Direct Measurement of the Mass Difference of ${}^{163}\mathrm{Ho}$ and ${}^{163}\mathrm{Dy}$ Solves the $Q$-Value Puzzle for the Neutrino Mass Determination

The atomic mass difference of ${}^{163}\mathrm{Ho}$ and ${}^{163}\mathrm{Dy}$ has been directly measured with the Penning-trap mass spectrometer SHIPTRAP applying the novel phase-imaging ion-cyclotron-resonance technique. Our measurement has solved the long-standing problem of large discrepancies in the $Q$ value of the electron capture in ${}^{163}\mathrm{Ho}$ determined by different techniques. Our measured mass difference shifts the current $Q$ value of 2555(16) eV evaluated in the Atomic Mass Evaluation 2012 [G. Audi et al., Chin. Phys. C 36, 1157 (2012)] by more than $7\sigma$ to $2833({30}_{\text{stat}})({15}_{\mathrm{sys}})\mathrm{eV}/c^2$. With the new mass difference it will be possible, e.g., to reach in the first phase of the ECHo experiment a statistical sensitivity to the neutrino mass below 10 eV, which will reduce its present upper limit by more than an order of magnitude.

Figure 1

(a) The $Q$ value of the electron capture in ${}^{163}\mathrm{Ho}$ taken from Ref. [24] and obtained in several experiments from the analysis of the electron-capture spectrum (Andersen [15, 17], Baisden [16], Laegsgaard [17], Hartmann [18, 20], Yasumi [19, 22], Bosch [21], Gatti [23], Ranitzsch [7]) plotted according to the publication year. Different symbols indicate different experimental methods. The $Q$ value recently measured with TRIGA-TRAP [25] is not shown in the plot due to its rather moderate accuracy of 700 eV [26]. The red line and shaded band correspond to the recommended $Q$ value and its uncertainty, respectively [24]. The recommended $Q$ value was obtained by averaging only the data points which are colored blue in the plot. (b) Statistical sensitivity of the ECHo experiment [8] to the electron-neutrino mass as a function of the $Q$ value of the electron capture in ${}^{163}\mathrm{Ho}$ for several numbers $N$ of the acquired electron-capture events in the full energy spectrum (see text for details).

Figure 2

Schematic of the SHIPTRAP setup used for the determination of the $Q$ value of the electron capture in ${}^{163}\mathrm{Ho}$. Note that while the ions perform cyclotron and magnetron revolutions in the same sense, their cyclotron phase image is inverted during the cyclotron-to-magnetron conversion [31]. For details see text, dimensions not to scale.

Figure 3

(a) An exemplary 5-hour measurement period of the cyclotron frequencies ${\nu }_c$ of the ${{}^{163}\mathrm{Dy}}^{+}$ and ${{}^{163}\mathrm{Ho}}^{+}$ ions. The ratio $R_{5\text{hour}}$ of the cyclotron frequencies ${\nu }_c$ of the ${{}^{163}\mathrm{Dy}}^{+}$ and ${{}^{163}\mathrm{Ho}}^{+}$ ions was obtained along with the inner and outer errors [36] by fitting to the ${{}^{163}\mathrm{Ho}}^{+}$ frequency points a fifth order polynomial $P_1(t)$ and to the ${{}^{163}\mathrm{Dy}}^{+}$ frequency points a polynomial $P_2(t)=R_{5\text{hour}}{P}_1(t)$. (b) The mass difference of ${}^{163}\mathrm{Ho}$ and ${}^{163}\mathrm{Dy}$ calculated from the cyclotron-frequency ratios $R_{5\text{hour}}$. The red line and the red shaded band are the average mass difference value and its uncertainty of the work reported here.