  A qualitative study of the lightest glueball states in Euclidean SU(2)
Yang-Mills theory quantized in the maximal Abelian gauge is presented. The
analysis is done by generalizing to the maximal Abelian gauge the so-called
replica model, already successfully introduced in the Landau gauge. As it will
be shown, the gluon and ghost propagators obtained from the replica model are
of the same type of those already introduced in Phys. Rev. D77, 105023 (2008)
[arXiv:0801.0566], whose behavior turns out to be in agreement with that
available from the lattice data on the maximal Abelian gauge. The model turns
out to be renormalizable to all orders, while enabling us to introduce gauge
invariant composite operators for the study of the lightest glueballs
$J^{PC}=0^{++}$, $2^{++}$ and $0^{-+}$. The spectral representation for the
correlation functions of these operators are evaluated to the first order, and
the corresponding spectral densities are shown to be positive. Under the
assumption of Abelian dominance, it turns out that the hierarchy for the masses
of the lightest glueballs in the maximal Abelian gauge is in agreement with
that already obtained in the Landau gauge, a feature which provides evidence
for the gauge independence of the spectrum of the theory.
