  Magnetic Feshbach resonances play a central role in experimental research of
atomic gases at ultracold temperatures, as they allow one to control the
microscopic interactions between ultracold atoms by tuning an applied magnetic
field. These resonances arise due to strong hyperfine interactions between the
unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A
major thrust of current research is to create an ultracold gas of diatomic
alkali-metal molecules in the ground rovibrational state of the ground
electronic $^1\Sigma$ state. Unlike alkali metal atoms, $^1\Sigma$ diatomic
molecules have no unpaired electrons. However, the hyperfine interactions of
molecules may give rise to magnetic Feshbach resonances. We use quantum
scattering calculations to study the possible width of these resonances. Our
results show that the widths of magnetic Feshbach resonances in ultracold
molecule-molecule collisions for $^1\Sigma$ molecules may exceed 1 milliGauss,
rendering such resonances experimentally detectable. We hope that this work
will stimulate the experimental search of these resonances.
