by Deutsche Forschungsgemeinschaft

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Section: Introductioncontrasting

confidence: 79%

mentioning

confidence: 81%

Anomalous processes in effective chiral theories at high temperatures

1996

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“…Such a situation could take place in a neutron star, or in a cosmological hadronic medium below the chiral phase transition point [3] [6] [7]. In agreement with previous studies of the π 0 → γγ decay at finite temperature [8], one expects to find non-vanishing T -corrections. In addition such corrections should be ultraviolet finite and no renormalization of the anomaly at finite…”

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confidence: 83%

One loop calculations on the Wess-Zumino-Witten anomalous functional at finite temperature

Alvarez‐Estrada¹,

Dobado²,

Nicola³

1994

Physics Letters B

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We analyze the finite temperature (T) extension of the WessZumino -Witten functional, discussed in a previous work, to one loop in chiral perturbation theory. As a phenomenological application, we calculate finite temperature corrections to the amplitude of π 0 decay into two photons. This calculation is performed in three limits : i) T /M π << 1 , ii) the chiral limit at finite T and iii) T /M π >> 1 (M π being the pion mass). The T -corrections tend to vanish in the chiral limit, where only the kaon contribution remains (although it is exponentially suppressed).

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“…The same diagram has been calculated in the real time formalism by [7,8], and also by Gupta and Nayak (GN in the following) in [9] who studied the zero momentum limit of this diagram. GN's result for this diagram in the zero external momentum limit is proportional to m/mT .…”

Section: Introductionmentioning

confidence: 68%

“…To that effect, we perform this calculation in the "retarded-advanced" version of the real time formalism, but we stay at a more general level than [1,7,8,9] concerning the kinematical configuration of the external particles. In particular, we don't assume that external particles are on-shell.…”

Section: Introductionmentioning

confidence: 99%

Ambiguities in the zero momentum limit of the thermalπ0γγtriangle diagram

Gelis

1999

Phys. Rev. D

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Modifications of the π o → 2γ decay amplitude by thermal effects have already been considered by several authors, leading to quite different results. I consider in this paper the triangle diagram connecting a neutral pion to two photons in a constituent quark model, within the real-time formulation of thermal field theory and study the zero external momentum limit of this diagram. It appears that this limit is not unique and depends strongly on the kinematical configuration of the external particles. This non-uniqueness is shown to explain the contradiction between existing results. I end with some considerations suggesting that this decay amplitude may be significantly modified by the resummation of hard thermal loops, due to infrared singularities.hep-ph/9806425 LAPTH-689/98

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The triangle diagram at finite temperature

Cited by 22 publications

References 18 publications

Anomalous processes in effective chiral theories at high temperatures

Anomalous processes in effective chiral theories at high temperatures

One loop calculations on the Wess-Zumino-Witten anomalous functional at finite temperature

Ambiguities in the zero momentum limit of the thermalπ0γγtriangle diagram

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