  Neutrinoless double-beta decay is a predicted beyond Standard Model process
that could clarify some of the not yet known neutrino properties, such as the
mass scale, the mass hierarchy, and its nature as a Dirac or Majorana fermion.
Should this transition be observed, there are still challenges in understanding
the underlying contributing mechanisms. We perform a detailed shell model
investigation of several beyond Standard Model mechanisms that consider the
existence of right-handed currents. Our analysis presents different venues that
can be used to identify the dominant mechanisms for nuclei of experimental
interest in the mass A$\sim$130 region ($^{124}$Sn, $^{130}$Te, and
$^{136}$Xe). It requires an accurate knowledge of nine nuclear matrix elements
that we calculate, in addition to the associated energy dependent phase-space
factors.
