Week 9: Lecture 44: Double Beta Decay (DBD) and Neutrinoless DBD (NDBD) – Part 2

In this lecture, we will uh go ahead with uh where we left off in the last one where we looked at uh you know the the rationale for studying neutrinos double beta decay. uh what are the ways you can go about uh measuring this nutrralless double bet which nuclei are used and so on. Uh today we will discuss a little bit more in detail uh results from some of the uh nuclear double beta experiments. Also we will uh mention a method that has been suggested not too long ago uh which is an alternate way of determining whether the neutrino is a mirana or a datac particle. And this just relies on the fact that it has a however tiny a mass and it's a marana particle then it has a certain correlation. On the other hand if it's a direct particle it would have a certain different correlation in the decays of heavy meons. Okay. So we start off with the the one of the most popular uh probes for nuclear double beta decay namely 76 germanmanium. Now 76 germanmanium uh the level scheme is shown here. It double beta decays to 76 selenium and the Q value is about 20 40 KV. uh it's a 0 plus to 0 plus decay as is so for all the even even nuclei and uh of course there are many experiments before this but the mayorana I'll give couple of examples the mayora demonstrator uh was one such uh reasonably new detector and uh it searched for nuclear double bet this is the reference the uh the setup itself self. Uh this is the reference uh in advances in high energy physics in 2014. Uh so the uh demonstrator has two cryostats. One which has 35 high purity germanium detectors and another which has 23 high purity germanmanium detectors and this second one has natural germanmanium. Uh we know that the abundance of 76 germanmanium in natural germanium is about 7.8% 8% whereas the 35 HPG detectors had 76 gmanium enriched to about 88%. And this is the total mass 29 and this is 14.4 kg. So of course you can estimate how much is the total amount of Germanium 76 in all of this. It would come out to be 30 plus kilograms. uh the background in this demonstrator was shown to be uh of the order of about um a little less than two counts into 10 the minus3 uh per k per kg per year. Okay. And this was consistent with another competing experiment called GA. So this demonstrated a uh a spectrum from uh all the six runs that they had uh from that reference from this reference here the final result of the Marona demonstrator search for NDBD in 76 germanmanium uh that some spectrum is given here. Now uh this uh is something which is due to cosmic rays induced or direct and so on and then that can be vetoed using a cosmic ray V2 detector and uh so the red uh plot shows uh sorry this is six runs with black this one and this should be with the cosmic ray detector. This should be with uh the cosmic ray veto and the inset of course shows the uh region of interest uh that is these uh that is at 20 39 as we saw and this is somewhere here. The background is of course taken from other regions and uh so the same thing is shown here but with different set of runs. Uh DS0 DS5A that is in black and uh the other runs 1 to 4 and 5B is in red and that has somewhat uh less background. So uh the blue region in the inset is uh can you can set a bound of about two counts at 90% confidence level and with a total exposure of about 64.5 kg year it gives a halfife of about half 10^ the 25 and the limit on the effective mass of the uh maron nutrino to be between 113 and 269 mill electron volts by c^². The legend 200 experiment builds on this uh marona demonstrator and uh this is the short form for a large enriched germanium experiment for nutrino double beta decay. Uh it is set up in grand saso. It has about 142 kg of uh so about uh what about five times the uh amount that we had in the uh demonstrator. But of course all of it is now enriched germanmanium 76 and legend thousand is supposed to be a one ton class uh search in Germanium 76 uh for NDBD this should have a sensitivity of this order 10 the 28 years and the sensitivity for the mu is if it is larger than 10 to 20 m electron volt by c^² it should be able to find this signal and these are the typical spectra So this this one corresponds to actually uh the two neutrino uh double beta decay and uh this is where you expect uh counts from the nutrino less double beta decay and so this is blown up in this. So before various cuts uh this is the spectrum in uh black and uh after the cuts the one this is shown in red uh red plot and so from there you can extract a half-life and extract a lower bound uh on the effective mass and so so it is below uh between 75 and 200 and this of course this uncertainty arises mainly because of the u uh uncertainty in the nuclear matrix element because when you go from here to here there is a nuclear matrix element involved and there are uncertainties in that up to a I mean in some cases even up to a factor of uh three. So when you square it you get 10 in terms of the half-life but for m new uh you you get this kind of uncertainty and this is the reference here. This is a 2026 very recent reference the first results uh on NDBD search in legend 200 experiment. Okay. The next nucleus that we will see is 82 selenium. 82 selenium has a higher uh endpoint energy. Q beta beta is about 3me or so and uh this is the level diagram the relevant level diagram uh of course as you notice in all these double beta DK cases the single beta DK is energetically disallowed uh that's shown here you will see always that the intermediate nucleus which could have been populated by single beta decay uh it cannot populate it because it's energetically uh not allowed Okay, so this cupid is the leading experiment in this uh for this nucleus. Uh it has a scintillating bolometer and it uses the cure cryogenics. So you can cool things down to 10 ml and you can get a bometric signal but it is also scintillating. So you can also get the cintillation signal and that's collected by this germanium disc plus a silicon coating to reflect the uh the light that is collected from the cintillation signal and uh that way you get a scintillation signal as well as a volutric signal and you can do a two-dimensional plot and you will see that alpha activity comes in a region which is different from the uh beta signal the two electron signal And of course as was done in the turum oxide experiment of cure the temperature sensor is a neutron transmutation doped germanmanium crystal. Uh the halflife extracted was uh such that there is a lower bound on the halfife which is 1.6 10 to the 23 years at 90% confidence level and then there would be a corresponding uh mu for that the lower bound on sorry the mu would be less than something. So uh it would be a upper bound for the mu somehow I've forgotten to give it here. Uh maybe I'll put it in the final slides but there these bounds are somewhat poorer than the ones which you saw in the case of germanium. This is of course cupid zero. they will go ahead with a bigger version of uh cupid uh and uh then of course the bounds will be become competitive with the other probes. Okay, we come next to 100 mibdinum. 100 mibdinum has a similar advantage to selenium in that the Q value is 3 MAV or so more a little more than 3 MV and this means that it is above the 2.614 614 KV gamma array that comes about from talium 28 decay which is the background in most of the uh double beta decay searches which have Q values less than that less than 2.6 actually the compton of 2.615 uh is what comes in and so if you have less than 2.4 MV or so then that background from that gamma becomes important but in this case for things which are above 2.6 six that is not a problem. Uh the only problem then would be cosmics and some other cosmic ray induced activities. So what is shown from this reference is a spectrum uh of uh the physics data blue and then after uh you know treating it and uh uh sub uh you know so this is the thallium induced background that you have and then that is suitably subtracted from here and so once you do that in the region of interest which is around uh let me see this is around 3 MV or so 3.23 MEV. So somewhere here in between these two black lines uh that is the region of interest and uh so this this will help in put a uh limit on the uh half-life and uh also on the uh the effective mass of the marana nutrino the bound on that. the upper bound. So just as uh the in 130 toum of course we have seen in the earlier lecture uh the limits on the half-life and of course the uh bound on the uh the effective mass and that is effective mass uh there is an upper bound of about 90 to 305 mill electron volt by C^² squ of course depending on the matrix element again u so so this was something that we saw with the cryogenic bometer now there is a very different technique which is used in the snow plus experiment and they they have a uh a huge uh linear alkyle benzene short form is lab based liquid cintilator where you put in about a half a percent of natural tunium but the idea is that you can put in an even smaller quantity of percentage but of enriched uh torium oh sorry neodymium as well. So they have these two possibilities uh they have not reported uh either of these results because the experiment is ongoing and uh neodymium of course we'll see in the next one. So f their first uh goal was to actually put in uh natural toum and then enriched torium. Uh however the enriched delium doesn't give that much of an advantage because after all you can only increase the sensitivity by about a factor of three. Uh whereas the neodymium of course has some other advantage which we I don't know whether we'll come to that in the next one next slide. In any case these are the two that they want to attack. The advantage here is that even if this looks like a small percentage, the detector itself is huge. So it's you know of the order of8 kiloton and in that if you put a.1% that's like uh 780 kg. Okay. So uh this can give you very competitive bounds uh or you might find evidence for uh nutrientless double bet as well. Okay. Then we come to Zenon 136 experiments. Now zenon 136 somehow is very popular and there are several groups attacking the zenon and one of the reasons is that you can make uh tpcs so-alled time projection chambers in which you get reasonably good resolution energy resolution I mean but you also get spatial resolution and to top it all there is the possibility that you can actually look at the daughter product which means uh 136 barerium And you can shine a laser on it and make sure that uh the decay I mean the daughter product is also seen. So that way you reduce the background hugely. It becomes almost background free. Okay. So that is the advantage. So there are several experiments. Kamland Zen was the first one. Then there is a Kamland Zen 400 and Kamland Zen 800. Uh I will show some results on that. Then there is the exo 200 and the next exo. Then there is a Chinese experiment in the deepest lab in the world the jinping lab at 2 and a half 2.4 kilometers depth. So this is panda x4. The idea is to have about 4 tons of uh zenon. Then there is the next experiments next next 100 and the future next bolt. Then there is Zenon NT, Zenon 110 ton and finally they want to combine Kamlan Zen and Exo 200. Okay. Uh combine meaning data wise. Uh look at it because many of the probably group members are uh common to these experiments. Okay. Okay. So, Kamlan Zen builds on an idea which is due to Raju Raghavan uh who was earlier at Bell Labs and then was at the Virginia Tech uh inst Virginia Institute of Technology and uh he he wrote this paper which basically pointed out that zenon dissolves by up to about 2% by weight in a liquid cintilator. Okay, it's a rare gas but it dissolves in a liquid organic cintilator and this was implemented in Kamland Zen 800. So Kamland Zen uh if you remember was a one uh kiloton uh liquid cintilator detector and that measured the reactor uh anti-utrinos to great precision. Uh so if you put a small amount of uh small in terms of fraction in this uh 1 kiloton cintilator so 745 kg of 90% enriched 136 zenon uh in a inside vessel okay this is the kamland cintilator the 1 kiloton detector and this is what you put inside of it uh which is a smaller volume is so called the the inner detector So this could act like a veto for instance both for radioactivity as well as for the remaining cosmics and then you can uh of course there is also the shield the water shield which also can be used as a cosmic V2 detector but the cintilator also can be used if you're looking at the inner detector and so this is the typical uh spectrum uh with uh you know two kinds of uh uh conditions and uh so the so-called SD and uh LD uh and from this data uh they have extracted the best uh bound on the lifetime for zenon 136 that is uh of the order of 4 into 10 the 26 years at 90% confidence level and the uh sorry this yeah the effective mass uh the effective myon mass is between is less than between 28 and 122 mill electron volts by c². Of course again this uncertainty comes about partly from the uh extraction of uh the uh counts uh which come from 136 uh or or you're bound on that but also significantly from the nuclear matrix element. Okay, there is the EXO 200 and Nexo. This is a US-based experiment and this is this is the reference for that. Uh so this is the detector again this is a uh TPC kind of detector. So uh the there are certain bounds that you get from it but basically this was to do R&D for the NXO which will be a 5 ton 90% enriched liquid 136 zenon uh detector TPC at snow lab. So earlier they had it in lab in the US in one of the waste radioactive waste facil facilities. uh but that was just the R&D phase and now they will take such a detector to snow lab which is one of the deepest uh labs in the world the second deepest after Jinping and again they will implement this berium plus ion detection for which they are doing R&D uh and so that you can go to almost zero background so these are the references here given and uh uh the next we come to this pand about a 4 ton liquid zenon uh time projection chamber based detector. And so one of the early runs which is a kind of test run you might say uh with this very small exposure they could show that they already have a decent bound on the half-life about few * 10 2 * 10 24 years at 90% confidence level and the effective mu of about42 to 1.6 ev by c². Of course, this doesn't compete very well with the others, but this is just a very early run and uh this is the reference 2024 reference. Uh, of course, they will count for much longer periods and presumably also with enriched uh Zenon 136, which will improve the sensitivity. The the big advantage of this uh Panda X40 is that it is located at a depth of about 2.4 km. It's the deepest anywhere. So basically they don't have to worry about cosmic rays. They only have to worry about uh radioactivity uh which uh of course they will uh perhaps in future they might also implement the berium ion because once somebody finds a neat way of killing the background uh and making it almost background free I think all the you know zenon based detectors will do that except for the cintilation one. the cintilation one probably it would be a little harder. Okay, then we come to the next collaboration. The next collaboration is a European based I think collaboration. It uses about 100 kilogram of xenon and a gaseous TPC uh but at at a very high pressure of 15 bar. The expected sensitivity if you run it for 5 years is something like 70 to 130 m electron volts. uh uh so if it is above that they would find it. The next HD is uh is about 10 times larger so it would have a sensitivity to the halflife of about if if a halfife is less than 1.4 4 10^ the 27 years they would find it and I if I remember right this was the first collaboration which actually or one of the first which uh looked at this berium plus iron decay and uh almost getting a background free measurement and with this of course you would get a sensitivity of uh something like less than 50 15 mill electron pools and this is shown here. So this is a laser setup. So once the TPC uh detects uh electrons then of course what you do is you you know the position from where it started and then you uh excite the berium plus ions using a laser using this setup and then it flourishes and that image can be taken by CCD cameras all around the detector and this is a demonstration of that that you can see that these darker dots are in the foreground. They're on the surface of the uh Xenon TPC and the fainter ones are the ones behind in the background and the dot size is of the order of about.3 microns. So uh that is the kind of uh you know positional precision that you can get uh if you had a neutral double beta event. So that will reduce the background which can come of course from all parts of the detector. So you you detect the two betas but you can also pinpoint the position and that helps. So this is a kind of uh uh you know an improvement on the nemo kind of detectors that we saw some time before where you had uh basically a magnetic field and a spectrometer to look at both tracks. Okay. So uh this is the reference We go to the next nucleus namely 150 neodymium and this is the level scheme. So again the energy is very high 3.37 me and this is the ground state to ground state decay. So Nemo3 of course measured the uh double beta decay the normal double beta decay 2 neutrino 2 beta and then it also searched for nutrino less double beta decay. So the half-life bound was that it was greater than 3 10 22 but this basic this number is of course limited by the uh you know kind of foils that you have to use uh you can't go to you know a ton scale experiment certainly with this. So superu will of course push these bounds further but the snow plus would push it much further. Uh so this is the kind of uh uh you know spectrum that was seen by an MO3 uh the two neutrino part and the uh the green one shows the thallium background uh and so on. So uh the search was also carried out with the full exposure of Nemo and they have some bounds on that which is of course here I haven't given the bound on MU but again they would be a little less competitive than the ones which we saw in the earlier cases. Okay. Now we'll come to a completely different method of trying to probe the dra or my nature of the neutrino. Okay. So uh if you remember uh if the nutrino is a direct particle then it is defined by whether it's a particle or antiparticle and whether it is spin up and spin down. So it is in fact it would be then represented by a four component spinner. Okay. Uh on the other hand if the nutrino is its own antiparticle which means it's a marona particle and that can happen if uh the nutrino has a mass ever so tiny mass uh then it can only then it can be described by just two components. Okay. So because you don't need the other two components for telling you whether it's a particle or antiparticle that you're talking about and uh it just has uh a helicity which is uh either plus or minus. Okay. So the you the spin up or spin down that that's all or spin along the uh momentum or reverse with respect to it momentum that's all that you need. Okay. So this cute method uh looks at uh as I said not nuclei but it looks at neutral mezons and this is just one example of that. B 0 is an example of a neutral mezison and looks at a higher order process not uh so where you have actually two muons of opposite charge and then you have also have correspondingly uh neutrinos so new mu in this case if you have a mu plus mu minus then you would have a new mu and a new mu bar okay this would be for a direct kind of situation uh and you choose kinematically those events in which the uh momentum of the mu plus is opposite to the momentum of the mu minus. Okay, so the sum of their two momenta is zero. They're they're moving in opposite directions. Okay, so they have roughly equal and opposite momenta. Of course, such events are very few in number and they have branching ratios which are very small. It could be of the order of 10us2 and so on. So that makes it hard to measure such thing but at least in principle this is a measurement that just requires you to know uh quantum statistics that's all and so uh that is stated here if the nutrinos are marona particles mass not equal to zero and new mu is equal to the anti-new mu and obey firm direct statistics the probability amplitude for these two neutrinos which would also come out in opposite directions uh that would have to that probability amplitude would have to be anti-ymmetric just because it is a firmion. Okay, this is not so for a direct new because of course the neutrino is different from the antiutino. So you don't have to antiymmetize it. Of course the neutral mezison could be a jai or a d0 a mixed charm strange d0 and whatnot. Uh similar similar story with the ji or even perhaps a k0. Okay. And this is the reference here. This is a 2022 reference. uh and uh earlier reference which actually alluded to this possibility uh the in 1992 that is also given here. Okay. So the uh helicity configurations are like this. If this is a direct uh case then of course uh if muon is moving in this direction then it spin uh is opposite uh sorry this is the neutrino. If the neutrino is moving in this direction then it spin is opposite to that is a left-handed particle and in the other one the antiparticle that is right-handed. So the spin is in the same direction as the momentum and this is the muon direction. Of course the nutrinos would be very hard to measure. I mean it's almost impossible with present day technology. But who knows things might change if you choose proper systems and with improvements in detector technology and so on. But as of now you would want to detect the charged particle which is the mu minus and the mu plus. And these are the helicities of the mu plus and the mu minus. Okay. So if the particle is a mayorana particle then these are the helicity configurations. uh uh this is uh the momentum of the mu minus and this is the momentum of the mu plus and again the spin uh of the muon and the uh sorry mu minus and the mu plus they're given here and this is the helicity with of the neutrinos the maroner nutrinos okay so new mu and uh you know new new m this is the same new R M is the same as new M. Okay. So uh this is so here and this is the exchange amplitude. So if if it is uh if this is a theta then this is corresponds to pi minus theta. Okay. Here so then you have to add these two uh uh I mean add with of course a minus sign and then uh get a probability uh for such a process. Okay. So if you were to do that then the angular distribution of this uh with plotted with respect to sin theta where theta is the angle between the neutrinos and the muon momenta because we have chosen them back to back and similar momenta it is basically these two which are making an angle and so you can plot that and you get a very different uh distribution if it is a marona particle this is a 1 + cos² theta Okay. And uh the drack one is given here. You get basically a zero at sin theta equal to0. However, as I said before, you cannot easily measure the uh neutrinos and certainly not two neutrinos. Uh so of course if you measure the muons and are able to measure one neutrino then you know what has happened to the other neutrino. But this is as I said very difficult. So instead you would like to see if there is any signal on the charged muon front and indeed there is the energy distribution of backto-back muons is uh shown in the blue line for the direct case and in the dashed red line for the meona case. This is something that is measurable. Okay. Uh at least in principle as of now. As of now, the luminosity of the super KKB, which is the uh beam Amazon factory in Japan, is smaller than that required to measure this distribution by about 3 to four orders of magnitude. Okay, things might change in the future. Maybe they will enhance their luminosities by another factor of 10 or even 100 perhaps. In that case, this if you count for a long time, then maybe you might get some uh small signal. However, there is a better option uh in LCB uh with the highintensity uh large headron collider uh which is now uh coming into uh which is coming online uh you will be able to produce about a million times more B 0 as compared to in super KKB. And if you uh if if this experiment can actually be tuned to measure these things then maybe you will you will be able to measure this energy distribution and uh this is a huge difference. I mean you can see that this difference is almost like a factor of 20 or 30. Okay. So I mean if you get this uh you know even with relatively poor statistics a few points on this curve and if you will be able to tell whether it lies here or it lies here and therefore whether it's a marona particle or a direct and this is this is a very cute method of uh finding out whether it's a marona or direct particle from a completely different uh uh experiment. Okay. So in summary we have discussed nutrinolless double beta DK searches which are carried out using various nuclei. While no nuclear double beta DK case has yet been found the limits are being pushed uh and the detectors are becoming ton scale detectors. If these experiments do not find evidence for the maronal nature of the nutrino then of course the inverted mass ordering or the inverted mass hierarchies is as it is called will be disfavored and the next generation will have to probe lower effective masses and normal ordering uh so-called NH normal hierarchy. Now I also talked about a very recent proposal to probe the maron nature of the nutrino based on just quantum statistics and you just need a very tiny mass however tiny it is uh using heavy meon decays and we discussed this briefly uh just to indicate the power of this method. Thank you.