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One-loop photon-photon scattering in a thermal, deconfining SU(2) Yang-Mills plasma

For a deconfining thermal SU(2) Yang-Mills plasma we discuss the role of (anti)calorons in introducing non-thermal behavior effectively described in terms of Planck's quantum of action $\hbar$. This non-thermality cancels exactly between the ground-state estimate and its free quasiparticle excitations. Kinematic constraints in 4-vertex scattering and the counting of radial loop variables versus the number of independent constraints on them are re-visited. Next, we consider thermal 2$\rightarrow$ 2 one-loop scattering of the modes remaining massless upon the (anti)caloron induced adjoint Higgs mechanism (thermal ground state after spatial coarse graining). Starting with stringent analytical arguments, we are able to exclude the contribution to photon-photon scattering from diagrams containing at least one three-vertex and, in a next step, a vast majority of all possible configurations involving two four-vertices. By numerical analysis we show that the remaining contribution of the overall S channel is severely suppressed compared to that of the T and U channels, meaning that the creation of a pair of massive vector modes by a pair of photons and vice versa practically does not occur in the Yang-Mills plasma. For the T and U channels the domain of loop integration represents less than $10^{-7}$ times the volume of the unconstrained integration region. The thus introduced photon-photon correlation should affect the Cosmic Microwave Background's polarisation at low redshift. An adaption of the here-developed methods to the analysis of irreducible bubble diagrams could prove the conjecture of hep-th/0609033 on the termination of the loop expansion of thermodynamical quantities at a finite irreducible order.