Transient photon production in a QGP

Abstract

Abstract.We discuss the shortcomings of a formula that has been used in the literature to compute the number of photons emitted by a hot or dense system during a finite time, and show that the transient effects it predicts for the photon rate are unphysical.Electromagnetic radiation has long been thought to be a good probe of the early stages of heavy ion collisions [1]. In recent years, a new "real-time" approach has been proposed in order to compute out-of-equilibrium effects for photon production in a dense equilibrated quark-gluon system, which originate in its finite life-time [2]. The result was that there are important transient effects that make the yield much larger than what would have been expected by simply multiplying the equilibrium rates by the corresponding amount of time. This unexpectedly large photon yield was the starting point of many discussions regarding the validity of this approach [3,4].In this note we show in a systematic and simple way that the expression of the photon yield obtained in [2] relies on unphysical assumptions. We show that the standard canonical formalism in the S-matrix approach leads to this expression, provided the electromagnetic interactions are unduly turned on and off at finite initial and final times. The simplicity of this derivation allows us to exhibit the illegitimate character of the expression used to predict the transient effects (For details, see Ref. [4]).Let us consider a system of quarks and gluons, and denote by L QCD its Lagrangian. We couple the quarks to the electromagnetic field in order to study photon emission by this system, and denote L e.m. the Lagrangian of the electromagnetic field, and L qγ the term that couples the quarks to the photons. The complete Lagrangian is thereforeHere G µ and G a µν are respectively the gluon field and field strength, A µ and F µν the photon field and field strength, and ψ the quark field (only one flavor is considered here). g is the strong coupling constant, and e is the quark electric charge. We denote collectively by L int the sum of all the interaction terms. The number of photons measured in the system at some late time is given by 1 Presented at the Hadron Physics

Off-equilibrium photon production during the chiral phase transition

“…Moreover, the consideration of the 'photon number-density' at finite times effectively comes along with a violation of the Ward-Takahashi identities. Our investigations hence support the respective concern raised in [33,34] towards [30,31,32].…”

“…Later on, the topic was also picked up by Fraga et al [33,34] where the ansatz used in [30,31,32] was considered as doubtful, as it came along with the mentioned problems. In particular, the concerns raised in [33,34] were the following:…”

“…The authors of [33,34] did, however, not provide an alternative approach for how to handle the mentioned problems in a consistent manner. Solely in [35] it was indicated that the question of finite-lifetime effects could be addressed within the 2PI (two-particle irreducible) approach even though the conservation of gauge invariance remains challenging.…”

Non-equilibrium photon production arising from the chiral mass shift

“…Solely in [35] it was indicated that the question of finite-lifetime effects could be addressed within the 2PI (two-particle irreducible) approach even though the conservation of gauge invariance remains challenging. Later on Boyanovsky et al insisted on their approach [36] and objected to the arguments by [33,34] as follows:…”