Abstract
We present an analytic method to compute the one-loop magnetic correction to the gluon polarization tensor starting from the Landau-level representation of the quark propagator in the presence of an external magnetic field. We show that the general expression contains the vacuum contribution that can be isolated from the zero-field limit for finite gluon momentum. The general tensor structure for the gluon polarization also contains two spurious terms that do not satisfy the transversality properties. However, we also show that the coefficients of this structures vanish and thus do not contribute to the polarization tensor, as expected. In order to check the validity of the expressions we study the strong and weak field limits and show that well established results are reproduced. The findings can be used to study the conditions for gluons to equilibrate with the magnetic field produced during the early stages of a relativistic heavy-ion collision.
Highlights
The production of hot and dense strongly interacting matter in heavy-ion reactions at high energies constitutes a driving force for the formulation of novel approaches to study QCD subject to extreme conditions
We present an analytic method to compute the one-loop magnetic correction to the gluon polarization tensor starting from the Landau-level representation of the quark propagator in the presence of an external magnetic field
When the field is not as intense, it is important to perform a sum over Landau levels to capture effects that may be missing from expressions restricted to the LLL, in particular, the emergence of tensor polarization structures other than the parallel one that makes up the full polarization tensor
Summary
The production of hot and dense strongly interacting matter in heavy-ion reactions at high energies constitutes a driving force for the formulation of novel approaches to study QCD subject to extreme conditions. When the field is not as intense, it is important to perform a sum over Landau levels to capture effects that may be missing from expressions restricted to the LLL, in particular, the emergence of tensor polarization structures other than the parallel one that makes up the full polarization tensor These kinds of calculations have been performed at one-loop level for the photon polarization tensor [17] in the context of the vacuum. We undertake such task and present an analytic method to perform the sum over all Landau levels for the coefficients of the tensor structure that make up the gluon polarization tensor in the presence of a magnetic field of arbitrary intensity. We show that by this procedure one obtains the usual fermion contribution to the vacuum polarization tensor, together with a second term that is shown to vanish, given the properties of its coefficient under scaling transformations.
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