Regularized non-Abelian chiral Jacobian factor at finite temperature

Rong-tai, Wang

doi:10.1088/0305-4470/23/23/027

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…It is well established in the literature that the axial anomaly has a temperature independent form [1][2][3][4][5][6][7][8][9][10][11][12][13]. This result is consistent with our present understanding of anomalies, since they are induced by the ultraviolet divergences present in the theory whereas the finite temperature modifies the infrared sector only, namely, by imposing periodic or antiperiodic boundary conditions in the Euclidean time direction [14][15][16].…”

Section: Introductionsupporting

confidence: 84%

“…The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.Typeset using REVT E X It is well established in the literature that the axial anomaly has a temperature independent form [1][2][3][4][5][6][7][8][9][10][11][12][13]. This result is consistent with our present understanding of anomalies, since they are induced by the ultraviolet divergences present in the theory whereas the finite temperature modifies the infrared sector only, namely, by imposing periodic or antiperiodic boundary conditions in the Euclidean time direction [14][15][16].…”

supporting

confidence: 86%

“…Such formalism gives directly the effective action as the integral of a (d + 1)-form, as in eqs. (8,9). One advantage of this procedure is that enforcement of vector gauge invariance is sufficient to fix the action without introducing a ζ-function regularization, but working in more spacetime dimensions is also more involved.…”

Section: Calculation Of the Effective Actionmentioning

confidence: 99%

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Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Salcedo

1998

Phys. Rev. D

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The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four dimensions. The calculation preserves chiral symmetry and confirms that a temperature dependence is compatible with axial anomaly saturation. The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.

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Section: Introductionsupporting

confidence: 84%

supporting

confidence: 86%

Section: Calculation Of the Effective Actionmentioning

confidence: 99%

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Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Salcedo

1998

Phys. Rev. D

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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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Howπ0→γγchanges with temperature

1997

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At zero temperature, in the chiral limit the amplitude for 0 to decay into two photons is directly related to the coefficient of the axial anomaly. At any nonzero temperature, this direct relationship is lost: while the coefficient of the axial anomaly is independent of temperature, in a thermal bath the anomalous Ward identities do not uniquely constrain the amplitude for 0 →␥␥. Explicit calculation shows that to lowest order about zero temperature this amplitude decreases. ͓S0556-2821͑97͒00423-2͔

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Regularized non-Abelian chiral Jacobian factor at finite temperature

Cited by 4 publications

References 13 publications

Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Anomalous processes in effective chiral theories at high temperatures

Howπ0→γγchanges with temperature

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