 We're going live. So I think we are live. So hello everyone, welcome back the Latin American webinars on physics. My name is Joel Jones from the PUCP in Peru and I will be your host today. This is webinar number 156 and we're having Diego Portillo as a speaker. Diego is currently a third year PhD student working at the same staff in Mexico under the supervision of Gabriel López Castro and Gerardo Hernández Bon. So today, Diego will give us news about attempts to distinguish between Dirac and Majorana neutrinos in leptonic four-body decays. We are very happy to have him as a speaker today. Now, before we begin, let me remind all viewers that you can ask questions and make comments via the YouTube live chat system. This question will be passed on to Diego at the end of the talk. So, we're all yours, Diego, you're muted, sorry. I will start sharing my screen. Here's it, you can see it. Everything. Okay, so let's start. We'll screen. Here's, now you got it, right? Okay, well, once again, my name is Diego Portillo Sanchez from same staff, and I really wanted to thank Joel for the invitation to give this seminar and sorry for all the inconvenience. Well, today we'll talk about on the Dirac Majorana neutrinos distinction in four-body case and also want to mention that this work was in collaboration with Juan Manuel Marquez and Pablo Roig Garces. And here's the reference you wanna take a look. Okay, well, the motivation, well, the outline of the talk will be as follows. I will give you a brief introduction and motivation for the work and present basically the problem that we want to solve here. After that, I will give you some information about the Majorana versus Dirac observables that we currently have. And after that, I will give you the introduction to the four-body case that we want to study here. Basically, it is the radiative leptonic decay. And after all that, I will give you a brief summary of all that I saved here. Okay, as is usual in this kind of talks, let's start briefly with the standard model just to give some context. Well, as you already know, the standard model is a guess theory with these local groups over here, but we also have another kind of symmetry like the accidental ones like the lepton number, barium number, et cetera. And regarding the matter content of the model, we know that the neutrinos are matterless particle in the standard model, but nevertheless, due to the experimental observation of the neutrinos relation, we know that the neutrinos must have mass. And this opens on questions in the neutrinos sector as we show here, as I show here. First, are the RAC or Majorana fermions? These neutrinos are the RAC or Majorana fermions? Or, and what is the mechanism that the neutrinos have to, in order to acquire mass? Well, I will focus in on the first one, but for this, I will give a brief introduction of what is the mechanism of the mass energy. Well, basically, we have to add a right-handed neutrino to the standard model in order to give a Yukawa coupling with the Higgs in order to, after the spontaneous symmetry baking, obtain a direct mass for the neutrino. And given that this right-handed neutrino is a singlet of the gauge group of the standard model, we also can write the corresponding Majorana master. And this is basically one operative that breaks the left-hand number into units, okay? Then we can use this breaking of this accidental symmetry that does not represent any inconsistency of the model, but give us with really interesting phenomenology in order to distinguish between Dirac or Majorana fermions for the endurance. Okay. There are several observables that let us distinguish between these, but as I will say later, these are really suppressed and the most promising one are the neutrino less double beta decay. Essentially, this observable is the search of a process that I show here. We have a nucleus with C number of protons that decays into another that have two more protons and two electrons. And basically this is a left-hand number process, left-hand number violation processes and essentially because we have this theorem that we described here in this reference, if we observe the neutrino is double beta decay, then we will be sure that the neutrinos, at least one neutrino is Majorana fermion. How does this theorem work? It's basically because if we allow this operator over here to describe this transition, then we can go to a radiative correction of this kind and obtain a Majorana mass for the corresponding neutrino. Also, apart from these observables, we have all the left-hand number violation processes that we can apply this specific theorem. And on other observables are the electric default moments or the magnetic default moments that we will discuss a little bit later. Well, what is the problem with the neutrino is double beta decay? Basically it's that the neutrinos, well, these processes have an amplitude that is proportional to this factor that we call effective Majorana mass described by this equation three over here. And essentially, depending on the combination of the Majorana mass phases that appears once we consider Majorana fermions, we can have different behavior for this parameter. Essentially in the inverted hierarchy, we have the green light over here and for the normal hierarchy, we have the red one over here. And as we can see, the red one is compatible with zero with values of the Majorana mass equals zero. And even if we cannot observe the neutrino of the double beta decay, we cannot say anything about the neutrinos or the nature of the neutrinos. Another important feature of here is that this matrix element that appears for the nuclear transition have a lot of uncertainties coming from the computation of this nuclear process. Then in order to have another kind of observables, well, this kind with lepton number violations, we also have the one that came after the decay of mesons and tau. Well, just to summarize this, all this process with Majorana fermion in this transition can be described by this diagram over here at field order where we have a massive neutrino propagated in this as it can see in this diagram over here. And essentially, we have different behaviors of this amplitude depending on the range of the mass of these massive states. For like neutrinos, we have the one that we call effective Majorana mass, but if we go to a more heavier state, we can integrate it out and obtain that the Wilson co-efficiency are essentially an inverse of the mass of this new state. And well, we also have another kind of processes where we can produce this neutrino on shell and have a resonant effect on the amplitude. Well, summarizing this, we have the meson decays with lepton number equals two, the tau decays with this diagram also with lepton number violation equals two. And the current experiments, the current experiment that tried to measure this specific process I described in this table over here where the more restricted one upper limited are described by the kaons decays. But we also have some restrictive quotes coming from the B mesons and the tau decays. Well, going to another kind of observable that let us distinguish between Dirac and Majorana, we also have that if we measure the electric depot moment or magnetic depot moment different from zero of the neutrinos, we can be sure that the neutrinos are Dirac particles. Essentially, the current upper limited that we have for these two quantities are of really, really restricted ones. We have that the magnetic depot moments are around 10, the upper limit for this is around 10 to minus 11 more magnetons or for the electric depot moment, we have this upper limit over here. So as we can see any of those observables that we are talking about are really suppressed and experimental balls cannot say anything about these two natures of the neutrinos nowadays. So another alternative to measure or to distinguish Dirac and Majorana are using the statistics, the quantum statistic of the neutrinos with two neutrinos in the final state with that process. Essentially, if we have two neutrinos, one neutrinone, one antineutrino, if those are Majorana fermions, then we have to antrisiometricize the amplitude in order to satisfy the spin quantum spin statistics. So instead of having for Dirac fermions, this amplitude over here, we have a second contribution coming for the exchange of the two particles in the final state. And as we can see later, as we will see later, these difference between these two different natures are also proportional to mass of the neutrinos. So if we are taking into account only like neutrinos, we will have a really suppressed observable for this. So basically here in the practical Dirac Majorana confusion term, what we're trying to say here is that if we integrate all the variables of the neutrinos, we only have 10 terms that are proportional to the masses and the energies. And then it will not be possible to distinguish in future or present experiments. So some alternatives to overcome this problem is to add new physics effects to the specific problem that we want the specific process that we want to study. Or on the other hand, try to measure any of the variables of the neutrinos in order to distinguish this. And we have several works about it, references here. Essentially, the new physics effects are also really suppressed by the coupling of these new interactions. And we will have more interest about the measurement of the variables or trying to infer the variables of the neutrinos in any specific configuration as we will see later. Well, another method proposed last year is to try to measure the B0D case into a muon, into a two muons and two neutrinos and go into the back-to-back kinematic scenario, which I will discuss later in order to avoid the practical Dirac Majorana confusion theorem and give an observable that it is not suppressed by any mass of the neutrinos. Okay, using this specific idea, what we try to do is to reproduce this computation using this less suppressed decay, which is the radiative left and right decay. Well, L can be muon or tau. And, well, that's it. So the things that we have to do for now is to have a process with two neutrinos in the final stage and compute the corresponding Dirac amplitude and the Majorana amplitude. After that, compute the corresponding differential decay rate and apply the back-to-back configuration in order to see if there is any difference between these two differential decay rates. Well, let's start. Well, before going specifically to the left-on, radiative left and decay, we have to go to the Majorana, well, to the mass basis where we can see that essentially the left-handed neutrinos or the flavored one neutrinos can be described as a sum or as a linear composition of the massive states where this U basically is the PMNS matrix as we know. And essentially this computation can be used in any value of these massive states, but we only consider three neutrinos. Okay, essentially if we add inquirently all these quantities over here, we can have the estimation of the total decay weight for the process that we are interested in. Well, essentially for this specific process, we have two different diagrams described here for the initial radiative transition and the final radiative transition. And we, for use a simplified notation, we will use the question 10 that we have the indices for the massive states described here and the momentums of the final state described by this order over here. Well, essentially if now we are considering Majorana neutrinos, what we have is two anti-symmetricized these amplitudes and obtain these four diagrams over here. Then basically the Majorana mass, well, the Majorana amplitude can be described by this permutation of the neutrinos for the second term where we have JK P2 P3 for the data case and the exchange one, it will be KJ P3 P2. And in order to be consistent with the Kaiser theorem and et cetera, we also compute the interference once we square the amplitude and obtain that this interference term is proportional to the mass of the neutrinos square. And for small neutrinos, we can neglect it or taking it equals here. Well, then the amplitude square for the Majorana case can be described by these two terms over here and the direct case will only have one term described here. Okay, now the second point that we did was to sum over all the possible massive states as we can see here in equation 40 and equation 50. And this factor, one and a half comes by the double cone of this sum over J and K, basically. As we can see, if we integrate out, well, if we integrate all the momentum P1 and P3 in all the possible configurations, this will be domain indices. And basically, the Dirac and Majorana, once we integrate the neutrinos variables will be the same, the differential decorates. Then basically, again, the Kaiser theorem is wall-side fire here. But in order to go to the specific enigmatic configuration, we need to describe our phase space in a specific way. So we use this variable described by this figure over here where phi basically is the angle that describe these two planes for the neutrinos and the lepton gamma. And the angle theta nu and theta L are the one that is described by the momentum of the final lepton and the boost corresponding to go to the center of mass frame of this system. Well, as we already know, all of these four body decays phase space are described by only five independent variables. And in order to give a simplified expressions we use two energies of the neutrinos, well, the energy of the neutrino and the anti-neutrino, the cosine of the angle between these two particles. And basically, these two angles are variables that are described in this figure over here. Well, essentially, we can then describe the differential decorate for Majorana and Dirac case in equation 17. And once again, because it is not enough to prove the practical Majorana confusion theory in one, we want to use as many as is possible. And once again, with this specific configuration, we obtain that the difference between Dirac and Majorana integrating over all the variables of the neutrinos is equal to here. Once we neglect the mass of the neutrinos. But now what about the back-to-back configuration? Well, the back-to-back configuration basically is the one that is described by these two equations over here, where we have that the two neutrinos goes in opposite directions and the left-on and the gamma also in opposite direction. And these two equations over here basically give us some restriction of the phase-based variable that we choose. And we have this one described here. Where the energy of the photon and the energy of the final left-on is equal once we neglect the mass of this left-on. And basically we have a relation between the energy of the neutrinos and the energy of the final left-on, as we can see here. Then if we measure the angle, well, the energy of this particle, we can infer with this relation a variable that is related with the neutrinos. That is one of the things that we want to compute. And on the other hand, the other two angular variables that we have for the phase-based are fixes to be equals pi in order to have these restrictions of the back-to-back scenario. Well, with all that, then we can fix the differential decay rate in this specific back-to-back kinematic scenario and obtain basically the equation 20. Where clearly we have a completely different relations for Dirac and Majorana case. And once we use this difference over here between Dirac and Majorana, we obtain an expression that is now not proportional to any mass of the neutrinos. So in principle, it is not suppressed by any other factors. But it is important to remark here that all of this difference is proportional to this angle that we call theta. That is essentially the angle between the lepton and the neutrino. And because we cannot measure this variable, we have to integrate it and see what is the spectrum of the energy in this specific kinematic configuration. Well, in order to write this angle in terms of the phase space variable that we described before, we have this relation over here in the back-to-back where we have essentially a non-trivial description or relation between the angle theta and the angle theta L, theta nu and phi. Okay, it is important to mention that this angle theta nu, basically we don't have any restriction over it. So we can fix it in any possible because what we want is the difference between the angles of the neutrino and the final left. Okay, I'm sorry, here I have a typo. I want to say that if we integrate over the theta angle, then we can plot the differential decay rate in terms of the energy of the two neutrinos and obtain that the Dirac and Majorana are basically the same spectrum. Here we have basically the spectrum that we will have and here basically is the infrared regime for this radiative decay. Well, but what happens if we are interested on the difference between Dirac and Majorana that are not proportional to Majorana? I mean, let me say it again. Yeah, let me say it a little bit different. What we're trying to say here is that essentially motivated by the word proposed in this reference over here, we expect that the difference between Dirac and Majorana will be not identically clear, but nevertheless given by all the detailed explanation that I have for the phase space integration, we obtained that the difference is equal zero. So we have to track the difference with the method used in this reference and the ones that we use. And basically we found that the relation that we are using for the angle between the leptone and the neutrino is different from us and from the Key and Semi method. Basically we have to say here that the angular variable phi, it is fixed in this case, but it's not fixed in our case. And we don't have any restriction in this angular variable as I said before. So essentially if we fix using all the results that we have, if we fix this phi equals zero, we obtain different energy spectrum for the Dirac and Majorana case in this radiative leptonic decay that can be measured in four common experiments. So what is the problem here is that basically phi cannot be fixed by any restriction for the back-to-back isn't that. Essentially as we can show before, the only restriction that we have for the back-to-back scenario is that the two energy of the neutrinos are identically between them and the angle between the two, the one of them are equals five. But we don't have any other restriction for the angle phi over the angle theta nu, et cetera. And as we say before in the next slides, if we fix this angle of phi equals zero, we will do some other configuration that can be described by one plane described by the neutrinos and the lepton gamma system, okay? I will try to summarize here what we are trying to do is that here is the general schematic scenario. If we go to the back-to-back scenario, then we have to neglect this boost that we have that connects the rest frame of the particle that decays and the corresponding center of mass frame for the neutrinos and this lepton gamma. And essentially we have a corresponding relation that we have for the angular variable that we are trying to describe and the different plots or the different planes that describe these two vectors over here. And essentially the most important thing here is that for any value of phi and theta l that we have, we always can reproduce a back-to-back scenario. So any of these planes can be considered in the total decay width and not only the one that is described here in this diagram A, where it's coming from the phi equals zero isn't it? Well, I also want to say that apart from the angular treatment that we have in the phase-based integration, we also made some consistency tests in the corresponding reference that I mentioned here and we obtained that basically the branching radio of this back-to-back scenario is really, really suppressed compared with the ones that we could obtain in experiments, in four common experiments. So basically this is of order 10 to minus 10. And I also want to say that a fixed in phi equals zero fixed, well, it is compatible with all other observable that we have. Well, all the consistency tests that we made. Well, I think I went too fast. But a summary of this is that basically in this paper, we consider the radiative lift and decay as an independent approach in order, as an independent approach for this novel method proposed in this reference over here and try to see if we can obtain any observable little distinguish between Dirac and Majorana. And the main conclusion here is that using the phase-based integration that we made and doing any consistency test that we did is that we do not obtain any difference between Dirac and Majorana in this specific scenario with two back-to-back configurations. Well, we also want to mention that we discussed in our paper the detailed arguments that why phi could not be fixed by any kinematic restrictions and also say that the problem is still open for trying to search any observable that are not neglectable once we take the mass of the new trinium sequels here for this Dirac-Maiorana problem. Well, I also want to mention that this novel idea could be applied in any other kinematic configuration, not only the back-to-back or not only the forebody decays, whereas we can show that it is not the case. We probably in forebody or three-body decays, we can find a configuration that let us distinguish because essentially the amplitude is not proportional to any mass of the neutrinos, the difference of this amplitude, but once we integrate again the inaccessible angles of the neutrinos, we have the same result that we have for all other processes that try to distinguish between Dirac and Maiorana. And that's it. Thank you. Thank you very much, Diego, for the very nice talk. So usually we get questions from the YouTube audience, but there is a time delay. So let's start by answering questions from the Zoom audience. So I'm wondering if there's anybody else who has a question who would like to start? I have a couple, but... Okay, let me start. Okay, so first question is when you're calculating the forebody decays, you are attaching... So you're taking the forefirmion operator and you're attaching a photon on the charged leptons, right, on the initial and final charged leptons. But in principle, this forefoton operator... Yeah, exactly, right? Slide 15, yeah, there. So in principle, this forefirmion operator, it's built with an intermediate Z or an intermediate W, right? So in the case of the W, attaching the photon there also, I mean, would that give a difference in your result? Yeah, we're not considering here the intermediate radiation because basically it could be neglectable because it is one order of magnitude suppressed by... Let me say it again. Basically, this diagram with the intermediate state radiation could be neglectable because it's proportional to a power of G-fermie more than this one, yeah, exactly. So we are only thinking to account the leading contributions. Yeah, you have an extra W, you know? Yeah, exactly, yeah. You have another Fermi constant in the amplitude, yeah. But it's true, we have to add it in order to have all these gauge invariance and all these relations to be, yeah. Yeah, that was the second thing I was thinking, right? Making the diagram gauge invariant. Yeah, but essentially it is neglectable so we cannot add it here. Yeah, so then, yeah, and given it has got a different structure, maybe the gauge invariance can like, cancels, the non-invariance cancels between itself. Yeah, that's what I would expect. Yeah, bro. Coming right up. Okay, so thanks for that one. I'm wondering if your result, it's a shame that at the end of the day the branching ratio is so small, but I was wondering if you still have your Rana neutrinos, but you replace one of them by a heavy neutrino, like the ones coming up. CISO model. Would you get information from that? Maybe having the heavy neutrino being produced elsewhere and then decaying into a tau instead of having the tau decaying into the heavy neutrino or something like that? Yeah, thank you. That's a very nice question. Basically here we are interested only in the light, the neutrinos, because if we add another massive state, we have to deal with the suppressed mixing angle that I have here. So basically we are trying to have only diagrams that are not suppressed by any other sources, that are only the Fermi constant, and that's it. But it's true. We can add another massive state, but it will be suppressed by the current experimental bounds for the mixings of these states. Yeah, the thing I was wondering is that if there you can get more information. Yeah, but after the decay of this, yeah, probably, but it will not be a four-body decay, it will be a five-body or, well, yeah. But thank you, it's a nice. So I don't know if there's any other question from the audience? I have a question for Diego. Diego, maybe you mentioned that I didn't get it. Is there any role for the CP violation phases here? Well, I didn't mention it, but essentially, let me go to this. When we zoom over all the massive states, basically we have the PMNS matrix square, and we use the unitary relations to, in order to only have this expression mentioned here. But yes, we use the unitary relation for the PMNS matrix in order to have these results. So it is considered, but once again, I will only take into account that this. Okay, thank you. Thank you. Okay. I don't know if there's any other questions. There's none from the YouTube transmission so far. So I guess that would be because I don't have any more questions. It was pretty clear. Well, if you have any other, later in the day, you can send me an email and we can discuss it. Excellent. So I guess that would be it. So thanks everybody watching for being here. And I'd like to remind everyone that this is our last webinar of the year. We're going to take a break. And we start next year probably mid January. We still haven't announced our list of speakers, but please stay tuned as we'll probably announce it soon. Okay. And well, yeah, hope you have a good holiday. I think I can, I can put a little emoticon here. Yeah. I think I hope you're seeing this. All right. And enjoy your, your holidays and we'll, we'll see you next year. See you and thank you again. Thank you again for the invitation.