  The Pierre Auger Collaboration has reported an excess in the number of muons
of a few tens of percent over expectations computed using extrapolation of
hadronic interaction models tuned to accommodate LHC data. Very recently, we
proposed an explanation for the muon excess assuming the formation of a
deconfined quark matter (fireball) state in central collisions of
ultrarelativistic cosmic rays with air nuclei. At the first stage of its
evolution the fireball contains gluons as well as $u$ and $d$ quarks. The very
high baryochemical potential inhibits gluons from fragmenting into $u \bar u$
and $d \bar d$, and so they fragment predominantly into $s \bar s$ pairs. In
the hadronization which follows this leads to the strong suppression of pions
and hence photons, but allows heavy hadrons to be emitted carrying away
strangeness. In this manner, the extreme imbalance of hadron to photon content
provides a way to enhance the muon content of the air shower. In this
communication we study theoretical systematics from hadronic interaction models
used to describe the cascades of secondary particles produced in the fireball
explosion. We study the predictions of one of the leading LHC-tuned models
QGSJET II-04 considered in the Auger analysis.
