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Background: Ultra-low $Q$-value $\beta$-decays are interesting processes tostudy with potential applications to nuclear $\beta$-decay theory and neutrinophysics. While a number of potential ultra-low $Q$-value $\beta$-decaycandidates exist, improved mass measurements are necessary to determine whichare energetically allowed. Method: Penning trap mass spectrometry was used todetermine the atomic mass of $^{89}$Y and $^{139}$La, from which $\beta$-decay$Q$-values for $^{89}$Sr and $^{139}$Ba were obtained to determine if therecould be an ultra-low $Q$-value decay branch in the $\beta$-decay of $^{89}$Sr$\rightarrow$ $^{89}$Y or $^{139}$Ba $\rightarrow$ $^{139}$La. Results: The$^{89}$Sr $\rightarrow$ $^{89}$Y and $^{139}$Ba $\rightarrow$ $^{139}$La$\beta$-decay $Q$-values were measured to be $Q_{\rm{Sr}}$ = 1502.20(0.35) keVand $Q_{\rm{Ba}}$ = 2308.37(68) keV. These were compared to energies of excitedstates in $^{89}$Y at 1507.4(1) keV, and in $^{139}$La at 2310(19) keV and2313(1) keV to determine $Q$-values of -5.20(37) keV for the potentialultra-low $\beta$-decay branch of $^{89}$Sr and -1.6(19.0) keV and -4.6(1.2)keV for those of $^{139}$Ba. Conclusion: The potential ultra-low $Q$-valuedecay branch of $^{89}$Sr to the $^{89}$Y (3/2$^-$, 1507.4 keV) state isenergetically forbidden and has been ruled out. The potential ultra-low$Q$-value decay branch of $^{139}$Ba to the 2313 keV state in $^{139}$La withunknown J$^{\pi}$ has also been ruled out at the 4$\sigma$ level, while moreprecise energy level data is needed for the $^{139}$La (1/2$^+$, 2310 keV)state to determine if an ultra-low $Q$-value $\beta$-decay branch to this stateis energetically allowed.

Investigation of potential ultra-low $Q$-value $\beta$-decay candidates $^{89}$Sr and $^{139}$Ba using Penning trap mass spectrometry