Reply to “Comment on ‘Hadronic production of thermal photons’”

Abstract

We address a recent comment by Alam et al. [Phys. Rev. C 71, 059802 (2005)], on our work of thermal photon emission rates from hadronic matter. Specifically, we explain how t-channel ω exchange in the πρ → πγ reaction arises as a dominant contribution to the rates at high energy and why hadronic form factors cannot be neglected in this assessment. [2], namely that t-channel ω exchange is a dominant source of high-energy photons from a thermal hadronic gas. In their reasoning, they intentionally omit the insertion of form factors (FFs) at hadronic vertices to "understand the relative importance of ω and a 1 exchange processes" [1].Hadronic FFs are a conventional way to incorporate finitesize effects in describing hadronic reactions, especially at high momentum transfer, where hadronic substructure becomes important. They arise naturally and are ubiquitous in field theories with emergent degrees of freedom. In Ref.[2] we have calculated photon-generating processes including the exchange of a 1 , ρ, and π mesons within the massive Yang-Mills (MYM) approach [3,4], as well as the πρω vertex as given by the Wess-Zumino Lagrangian [5], augmented by standard (dipole) FFs [2,6] that are unity on-shell. The four parameters of the MYM Lagrangian can be fit using measured values [7] of m ρ , m a 1 , ρ→ππ , and a 1 →ρπ , whereas the coupling constant g ωπρ is fixed by the decay ω → πγ . The latter is an off-shell decay (proceeding via an intermediate ρ meson) with the FF entering the decay width as ω→πγ ∝ (g ωπρ F F ωπρ ) 2 . We obtained g ωπρ = 22.6 GeV −1 (with a typical FF cutoff of 1 GeV), as compared to g ωπρ = 11.93 GeV −1 with F F ωπρ ≡ 1. The presence of the FF clearly and simply increases the coupling constant. Our procedure is corroborated by inspecting the triple-pion ω decay channel. In the gauged Wess-Zumino Lagrangian [5] that reproduces the radiative decay of the ω, the width for ω → πππ is ω→πππ = 5.1 MeV (with FF = 1), whereas the experimental result is 7.49 ± 0.08 MeV. Once the FF is implemented at each vertex of the reaction, we find ω→πππ = 7.47 MeV. The presence of the FF obviously increases the value of the coupling constant g ωπρ , but of course the full effect has to involve both coupling and FF. The net effect is an increase of the width for ω → πππ and this enhancement carries over to the π + ρ → π + γ reaction with ω exchange.As discussed in Ref.[2], for the case of ω exchange an incoherent addition of the s-and t-channel contributions is justified. This is illustrated in the top panel of

The theory and phenomenology of perturbative QCD based jet quenching

“…This expression may be easily generalized from Eqs. (26,25,38) The δ-function δ(l ⊥ + l q ⊥ ) is shifted to δ(l q ⊥ ) and is then broadened by multiple scattering as in Eq. (38).…”

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Quark matter 2006: high- and jets

“…The data indicate that there may be a small suppression at high p T , but there is no indication of the expected in-medium suppression at lower p T , albeit with large uncertainties. It has also been suggested that quark-photon conversions in the medium could lead to an enhancement of direct photon production at intermediate p T [33]. There is no evidence for such an enhancement in the data.…”

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