Week 9: Lecture 43: Double Beta Decay (DBD) and Neutrinoless DBD (NDBD) – Part 1

So this is the first of two lectures on double beta decay and nutrinoless double beta decay. So this is part one of that. So uh what is shown here is the uh in italics uh that I will talk about in the next lecture. So in this lecture I will uh look at the motivation for studying neutralless doublebdk uh and what are the strategies used for such measurements u and which nuclei of course can be studied. So the idea is that the the main goal of the uh double neutrinus double beta decay is of course to find out if the neutrino is its own antiparticle. Namely is it a mayorana particle or not. So it goes like this. uh if you have a nucleus of mass number A and proton number zed then it can decay to a mass number A but a proton number which is Z +2 two betas two negatively charged beta particles are emitted and then there are two anti-utrinos of the electron type so this is the normal uh leptton conserving uh double beta DK uh this minus should not be Here this is okay. On the other hand, if the nutrino is its own antiparticle, it's a marona particle, then you can have a situation where you have only two betas and nothing else. So no neutrinos are emitted. So the virtual uh neutrino that is emitted uh in this uh process is also absorbed by the nucleus and that is of course to do with the uh it is related to the helicity of these nutrinos. So of course it is uh related to the effective mass of the neutrino squared. Okay. So how do you look for this? So the scheme is given here. So you have a nucleus AZ and you're looking for such a decay. Uh this is the Q value for that reaction. And ideally you this uh intermediate state Z + 1 A should be above this so that this decay is forbidden. Only virtual transitions are of course possible. and then it comes to this. So a real decay to this is uh energetically disallowed and that would be best for looking for such very rare decays. Uh what you look for of course in the in this lepton number violating double BTDK in case the neutrino is its own antiparticle is that you have the normal 2 beta 2 neutrino decay spectrum. Okay. So this is the sum energy of the two electrons plotted as a function of the counts let's say in some energy bin. Uh so this is a continuum spectrum. Uh and then you have a peak if this lepton violating uh double beta decay process is there. So the so-called neutrinoless double beta decay then you would see a peak at the end point. Okay. The sum energy of these two betas would correspond to the Q value of this. Uh so of course you might you might you can see that uh if for instance you have a certain energy resolution then this the width of this peak uh is given by that resolution. Uh on the other hand if you have a poor resolution detector then this spreads out and so you got a broad peak and so you can get the tail of this contributing here. So ideally you you should have a very good resolution uh detector number one. Also if you can identify these two beta particles that are coming out and measure their let's say uh angles measure their momenta then of course you have one more handle to reduce the background that might come in uh into play when you're looking for such a rare process. uh this double beta decay was was uh first talked about by Maria Meyer who in fact uh this is the 1935 paper where she talks about double beta disintegration. So that's the normal uh 2 beta 2 neutrino decay that she's talking about. uh Mayorana considered the possibility that since the nutrino is a neutral particle. By the way, this had not yet been detected but had been proposed by Pi and then a theory of weak interactions was written down by Enrio Fermy in fact his classmate. Uh he wrote a paper saying that what is the possibility? So when when Fermy wrote his paper he of course assumed that the neutrino is a uh is to be represented by a four component spinner uh corresponding to spin up spin down and it's also it's antiparticle whereas my considered the possibility that since the nutrino is a neutral particle is it possible that it is its own antiparticle so then the description becomes simpler then it's only spin up and spin down so it's a two component spinner instead of a four component dra spinner. So this is the reference to this uh 1937 and later uh furry uh I don't know how it's exactly pronounced but uh he wrote a paper about a couple of years later on the transition probabilities in double beta disintegration where he also took into account the possibility of nutrinoless double beta decay uh as uh envisaged or as some something that can happen if the nutrino you know is its own 90 particle. So this is a brief uh uh you know uh history of the references. Uh there are other papers as well but these are the key ones. Okay. So the double beta decay is of course a second order process and the nutrino less double beta decay is a second order process where a virtual neutrino emitted by another nucleon uh is absorbed by another nucleon and then the energy is released is given to the two beta particles. Uh the nutrinous double beta dk is forbidden in the standard model. Uh so since uh new e is not the same as new e bar uh that's you would call that a direct particle. However, if new e is the same as new e bar then it's a marona particle and then this process is allowed. So if you were to measure this, this would tell you whether the nutrino is a marona particle or a direct particle. So if you find that there is nutrino double beta decay, then it's a marona particle. Of course, if you don't see this, it doesn't tell you whether it is not a marana particle. Okay, it just it means that you haven't found it at the experimental level. Uh but it could still be there. uh since virtual emission and absorption of neutino is governed by different helicities this amplitude is of course proportional to m new. So the width for this the partial width for this decay which is the 2 beta 0 neutrino decay is proportional to the phase space since there are only two particles involved it is uh Q value to the^ of 5 Q to the^ of 5 just as in the normal first order beta DK okay there there are also two particles in the final state the beta and the neutrino and that is also proportional to Q to the 5. Then there is a nuclear matrix element which is the overlap between the initial state and the final state which is Z +2 the nucleus and then something proportional to MU^² because of course in the uh in the picture of quantum field theory the nutrino that is emitted also is absorbed and that is as I said proportional to mu squar because of the helicity factor. Now the nuclear matrix element of course there are uncertainties up to about a factor of three which means uh in the mu squar this would give an uncertainty of about a factor of 10 although if you take the square root of that then still a factor of three or so uh the phase space of course is well known you just need to know the uh q values for this and of course when you get the effective mnu squar then this mu is related to each of these massag states times a matrix element. The overlap between E and I the lepton flavor and the uh mass state the corresponding matrix element in that piny matrix that we saw and uh so UE1 is just C12 C13 U2 is S12 C13 U3 is proportional to this E to the I delta minus I delta and S13. So uh depending on what that mass is uh this uh effective nutrino mass that comes in here is high. If it is the inverted hierarchy, of course, if it is degenerate, then it is fairly high. But I think at the experimental levels that we have, we probably have ruled out most of this degenerate region. And uh however, we don't know whether is the inverted mass hierarchy or the normal hierarchy. uh other experiments of course such as accelerator based experiments will tell us eventually whether it's the inverted or the normal hierarchy or the Juno experiment which if that uh if they see a signal uh then they will be able to tell at a three sigma level. So in any case uh the effective mass square depends on whether it's a normal or the inverted hierarchy. uh if it is a normal hierarchy then of course it becomes very difficult for experiments but maybe the next generation or the next to next generation will be able to address the uh normal mass hierarchy for the at least for the neutralless double beta decay. So anyway, so again this is the kind of processes the normal leptton conserving double beta dk is this. uh the lepton violating WDK the nor neutrino less double bet is this and uh for the two neutrino process this is q to the 9 whereas the zero neutrino is proportional to q to the 5 the partial width uh in addition to the you know 2 beta or 2 beta 0 nutrino cases 2 beta 2 or 2 beta 0 nutrino cases there is also the corresponding second order process where two beta pluses are emitted and two electron neutrinos are emitted rather than the antiparticle here. Uh so similarly you can have a process where you don't have the neutrinos and this is the uh neutrinless double breed decay but for the p positron channel two positrons in the final state. Finally of course you can have a electron capture double electron capture process. So the normal uh double electron capture process would emit two neutrinos. Uh you don't see these neutrinos. You'll only see a recoil spectrum of this az minus2. And of course there'll be vacancies in the kk or the kl shells. So you'll either get two kxrays or the k and the l x-ray. uh but if you have no neutrinos so neutrino or less electron capture decay then of course you will have just AZ going to AZ minus2 and then there will be holes in the k or in the uh l shells so there there's no other signal that you have so this is of course a very hard thing to detect uh even in those cases where such a decay is in principle energetically allowed So this is a list taken from some reference. I've uh not given the reference here but uh double beta decay transitions for naturally occurring parent isotopes. So this is the double beta decay cases or the nutrinalist double beta decay cases. So there are several of them and the ones which have high Q value of course are the ones which are candidates for experimental searches such as for instance uh the germanium 76 calcium 48 then selenium 82 zirconium 96 uh then 100 malibdinum uh then there is of course this 130 uh similarly zenon 136 X and this about exhaust the thing because these 150 neodymium the others are of course uh much smaller Q values and they are uh troubled by the background that we have the natural radioactivity background. Uh similarly there is a table for beta plus or uh beta uh plus EC or the ECE cases and uh this is a list of that right from 36 argon to 112 tin and uh 120 toum to uh 196 mercury. So of course the ones with higher Q values are the ones where one could possibly search for that because uh as we saw in the B2B plus two neutrino case uh you have something proportional to Q to the 9 and in any case neutrino less also is proportional to Q to Q to the 5. So you would look for the high Q value cases and so that in this case is about uh 136 serium but that's a very small abundance. Uh 12 for zenon has about 2.9 u me and so on. Uh maybe I should go back in the earlier table. uh the other ones with the high Q value are 78 krypton but then its abundance is only point uh naturally occurring krypton is only.35%. Uh in the case of let's see there's no other about 2 m uh 76 ruinium is there that has a reasonable abundance of 5.5% and it has a reasonably high Q value of 2.7 MV uh similarly 106 cadmium this is only 1.25% 25% but 2.77 7 MV 108 cadmium uh no sorry 108 cadmium is very low uh so anyway these are there is another 96 routinium and 106 cadmium okay so there are three cases in this page uh and maybe one or two cases in the other one so there are fewer cases of uh candidates for searching for nutrinoless double beta plus decay or beta plus EC and so on. So let's take the case of 2 beta minus uh zero neutrino uh decay. Then this is a plot of the abundance the natural abundance uh and the Q value. So of course the highest one is 48 calcium but then it has a very low abundance something like only 2% or so. Uh 130 toum of course has a reasonably high abundance of about 35% or so and it has a moderate uh moderately high Q value of the order of about 2.5 MAV. Uh malibdinum has a higher uh Q value but then it has a lower abundance of the order of 10 to 10% or so. uh 82 selium is again the same category 136 xenon is again 2.5 MV or so which has a reasonable abundance of 10% germanmanium uh about 8% and a low Q value but of course you can get semiconductor detectors which are very high resolution so uh I've listed some of these 130 toum it has a high abundance 100 mibdinum has a high Q and also a reasonably high abundance uh that's here of the order of 10 to 10 to 11%. 150 neodymium high Q moderate abundance 48 calcium is the highest Q but it is rare you would have to enrich that and to get enriched samples in large quantities is that much more difficult. So the detector strategies for looking for double beta decay and neutrinless double beta decay is that you can either make that nucleus as part as an integral part of the detector such as in let's say 76 germanmanium. So we have uh germanmanium semiconductor detectors high purity ones which are used in gamar spectroscopy. So this is an advantage. The technology already exists. Or you can make a cryogenic bolometer of 128 or 130 toum. You can also in principle enrich it so as to increase the signal to background ratio somewhat. Uh you can do calorimetry. You can measure the temperature rise in a uh you know let's say cryogenic sample of which has 130 toum or you can do ionization if you have a gas sample then you can look at uh you know ionization detectors of the even of the TPC types or a scintillation if you can make a cintilator of tourum then of course you can look at the scintillation signal as uh typical uh full width that have maxima are for measurements involving a cryogenic bometer they're of the order of 10 KV uh if you have uh let's say a cintilation ionization which means you can look at the electron whole pair then that is of the order of 3 KV or so and if you have a cintilation detector that resolution about 2 MV is about 100 KV so you can see the range of resolution that you have this is the best uh TPC's or a bometer is about 10 KV and cintillation is higher or you can even have simultaneous measurement of let's say temperature rise or ionization or ionization and cintillation at least two to reduce the background because then you you can eliminate some kinds of backgrounds if you have multiple u signal measurements. uh these can also be external to a detector and for instance there you can do tracking of the uh beta minus particles in a for instance in a magnetic field and you can look at the angular correlations as well uh of these two betas. You can identify the vertex. So that helps again in reducing background. You can do a fast coincidence between these two betas that also helps in reducing background. However, when you have a a a target or some material in the form of a foil, uh then in order to increase the you know the number of atoms, you have to make a reasonably thick foil. If you make a very thin foil, then you have to put multiple thin foils and then it becomes a little inefficient. So there is an optimization process involved. So if you use for instance typical values like a few tens of mig per square centimeter of foils then the you get a poorer energy resolution of the order of about 10% or so. So let's come to the semiconductor detectors. Germanmanium is the most popular choice as of course as I said the technology for high purity germanmanium detectors already exists because it is extensively used in gammaray spectroscopy high resolution gammaray spectroscopy. So uh for instance the mayorana demonstrator has a bulk high purity germanmanium in which the contact here is blown up here and shown there's a dimple and then there is a contact here which enables this thing to be by applying a voltage you remove the uh electron hole pairs from this bulk material. And so if there is any decay it gives rise to electron hole pairs which are then uh which they drift to the respective cathode anode uh and then you get a charge signal. So uh this is the reference for the marona demonstrator and this is the search for nutrinoless double bet and 76 germanium using this marana demonstrator. So the other way of doing it is you have a cryogenic bometer. The idea is simple uh at least in principle. Of course in practice it's uh it's a lot of work and a lot of things had evolved over a period of time over something like 30 years or so. Uh so the idea is that you have a you have a material which contains the NTBD nucleus of interest. uh if it you you take it down to cryogenic temperatures of the order of millich keelvin. So in insulators at low temperature the specific heat goes like uh t cubed. So if you go to very low temperatures then the specific heat is very tiny and the temperature rise is because of the energy deposit divided by the specific heat and that therefore goes like 1x t cubed. So if T is very small then the temperature rise is large. So in practice it means that you get a thermal pulse which of course lasts for times of the order of hundreds of milliseconds or seconds and you get this thermal pulse which has to be measured and that is measured by a sensor a temperature sensor. This is basically a thermometer but not of the type that we use to measure body temperatures. Of course, this is a much more sophisticated device and this has to work at 10 ml also. So, uh the uh the the two betas uh which come out of this uh NTBD decay uh they produce uh phonons and then these phonons thermalize. They lead to a small rise in temperature of this bulk material which shows up in the sensor the temperature sensors and uh then you get this thermal pulse. Of course in order to cool this to millvin temperatures you have to have a thermal bath which is operating at uh quite low temperatures and there is a thermal coupling here. So you take this down to 10 ml and then this comes down ultimately. So this can take days if not weeks to bring this down to 10 mic kelvin temperatures. And at the same time therefore if there is something that uh causes a small rise in temperature then this goes through the same thermal coupling and this energy is dissipated. This small temperature rise the heat is dissipated in this thermal bath. Okay. So uh this is one way of doing it. You have an insulator and typically you can have a either a metal oxide or a semi- metal oxide and you make crystals of that and then uh this this is basically an insulator and then the uh you get a thermal pulse in that. Uh the other way of doing it is that you if you take a superconductor then it can be a normal metal uh where you know the uh C goes like T but if you take it below the superconducting uh transition then this falls exponentially with temperature. So as uh temperature falls then this goes up exponentially and so uh goes down exponentially. So the sea falls very fast. And so you can use again the same idea that you have a sensor a thermometer you can cool it to millich keelvin temperatures and then you have a sensor again which measures. Now there are two kinds of sensors essentially there might be more in future but the the sensors that are used normally are the so-called neutron transmutation doped geranium sensors where uh ideally of course a semiconductor has a very large resistance the resistivity goes to infinity if it is ideally pure uh but in practice also it's uh it has a very high resistivity at low temperatures. On the other hand, if you neutron trans if you dope it with some material and that you can do by actually irradiating it with neutrons, you produce both the P type and the N type impurities in this and so then you can actually get a variation of this resistance which is something in the measurable range. Okay. So the resistance of course comes down but it also changes with temperature and then that can be measured. The response time of these NTD germaniums are of the order of milliseconds. There are also transition edge sensors where you have very thin films of some material that you can make uh which can go superconducting but because of the finite and small size of this the transition is not uh infinitely sharp and there is a you know it's a it's a smooth transition uh to the superconducting state and so then you can actually operate this somewhere halfway and that uh said there's advantage that you can tune it, you can change the material, you can change the thickness and so you can have response times of course which are much faster. They are in fact in the range of hundreds of nanconds or even faster depending on the material and uh so on. So these are the two types of temperature uh therm temperature sensors or thermometers you might call it and uh a review article or a talk in 2008 this is this picture is taken from there but there are several now reviews of such cryogenic bometers so one of the most well-known cryogenic bometer is the one based on toum oxide and this is called cure. So this is the vessel the cryogenic vessel which cools this uh tower of turum oxide crystals uh to about 10 ml or so. Uh so this is a picture of just the turum oxide uh about 742 kgs of natural turum oxide operating at about 10 ml 19 towers of 52 crystals of this size 5x 5 x 5 cm and they are equipped with a NTD germanium sensors each one of them I think there is a redundancy probably two of them are there for each of these crystals and the the the measurement reported here in 2022 two uh was to search for marijuana uh neutrinos in this double bet nutrinless double bet in cure and they found a limit or t half is greater than about 2 * 2 into 10 ^ 25 years at 90% confidence level uh this an example of one of the parameters the temperature stability of this cure detector and uh in fact the projection of that is shown to be almost like a gaussian And so it is stable at 10 ml plus minus something a fraction of that uh millich keelvin. And some of these actually events these glitches are because of some uh coupling from the mechanical side to this. I think there is evidence that an earthquake far away from this place actually caused a glitch. it correlated well with the uh time stamp of these uh temperature signals. Okay. The other type of detector is the so-called uh tracking detector and the best example of this is the so-called super memo. Uh it is this is the detector. uh I don't uh there is no human beside that but it's a very large detector of the order of about 3 m on a stand and uh uh it's about 2 m or so uh uh this is two about 2 m or so this is these are the uh uh racks of uh the material as well as the geer muller counters and the cintilators behind them. So this can hold a stack of uh potentially neutronless double beaded decaying material. But of course they see uh the normal double bet and they have put uh they have measured these half- livives with reasonable accuracy. So as you can see there are several isotopes here uh 48 calcium, 96 zirconium, 150 neodymium and so on uh 82 selenium. So this is a example of a track of the two betas in the normal beta decay. The energy resolution is given by 15% by square root of E. So if you take E to be about 2.5 me then this comes out of the order of 10% or so energy resolution. This is full width at half uh this is probably uh delta E is uh uh probably the full width at half maximum. uh the uh sigma for t so the time resolution is about 250 picoscond or so the vertex resolution is on the in the xy plane is about 3 mm in the z direction it's about 10 mm uh in this super nemo they have used 60 mg per square cm foils and the total mass of all these foils put together all these uh samples is of the order of 10 kilogram so this is taken from this reference This is a summary of the half- lives. This is of course a slightly dated uh reference 2004 reference where many of these half- livives have been measured to fairly good accuracy. Okay, this is for normal double beta decay not the nutrinoless one. Nutrinoless double bet we haven't still found and searches are still ongoing. So of course the very important thing in these measurements is the uh reduction of background. So you have to choose materials very carefully so that they don't have uh any radioactivity in them. Of course these radioactivity means very small levels of natural radioactivity. So you have to choose materials where even that is lowered by factors of 10 100 or thousand even. Uh so you have to uh choose the materials carefully both on the detector environment as well as the outer shielding. Uh an underground location of course helps reduce the cosmic ray background due to muons. Then of course you have to use electronic rejection of background events because they might have a different uh signature as compared to the real events that you want. uh if a dual signal is there is that due to electron whole pair in a semiconductor plus cintillation or a cintilation plus calorometric signal this helps also reduce the background considerably and uh recently this uh there has been a pioneering effort looking for double beta DK neutrinverse double bet and 136 zenon by actually following the 136 berium ion and doing uh resonance exitation of that using a laser uh and also some other technique to do single atom detection. So the experiment the experimental group uh actually says that they can get a zero background situation by doing all of this. So these are the various ways in which people have attacked this background reduction problem. So in summary I would say that uh we have just discussed what is double beta decay and what is neutrino less double beta decay. uh what are the possible nuclei for searching for double BTDK and neutrino or less double bet strategies employed in the searches and some examples of uh double betk measurements and also a couple of examples of the best limits that we have uh on the the lower limits on the possible half-life for nutrino less doubled. Thank you.