  Excitonic properties of Ge$_2$H$_2$ and Sn$_2$H$_2$, also known as Xanes, are
investigated within the effective mass model. A perpendicularly applied
magnetic field induces a negative shift on the exciton center-of-mass kinetic
energy that is approximately quadratic with its momentum, thus pushing down the
exciton dispersion curve and flattening it. This can be interpreted as an
increase in the effective mass of the magneto-exciton, tunable by the field
intensity. Our results show that in low effective mass two-dimensional
semiconductors, such as Xanes, the applied magnetic field allows one to tune
the magneto-exciton effective mass over a wide range of values.
