Ambiguities in the zero momentum limit of the thermalπ0γγtriangle diagram

Abstract

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

Response of strongly interacting matter to a magnetic field: Some exact results

“…This model was employed before to understand the effects of temperature on anomaly [9]. Furthermore, the finite-temperature π 0 → 2γ amplitude has been computed in this model in various kinetimatic limits, including the limit where the outgoing photons are at zero frequency [4,10]. Thus, we can confirm our result (6) by calculating the axial magnetic susceptibility in this model.…”

“…As noted in Ref. [4], there is an ambiguity with the zero momentum limit. We choose the following definition.…”

“…The way we define g π 0 γγ corresponds to the π 0 → 2γ amplitude in the spacelike region of Ref. [4].…”

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“…In particular these terms modify the π → γγ amplitude which is no longer determined by the chiral anomaly [30]. The calculation in [28] confirms previous results [31,32] that this amplitude vanishes in a chiral symmetric phase (see also [33,34]).…”

Anomalous processes at high temperature and density in a two-dimensional linear σ model

“…The reason why the on-shell value is so singular when m → 0 is related to collinear singularities: in 1 + 1 dimensions, all the spatial vectors are aligned, so that we are always at the most singular point 5 . Here also, in order to be able to apply Pisarski's argument, one should first regularize the theory by resumming a thermal mass [13,17]. Then, all the powers of m in the denominators would be replaced by powers of the thermal mass, leaving an uncompensated power of m → 0 in the numerator.…”