  Recent tunneling conductance measurements of Majorana nanowires show a strong
variation in the magnetic field dependence of the superconducting gap among
different devices. Here, we theoretically study the magnetic field dependence
of the gap closing feature and establish that the degree of convexity (or
concavity) of the gap closing as a function of Zeeman field can provide
critical constraints on the underlying microscopic parameters of the
semiconductor-superconductor hybrid system model. Specifically, we show that
the gap closing feature is entirely concave only for strong spin-orbit coupling
strength relative to the chemical potential. Additionally, the non-linearity
(i.e. concavity or convexity) of the gap closing as a function of magnetic
field complicates the simple assignment of a constant effective $ g $-factor to
the states in the Majorana nanowire. We develop a procedure to estimate the
effective $ g $-factor from recent experimental data that accounts for the
non-linear gap closing resulting from the interplay between chemical potential
and spin-orbit coupling. Thus, measurements of the magnetic field dependence of
the gap closure on the trivial side of the topological quantum phase transition
can provide useful information on parameters that are critical to the
theoretical modeling of Majorana nanowires.
