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A precise determination of the atomic mass of $^{75}$As has been performedutilizing the double Penning trap mass spectrometer, JYFLTRAP. The mass excessis measured to be -73035.519(42) keV/c$^2$, which is a factor of 21 moreprecise and 1.3(9) keV/c$^2$ lower than the adopted value in the newest AtomicMass Evaluation (AME2020). This value has been used to determine theground-state-to-ground-state electron-capture decay $Q$ value of $^{75}$Se and$\beta^-$ decay $Q$ value of $^{75}$Ge, which are derived to be 866.041(81) keVand 1178.561(65) keV, respectively. Using the nuclear energy-level data of860.00(40) keV, 865.40(50) keV (final states of electron capture) and1172.00(60) keV (final state of $\beta^-$ decay) for the excited states of$^{75}$As$^*$, we have determined the ground-state-to-excited-state $Q$ valuesfor two transitions of $^{75}$Se $\rightarrow$ $^{75}$As$^*$ and one transitionof $^{75}$Ge $\rightarrow$ $^{75}$As$^*$. The ground-state-to-excited-state $Q$values are determined to be 6.04(41) keV, 0.64(51) keV and 6.56(60) keV,respectively, thus confirming that the three low $Q$-value transitions are allenergetically valid and one of them is a possible candidate channel forantineutrino mass determination. Furthermore, the ground-state-to-excited-state$Q$ value of transition $^{75}$Se $\rightarrow$ $^{75}$As$^*$ (865.40(50) keV)is revealed to be ultra-low (< 1 keV) and the first-ever confirmed ECtransition possessing an ultra-low $Q$ value from direct measurements.

Observation of an ultra-low $Q$-value electron-capture channel decaying to $^{75}$As via high-precision mass measurement