 Hello everyone and welcome to the Latin America and webinar of physics. I am Roberto Linero from Instituto de Física Corpuscular in Valencian Spain and I will be the host of the first webinar of the session 2 which is in fact the 10th webinar of the series. So today we have a very interesting talk in the line of neutrinos and LHC signatures but before we start with the talk itself I want to tell you about how to contact us in case if you want to make questions you can use the Q&A system and the hashtag layer OP in Twitter you can see here in this part of the screen and if you want to contact it in case if you want to give up some comments or you are interested to give a seminar, a webinar you can contact it here to Twitter or via email to this Gmail address. So now we start again, we pass with Joel that is going to be at the speaker. He is from Pontifici Universidad Catolica del Perú where he is currently a professor there and that is an institution. He obtained a PhD at the University of Valencia and after that he realized a postdoc at INFN in Frascati in Italy and after that a postdoc at CERN thanks to the Valencian program Balimazde. So his title is Proving the Type 1 CISO Mechanism with Displaced Vertices at LAC and I guess now Joel you have all the power on the webinars. Please. Okay. Thank you very much. Everybody can see me. So let me try to share my screen. So I'll share my desktop and here we go. Okay. So everything's okay. Everybody can see this? Yes. We can see. Okay. Fantastic. So thanks everybody for being here. My talk is titled Proving the Type 1 CISO Mechanism with Displaced Vertices at LAC. It's a work already on the archive and has been submitted for publication and it has been done in collaboration with Alberto Gago, Pilar Hernandez, Marta Lozada and Alex Moreno. So this talk is based on a CISO model, a Type 1 CISO model called the 3 plus 2 minimal neutrino model. It's basically a Type 1 CISO with just two heavy fermionic singlets that we call right handed neutrinos or sometimes sterile neutrinos. You can see the Lagrangian from the model right in front of you. So basically you have the standard model Lagrangian. You add a kinetic term for the sterile neutrinos. Furthermore, you are adding a Yukawa coupling between the active neutrinos, the heavy neutrinos and the Higgs. And finally a Majorana mass term for the sterile neutrinos. You proceed the procedure is standard, right? So after electroic symmetry breaking, you can reconstruct the CISO mass matrix and then a diagonalization of this matrix gives you a mass matrix for the light neutrinos that follows more or less this structure. So mainly the idea here is that the lightness of the neutrinos that we observe is due to the heaviness of the sterile neutrinos. So after the diagonalization, we initially have the three active neutrinos and the two sterile neutrinos. So after the diagonalization, we get one massless neutrinos because we're only adding two heavy neutrinos, so one active becomes a massless. We have two light neutrinos and two heavies. The light ones are mostly active, the two heavy ones are mostly sterile, but they have mixed components. This mixing is described by the 5x5 mixing matrix, which is decomposed into four blocks as shown on the right side of the slide. So we have a mixing between the actives and the lights, which is the upper left part. You have a mixing between the actives and the heavies, the sterile and the lights, the sterile and the heavies. So how can we actually test this model? In order to test it, what we should do is we should actually, after observing the heavy neutrinos, we should observe the coupling between the Higgs bosons, the active neutrinos, and the heavy neutrinos. This is the ultimate test for the seesome model. Nevertheless, this is generally expected to be impossible. The standard law is that if we want to make the Yukawa couplings large, then the singlet masses must be unreachable. So here's again the neutrino mass matrix, and here we can see that if the Yukawa's are of order one, then the right-handed neutrino masses need to increase. In order to keep the light neutrino masses small enough. So then one would expect the seesome mechanism to be impossible to test. If one makes the heavy neutrinos light enough, then the Yukawa couplings are too small and the coupling is unmeasurable. We're going to argue that this is not the general case. There are specific models, specific realizations of the model, where you can actually have light masses and large couplings too. So then the question is, if these heavy neutrinos are light enough, such that they could be produced at LHC energies, then is it actually possible to measure their coupling with the Higgs bosons? So this is the main objective of this work. So this is the outline of the talk. So first of all, I'm going to talk about the parameter space of the model. Then we shall apply some constraints on it. And then we'll go into the observables that we're interested in. Namely, we shall study the Higgs decays into heavy neutrinos. So we'll assume that the heavy neutrinos are lighter than the Higgs. And then we shall concentrate on the decay of the heavy neutrinos through a displaced vertex signal. So this is a parameter space. Well, these are the blocks that we care about in the parameter space. So here we have the active light mixing and the active heavy mixing. And we see several components here. So first of all, we have a unitary mixing matrix, UPMS. And we have also a Hermitian matrix H, which will describe non-unitary effects in the active light mixing. The active light mixing is the one that we actually observe in neutrinosilations. And generally, it can be very well approximated by a unitary mixing matrix, just a PMMS matrix. The Hermitian matrix A shall generally be almost the identity matrix. Furthermore, on the active heavy mixing, we find the two diagonal, two times two mass matrices. So ML has got the light neutrino masses, and MH has got the heavy neutrino masses. So here we see the suppression appearing in the active heavy mixing. We see that the suppression goes like the light mass over the heavy mass square root of that. So this is the main suppression that we get in the active heavy mixing. It's a very strong suppression. Finally, we find a complex orthogonal matrix. This can be parameterized through the sine and cosine of a complex angle. The real part of this complex angle, we call theta 45. And the imaginary part of this complex angle, we call gamma 45. And it's this gamma 45, the most important part of this model. If we have an imaginary angle, then the sines and cosines shall be related to hyperbolic sines and hyperbolic cosines. So that means that we can get an exponential enhancement on the active heavy mixing. So the idea is if we enhance gamma 45, then we can get an exponential enhancement to the active heavy mixing. Now let's understand this a bit better. We can go to the limit where gamma 45 is large and where the H matrix is identical to the identity matrix. So in this case, if we have gamma 45 large, say larger than 3, and the H approximately the identity matrix, we come in the right way. So here we see that we have the exponential enhancement due to the hyperbolic cosine of gamma 45. We also see the suppression where we find the square root of the light neutrino masses. In this case, it's M3, which is equal to the square root of the atmospheric mass difference. And that is divided by each of the heavy masses. We also see that there's no relevant role for theta 45. It's just a phase. So since we're going to be taking the modular of this mixing, then this phase shall disappear entirely. And finally, we have this Z factor, which is more or less an order one. It depends on the mixing angles and on the ratio between the masses. So it's a very easy way to understand how the active heavy mixing behaves. Nevertheless, in this work, we shall use the full active heavy mixing matrix. The story is the same for the Yukawa couplings. One can rebuild them and one can see that they have this shape. That term that we care about is this one. So we can see that if we want to increase the size of the Yukawa couplings, we need either to increase the heavy masses or we need to increase the parameters within the R matrix. So since we want to keep MH small enough, then what we need to do is increase R. So the same as before, we can increase gamma 45 and take H similar to the identity and we can reconstruct the Yukawa matrix and prove that they have more or less this shape. So again, we see directly that we can maximize this by maximizing gamma 45. So that's going to be our objective from now on. We're going to try to maximize gamma 45. So what kind of structure does this lead us into? So we can prove that for large gamma 45 and degenerate Majorana masses, we can perform a change of basis and write the neutrino mass matrix as an inverse CISO-like matrix. So this more or less explains why we're having these very large Yukawa's and these light masses. This situation is common in an inverse CISO scenarios. If we do not have degenerate Majorana masses, we can still write it in a similar way. In this case, we find we have a large ish element on the say 2-2 part of the matrix. So we have an extended CISO-like structure. All of these structures can be justified by assuming, say, a lepton number symmetry of the high scale, which is at some point broke. So the mu and mu prime parameters are those that can break this lepton number. So let's go into the constraints. First of all, we shall consider neutrino less double beta decay. Then we shall take into account lepton flavor violation and direct searches. Even though loop corrections are also important, we shall not take them into account as they will be taken care of when we solve the constraints of neutrino less double beta decay. So let's go with the first constraint. We find that the non-observation of this process can constrain very strongly gamma 45. So the plot here shows the space of the two heavy masses M1 and M2. And the contours indicate the maximum value that gamma 45 can have provided that the neutrino less double beta decay is not observed. So we see that for light heavy neutrinos, the maximum value of gamma 45 we can have is about, say, 5 or 6. That will not be very good. Nevertheless, if we go to the limit where M1 is equal to M2, so we go to the diagonal of this line, we see that the bounds are greatly weakened and we can go to gamma 45 larger than 10. So that's more or less what we're going to do. The reason for this is that when we go to degenerate neutrino masses, we only have one parameter breaking lepton number. And that is the one that will give the light neutrinos their mass. So the contribution to neutrino less double beta decay shall always be proportional to this number. So here we have the situation in formulas. So here in this capital M beta beta, we have the lowercase beta beta, which is a standard contribution to neutrino less double beta decay from light neutrinos. And then the second term gives us that contribution from the heavy ones. On the square brackets, we see why gamma 45 is so strongly constrained. We see here that we also have an exponential enhancement. These terms are smallish terms that we don't really need to worry about too much right now. But we see that multiplying the square brackets, we have this delta M term. And that is the difference between the matrix elements. So when the two neutrino masses are equal, this term vanishes. And the neutrino less double beta decay is under control. This again is due to having only one parameter breaking lepton number. So that's why we still get the M beta beta contribution. So this is one situation that we're going to face. So what we're going to do is we're going to set M1 equal to M2 for definiteness. That's the only parameters that we care about are M1 and gamma 45. So the active heavy mixing becomes the same, both for the neutrino, say 1 and the neutrino 2. Okay, now comes lepton flare violation. We see that here again we have an enhancement for the processes. The processes we care about are those like mu e gamma decay and mu e conversion in nuclei. And here we get a bound even if the neutrinos are degenerate. On the plot we see the rates for mu e conversion, which imposes the most stringent constraint on our parameter space. The current bound, which comes from the syndrome experiment with gold, doesn't allow gamma 45 to be larger than 10. In the future, maybe the mu 2e experiment and the comet experiment, I believe, shall try to probe mu e conversion using aluminum. And given their expectations, we might be able to bound gamma 45 up to values of 8 more or less. Okay, so that's an important constraint that needs to be taken into account. Nevertheless, the most important constraint is the one that comes from direct searches. Here we have many experiments that have tried to directly produce the heavy neutrinos. The important constraints for our work will be those, for instance, of Charm and Delphi. Here we see that we're constraining the mixing between the electron neutrino and the lightest heavy neutrino. So we have put here u e4 squared. We also have analogous constraints for the mixing between the muon neutrino and the heavy neutrinos. What we find is that in our model, this is the most stringent one. The bound on the mixing between the muon and the heavy neutrinos. So this is the one that we're going to use in the following, as it is. Okay, so these are the constraints that we're imposing. Let's now have a look at Higgs decays. So possible scenarios are the Higgs decaying into two light neutrinos. The Higgs decaying into a light neutrinos and a heavy neutrinos, or the Higgs decaying into two heavy neutrinos. What we find is that the largest contribution to the Higgs branching ratio comes from Higgs going into one light neutrinos and one heavy neutrinos. So here is the partial width for this decay. It might give you the impression that this decay will be proportional to the heavy neutrinomass divided by the W mass squared. Since there's a term like that right in front of it. Nevertheless, there's a Cij term, which is a matrix, and from there one sees that one gets a suppression that goes like the heavy neutrinomass. So at the end of the day, what one observes is that this process shall be proportional to one power of the light neutrinomass, one power of the heavy neutrinomass divided by the W mass squared. This is a very strong suppression. Nevertheless, it's the least suppressed of all of the decays, and it can be enhanced by gamma 4 or 5 as we see that the R matrix is appearing there. So this is the decay that we're going to explore. Now we'll see the values of the branching ratio within the parameter space. So here we have again the mixing between the active neon neutrinos and the neutrino 4 versus the heavy neutrinomass. The blue region is excluded by direct searches, as I showed you before, and the red region is excluded by mu A conversion in gold. So we see that these exclusion regions don't allow us to have branching ratios larger than 10 to the minus 2. So we're talking about small branching ratios here. We can see branching ratios as low as 10 to the minus 4, 10 to the minus 6. This shall not worry us too much. 10 to the minus 4 is the branching ratio for Higgs decay into two muons, and we expect to be able to measure that at the LHC. We shall consider branching ratios as small as 10 to the minus 5 in the following. So that's that. Now which channel are we going to choose? What we're going to do is we're going to have the Higgs decaying into a light neutrinomass and a heavy neutrinomass, and then we shall allow the neutrinomass to travel a macroscopic distance between 1 mm and 1 m. And then the heavy neutrinomass shall decay. This is an example of what you see on the screen. You can see a decay into a charged lepton and two jets. So in this case, for example, the signature would be Higgs going into charged lepton, two jets missing energy from the initial light neutrinomass and the displaced vertex. Now the question is in what part of the parameter space can we actually measure this sort of signature and how to actually model it. Now trying to reproduce displaced vertices is not very easy. Generally, one says, oh yeah, displaced vertices are background free, but this is not really true. Sometimes, in some cases, you have interaction in normal standard model particles and the material within the detector. So if we want to do a serious study of this, we would need to simulate the whole detector. And that is something that was beyond the scope of our work. We might want to do this eventually in collaboration with an experiment, but for this work we decided to stop and not do that. So we shall carry out a simpler analysis that can be used as a guide for experimental collaborations so they can actually put the appropriate triggers and cuts later. So the objective now is to first of all present the region of the parameter space where actually we can see displaced vertices, then study the branching ratios and see which channels are the ones that would give us a larger number of events. And then we'll put some representative LHC cuts just to see what happens. So first of all, for the first part of the study, we use this formula to get the number of events with displaced vertices. So first of all, you see this is not as complicated as it looks. This is basically a large integral that includes Higgs production through glue and fusion and then the decay of the Higgs into a heavy notrino and a light notrino. So here we have in L the LHC luminosity which we take equal to 300 inverse femtovarnes. The last term on the first line is Higgs production differential distribution which depends on the Higgs transverse momentum and the Higgs rapidity from the code Sushi and the code more Sushi combined. Then we have a notrino decay differential distribution which depends on the notrino transverse momentum and the angle between the Higgs and the heavy notrino transverse momenta. We also need to include some Lorentz factors there and well, the notrino decay distribution we have calculated it by hand. Furthermore, we impose the allowed decay lengths using heavy side theta functions between one millimeter and one meter. So we use this formula and we find that the region of the parameter space that would lead us to having displaced vertices is the one that you're actually seeing on the screen. This of course doesn't involve the posterior notrino decay so it's kind of like a preliminary plot of what we're actually interested in. The red region has got more than 250 events, right? 250 Higgs decays into a heavy notrino giving us a displaced vertex at the LHC with 300 inverse factor bands. The orange region is the same but will give us more than 50 events. The dashed line over there is the future prospect for newly conversion. So for instance, if nature decides to be for instance on the dot that you see on the screen which is a benchmark point that we use on the paper, we would find a nice cross check between newly conversion and the search for displaced vertices so we would have an interplay between low energy and high energy experiments. So that of course is not the end of the story. We need to make the notrino decay. So first of all we need to understand what are the notrino branching ratios. So these are all of the branching ratios that we have taken into account and we shall choose one channel for definiteness and the one that we shall choose is a decay into a muon and two jets. We did this because there was a similar analysis done by Atlas and we tried to use it as a guide at that point. We later found out that it wasn't an appropriate guide but at least it will help us understand what the problems are with this image as we shall see in a moment. So in this case the formula becomes slightly more complicated but not too bad. The upper part of the formula you have seen, you have the Higgs production and decay again. The lower part has got the heavy notrino decay distribution. This one is a bit more complicated in order to actually calculate this is a three body decay. We need to go into different frames at some point so we need to do Lorentz transformations within the differential distribution. It's not a simple calculation. Nevertheless we have done it analytically. In the final part we have a function that will impose all of the detector constraints. So our requirements on the displaced vertex shall be within this function which we can also impose constraints from pseudo-rapidity because of course not every part of the detector is sensitive to our final states. And then we shall also put some other additional cuts there just to understand what's going on. So if we do not impose any cuts at all, this is the situation. So here the only difference that we have with respect to the previous plot is that we're adding the branching ratio from the notrino into one muon and two jets. This is the only difference. So the brown region has got more than 100 events and the green region has got more than 10 events. So this is a starting point. Now we're going to add the constraints coming from the pseudo-rapidity constraints of the detectors. So we cannot allow the muons to have a pseudo-rapidity larger than 2.4 and the quarks, the jets cannot have a pseudo-rapidity larger than 2.5 for instance. So if we impose those constraints, this region of course is reduced. We get this one. So we see that only now a very small area of the parameter space has got more than 100 events and most of them have got more than 10. Now it's absolutely legal to ask, well, is 10 events good enough? Of course, at this point we don't really know. It depends on the posterior cuts and how the backgrounds behave with those cuts. Nevertheless, if we manage to reduce these cuts, then say 5-10 events is generally considered to be good enough. So what happens when we add cuts? Let's suppose that we're adding a cut on the muon transverse momentum. And on this plot we see how the number of events changes as a function of the cut. Here we're sampling two values of the heavy neutrino mass. So the yellow dots have got a mass of 3 GV, the blue dots have got a mass of 15 GV. So we see that they don't change very much. We see that the ratio of events is decreased very strongly as we increase the cuts. For instance, if we impose a cut of 20 GV on the PT of the muon, which is a typical trigger from the first run of the LHC, we see that our number of events is reduced down to 40%, which is not good at all. If we try instead to impose a 30 GV cut on the muon transverse momentum, which is an expected cut for the run-through of the LHC, we see that the number of events is reduced down to 20%. So if we initially had, say, 50 events, then we shall end up with 10, which is not very good considering that we are not adding any cuts on the jets and no efficiencies. So the main conclusion is that these PT cuts are just too strong. We shall need to require dedicated triggers for this kind of signature. The study of such dedicated triggers was out of the scope of this work, as I mentioned previously. We're actually doing some literature search to see if we can actually propose some better triggers. Nevertheless, we did study the impact of some other constraints. For instance, a cut on the missing energy is much better. We see that we can impose a cut up to 40 GV without reducing the number of events lower than 80%. Unfortunately, this is not good enough for triggering. This could be used for a posterior analysis after the triggers. We also can apply cuts on the effective mass, which is the sum of all of the transverse momenta and the missing energy. Here we can go up to 80 GV without drastically reducing the number of events. Nevertheless, this is as far as we went. So a posterior analysis should be done with much more detail in the future. This is where we stop, and let me conclude for now. In total, we see that if we want to actually test a seasonal mechanism, we want to test the Higgs and Neltrino coupling. If we actually want to generate these heavy Neltrinos at the GV scale, there are some schemes where one can actually enhance the coupling and avoid all constraints, constraint from Neltrino's little beta decay, lepton flare relation, and direct searches. If the heavy Neltrinos have masses between say 2 and 20 GV, the best way to actually see them is with displaced vertices. For heavier Neltrinos, there are other possibilities. Now this, as you have seen, will be very difficult to accomplish, but of course, the story has not been written yet. There are works coming out in studying other sort of models that have also got this problem of having two strong triggers, but displaced vertices. So maybe in the coming year, you might find some important progress done in this, and this observable might actually be observable soon. So thank you very much for your attention. Thank you very much for this interesting talk. So now it's time for questions. But before, just to remind the public that is watching the streaming of this webinar, that you can make questions using the Google Plus Q&A if you enter to the Google Plus page, the page of the Latin American Webinar of Physics, or via Twitter with the hashtag LAWOP. So now maybe we can start with the question from the people that are participating on this Hangout. So I don't know, you can unmute yourself and make the questions. I have a question for you. Yes, can you hear me? In this parametrical region that you focus where the units are degenerated, you avoid limits from nutrients less than the decay, right? Yeah. My question is, are other left and right signal also suppresses, for instance, like sine left and plus two jets at LHC? Yeah, I would expect so. I would expect so because here, in this limit, what we're having are pseudo-DRAC heavy nutrients. So I understand that whenever you have pseudo-DRAC heavy nutrients, all of these signatures are erased. Yeah. So you would expect only have a different sine left on at the LHC because you don't have the problem because your signal does not violate left number. But if you want to search for two left plus two jets at the LHC, you could only search for opposite sine left on. Exactly. Yeah. I wouldn't know how to actually get the same sine left on without having problems with nutrient less L beta and more importantly with the loop corrections. The loop corrections are very strong. They're stronger than the bounds from nutrient less L beta decay. Nevertheless, the same thing applies. If you impose the degenerate neutrino masses, then the loop corrections are also avoided. Yeah. Okay. So someone else has a question for Joel? I don't know. Anyway, I have some questions for Joel. So one is just the rough estimator, which is the lowest value that you could have with this right-handed neutrino, the lowest and the highest possible in order to have observable effects? In the mass? Yeah, the mass, yes, in the heavy states. Right. So it depends what kind of search you're doing. If you want to stick with this place vertices, you want the masses between 2GV and 20GV. Right. Not only for this kind of search coming from Higgs decays, but also coming from direct production or production through double decay. Right. This is due to the lifetime of the heavy neutrinos. Now, if you have heavier neutrinos, there are other kind of signals that you might want to look out for. Like decays, direct decays without the displaced vertex into, say, two charged leptons and missing energy. That has also been done. Also, other kind of signals that have been studied is a decay into a charged lepton and two jets, for example. Those involve higher mass neutrinos, say higher with masses higher than 50GV more or less. And then, of course, for lower mass neutrinos, you have had searches like the ones done before, like the Nutev experiment and things like this or Delphi, that can probe lower masses. I'm not sure if there's currently any experiment that can probe even lower masses. A ship experiment might be able to check lower masses, but I'm not really sure about that. That's more or less my understanding of the situation. Okay, thank you. Someone else has a question? I still have many. I don't know if Nicolás or Federico or Diego may have some questions. You can ask now. Another question, because you were talking about in case you go to the heavier states, heavier than the stuff in the range that you are checking, I was wondering if it is possible to make a scheme compatible, for instance, with leptogenesis, in which at least one of these states has to be very heavy. So I'm not very... I don't know much about leptogenesis. What I understand is that... I guess we... Hello, hey. I guess Joel went out of the connection. It seems that he was talking about forbidden work. Yeah, we can hear you now. Oh, you can hear me. I guess someone was avoiding that you speak about leptogenesis. Yeah, I don't know. Maybe that's one of my collaborators. I don't! So my understanding of leptogenesis, I don't really know much about this. So my understanding is that in this region there is a possibility of having leptogenesis through oscillation of the heavy states. Nevertheless, I think that in order to have correct leptogenesis, you need smaller mixings. So I'm not really sure if it's actually possible. Smaller mixing is the one that we were trying to probe. So in that case, we would need a much higher luminosity to actually get down to that leptogenesis region. But I might be completely wrong here. So let's don't take my comments with a pinch of salt. Right? Yeah, okay. Maybe we can pass now to the questions that are in the table. Let's start with a question from Diego Rostrepo that he's asking. Do you have any definitive prediction for the flavor of the final charged leptom? Oh, right. So that depends on the hierarchy that you're in. So it depends if you're in normal hierarchy or inverted hierarchy. The results I presented for you are those for the normal hierarchy. And here, just due to the structure of the PMS matrix, which appears on the mixing, the most important decay is due to, is into muons, right? These changes if you go into the inverted hierarchy. And unfortunately, don't have any plot available for that. But yeah, that is hierarchy dependent. So mostly it's muons, right? Muons and towels. Those are the ones with the largest mixing in the normal hierarchy. Electrons first of all. Okay, so we did this question. So we have another question that is, if it is possible to distinguish this frame from other point-and-sussy models in which you have broken your parity. In that case, the right-handed neutrino, the role of the right-handed neutrino is taking the place by the neutralino. Yeah, in this case, a main difference, I believe, is that we have a missing energy, right? So most of the parity, the broken parity searches I see and are into basically checks, right? Or maybe checks and charge leptons. This could be mimicked, I think, if you have a neutrino, a light neutrino in the final state. Yeah, this is the only possibility I can think about right now. Nevertheless, I have never seen such a search. Yeah, I think that's the main difference, right? The missing energy. The parity-violating case. Okay, so in principle, both models have different signatures. I mean, can be searched in different ways or can be possible to distinguish both? Yeah, I believe so. Okay, so another question is, and I have one here that I noted with my hand, that is, I mean, maybe this is not a question about your talking exactly, but if you know about what happened in other kind of seesaw mechanisms, instead of having a single right-handed neutrino, you have a triplet leptons or whatever that can have all the type of things. No idea at all. I think this is not really feasible on the type II seesaw, but I'm not really sure. But yeah, I haven't really considered other seesaw models. I think that there have been some works on the type III seesaw scenario. So yeah, I would expect something over there, too. But I wouldn't know about the type II. Okay, we have a fast question from Diego that he's asking, what happened with the flavor? Maybe it was related with the previous question. He's completing the question afterwards. What happens with the flavor of the final charged lepton in inverse hierarchy case? Okay, sorry. No, that's basically what I said previously. There you can have the electron coming out with larger rates than the ones. Maybe we can go back to... You can show the slides if you need. Yeah, let's see. Let me go back to those of the branching ratio. So am I sharing the screen or are you sharing the screen? Can you actually see me? I can see you, but you have to turn off your camera and share your screen. Okay, let me do that. Turn camera off. Let me screen share. Okay, so do you see this? Yes, we saw. Okay, so here what we see, for instance, is the green curve. It's the one that involves a muon. Then you have the orange curve giving you the muon. Then you have the green one involving tals. And then down here, right, the red gives you the electrons. This is due mainly to the structure of the mixing. So let's go back to the beginning. Okay, so here we see why this is the case. So for instance, if we replace here, say, on the active heavy mixing, electron to one, right, E1, which is a mix between the electron and the heavy neutrino, you find that what you care about here is the 1, 3 element of the PMNS matrix. So that is sine 1, 3. So that's why this is very much suppressed with respect to the other flavors, right? With respect to 2, 3 or 3, 3, which are much larger. Now, if you go into the inverted hierarchy, these changes, I'm not exactly sure what was the prediction for the inverted hierarchy. I think that you had a 2, 3 element here for the, sorry, an L2 element here, right? So here then the column of the PMNS matrix that is involved is different, right? So here you have a much more democratic distribution between the flavors. This is just a problem of the normal hierarchy. So I'm hoping I was clear on this. I hope so. I hope they all can give a thumb up about the answer of the question. Okay, maybe. We still have more questions here. So one is one that, my mistake, it's selected, but it was not, I didn't ask, was the, maybe it's a kind of a goal about the experimental side. What is the status of this displaced vertex analysis? Because it's kind of, it's not so popular to do it now. Currently, or in the previous analysis at the LHC, they haven't done. So there is some... On previous analysis, they have all considered very high mass particles decaying. So that's why they didn't worry too much with the triggers, right? With the muon triggers. So all of the things, all of the constraints had very high PT, right? Had very high PT requirements. Now that the Higgs has been found to be lightish, right? People are considering this kind of the case, not only into heavy neutrinos, but also into hidden valet particles or some other things that I don't really know about. But all of the things share the same feature that they are light and their final momentum is very, the transfer of momentum of their final state is very soft. So I have seen recently, say a couple months ago, some new papers coming out trying to propose new triggers. How this is being taken by the experimental collaborations, I don't know. I'm hoping to talk with somebody involved in these things in the coming weeks, but I really, at the moment, I'm unable to tell you how the experimental collaborations are taking this into account. Yeah, okay. In the future, we will know. We will know for sure. So the situation right now has been, unfortunately, not very encouraging since most of the searches have been focusing on very large mass particles. So another few small questions, is if these CP phases in the neutrinos sector may have a role, take a role in this kind of, not in this case observable. Not in this place vertices because you don't have any interference effects here. So then it's just a moduli squared and that's about it. Now, there's an interesting thing. Actually, no, actually, this is something else. Let me correct myself. So let's go back to my slide. I'm so sorry I'm doing this today. So let's see. Let me turn off my camera. Okay, let me share my screen desktop. And let's go back to the slides. Okay, so here you see the active heavy mixing again. Does everybody see this? Yes, I guess everybody is looking at that. So here what you can see actually is that the mixing will involve the phases of different PMNS elements. So here when I'm talking about the PMNS matrix, I'm also including the Majorana phases. So when you square this, you might have some interference effects between one part and the other. Of course, since you have the suppression of the neutrino masses, this is not very encouraging, but in principle you could get some effect due to the interference between these elements. But that's as much as I can tell you. Now the Higgs decay on the other hand, let me show you, the Higgs depends on this Cij element. So Cij doesn't depend on the PMNS matrix at all. It's only the posterior decay of the heavy neutrino, which might have some very small sensitivity to the CP phases. So for instance, this might be measurable with the W's, but not with the Higgs. But still, I expect this to be a very small effect. Okay, so it's in principle a small effect. It may be important, maybe in the case where you go to very high energies like in the leptogenesis scenarios, because usually at that point everything is available at the energy scale is so large that you can have it. So I don't know if the rest of the people have some other questions for Joel. Just let me check if Twitter we have some questions there. No, it seems that we don't have. I don't know, Nicolas or Juan Carlos, Federico or Diego, if you have some many questions. I guess no. So let's start to close this webinar. So first of all, I want to remind everybody to... First of all, I want to acknowledge Joel for this nice webinar. And also to remind that if you want to contact us for any doubt, suggestions or comments or if you want to propose a webinar that we can host, in this size you can see the Twitter address or Twitter address and our Gmail address in order to contact. So I hope that you have enjoyed this webinar and don't forget also to subscribe to our YouTube channel in which you can find all the previous webinars and you can watch it again and maybe to have some questions, you can address questions directly with the speaker. And I hope to see you again in the next Latin American webinar of physics that in principle is going to be the 7th of October where the speaker is going to be Diego Aristizaval from the University of Liege and he will talk about something related with leptogenesis. Many of the questions that I was doing before to Joel. So see you in the next opportunity and bye to everybody and also to the people that follow this streaming internet.