New limits from the Milano neutrino mass experiment with thermal microcalorimeters $

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1 Nuclear Instruments and Methods in Physics Research A 520 (2004) New limits from the Milano neutrino mass experiment with thermal microcalorimeters $ M. Sisti a, *, C. Arnaboldi a, C. Brofferio a, G. Ceruti a, O. Cremonesi a, E. Fiorini a, A. Giuliani b, B. Margesin c, L. Martensson a, A. Nucciotti a, M. Pavan a, G. Pessina a, S. Pirro a, E. Previtali a, L. Soma a, M. Zen c a Dipartimento di Fisica dell Universit"a di Milano-Bicocca and Sezione di Milano dell INFN, Milano I-20126, Italy b Dipartimento di Scienze Chimiche, Fisiche e Matematiche dell Universit "a d Insubria I Como and Sezione di Milano dell INFN, Milano I-20133, Italy c ITC-irst, Microsystems Division, Povo TN, I-38050, Italy Abstract In the Standard Model ofelectroweak interactions an important input parameter is still missing: the absolute value of the mass ofone ofthe neutrinos. In this paper we report the final results ofthe Milano electron anti-neutrino mass experiment after having measured for about one year the beta spectrum of 187 Re with 10 AgReO 4 microcalorimeters. We describe the experimental set-up, the detector performance and the measuring conditions. We present the updated limit on the electron anti-neutrino mass which is the most stringent so far obtained with thermal detectors. We also give the most precise estimates for the 187 Re transition energy and lifetime. r 2003 Elsevier B.V. All rights reserved. PACS: Pq; Bw; Ff; t Keywords: Neutrino mass; Thermal detectors; Beta decay; 187 Re 1. Introduction Recent exciting results from solar and atmospheric neutrino experiments prove that neutrinos are indeed massive particles. On the other hand, neutrino flavour oscillations are sensitive only to Dm 2 n values. To assess the absolute neutrino mass scale it is therefore important to carry out a direct measurement of m n ; by studying the kinematics of nuclear b decay. Calorimetric techniques, where the b source is contained in the detector, are quite appealing in this respect, since they allow the measurement ofthe entire energy emitted in the decay, except that carried away by the neutrino. $ This experiment has been supported in part by the Commission ofeuropean Communities under Contract HPRN-CT *Corresponding author. Tel.: ; fax: address: monica.sisti@mib.infn.it (M. Sisti). 2. The Milano experiment set-up The Milano group is performing an experiment with thermal microcalorimeters to carefully /$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi: /j.nima

2 126 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) measure the b decay spectrum of 187 Re; which has the advantage ofthe lowest known transition energy. To compensate the intrinsic slowness of thermal detectors we operate arrays of10 microcalorimeters. Our detectors are made ofagreo 4 absorbers, with masses ranging from 250 to 300 mg to avoid event pile-up, coupled to silicon implanted thermistors. The natural fraction of 187 Re in AgReO 4 gives a decay rate ofabout 5: Hz=mg: A first array of10 AgReO 4 microcalorimeters was run at the end ofyear 2000 and the results were reported in Ref. [1]. The set-up for the new experiment is almost identical to the one described in Ref. [1]. Special care has been put in improving the purpose-built multi-line fluorescence source used for the periodical calibration of the energy scale and for the monitoring of the stability and the performance of all detectors. It consists of two primary 5 mci 55 Fe sources irradiating two composite targets, containing Al, CaF 2 ; Ti, and NaCl. Therefore the detectors are exposed to the Rayleigh scattered 5:9 kev K a X-rays ofmn and to the fluorescence K a X-rays at 1.5, 2.6, 3.7, and 4:5 kev excited in Al, Cl, Ca, and Ti, respectively. To shield the internalbremsstrahlung radiation accompanying 55 Fe E.C. decay which was producing an intense background in the first high statistics measurement reported in Ref. [1] the 55 Fe sources are mounted on a half-cylinder, made out of Roman lead, which has the lowest 210 Pb activity (p4 mbq=kg [2]). When acquiring pure b decay signals, the half-cylinder is moved to fit inside a massive shield, also made out ofroman lead, laterally displaced with respect to the detector holders. Several other improvements have been brought into the experimental set-up. First ofall, we replaced one ofthe refrigerator 1 K-pot needle valves by a fixed impedance. Then we constructed a more compact circuit for the electrical connection between the load resistors ofthe detector biassing network and the microcalorimeters, to diminish wire vibrations. As a consequence, the detectors showed a much reduced sensitivity to microphonic noise and a faster time response. A completely new acquisition system was also prepared. A VXI data acquisition system (DAQ) based on a 16-bit 16-channel transient digitizer capable of 100 ks=s per channel acquires asynchronously the different channels and saves to disk every triggered pulse even ifless than one record length apart. For the experiment described here, the chosen record length is 2048 channels the first 256 used as pre-trigger with a time base of26 ms; each pulse is then 53 ms long. The analog discriminator is set to have a 40 ms non-paralyzing dead time to prevent DAQ breakdown in case ofsudden noise bursts. The acquisition sequence starts with 25 min of X-ray source calibration followed by 2 h of pure b decay measurement and then goes on cycling (see Fig. 1). The DAQ controls the motor moving the source holder and properly flags the events acquired in the source-open and source-closed periods. In order to monitor the evolution ofthe noise ofeach detector during the entire measurement, random triggers are collected every 10 s during source-open periods and every 60 s during source-closed periods. Measurements are on a one-day basis (for dilution refrigerator daily service) and have always to finish with a source-open period, to be able to eventually apply off-line gain drift corrections. Typically blocks ofabout one month measurements are then analysed altogether time [days] 100 counts Fig. 1. A sample one day measurement, after gain stability correction, showing the periodical exposure to the source

3 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) Data analysis The off-line data analysis extensively applies the optimal filter (OF) technique, which maximizes the signal-to-noise ratio to get the best estimate of the pulse amplitude. To evaluate the OF transfer function H OF ðoþ it is necessary to know the signal in a zero noise condition, and the noise. Therefore the first step ofthe analysis is the creation, for each detector, ofan average b pulse SðtÞ and ofa noise power spectrum NðoÞ from all the source-open and the source-closed periods. This procedure is repeated for each one-day measurement of a block to obtain an overall average. The OF transfer function is then given by H OF ðoþpsðoþ =NðoÞ: The next step is the calculation of n-tuples (one for every measurement) from each digitized pulse. They contain all useful pulse parameters, like the channel number, the absolute time, the OF amplitude, the signal rise and decay times, some shape factors (see later), the amplitude and delay ofany post-trigger secondary pulses (pile-up events), etc. The identification ofsecondary pulses with the smallest possible time separation is crucial in a neutrino mass experiment, to avoid deformation ofthe measured b spectrum: the best results are obtained searching for secondary pulses exceeding a threshold offew times the RMS noise after applying the optimal Wiener Filter (WF), whose transfer function H WF ðoþ is given by H WF ðoþpsðoþ =ðjsðoþj 2 þjnðoþj 2 Þ: Afterwards the n-tuples are divided into single channel ones requiring a detector multiplicity o4 for each event in order to reject electrical disturbances triggering more detectors at once. The next step is the gain drift correction by means ofx-ray peak position stabilization. The higher energy X-rays (Al and Cl lines are never employed in this procedure) are then used to correct any system instabilities by fitting the time behaviour ofthe peaks and stabilizing them to straight lines. The result is shown in Fig. 1. Finally source-open and source-closed n-tuples (as tagged by the acquisition) are generated for each channel. The source-open n-tuples serve to create X-ray spectra, whose energy scale is then obtained by fitting the Al, Cl, Ca, and Ti K a peak positions with a second order polynomial. The source-closed n-tuples are used to create the b spectra. This is the most delicate point, because it is very important to carefully select only true b decay pulses and not to apply cuts which could differently weight the various energy bins of the Kurie plot. For this purpose several pulse shape parameters are calculated by comparison with the average pulse SðtÞ: the most sensitive parameters are the root mean square deviation ofthe optimally filtered pulses and the output ofan Artificial Neuronal Network (ANN). The ANN is a 3-layered network whose 60 input nodes are fed with 600 pulse samples averaged to 60 and taken in a window which extends from 1:5 ms before to 14 ms after the pulse starting point. One single ANN is used and is trained with good b pulses and a collection ofvarious identified spurious pulses from all channels. The combined use of the ANN and ofthe pile-up identification algorithm in most cases rejects all spurious pulses (silicon thermistor hits, electrical disturbances, etc.) and removes pileup events with a time separation as small as about 3 rise times, with an efficiency better than 99%. Once the pure 187 Re decays are selected, calibrated b spectra are generated for each detector using the energy scale previously calculated from the source-open periods. The spectra are then added to create the sum b spectrum. The b spectrum is fit with the function F ¼ ð f th þ f pup þ f bck Þ#f det ; where f th is the theoretical spectrum calculated by W. Buhring [3] for first forbidden unique b transitions, f pup pf th #f th is the pile-up spectrum, f bck is the unknown background, and f det is the detector energy response function. For the present data, the background is typically supposed to be constant, as it appears to be above 5 kev (Fig. 4), where the contribution from the pile-up spectrum is not present. f det is assumed to be constant in energy and equal to a Gaussian with the FWHM as obtained by extrapolation at the b end-point ofthe X-ray peak FWHMs (see Section 3.1). The b end-point, the b- and pile-up-spectrum normalizations, the background level, and the squared electron antineutrino mass m 2 %n e are all free parameters of the fit. The fit procedure uses the estimator X 2 ¼ 2 P i ½F i s i s i ln ðf i =s i ÞŠ; where s i are the experimental spectrum bins and F i are counts predicted

4 128 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) by the model function F in the same bins. For the evaluation ofthe neutrino mass upper limit the Bayesian approach is used for non-physical regions (i.e. m 2 %n e o0). By varying both the upper between 3 and 5 kev and the lower between 0.7 and 2:1 kev limits ofthe fitting interval, all fit parameters remained stable within the errors, thus confirming the good description of the data given by the function F: Systematic sources ofuncertainties in the evaluation of m 2 %n e ; as well as ofthe end-point, are determined varying some ofthe fit hypotheses: (i) the detector energy resolution (see Section 3.1); (ii) the detector response function (see Section 3.1); (iii) the background shape below the b spectrum; and (iv) the parametrization ofthe theoretical b spectrum. Finally, 187 Re half-life t 1=2 is calculated by fitting the distribution ofthe time intervals Dt between two successive b decays, which is given by NðDtÞp expð rdtþ; where rp1=t 1=2 is the decay rate. To obtain this distribution source-closed n-tuples without pile-up rejection are created. Since the DAQ saves in a separate record the event which caused pile-up, provided it is separated by more than 40 ms; intervals DtX40 ms are correctly counted. Nevertheless a correction must be introduced to account for the fixed 40 ms dead time: a Monte Carlo simulation gives a correction ofless than 0.1% on the measured counting rate. 4. Experimental data The new high statistics measurement started on June 2002 with a partially renewed array of 10 AgReO 4 microcalorimeters, and was stopped on April 2003 due to a problem in the fluorescence source moving mechanism. The data from two detectors, with poorer resolution, are not included in our statistics, so the effective total mass of the array is 2:174 mg; for a 187 Re activity of1:17 Hz: The total live time adds up to 210 days, 42 of which have been devoted to the periodic calibrations while 168 days correspond to pure b acquisition. The total efficiency of this run is therefore of 67%, which includes daily servicing to our refrigerator (B2 h a day), calibration test measurements and a few lab power failures; the pure b acquisition efficiency is of 54%. The final beta and calibration spectra obtained from the sum ofall 8 detectors correspond to 8751 h mg and 2168 h mg; respectively. The performance of the detectors were quite stable during the run. The FWHM resolution at 1:5 kev in the single detector final spectra ranges from 21.3 to 29:3 ev; with an average of25:5 ev: The 10% to 90% risetime ofthe 8 detectors is in the range ms; with an average value of 492 ms: Fig. 2 shows the X-ray calibration spectrum obtained from the sum of the 8 working detectors. The FWHM resolution ofthe entire array extrapolated at the energy ofthe b end-point ð2:46 kevþ is 28:5 ev: Besides the K a lines, and corresponding K b ; produced by the fluorescence source, there are several other peaks due to fluorescence ofthe materials surrounding the detectors. One can recognize the M lines ofpb (at 2.35 and 2:44 kev) and the Cr K a peak (at 5:41 kev); with smaller statistics, there are probably the fluorescence lines ofk, Au, Sn. These peaks are not present when the source is inside the lead shield Detector response All X-ray peaks show tails on the low energy side and cannot be fit by a symmetric Gaussian (Fig. 2). A possible way to satisfactorily reproduce the peak shape is to fit with two symmetric Gaussians ofequal width. At the b end-point, counts Al Kα Al Kβ Pb M Cl Kα Cl Kβ Ca Kα Ca Kβ Ti Kα Ti Kβ Cr Kα Mn Kα Fig. 2. Total X-ray calibration spectrum. Mn Kβ

5 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) the two symmetric Gaussians are separated by 37 ev; the area ratio between the left and the right one being 3.4%. With this detector response function, the displacement of the Cl K a line from its nominal position in the sum spectrum is 0:5 ev: Other fit solutions, for example a symmetric Gaussian with exponential tails, are presently under study. A physical motivation for such a behaviour is not yet known. The attenuation length ofa 6 kev photon in AgReO 4 is E3 mm; so all calibration X-rays do not penetrate much in the absorbers the AgReO 4 absorbers have linear dimensions of about 300 mm: Since AgReO 4 single crystals present quite rough surfaces and they are slightly hygroscopic when exposed too long to air, a yellowish patina forms which can be removed by ethanol the peak shape could reflect a surface effect and not a detector characteristics. Therefore electrons from 187 Re b-decay, which are emitted all over the volume, could in principle still give a pure Gaussian response. The fit ofthe Kurie plot is then made under both assumptions: a single symmetric Gaussian and two symmetric Gaussians with distance and area ratio as explained before. The differences in the fit results are included in the quoted systematic errors (see Section 2). Moreover the peak FWHMs have an energy dependency which can be described by DEFWHM 2 ðeþ ¼ a þ be þ ce 2 : We attribute the linear term to statistical fluctuation in the thermalization in AgReO 4 and the quadratic term to uncorrected gain instabilities (Fig. 3). The latter in particular E FWHM 2 [ev 2 ] Fig. 3. Energy dependence ofthe peak FWHM in the total calibration X-ray spectrum. E FWHM [ev] contribute to about 0.2% ofthe peak broadening. For sake ofsimplicity, the Kurie plot is fit assuming an energy constant peak width as obtained by extrapolation of DEFWHM 2 ðeþ at the b end-point: the effect of this simplification has been tested by Monte Carlo simulations and the estimated uncertainty is included in the systematic errors (see Section 2). We have devised a possible tool to establish the true detector response to electrons from 187 Re b decay: it consists in the use ofthe X-ray escape process. In such a process, a photon with energy above the Re K-edge at 71:7 kev undergo a photoelectric interaction on a K Re electron: for an energy ofabout 70 kev the attenuation length in AgReO 4 is about 400 mm and the interactions are therefore uniformly distributed in the absorber. Ifthe Re K X-ray, emitted while filling the vacancy left over by the photoelectric effect, exits the absorber, one observes a so-called escape peak at an energy equal to the difference between the energy ofthe incident photon and the energy of the escaping X-ray. Properly choosing the energy ofthe incident photon, the escape peak can be in the region ofinterest. We are planning an experiment using a 44 Ti ðt 1=2 E62 yearsþ source which emits g rays with an energy of78 kev: from MonteCarlo simulation it seems possible to observe peaks at about 18, 17, and 9 kev due to the escape ofk a2 ; K a1 ; and K b Re X-rays respectively. The main difficulty will consist in the deconvolution ofthe intrinsic Lorentzian broadening ofthe Re X-ray line ofabout 42 ev to extract the detector response Experimental results The background level achieved in this run is practically constant at 0:007 c=kev=h up to 20 kev; thus demonstrating the efficiency of the new source shield. In the 30 ev (B one resolution width) below the 187 Re end-point, the ratio between the b decay signal and the background fluctuations is The lower curve of Fig. 4 shows the 2003 background just above the b endpoint. From this figure it is possible to see the contribution of 187 Re event pile-up, which extends up to B5 kev (twice the energy ofthe b end-point)

6 130 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) counts/kev/h RUN 9 RUN Re β spectrum fit Fig. 4. Background in the 2000 and 2003 measurements. N(E) pef(z,e)s(e) N(E) pef(z,e)s(e) and the flat residual background mainly caused by cosmic rays and environmental radioactivity. The final Kurie plot resulting from the sum of the 8 detectors is shown in Fig. 5. It corresponds to B6: Re-decays above the common energy threshold of700 ev: The spectrum was fit in the energy interval kev (see Section 2) and the w 2 /DOF ofthe fit is The preliminary measured value for the end-point is 2465:370:5ðstat:Þ71:6ðsyst:Þ ev: In the chosen fitting interval, the systematic error is determined by the uncertainties in the energy resolution, in the detector response function, and in the shape of the background below the b spectrum. By fitting the distribution ofthe time intervals between two successive b decays (see Section 2), we could precisely determine the 187 Re half-life, which was fit residuals Fig. 5. Sum Kurie plot, where p and E are, respectively, the b momentum and kinetic energy, FðZ; EÞ is the Coulomb factor and SðEÞ is the shape factor. fit residuals found to be ½43:270:2ðstat:Þ70:1ðsyst:ÞŠ 10 9 years. Here the statistical error is due to the uncertainties in the measurement ofthe mass of the absorbers and the systematic error is due to the uncertainties in the pile-up discrimination. The values for the end-point energy and for the half-life are the most precise existing in the literature. The latter has considerable impact in geochronology. The squared electron antineutrino mass m 2 %n e is ðstat:Þ790ðsyst:Þ ev 2 ; where the systematic error has the same origin as for the endpoint energy quoted above. The 90% C.L. upper limit to the electron antineutrino mass is 15 ev: This result is in agreement with the expected sensitivity deduced from a Monte Carlo simulation ofan experiment with the same statistical significance as our data set [5]. The fit residuals in the energy interval between 470 ev (the common energy threshold for 7 of the 8 detectors) and 1:3 kev show a clear evidence of an oscillatory modulation ofthe data due to the Beta Environmental Fine Structure (BEFS) in AgReO 4 (Fig. 6). This important effect was first observed for metallic rhenium [4]. A quantitative analysis in terms ofagreo 4 lattice structure is presently on the way. 5. Conclusions Fig. 6. Experimental BEFS superimposed to the theoretical prediction for DE FWHM ¼ 30 ev: The limit on m n reported in this paper, even if not yet competitive to the limit ofabout 2 ev

7 M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) obtained with spectrometers for 3 H b-decay [6], shows the potential offuture bolometric measurements ofthe neutrino mass, which is further discussed in [5]. References [1] A. Nucciotti, et al., in: F. Scott Porter, D. McCammon, M. Galeazzi, C.K. Stahle (Eds.), Proceedings ofthe 9th International Workshop on Low Temperature Detectors LTD-9, 2001, Madison, Wisconsin (USA), American Institute ofphysics, Vol. 605, 2002, pp [2] A. Alessandrello, et al., Nucl. Instr. and Meth. B 142 (1998) 163. [3] W. Buhring, Nucl. Phys. 61 (1965) 190. [4] F. Gatti, et al., Nature 397 (1999) 137. [5] A. Nucciotti, et al., How to improve the sensitivity offuture neutrino mass experiments with thermal calorimeters, Nucl. Instr. and Meth. A 2004, these Proceedings. [6] J. Bonn, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 273; V. Lobashev, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 280.