- Email: [email protected]
New limits from the Milano neutrino mass experiment with thermal microcalorimeters
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
New limits from the Milano neutrino mass experiment with thermal microcalorimeters$ M. Sistia,*, C. Arnaboldia, C. Brofferioa, G. Cerutia, O. Cremonesia, E. Fiorinia, A. Giulianib, B. Margesinc, L. Martenssona, A. Nucciottia, M. Pavana, G. Pessinaa, S. Pirroa, E. Previtalia, L. Somaa, M. Zenc Dipartimento di Fisica dell’Universita" di Milano-Bicocca and Sezione di Milano dell’INFN, Milano I-20126, Italy Dipartimento di Scienze Chimiche, Fisiche e Matematiche dell’Universita" d’Insubria I-22100 Como and Sezione di Milano dell’INFN, Milano I-20133, Italy c ITC-irst, Microsystems Division, Povo TN, I-38050, Italy a
b
Abstract In the Standard Model of electroweak interactions an important input parameter is still missing: the absolute value of the mass of one of the neutrinos. In this paper we report the final results of the Milano electron anti-neutrino mass experiment after having measured for about one year the beta spectrum of 187 Re with 10 AgReO4 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: 14.60.Pq; 23.40.Bw; 12.15.Ff; 0.7.05.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 Dm2n values. To assess the absolute neutrino mass $ This experiment has been supported in part by the Commission of European Communities under Contract HPRN-CT-2002-00322. *Corresponding author. Tel.: +39-02-6448-2331; fax: +3902-6448-2463. E-mail address: [email protected] (M. Sisti).
scale it is therefore important to carry out a direct measurement of mn ; 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 of the entire energy emitted in the decay, except that carried away by the neutrino.
2. The Milano experiment set-up The Milano group is performing an experiment with thermal microcalorimeters to carefully
0168-9002/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2003.11.273
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
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 if less 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 of 26 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 of sudden 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 of the noise of each 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 of about one month measurements are then analysed altogether.
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measure the b decay spectrum of 187 Re; which has the advantage of the lowest known transition energy. To compensate the intrinsic slowness of thermal detectors we operate arrays of 10 microcalorimeters. Our detectors are made of AgReO4 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 AgReO4 gives a decay rate of about 5:4 104 Hz=mg: A first array of 10 AgReO4 microcalorimeters was run at the end of year 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, CaF2 ; Ti, and NaCl. Therefore the detectors are exposed to the Rayleigh scattered 5:9 keV Ka X-rays of Mn and to the fluorescence Ka 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 of Roman lead, laterally displaced with respect to the detector holders. Several other improvements have been brought into the experimental set-up. First of all, we replaced one of the 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 of the 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
energy [keV]
126
0
Fig. 1. A sample one day measurement, after gain stability correction, showing the periodical exposure to the source.
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
3. 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 HOF ðoÞ it is necessary to know the signal in a zero noise condition, and the noise. Therefore the first step of the analysis is the creation, for each detector, of an average b pulse SðtÞ and of a 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 HOF 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 of any post-trigger secondary pulses (pile-up events), etc. The identification of secondary pulses with the smallest possible time separation is crucial in a neutrino mass experiment, to avoid deformation of the measured b spectrum: the best results are obtained searching for secondary pulses exceeding a threshold of few times the RMS noise after applying the optimal Wiener Filter (WF), whose transfer function HWF ðoÞ is given by HWF ðoÞpSðoÞ =ðjSðoÞj2 þ jNðoÞj2 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 of X-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 of the 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 Ka peak positions with a second order polynomial.
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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 of the optimally filtered pulses and the output of an 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 of various identified spurious pulses from all channels. The combined use of the ANN and of the 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 fth þ fpup þ fbck Þ#fdet ; where fth is the theoretical spectrum calculated by W. Buhring [3] for first forbidden unique b transitions, fpup pfth #fth is the pile-up spectrum, fbck is the unknown background, and fdet 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. fdet is assumed to be constant in energy and equal to a Gaussian with the FWHM as obtained by extrapolation at the b end-point of the 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 m2n% e are all free parameters of the fit. 2 The P fit procedure uses the estimator X ¼ 2 i ½Fi si si ln ðFi =si Þ ; where si are the experimental spectrum bins and Fi are counts predicted
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
Mn Kβ
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Ti Kα Ti Kβ
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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 of equal width. At the b end-point,
Cl Kβ
The new high statistics measurement started on June 2002 with a partially renewed array of 10 AgReO4 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 of 1:17 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
4.1. Detector response
Al Kα
4. Experimental data
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 of all 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 of 25:5 eV: The 10% to 90% risetime of the 8 detectors is in the range 340–680 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 of the entire array extrapolated at the energy of the b end-point ð2:46 keVÞ is 28:5 eV: Besides the Ka lines, and corresponding Kb ; produced by the fluorescence source, there are several other peaks due to fluorescence of the materials surrounding the detectors. One can recognize the M lines of Pb (at 2.35 and 2:44 keV) and the Cr Ka peak (at 5:41 keV); with smaller statistics, there are probably the fluorescence lines of K, Au, Sn. These peaks are not present when the source is inside the lead shield.
Al Kβ
by the model function F in the same bins. For the evaluation of the neutrino mass upper limit the Bayesian approach is used for non-physical regions (i.e. m2n% e o0). By varying both the upper—between 3 and 5 keV—and the lower— between 0.7 and 2:1 keV—limits of the 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 of uncertainties in the evaluation of m2n% e ; as well as of the end-point, are determined varying some of the 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 of the theoretical b spectrum. Finally, 187 Re half-life t1=2 is calculated by fitting the distribution of the time intervals Dt between two successive b decays, which is given by NðDtÞp expðrDtÞ; where rp1=t1=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 of less than 0.1% on the measured counting rate.
counts
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Fig. 2. Total X-ray calibration spectrum.
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ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
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contribute to about 0.2% of the peak broadening. For sake of simplicity, the Kurie plot is fit assuming an energy constant peak width as 2 ðEÞ at the obtained by extrapolation of DEFWHM 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 of the 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 of about 70 keV the attenuation length in AgReO4 is about 400 mm and the interactions are therefore uniformly distributed in the absorber. If the 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 of the incident photon and the energy of the escaping X-ray. Properly choosing the energy of the incident photon, the escape peak can be in the region of interest. We are planning an experiment using a 44 Ti ðt1=2 E62 yearsÞ source which emits g rays with an energy of 78 keV: from MonteCarlo simulation it seems possible to observe peaks at about 18, 17, and 9 keV due to the escape of Ka2 ; Ka1 ; and Kb Re X-rays respectively. The main difficulty will consist in the deconvolution of the intrinsic Lorentzian broadening of the Re X-ray line of about 42 eV to extract the detector response. 4.2. Experimental results
∆E FWHM [eV]
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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 Ka 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 of a 6 keV photon in AgReO4 is E3 mm; so all calibration X-rays do not penetrate much in the absorbers— the AgReO4 absorbers have linear dimensions of about 300 mm: Since AgReO4 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 of the 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 2 which can be described by DEFWHM ðEÞ ¼ a þ bE þ cE 2 : We attribute the linear term to statistical fluctuation in the thermalization in AgReO4 and the quadratic term to uncorrected gain instabilities (Fig. 3). The latter in particular
129
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 energy [keV]
Fig. 3. Energy dependence of the peak FWHM in the total calibration X-ray spectrum.
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 12.4. 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 of the b end-point)
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
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Fig. 5. Sum Kurie plot, where p and E are, respectively, the b momentum and kinetic energy, F ðZ; EÞ is the Coulomb factor and SðEÞ is the shape factor.
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 B6:2 106 187 Re-decays above the common energy threshold of 700 eV: The spectrum was fit in the energy interval 0.9–4 keV (see Section 2) and the w2 /DOF of the fit is 0.905. 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 of the time intervals between two successive b decays (see Section 2), we could precisely determine the 187 Re half-life, which was
-0.012 0.5
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Fig. 6. Experimental BEFS superimposed to the theoretical prediction for DEFWHM ¼ 30 eV:
found to be ½43:270:2ðstat:Þ70:1ðsyst:Þ 109 years. Here the statistical error is due to the uncertainties in the measurement of the 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 m2n% e is 1127207ðstat:Þ790ðsyst:Þ eV2 ; 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 of an 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 of the data due to the Beta Environmental Fine Structure (BEFS) in AgReO4 (Fig. 6). This important effect was first observed for metallic rhenium [4]. A quantitative analysis in terms of AgReO4 lattice structure is presently on the way.
5. Conclusions The limit on mn reported in this paper, even if not yet competitive to the limit of about 2 eV
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
obtained with spectrometers for 3 H b-decay [6], shows the potential of future bolometric measurements of the neutrino mass, which is further discussed in [5].
[2] [3] [4] [5]
References [1] A. Nucciotti, et al., in: F. Scott Porter, D. McCammon, M. Galeazzi, C.K. Stahle (Eds.), Proceedings of the 9th International Workshop on Low Temperature Detectors
[6]
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LTD-9, 2001, Madison, Wisconsin (USA), American Institute of Physics, Vol. 605, 2002, pp. 453. A. Alessandrello, et al., Nucl. Instr. and Meth. B 142 (1998) 163. W. Buhring, Nucl. Phys. 61 (1965) 190. F. Gatti, et al., Nature 397 (1999) 137. A. Nucciotti, et al., How to improve the sensitivity of future neutrino mass experiments with thermal calorimeters, Nucl. Instr. and Meth. A 2004, these Proceedings. J. Bonn, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 273; V. Lobashev, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 280.
Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
New limits from the Milano neutrino mass experiment with thermal microcalorimeters$ M. Sistia,*, C. Arnaboldia, C. Brofferioa, G. Cerutia, O. Cremonesia, E. Fiorinia, A. Giulianib, B. Margesinc, L. Martenssona, A. Nucciottia, M. Pavana, G. Pessinaa, S. Pirroa, E. Previtalia, L. Somaa, M. Zenc Dipartimento di Fisica dell’Universita" di Milano-Bicocca and Sezione di Milano dell’INFN, Milano I-20126, Italy Dipartimento di Scienze Chimiche, Fisiche e Matematiche dell’Universita" d’Insubria I-22100 Como and Sezione di Milano dell’INFN, Milano I-20133, Italy c ITC-irst, Microsystems Division, Povo TN, I-38050, Italy a
b
Abstract In the Standard Model of electroweak interactions an important input parameter is still missing: the absolute value of the mass of one of the neutrinos. In this paper we report the final results of the Milano electron anti-neutrino mass experiment after having measured for about one year the beta spectrum of 187 Re with 10 AgReO4 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: 14.60.Pq; 23.40.Bw; 12.15.Ff; 0.7.05.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 Dm2n values. To assess the absolute neutrino mass $ This experiment has been supported in part by the Commission of European Communities under Contract HPRN-CT-2002-00322. *Corresponding author. Tel.: +39-02-6448-2331; fax: +3902-6448-2463. E-mail address: [email protected] (M. Sisti).
scale it is therefore important to carry out a direct measurement of mn ; 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 of the entire energy emitted in the decay, except that carried away by the neutrino.
2. The Milano experiment set-up The Milano group is performing an experiment with thermal microcalorimeters to carefully
0168-9002/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2003.11.273
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
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 if less 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 of 26 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 of sudden 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 of the noise of each 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 of about one month measurements are then analysed altogether.
7
7
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5
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4
4
3
3
2
2
1
1
0.0
0.2
0.4 0.6 time [days]
0.8
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100 counts
energy [keV]
measure the b decay spectrum of 187 Re; which has the advantage of the lowest known transition energy. To compensate the intrinsic slowness of thermal detectors we operate arrays of 10 microcalorimeters. Our detectors are made of AgReO4 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 AgReO4 gives a decay rate of about 5:4 104 Hz=mg: A first array of 10 AgReO4 microcalorimeters was run at the end of year 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, CaF2 ; Ti, and NaCl. Therefore the detectors are exposed to the Rayleigh scattered 5:9 keV Ka X-rays of Mn and to the fluorescence Ka 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 of Roman lead, laterally displaced with respect to the detector holders. Several other improvements have been brought into the experimental set-up. First of all, we replaced one of the 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 of the 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
energy [keV]
126
0
Fig. 1. A sample one day measurement, after gain stability correction, showing the periodical exposure to the source.
ARTICLE IN PRESS M. Sisti et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 125–131
3. 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 HOF ðoÞ it is necessary to know the signal in a zero noise condition, and the noise. Therefore the first step of the analysis is the creation, for each detector, of an average b pulse SðtÞ and of a 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 HOF 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 of any post-trigger secondary pulses (pile-up events), etc. The identification of secondary pulses with the smallest possible time separation is crucial in a neutrino mass experiment, to avoid deformation of the measured b spectrum: the best results are obtained searching for secondary pulses exceeding a threshold of few times the RMS noise after applying the optimal Wiener Filter (WF), whose transfer function HWF ðoÞ is given by HWF ðoÞpSðoÞ =ðjSðoÞj2 þ jNðoÞj2 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 of X-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 of the 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 Ka peak positions with a second order polynomial.
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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 of the optimally filtered pulses and the output of an 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 of various identified spurious pulses from all channels. The combined use of the ANN and of the 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 fth þ fpup þ fbck Þ#fdet ; where fth is the theoretical spectrum calculated by W. Buhring [3] for first forbidden unique b transitions, fpup pfth #fth is the pile-up spectrum, fbck is the unknown background, and fdet 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. fdet is assumed to be constant in energy and equal to a Gaussian with the FWHM as obtained by extrapolation at the b end-point of the 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 m2n% e are all free parameters of the fit. 2 The P fit procedure uses the estimator X ¼ 2 i ½Fi si si ln ðFi =si Þ ; where si are the experimental spectrum bins and Fi are counts predicted
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Mn Kβ
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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 of equal width. At the b end-point,
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The new high statistics measurement started on June 2002 with a partially renewed array of 10 AgReO4 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 of 1:17 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
4.1. Detector response
Al Kα
4. Experimental data
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 of all 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 of 25:5 eV: The 10% to 90% risetime of the 8 detectors is in the range 340–680 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 of the entire array extrapolated at the energy of the b end-point ð2:46 keVÞ is 28:5 eV: Besides the Ka lines, and corresponding Kb ; produced by the fluorescence source, there are several other peaks due to fluorescence of the materials surrounding the detectors. One can recognize the M lines of Pb (at 2.35 and 2:44 keV) and the Cr Ka peak (at 5:41 keV); with smaller statistics, there are probably the fluorescence lines of K, Au, Sn. These peaks are not present when the source is inside the lead shield.
Al Kβ
by the model function F in the same bins. For the evaluation of the neutrino mass upper limit the Bayesian approach is used for non-physical regions (i.e. m2n% e o0). By varying both the upper—between 3 and 5 keV—and the lower— between 0.7 and 2:1 keV—limits of the 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 of uncertainties in the evaluation of m2n% e ; as well as of the end-point, are determined varying some of the 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 of the theoretical b spectrum. Finally, 187 Re half-life t1=2 is calculated by fitting the distribution of the time intervals Dt between two successive b decays, which is given by NðDtÞp expðrDtÞ; where rp1=t1=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 of less than 0.1% on the measured counting rate.
counts
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contribute to about 0.2% of the peak broadening. For sake of simplicity, the Kurie plot is fit assuming an energy constant peak width as 2 ðEÞ at the obtained by extrapolation of DEFWHM 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 of the 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 of about 70 keV the attenuation length in AgReO4 is about 400 mm and the interactions are therefore uniformly distributed in the absorber. If the 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 of the incident photon and the energy of the escaping X-ray. Properly choosing the energy of the incident photon, the escape peak can be in the region of interest. We are planning an experiment using a 44 Ti ðt1=2 E62 yearsÞ source which emits g rays with an energy of 78 keV: from MonteCarlo simulation it seems possible to observe peaks at about 18, 17, and 9 keV due to the escape of Ka2 ; Ka1 ; and Kb Re X-rays respectively. The main difficulty will consist in the deconvolution of the intrinsic Lorentzian broadening of the Re X-ray line of about 42 eV to extract the detector response. 4.2. Experimental results
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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 Ka 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 of a 6 keV photon in AgReO4 is E3 mm; so all calibration X-rays do not penetrate much in the absorbers— the AgReO4 absorbers have linear dimensions of about 300 mm: Since AgReO4 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 of the 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 2 which can be described by DEFWHM ðEÞ ¼ a þ bE þ cE 2 : We attribute the linear term to statistical fluctuation in the thermalization in AgReO4 and the quadratic term to uncorrected gain instabilities (Fig. 3). The latter in particular
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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 energy [keV]
Fig. 3. Energy dependence of the peak FWHM in the total calibration X-ray spectrum.
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 12.4. 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 of the b end-point)
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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 B6:2 106 187 Re-decays above the common energy threshold of 700 eV: The spectrum was fit in the energy interval 0.9–4 keV (see Section 2) and the w2 /DOF of the fit is 0.905. 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 of the time intervals between two successive b decays (see Section 2), we could precisely determine the 187 Re half-life, which was
-0.012 0.5
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Fig. 6. Experimental BEFS superimposed to the theoretical prediction for DEFWHM ¼ 30 eV:
found to be ½43:270:2ðstat:Þ70:1ðsyst:Þ 109 years. Here the statistical error is due to the uncertainties in the measurement of the 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 m2n% e is 1127207ðstat:Þ790ðsyst:Þ eV2 ; 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 of an 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 of the data due to the Beta Environmental Fine Structure (BEFS) in AgReO4 (Fig. 6). This important effect was first observed for metallic rhenium [4]. A quantitative analysis in terms of AgReO4 lattice structure is presently on the way.
5. Conclusions The limit on mn reported in this paper, even if not yet competitive to the limit of about 2 eV
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obtained with spectrometers for 3 H b-decay [6], shows the potential of future bolometric measurements of the neutrino mass, which is further discussed in [5].
[2] [3] [4] [5]
References [1] A. Nucciotti, et al., in: F. Scott Porter, D. McCammon, M. Galeazzi, C.K. Stahle (Eds.), Proceedings of the 9th International Workshop on Low Temperature Detectors
[6]
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LTD-9, 2001, Madison, Wisconsin (USA), American Institute of Physics, Vol. 605, 2002, pp. 453. A. Alessandrello, et al., Nucl. Instr. and Meth. B 142 (1998) 163. W. Buhring, Nucl. Phys. 61 (1965) 190. F. Gatti, et al., Nature 397 (1999) 137. A. Nucciotti, et al., How to improve the sensitivity of future neutrino mass experiments with thermal calorimeters, Nucl. Instr. and Meth. A 2004, these Proceedings. J. Bonn, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 273; V. Lobashev, et al., Nucl. Phys. B Proc. 91 (Suppl.) (2001) 280.