  Background: Low energy $\beta$ and electron capture (EC) decays are important
systems in neutrino mass determination experiments. An isotope with an
ultra-low Q value $\beta$-decay to an excited state in the daughter with Qes <
1 keV could provide a promising alternative candidate for future experiments.
$^{75}$Se EC and $^{75}$Ge $\beta$-decay represent such candidates, but a more
precise determination of the mass of the common daughter, $^{75}$As, is
required to evaluate whether their potential decay branches are energetically
allowed and ultra-low. Purpose: Perform a precise atomic mass measurement of
$^{75}$As and combine the result with the precisely known atomic masses of
$^{75}$Se and $^{75}$Ge, along with nuclear energy level data for $^{75}$As to
evaluate potential ultra-low Q value decay branches in the EC decay of
$^{75}$Se and the $\beta$-decay of $^{75}$Ge. Method: The LEBIT Penning trap
mass spectrometer at the Facility for Rare Isotope Beams was used to perform a
high-precision measurement of the atomic mass of $^{75}$As via cyclotron
frequency ratio measurements of $^{75}$As$^{+}$ to a $^{12}$C$_{6}^{+}$
reference ion. Results: The $^{75}$As mass excess was determined to be
ME($^{75}$As)= -73 035.98(43) keV, from which the ground-state to ground-state
Q values for $^{75}$Se EC and $^{75}$Ge $\beta$-decay were determined to be
866.50(44) keV and 1179.01(44) keV, respectively. These results were compared
to energies of excited states in $^{75}$As at 865.4(5) keV and 1172.0(6) keV to
determine Q values of 1.1(7) keV and 7.0(7) keV for the potential ultra-low EC
and $\beta$-decay branches of $^{75}$Se and $^{75}$Ge, respectively.
Conclusion: The $^{75}$Se EC decay to the 865.4 keV excited state in $^{75}$As
is potentially ultra-low with Qes $\approx$ 1 keV. However, a more precise
determination of the 865.4(5) keV level in $^{75}$As is required.
