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Direct Measurement of the Mass Difference of Ho163 and Dy163 Solves the Q-Value Puzzle for the Neutrino Mass Determination

The atomic mass difference of 163Ho and 163Dy 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 163Ho 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(30stat)(15sys) eV/c2. 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.

The atomic mass difference of 163 Ho and 163 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 Ho determined by different techniques. Our measured mass difference shifts the current Q-value of 2555 (16) eV evaluated in the AME2012 [1] by more than 7 sigma to 2833(30stat)(15sys) 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. One of the most interesting open questions in particle physics is the absolute scale of neutrino masses. Among several approaches to determine the absolute neutrino masses, the analysis of the β − decays of tritium and 187 Re and the electron capture (EC) in 163 Ho are considered model-independent, since they are based on a kinematic analysis of the decay. The presently best upper limits of about 2.12 eV and 2.3 eV (95% C.L.) on the electron antineutrino mass have been obtained in the "Troitsk ν-mass" and "Neutrino Mainz" experiments (see [2,3]), respectively, using the tritium β − decay. The best limit on the electron neutrino mass, obtained by the analysis of the X-ray emission following the electron capture in 163 Ho, is by far less stringent being about 225 eV (95% C.L.) [4]. Currently, several next-generation projects -KATRIN [5] and Project 8 [6] using tritium, MARE [7] using 187 Re, and ECHo [8,9], HOLMES [10] and NuMECS [11,12] using 163 Ho -are being developed with the goal to probe the electron-neutrino and antineutrino masses on a sub-eV level. In the kinematic analysis of the β − and EC spectra an accurate knowledge of the mass differences of the mother and daughter nuclides of the processes under investigation is essential for investigating systematic effects in the analysis of the endpoint region. Presently, only high-precision Penning-trap mass spectrometry is capable of determining mass differences of nuclides relevant to the neutrino-mass determination with the required uncertainty (see, e.g., [13][14][15]).
In this Letter we report on the first direct highprecision Penning-trap determination of the atomic mass difference of 163 Ho and 163 Dy. The Q-value has already been determined, but only indirectly from the analysis of the EC-spectrum in several independent experiments by different groups using different methods ( Fig. 1(a)) [4,8,[16][17][18][19][20][21][22][23][24]. The results fall in the range from approximately 2.4 keV to 2.9 keV, thus, exhibiting a substantial scatter of a few hundred eV. In particular, the Q-values obtained with cryogenic microcalorimetry [8,24] -the technique which forms the basis of all modern 163 Ho-experiments -are higher by about 250 eV than the recommended Q-value of 2555(16) eV of the Atomic-Mass Evaluation AME2012 [1], which was obtained by averaging only proportional counter data [19,21] and storage-ring measurements [22]. Even if all the available values had been used for the averaging, the result would only slightly have been affected and still quite incompatible with the values obtained with cryogenic microcalorimetry. Recently, it has also been measured directly with the Penning-trap setup TRIGA-TRAP [25], however, with an uncertainty of 700 eV [26], which is insufficient to resolve the Q-value puzzle. If the recommended Q-value is correct, then the large deviation of the microcalorimetry values may be a sign of  [1] and obtained in several experiments from the analysis of the electron-capture spectrum (Andersen [16,18], Baisden [17], Laegsgaard [18], Hartmann [19,21], Yasumi [20,23], Bosch [22], Gatti [24], Ranitzsch [8]) 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 [1]. 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 [9] to the electron-neutrino mass as a function of the Q-value of the electron capture in 163 Ho for several numbers N of the acquired electron-capture events in the full energy spectrum (see text for details).
an insufficient understanding of the corresponding measurements of the EC spectrum, i.e. of the de-excitation processes involved in the EC in 163 Ho. However, recent improved calculations of the probabilities of different atomic configurations in 163 Dy after the EC in 163 Ho [27][28][29] including 2-hole and 3-hole excitations show that the contribution of higher order structures in the calorimetrically measured spectrum is below a few percent. Therefore, these higher orders cannot explain the large discrepancy between the result obtained by calorimetric measurements and the recommended value [1].
Furthermore, the statistical sensitivity of the experiments to the electron-neutrino mass value is a function of the Q-value of the EC in 163 Ho. Fig. 1(b) shows the achievable statistical sensitivity (90% C.L.) of the ECHo experiment [9] to the electron-neutrino mass vs the Q-value for several numbers of acquired electroncapture events: a large uncertainty in the Q-value results in an unacceptably large uncertainty in the scale of the microcalorimetric experiment. Therefore, an accurate and independent direct measurement of the atomic mass differences of 163 Ho and 163 Dy is demanded.
The determination of the atomic mass difference of 163 Ho and 163 Dy was performed with the Penning-trap mass spectrometer SHIPTRAP [31] by measuring the cyclotron-frequency ratio of 163 Ho and 163 Dy ions, R = ν c ( 163 Dy + )/ν c ( 163 Ho + ), using the novel Phase-Imaging Ion-Cyclotron Resonance (PI-ICR) technique [30,32]. The cyclotron frequency ν c of an ion with mass m and charge q in a magnetic field with strength B, given by ν c = qB/(2πm), was determined as the sum of the two radial-motion frequencies of the trapped ions: magnetron frequency ν − and modified cyclotron frequency ν + , i.e., ν c =ν − +ν + . A schematic of the experimental setup is presented in Fig. 2. Singly-charged ions of 163 Ho and 163 Dy were produced with a laser-ablation ion source [33] by irradiating the corresponding Ho and Dy samples with a frequency-doubled Nd:YAG laser beam with a diameter of about 1 mm. This production mechanism of Ho-ions has already been demonstrated at the TRIGA-TRAP facility [26]. For a production of the Dy-sample, a few milligrams of natural Dy in powder form were spread over a 5x5 mm 2 large titanium plate. 163 Ho is radioactive with a half-life of 4570(25) years and thus first had to be produced in sufficient amount and in a high-purity form. The production of 163 Ho involved neutron irradiation of an enriched 162 Er sample in the high-flux reactor of the Institut Laue-Langevin and the subsequent electron capture decay of the resulting 163 Er (T 1/2 = 75 min) into 163 Ho. This was followed by a chemical separation based on ion-chromatography optimized to separate neighboring lanthanides. The resulting 163 Ho contained less than 0.4% 163 Dy -the only nuclide that cannot be resolved from 163 Ho in the Penning trap and hence can lead to a systematic uncertainty in the mass difference determination between 163 Ho and 163 Dy. Finally, the Ho-sample for the laser ion source was prepared by From the laser-ablation ion source 163 Ho + and 163 Dy + ions were alternately transferred into a preparation trap for cooling and centering via mass-selective buffer-gas cooling [35] and further transfered into a measurement trap for cyclotron-frequency determination with the PI-ICR technique [30,32]. The distance between the Ho and Dy samples on the target holder of the laser ion source was about 30 mm and thus a simultaneous irradiation of two samples and hence a simultaneous production of 163 Ho and 163 Dy ions were excluded. Other impurity ions were removed in the preparation trap with the buffer-gas cooling technique [35] prior to the transfer into the measurement trap. For the measurement of the ion cyclotron frequency "measurement scheme 2" as described in detail in [30] was applied: in short, the amplitudes of the coherent components of their magnetron and axial motions were reduced to values of about 0.01 mm and 0.4 mm, respectively, by simultaneously applying to the corresponding trap electrodes two 1-ms dipolar rf-pulses with certain amplitudes, initial phases and the corresponding frequencies. These steps were required to reduce to a level well below 10 −10 a possible shift in the cyclotron-frequency ratio of the 163 Ho + and 163 Dy + ions due to the anharmonicity of the trap potential and the inhomogeneity of the magnetic field. After these preparatory steps, the radius of the ion cyclotron motion was increased to 0.5 mm in order to set its initial phase of the cyclotron motion. Then, two excitation patterns, called in this work "magnetron phase" and "cyclotron phase", were applied alternately in order to measure the ion cyclotron frequency ν c . In the magnetron-phase pattern the cyclotron motion was first converted to the magnetron motion with the same radius. Then, the ions performed the magnetron motion accumulating a certain magnetron phase. After 600 ms elapsed, the ions' position in the trap plane perpendicular to the magnetic field was projected onto a position-sensitive detector by ejecting the ions from the trap towards the detector [36]. In the cyclotron-phase pattern the ions first performed the cyclotron motion for 600 ms accumulating the corresponding cyclotron phase with a consecutive conversion to the magnetron motion and again projection of the ion position in the trap onto the position-sensitive detector. The angular FWHM of the magnetron and cyclotron phase spots with respect to the trap-image center amounts to about 7 0 and 11 0 , respectively. The difference between the angular positions of the two phase images (see Fig. 2) is a measure for the ion cyclotron frequency ν c . One measurement of the ion cyclotron frequency consisted of a periodic sequence of the magnetron and cyclotron pulse patterns with a period of about 800 ms and a total measurement time of approximately 5 minutes. On this time-scale and with the obtained uncertainty the phase measurements can be considered to be performed simultaneously. Data with more than 5 detected ions (about ten loaded ions) per cycle were rejected in the data analysis in order to reduce a possible shift in the cyclotron-frequency ratio of the 163 Ho + and 163 Dy + ions due to ion-ion interactions. To eliminate a cyclotron-frequency shift The ratio R 5hour of the cyclotron frequencies νc of the 163 Dy + and 163 Ho + ions was obtained along with the inner and outer errors [34] by fitting to the 163 Ho + frequency points a fifth order polynomial P1(t) and to the 163 Dy + frequency points a polynomial P2(t) = R 5hour × P1(t). (b) The mass difference of 163 Ho and 163 Dy calculated from the cyclotron-frequency ratios R 5hour . The red line and the red shaded band are the average mass difference value and its uncertainty of the work reported here.
due to incomplete damping of the coherent component of the magnetron motion, the delay between the damping of the magnetron and axial motions and the excitation of the ion cyclotron motion was varied over the period of the magnetron motion. The positions of the magnetron and cyclotron phase spots were chosen such that the angle between them with respect to the measurementtrap axis did not exceed a few degrees. This procedure reduced the shift in the ratio of the 163 Dy + and 163 Ho + ions due to the possible distortion of the ion-motion projection onto the detector to a level well below 10 −10 [30]. The cyclotron frequencies ν c of the 163 Dy + and 163 Ho + ions were measured alternately for several days. The total measurement period was divided in 34 approximately 5-hour periods. For each of them the ratio R 5hour of the cyclotron frequencies ν c of the 163 Dy + and 163 Ho + ions was obtained along with the inner and outer errors [34] by simultaneously fitting a fifth-order polynomial to the 163 Ho + frequency points and the same polynomial multiplied by a further fitted frequency ratio R 5hour to the 163 Dy + frequency points (see Fig. 3(a)). The final cyclotron-frequency ratio R is the weighted mean of the R 5hour ratios, where the inverse of the squared maxima of the inner and outer errors of the R 5hour ratios were taken as the weights to calculate R. The associated Birge ratio is 1.09. Fig. 3(b) shows the mass difference of 163 Ho and 163 Dy corresponding to the cyclotron-frequency ratios R 5hour . The final frequency ratio R with its statistical and systematic uncertainties as well as the corresponding mass difference of 163 Ho and 163 Dy are R=1.000 000 018 67(20 stat )(10 sys ) and ∆m=2833(30 stat )(15 sys ) eV/c 2 , respectively. The systematic uncertainty in the frequency-ratio determination originates from the anharmonicity of the trap potential, the inhomogeneity of the magnetic field, the distortion of the ion-motion projection onto the detector, and a possible presence of 163 Dy in the Ho-sample [30].
Our result for the atomic mass difference of 163 Ho and 163 Dy deviates by more than seven sigma experimental uncertainty from the accepted value of the Atomic-Mass-Evaluation AME 2012 [1] while being in perfect agreement with the microcalorimetric measurements: Q = 2800(50) eV [24] and Q = 2800(80) eV [8] (see Fig. 1) -the Q-values, which were not included in the AME 2012 [1]. Thus, on the level of the present accuracy there are no unexpected deviations due to systematic effects of cryogenic microcalorimetry or of the theoretical description of the spectrum. With the obtained Q-value and a foreseen number of acquired electron-capture events of 10 10 in the first phase of the ECHo experiment (ECHo-1k) it will be possible to reach a statistical sensitivity below 10 eV to the neutrino mass, which will drastically, i.e., by more than an order of magnitude, improve the present upper limit on the neutrino mass. For the determination of the electron-neutrino mass with sub-eV uncertainty, the Q-value must be determined with a substantially lower uncertainty, too. This independently measured Q-value on the eV level will remove any systematic uncertainties due to possible solid-state effects. Mass-difference measurements with correspondingly high accuracy will become possible with the realization of the PENTATRAP [37,38] and CHIP-TRAP experiments [39]. Also the existing FSU-TRAP is in principle capable of determining the Q-value of the EC in 163 Ho with an eV-uncertainty [13].
In summary, the atomic mass difference of 163 Ho and 163 Dy has been determined with the Penning-trap mass spectrometer SHIPTRAP with the novel PI-ICR technique. The measurement has yielded the value of 2833(30 stat )(15 sys ) eV/c 2 , in perfect agreement with the Q-values obtained with cryogenic microcalorimetry. It thus solves the puzzle in the determination of the Q-value in the EC in 163 Ho and allows for defining the scale of the experiments on the determination of the electron-neutrino mass from the electron capture in 163 Ho.