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Gluon mass generation is investigated for 4-dimensional $SU(N)$ Yang-Mills inconventional covariant and in background field gauges within an effectivedescription that, through a parameterization, can be regarded as a massivegluon model, or as a Nambu-Jona-Lasinio-like expansion around a massive leadingorder while preserving the Yang-Mills Lagrangian. We employ a renormalizationscheme that introduces the ratio of the gluon mass parameter $m$ to thesaturation value of the gluon propagator. This, along with the mass $m(\mu)$and the strong coupling $\alpha_s(\mu)$, provided the fit parameters forcomparison with $SU(3)$ lattice results renormalized at the scale $\mu$. Weobtain two types of solutions with satisfactory fits. Within the proposedexpansion, we show the conditions under which it is possible to obtain anexactly vanishing longitudinal self energy for any gauge parameter $\xi$ in thebackground field case. However, such a result in conventional covariant gaugesis unattainable by the given expansion as it is, indicating that moresophisticated versions with dressed vertices are likely necessary. We arguethat the conditions under which transversality takes place are consistent withSchwinger-Dyson results for the ghost dressing function also.

Transversality of gluon mass generation through an effective loop expansion in covariant and background field gauges