New Lower Limits on the Lifetime of Heavy Neutrino Radiative Decay
S. Cecchini, D. Centomo, G. Giacomelli, R. Giacomelli, M. Giorgini, L. Patrizii, V. Popa, C.G. Serbanuut
aa r X i v : . [ h e p - e x ] D ec New Lower Limits on the Lifetime of Heavy NeutrinoRadiative Decay
S. Cecchini a,b,c , D. Centomo a , G. Giacomelli a,b , R. Giacomelli b ,M. Giorgini a,b , L. Patrizii b , V. Popa d,1 , C.G. S¸erb˘anut¸ e,f a Dipartimento di Fisica dell’Universit`a di Bologna, I-40127, Bologna, Italy b INFN Sezione di Bologna, I-40127, Bologna, Italy c IASF/INAF, I-40129 Bologna, Italy d Institutul de S¸tiint¸e Spat¸iale, R-77125, Bucharest-M˘agurele, Romania e Dipartimento di Fisica Generale dell’Universit`a di Torino, I-10125, Torino, Italy f INFN Sezione di Torino, I-10125, Torino, Italy
Abstract
The data collected during the 2006 total solar eclipse are analyzed in the searchfor signals produced by a hypothetical radiative decay of massive neutrinos. In theabsence of the expected light pattern, we set lower limits for the massive neutrinocomponents proper lifetime. The reached sensitivity indicates that these are thebest limits obtainable with this method.
Key words:
Solar neutrinos, Radiative decays of massive neutrinos, Neutrino mass andmixing, Total solar eclipses, Image processing
PACS:
1. Introduction
The evidence for solar and atmospheric neutrino oscillations [1-5] impliesthat neutrinos have non-vanishing masses, and that neutrino flavour eigen-states are superpositions of mass eigenstates. D.W. Sciama pointed out thepossibility of ν radiative decay and the observational and theoretical con-sequences [6]. Massive neutrinos could undergo radiative decays; a possibledecay mode is ν → ν + γ . Email address: [email protected] (V. Popa) Corresponding author
Preprint submitted to Astroparticle Physics November 5, 2018 he neutrino radiative decay requires a non-vanishing neutrino magneticmoment; stringent existing limits ( µ ν < . · − µ B , [7]) apply to neu-trino flavour eigenstates and cannot be directly extended to dipole magneticmoments of neutrino mass eigenstates.“Semi-indirect” limits on neutrino radiative decay have been obtainedfrom solar and atmospheric neutrino data. The current interpretation ofexisting observations is that of neutrino flavour oscillations, but the contri-bution from neutrino decays as a secondary effect cannot be excluded. Fromthe SNO solar neutrino data, in ref. [8] a lower limit of τ /m > . · − s/eV was inferred ( τ and m are the proper lifetime and mass of a decayingneutrino, respectively). By combining available solar neutrino data, limits of τ /m > . · − s/eV [9], or, following different assumptions, τ /m > − s/eV [10] were obtained.Direct searches for radiative (anti)-neutrino decays were performed in thevicinity of nuclear reactors (e.g. [11], yielding limits between τ /m > − s/eV and τ /m > . m/m between 10 − and 0.1); the BorexinoCounting Test Facility at Gran Sasso yielded limits at the level of τ /m ∼ s/eV [12].Cowsik [13] pointed out that astronomical observations at x-ray, opticaland radio-frequencies could be used to derive bounds on radiative lifetimeson the basis of the non-observation of the final γ -ray. More recently boundshave been deduced from infra-red background measurements. Such lowerlimits are large (e.g. τ /m > . · s/eV [14]), but they are indirect andrather speculative.The Sun is a strong source of ν e neutrinos; the expected flux at the Earth(neglecting oscillation effects) is Φ ≃ · cm − s − . If radiative neutrinodecays occur yielding visible photons, they would not be observable due tothe very large amount of solar light. During a Total Solar Eclipse (TSE) theMoon screens the direct light from the Sun, while it is completely transparentto solar neutrinos. An experiment looking for such an effect would thus besensitive to neutrino decays occurring between the Moon and the Earth.In a pioneering experiment performed in occasion of the October 24, 1995TSE, a first search was made for visible photons emitted through radiativedecays of solar neutrinos during their flight between the Moon and the Earth[15]. The authors assumed that all neutrinos have masses of the order of feweV, ∆ m ≃ − eV , an energy of 860 keV and that all decays yield visiblephotons, which travel nearly in the same direction as the parent neutrinos.From the absence of a positive signal they estimated a lower limit on τ (972) which, in view of the assumptions made, is now not reliable.We made a search for solar neutrino radiative decays during the June21, 2002 TSE, in Zambia [16] after a first attempt during the 1999 eclipsein Romania [17]. The proper lower time limits (95% C.L.) obtained for the ν → ν + γ decays of left-handed neutrinos ranged from τ /m ≃
10 to ≃ s/eV, for 10 − eV < m < .
2. The experimental setup
Our main system used a Matsukov-Cassegrain telescope (Φ = 235 mm, f = 2350 mm) equipped with a fast 16 bit Mx916 CCD camera. The originalfindscope was substituted by the digital videocamera used for data takingduring the 2002 TSE.The night before the eclipse we aligned the system, adjusted the focus andtook calibration images of some standard luminosity stars (SAO99215 andSAO99802). In order to avoid the over-heating of the telescope and CCD andto minimize the possibility of focus and alignment changes, the equipmentwas protected with aluminum foils. A photograph of the set up is shown inFig. 1. Pictures of our set ups as well as data evaluation may be found inref. [18].The telescope movement was set to follow the Sun in order to have alwaysthe center of the acquired images coincident with the Sun center. Further-more, we implemented a special CCD exposure algorithm in order to adaptthe exposure times to the luminosity level of the Moon image. The ashenlight (the Sun’s light reflected by the Earth back to the Moon) is one of themain background sources in such searches, but it allows the reconstruction,frame by frame, of the real position of the Sun behind the Moon, eliminatingthe risk of pointing errors due to undesired movements of the telescope. The digital video-camera used in occasion of the 2002 TSE was a smallbackup system. It produced a digital film of the eclipse that could confirmour earlier results [16]. 3 igure 1: A photo of the main system deployed in the Libyan Sahara desert. The telescope,the CCD and the digital videocamera are visible. The aluminum foil reduced the heatingof the apparatus. The solar filter on the top of the telescope was used only during thepartiality.
A smaller Celestron C5 telescope equipped with a manually controlleddigital camera (Canon D20) was also used. We obtained 50 digital picturesof the eclipse.In this paper we discuss only the data collected with the main system,which has a much higher sensitivity than the back-up systems.
3. The experimental data
On the 29 th of March 2006 we observed the total solar eclipse from alocation (17 . ◦ East longitude, 24 . ◦ North latitude and 465 m altitude)in the Libyan Sahara desert, practically on the totality line and very closeto the maximum eclipse point. The time of the totality was close to noon,so the Sun and the Moon were near their highest positions in the sky (about65 . ◦ ), corresponding to the minimum light absorption by the atmosphere.The data collected by the main system consist in 212 digital pictures ofthe central part of the “dark” disk of the Moon. We used a 2 × igure 2: One of the frames recorded during the 2006 TSE. The center of the imagecorresponds to the position of the center of the Sun behind the Moon. angle of 1 . × . ×
256 square pixels); the total coveragewas 8 . ′ × . ′ (the Moon apparent diameter is 31 ′ ).Fig. 2 shows one of the frames recorded during the totality phase; detailson the Moon surface seen in the ashen light are visible.In Fig. 3 the image of the Moon observed in the light of the Sun iscompared with one of our frames (in ashen light). The corresponding areaon the Moon is marked by a rectangle. Differences are due to the differentMoon lighting conditions; some small scale details can be located in bothimages.Dark CCD frames, used to eliminate the effect of some possible “hotpixels”, were recorded before and after the totality phase. The telescope was aligned the night before the eclipse using the NorthStar (in the same observation session in which the calibration pictures weretaken), and it was kept in position till the end of the eclipse.5 igure 3: A full Moon picture (left) compared to one frame (right). The differences aredue to the different lighting conditions: in the light of the Sun and in the ashen light,respectively. The rectangle on the Moon shows the area covered by the frame measuredduring the eclipse.
We continuously checked the Sun position, starting at the moment of thefirst contact, using a grid applied on the screen of the digital videocamera.We used 7 luminous spots on the frames (small Moon craters reflectingthe ashen light) as “fiducial” points to reconstruct for each frame the relativeposition of the center of the Sun. Although the telescope movement was set tofollow the Sun, the human activity around our apparatus caused some groundoscillations that were corrected using the fiducial points. For the analysis weretained 195 frames in which all 7 points were clearly determined. Fig. 4ashows the displacement of the fiducial points due to the relative movement ofthe Moon with respect to the Sun. The arrow indicates the North direction(for the Moon). In Fig. 4b the variation of the “x” coordinate with time isshown. The origin of the time axis is at 12 hours and 13 minutes local time,about 50 seconds before the second contact of the eclipse. Small oscillationscaused by human activity in the vicinity of the instrument are visible; theireffect was removed in the off-line analysis.The superposition of the selected 195 frames is shown in Fig. 5. All lunarlandscape details are washed away; the light gradient is due mostly to the6
Figure 4: (a) Map of the successive positions in the CCD of 7 fiducial points on the Moonsurface during the totality phase of the eclipse. The arrow indicates the Moon Northdirection. (b) “x” coordinates of the fiducial points versus time during the eclipse. asymmetry of the coronal light diffracted by the Moon border and reachingthe instrument. The small darker spot visible in the picture (at the centerof the image, ∼ The exposure time for each frame was computed to have the maximumcontrast avoiding at the same time saturated pixels. The algorithm analyzedthe previous frame, and computed the exposure time for the next one so thatthe average luminosity was in the middle of the dynamical range of the 16bit CCD. The exposure time and other information concerning the telescopemovement were registered in the headers of each frame.For most frames the exposure time was 0 . ÷ . ∼ igure 5: The superposition of the 195 selected frames used in the analysis. The center ofthe image corresponds to the position of the center of the Sun. Figure 6: The exposure rate for each frame after the correction discussed in the text.
As mentioned in Sect. 2.1, the calibration of the main system was donethe night before the eclipse using two standard luminosity stars, SAO99215and SAO99802. We took 20 frames, 2 s exposure each, for the first star and 30frames with the same exposure for the second star (which is slightly fainter).After the removal of the dark frames the astro-photometric measurementsindicate that one ADU corresponds to 6 . ± .
4. Monte Carlo simulations
The analysis of the data obtained by this experiment required a detailedMonte Carlo simulation, including the neutrino production in the solar core,its propagation, decay, and the detection by our telescope on Earth. Sucha code was developed for the analysis of the previous data collected duringthe 2001 eclipse [16] and was adapted to the conditions of the 2006 observa-tions. The model is described in detail in ref. [19]; here the main ideas aresummarized and the parts relevant for the 2006 eclipse.Solar neutrino production was simulated according to the “BP2000” Stan-dard Solar Model (SSM) [20] available in numerical form in ref. [21]. Wechose a specific reaction/decay yielding neutrinos (both from the p-p and theCNO cycles); the neutrino energy and the position of its production pointin the core of the Sun were generated according to the SSM. As we are in-terested only in neutrinos that could undergo radiative decays between thearea of the Moon seen by our experiment and the Earth, a decay point wasgenerated and the arrival direction of the decay photon was chosen. Once the9 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -4 -3 -2 -1 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -4 -3 -2 -1 Figure 7: (a) The Monte Carlo probability to have a visible photon arriving to the telescopefrom the ν → ν + γ radiative decay, versus the ν mass, in the conditions of the 2006experiment (solid lines), compared to similar probabilities in the 2002 experiment (dashedlines). The dashed lines correspond from up to down to left-handed, Majorana and right-handed neutrinos. The differences in the probabilities for the 2006 simulation for different ν polarities are too small to be seen in the graph. (b) The same as in (a) for the ν → ν , + γ decays. geometry of the event is known, the photon energy is computed taking intoaccount the Lorentz boost, and for visible photons the probability density ofthe angular distribution, depending on whether the neutrino is a Dirac neu-trino, left or right-handed, or a Majorana neutrino. The number of visiblephotons is about 5 · − of the total spectrum; this quantity is integratedover all directions accessed by the instrument aperture.The interpretation of solar neutrino oscillation data in the simplest twoflavour model (assuming that the electron neutrino ν e is a superposition oftwo mass eigenstates ν and ν ) yields a square mass difference ∆ m , =6 · − eV [1]. This value was used in simulating ν → ν + γ decays.The probabilities that the photon emitted in the space between the Moonand the Earth is a visible photon and reaches the telescope are shown inFig. 7a, versus the ν mass (solid line). For comparison, we also show thecorresponding probabilities obtained in 2002 with a different system. In theconditions of the 2006 experiment, differences among neutrino polarities aresmaller and cannot be observed in the scale of Fig. 7.Assuming a mixing among all 3 mass eigenstates with ∆ m , ≃ ∆ m , =2 . · − eV (as known from atmospheric neutrino [2, 3, 4] and long baselineoscillation experiments [5]), ν → ν + γ and ν → ν + γ decays shouldbehave in the same way. The resulting probabilities are shown in Fig. 7b.10he notation of the lines is as in Fig. 7a.The ν → ν + γ decays should produce a spot of light coincident withthe center of the Sun behind the Moon disk, about 60” large, while the signalfrom the ν → ν , + γ decays would consists of light rings about 20” thick,with diameters of about 200” and 250”, also centered in the Sun.
5. Data analysis
The search for ν → ν + γ and ν → ν , + γ signatures in the framesrecorded during the 2006 total solar eclipse is based on the wavelet decom-position of the compound image, shown in Fig. 5. We recall that this imageis a superposition of 195 selected 16 bit frames recorded during the TSE andaligned with respect to the center of the Sun position behind the Moon. Asin the case of the 2002 eclipse [16] we chose the Haar wavelet basis [22]. The n -order term of the decomposition is obtained by dividing the N × N pixels image in squares of N/ n × N/ n pixels and averaging the luminosity in eachsquare; the averages are then subtracted and the resulting image, the n -orderresidual, can be used to obtain the ( n + 1)-order term. Each decompositionterm is an image that enhances the features on the corresponding scale, whilethe residuals yield information for smaller dimension scales.The decay signal is searched for by averaging the luminosity of the imagesover concentric “rings” centered in the Sun. As the wavelet analysis requiresa dyadic dimension (the number of pixels has to be an integer power of 2),we considered four pixels adjacent to the image center as “central” and thenaveraged the obtained luminosity profiles.The image in Fig. 5 is 256 ×
256 pixels ; we used up to the 7 th order inthe wavelet decomposition. Fig. 8 shows the luminosity distribution for the7 th order residual, that may yield information on the smaller scale effects inthe original image. The profile is consistent with statistical noise; the largeramplitudes near the center of the Sun and near the edges of the image aredue to a smaller number of pixels available for the averaging.None of the image decomposition terms or residuals shows structures aswould be expected from solar neutrino radiative decays; thus a possible signalcannot be larger than the statistical fluctuations.
6. Results and discussions
The expected scale of the decay signal (few tens of arcseconds) suggeststhat the wavelet term most sensitive to ν → ν + γ and ν → ν , + γ decays11 Figure 8: Luminosity profile of the 7 th residual from the wavelet decomposition of thecentral part of the Moon image in Fig. 5. should be the 5 th order, with a typical scale of about 16”. The number ofvisible photons originating from solar neutrino radiative decays that couldbe recorded by the telescope CCD may be computed as N γ = P Φ (2 , S M t obs (cid:16) − e h tME i τ (cid:17) e − tSMτ (2 , , (1)where P is the mass-dependent probability shown in Figs. 7a,b and Φ (2 , represents the flux of ν or ν solar neutrinos at the Earth.Φ = Φ ν sin θ Φ = Φ ν sin θ , (2)where Φ ν ≃ · cm − s − is the expected solar neutrino flux at the Earth(neglecting oscillations) and θ is the mixing angle in the two flavour ap-proximation. For 3 neutrino flavours the mixing angle θ in uncertain; in ourcalculations we used sin θ = 0 .
1. If one used 0.06 as the 95% C.L. quotedby SNO [1], there would be only a slight reduction of sensitivity, while thereduction would be considerable in the case of sin θ = 0 .
02 [1, 7]. In Eq.1 S M is the area on the Moon surface covered by our observations, t obs is thetotal acquisition time, h t ME i is the average travel time of the neutrinos inthe observational cone from the Moon to the Earth (assuming that the decaypoint is uniformly distributed along that distance h t ME i is about one third12 -4 -3 -2 -1 -4 -3 -2 -1 Figure 9: (a) 95% C.L. lower limits for the ν proper lifetime. The differences betweendifferent polarization states cannot be seen at this scale. (b) 95% C.L. lower limits forthe ν proper lifetime, assuming sin θ = 0 .
1. The lines correspond from up to down toleft-handed, Majorana and right-handed neutrinos. of the flying time [16]), t SM is the flight time from the Sun to the Moon and τ (2 , the lifetime of ν and ν neutrino mass higher states. All time variablesin Eq. 1 are defined in the laboratory frame of reference.No structure compatible with ν or ν radiative decays was found in ouranalysis; lower limits for the lifetimes of the heavy neutrino componentswere obtained. The number of photons produced through radiative decaysbetween the Moon and the Earth reaching our detector is N γ ≤ σ T (95%C.L.), where σ T is the standard deviation of the luminosity of the 5 th termin the wavelet decomposition of the data. The 95% C.L. lower limits forthe ν proper lifetimes are shown in Fig. 9a. Although they were computedassuming three possible ν polarizations, the results are so close that cannotbe separated on the graph. For the ν proper lifetimes, the 95% C.L. upperlimits, computed assuming sin θ = 0 .
1, are shown in Fig. 9b. The solid linecorresponds to left-handed Dirac neutrinos, the dash-dotted line to Majorananeutrinos and the dashed line to right-handed Dirac neutrinos.
7. Conclusions
The analysis of 195 frames recorded in occasion of the 26 th of March 2006total solar eclipse in the Libyan Sahara desert did not evidence any signal13ompatible with the Monte Carlo predictions for the radiative decays of theheavier components of solar neutrinos [19].For ν → ν + γ radiative decay the 95% C.L. lower lifetime limits arein the range 10 ÷ s, for neutrino masses 10 − < m ν < . ÷ ν → ν , + γ , but the limits are tentativesince the mixing angle θ is still uncertain.The limits mentioned above are obtained from the fifth order wavelet termof the summed image of Fig. 5. The detection of the ashen light combinedwith the negative result prove that the searched signal should be fainter thanthe ashen light itself; we thus can state that the limits presented in this paperare the best obtainable using this technique, since there is no way to avoidthe ashen light background. Acknowledgments
We would like to acknowledge many colleagues for useful comments and dis-cussions. The experiment was funded by the University and INFN Section ofBologna. We acknowledge also the support from the Italian Institute of Culture ofTripoli. The analysis was partially funded under CNCSIS Contract 539/2009. Weare grateful to the organizers of the SPSE 2006 event for their efforts that allowedto perform our experiment. Special thanks are due to the Winzrik Group and tothe Libyan Air Force for their assistance.
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