 Okay, hello everyone and welcome once again to the Latin American webinars on physics. I am Joel Jones from the PUCP in Peru and I will be your host today. This is webinar number 68 and we're having Marisa López-Iváñez as a speaker. Marisa started her physics career in Murcia, Spain and moved to Valencia to do her PhD. During these studies she has had close collaborations with the KIES in South Korea and the University of Padova in Italy and she's currently doing a postdoc at Roma Tree in Italy. So today Marisa will tell us the latest news in effective theories of flavor in the context of the non-universal MSSM and we're very happy to have her as a speaker today. So before we begin let me remind the viewers that you can ask questions and comments via the YouTube live chat system and these questions will be passed on to Marisa at the end of her talk. So having said that I'll pass the microphone to Marisa. So let's see, here we go. Everything good? Yes, well first of all I would like to thank the organizers for inviting me to present this work and I'm going to share my screen like this. Everything fine? Okay, can you see it? Everything good. Okay, so I'm going to present the main results in these three references that have been a working collaboration with all these people and as you have said before I'm going to talk about the study of flavor symmetries in supersymmetry. In particular the main idea is seeing this like a very useful strategy because in this way we can get additional information about these two sectors. In particular what we can expect for this type of analysis are new flavor violating effects that can be translated in terms of correlations among observables and also as constrained over the parameter space in supersymmetric models. So this is the outline of my talk. I will start motivating the study of flavor symmetries in supersymmetry. Then I will show you the main implication of doing so and how all the flavor structures must be compute in order to account for all the possible effects. And finally I will show you some examples that we have studied for these flavor groups. And I will conclude with some remarks. So first of all why flavor symmetries? We know that one of the most intriguing and open question in the standard model is the fundamental origin of the flavor sector. We've been able to measure almost all the parameters related to fermion masses and some mixings but still there are just numbers that we put in our Lagrangian in our model. We don't know if there's some hidden principle behind it because in fact what we can observe too is that all these parameters are not just order one coefficient that would be like the natural option if we see the standard model as an effective theory at low energy but they obey some patterns. In particular we observe that the charge fermions have very hierarchical masses with small mixings among generations while for the neutrinos the masses seems to be more degenerated and the mixings are larger. So that the obvious question at this point is there any symmetry behind this pattern? And a nice solution to this question is the Frogan-Nielsen mechanism that suggests that the Yukawa coupling can be effectively generated as a power of this expansion of parameters once a flavor symmetry is spontaneously broken by the waves of some color that we will call flavons. So arranging the mass, the charges of these matter fields we will have diagrams of this type where these are the flavons, these are very heavy mediators and depending on this charge there is a number of insertions that number of insertions will be related with the power of this epsilon parameter with this expansion parameter which is just the ratio between the wave of these fields and the masses of this very heavy mediator. This has been a very useful strategy and a very well-known strategy. Many flavor groups have been proposed as flavor symmetries but still we are left with one question and it is how can we distinguish among all these models? They have excellent prediction but still they don't predict new effects that we can measure with which we could test this model and in this sense super symmetry can be very useful because in order to have prediction we need new observable, new flavor effects. Another reason why studied flavor symmetries in super symmetry can be very interesting comes from the experimental side. We know that the LHC will run until 2035 but still we don't expect that the mass limits of the SUZI particle increase. We expect more precision. We expect that the higher bounds of two TVs or so for gruinus for instance and for this particle will be extended for non-minimal model but we don't expect go beyond this. So we need indirect hints of new physics. We need to think about new ways of test the present of new physics and in this sense introducing flavor symmetries in our super symmetric model can be a way to proceed. So having said that I'm going to show you how this can be done. So let's consider a flavor symmetry in super symmetry. The first thing that we have to think about is about the scales. We know that super symmetry must be broken. We know also that this breaking must occur in a high-end sector and has to be transmitted somehow to the visible sector. That sets the first scale. The scale at which super symmetry breaking is transmitted. We have another scale in the model which is the scale at which the flavor symmetry is broken. And according to this we can have two scenarios. The first scenario is that in which the flavor symmetry is broken below the scale at which super symmetry the breaking of super symmetry is transmitted. In this case that means that we have soft terms above before the flavor symmetry is broken. And the soft term like the rest of the sector in the theory has to be symmetric under the flavor group. Once the flavor group is broken in the same way that the Yucavas had or inherited a non-trivial structure due to the flavor group, the soft term will inherit a similar one. The other possibility is this one. The other possibility is having the transmission of super symmetry breaking of course below the scale at which the flavor symmetry is broken. And in this case we will have not additional flavor structure to those which are already present in the standard model. An example of this type of scenario is super gravity. An example of this type of scenario could be gauge mediated model. Of course we will be interested in this possibility. So let's consider for instance a super gravity model. In order to be conservative we want to consider the simplest one in which the breaking of super symmetry is given by this single universal field. In this case this model will be defined by our super potential, our carol potential and the gauge kinetic function. And all this function can be written in terms of this supersymmetric part and this part that will break super symmetry. As we are considering a gravity mediated model, the terms that will break super symmetry are suppressed by the planche scale. From the super potential, from these yukawa like terms, we will obtain the tri-linear in the sub-breaking Lagrangian. And from these corrections to the color, we will obtain the sub-massage. Once the spurion field, the f term of the spurion field gets its depth different from zero. What is important to note here too is this is the unusual gravity mediated model. We haven't introduced yet any flavor symmetry. And what is important to note here is that no matter which fields we have in this term for instant, the proportionality factor that relates the tri-linear, which will be all this with the yukawa, which is this one, will be a constant factor which is given by this and the same for the sub-massage. What we claim and what I'm going to show you now is that this universal constant will not be universal in the presence of a flavor symmetry and it will change and this has important implications because this will generate flavor violating effects. So that is what I'm going to show you now. Let's consider my super-gravity-like model with a flavor symmetry. Now the yukawa cup that normally are in the super potential are no longer allowed, but I write my super symmetric super potential with a part which is renormalizable plus higher-order operators. And this higher-order operator contains the flavors and the heavy mediators that have been integrated out. So this operator could be written in terms of a super graph. Super graph of this type with a number of leonisertia which is related with this power and the heavy mediators. Now I want to compute the tri-linear term and as I have shown you before, what I have to do is multiply the spurion field by the super symmetric super potential. In terms of super graph, that means inserting the spurion field in the diagram that I had before. However, I have to do this very carefully because this has been done in many different ways. In principle, I could attach this X field in this vertex, but also in this vertex, in this vertex, etc. That means that now my tri-linear element will not be proportional just to this universal constant plus the corresponding yukawa coupling, but also I have this proportionality factor that accounts for the generacy of the diagram. It accounts for all the possible diagrams that I can write and contribute to the same element. And something similar happened for the color and the soft masses. In the presence of a flavor symmetry, I can write my color potential like this where this will be the canonical term. And these are higher-order terms that contain the flavor contributions. And this term comes from a living order, from diagrams of this type. I can put this bubble of flavors entering, this bubble of flavors leaving, connected by these mediators. I could have other type of diagrams with randomly distributed flavors entering and leaving, but they will be subdominant. So in principle, these are the leading order contributions to these higher-order operators. When I integrate out the heavy mediators, I obtain this. Each of these bubbles that I have shown you are just a set of flavors entering or flavors leaving with the heavy mediators here. Now I want to compute the soft masses. And for that, the only thing that I have to do is multiply the color by this spoon combination. In terms of superglue, that means inserting the eggs fill and eggs dagger fill to the previous diagram. Again, I can do this in different ways. And I have to consider all the possible contributions. The first one is attaching the eggs and eggs dagger fill to this heavy mediator. And this gives me this contribution. Now I can also attach the entering fill to this bubble and the leaving fill to this other bubble. And as I have told you, each of these bubbles is just a set of fills entering. For each bubble, I will have different contributions that can be 2N minus 1. Because for one flavoring session, I have two possibilities and at the end, just one. So 2N minus 1. And the same for the bubble of fills leaving. So with this, I will have the basic ingredients for computing the softness from the color and the superpotential to the yukaba couplings. And why is this important? Because as I have just shown you, all the term by term trilingual and soft mass elements will be proportional to the corresponding yukabas and color metric elements. If I look at the complete matrix, the trilingual and soft mass matrices are not directly proportional to the yukaba and color potential. That means that when I want to study the phenomenology of my model and I go to the physical basis where the color is canonical normalized because it is related to the kinetic terms. So it has to be the identity and I go to the mass basis where the yukabas are diagonal as these two matrices are not directly proportional to these two other ones. They will get not diagonalized and therefore new flavor violation effects will arise. And this is our plan, even for a very simplified SUZI model, like this super gravity like model, even having a single universal source of SUZI breaking. In general, we will have non-universal flavor structures. And that is what I'm going to show you now for some of the models that we have studied. So I'm going to explain this A4 model. This A4 model from Artarelli and Mironi is a new version of a previous one where they don't need a U1 continuous Frogan Nielsen symmetry to generate the hierarchy in the yukabas, but they just do it from the super potential. Symmetries, the right handed neutrinos will be in this triple representation, left handed leptons will be in another triple representation, and the chart leptons, right handed chart leptons will transform as single representation. This will be the flavons that break the symmetry and the two usual doublet peaks in supersymmetry. Now this model predicts a maximal mixing for the neutrinos at leading order, and they reproduce the theta 1, 3 angle, and actually leading order as proportional to epsilon prime. At leading order, this model generates the diagonal yukabas. This term generates the 3-3 element, this one the 2-2, and this last one the 1-1. Then considering corrections to the leading order super potential, we obtain the diagonal entries, which as you can see here, they are just the diagonal power multiplied by epsilon prime. So this line will be epsilon to the 3 by epsilon prime, this will be epsilon square epsilon prime, and this one epsilon epsilon prime. Another thing important here is that we can identify directly the power of this epsilon in the yukabas matrix with the number of flavon insertions that we will have in the diagonal. Because here epsilon to the 3 means that I have here 3 flavons. Here epsilon to means that I have here 2 flavons. Therefore, we can just use this expression that we have obtained before to compute the trilinear matrix. From this element, for instance, I will have the same by this pre-factor obtained like this. Here that I have epsilon square, I will have 2 flavon insertions with mean a pre-factor of 5, etc. So in this way, I compute my trilinear matrix. The same for the color. We take the fields with the chart assignment here in this table, and we compute all the leading order terms that enter the color for the left-handed fields and for the right-handed fields. And like this, we can compute the color metric. What I wanted to make you note here is that, for instance, while terms of this type could be removed, in principle, adding new symmetries, a term like this in the left-handed color cannot be removed. Because in principle, having L, Ldada, Fies, Fies-dada is a neutral contribution. So in principle, terms like this will be always present. And what I wanted to point out here, too, is the elements with this operator contribute in the color. Because it contributes to the left-handed color and to these elements here, which will be important when I discuss the results in the following slide. Now, having these structures, I can compute the soft masses. The soft masses for left-handed fields and for right-handed fields. I just have to use, again, this expression that we have obtained before to compute the proportionality factor. Here, I have, for instance, epsilon prime squared, which means, to play one insertion, one entering, one leaving. We did here this number, and I obtained the proportionality factor, and that can be done for element by element. And these are the results that we obtained for this A4 model. First form, for studying the phenomenology, I have to go, as I have said before, to the canonical basis where the calia are the identity. And then I have to go to the mass basis where the yukavas are the diagonal. And although I have not put here how are the final expression for these matrices, the effect that these rotations have are just a modification of the order 1 coefficient of these prefactors here. Now, we observe that the most sensitive observables are those related to muetransition. We represent here, in this plot, M0 and 1 half, which are the usual parameters for a mensugura model. And we compute the, we analyze the phenomenology for those reference values of tangent beta. We have for tangent beta 5, this contour and this one, and for tangent beta beta, this one, and this one. And we also observe that for currents bounds, the process mu e gamma is the one that is most constraining. And we obtain these two shapes, while for future bounds, the most sensitive process is mutually voting that give us this area for this excluded area for tangent beta 5 and this excluded area for tangent beta 20. This part of the parameter space will be related to the star of the LSP. And this part of the parameter space will not reproduce the correct electro-wix symmetry rating. So, in principle, we will live with this part, and this part will be excluded in the case of not finding any signal by these processes. Now this will be this part and this part, and in the future, this part. What can be also noted here is that even for small values of tangent beta, mu e gamma, the bound set by mu e gamma is already competitive with that coming from Atlas for mensugura models. Also, I would like to comment here that the shapes that we observe here are the typical one, the typical that we could expect in the presence of left-left mass insertions. In the mass insertion approximation, we have checked this numerical result with the analytic formulae and we obtain a good agreement. So, we observe that this big growth of the bounds with tangent beta is due to the tangent beta enhanced third present in the expressions due to the internal chirality flip. Also, I have put here this sentence about irreducible bounds related to the comment that I have made before relating to this. In principle, this type of operator cannot be removed from our color and it contributes to these terms in the color and in the left-handed soft mass set. The 1, 2, and 2, 1 entries are directly responsible for this type of transitions. So, in principle, this bound could not be improved even if we try to put additional symmetries to remove these terms. Another model that I want to show you is this S3 model from Meloni. In this type of model, we have just doublet representation, the right-handed neutrino will be given in this doublet representation. The left-handed leptons will be given in doublets for the mu or for the tau and the right-handed and left-handed electron will be given in this ultransfor and single representation like this. This will be the flavors that break the symmetry and the hexes. In this model, the superpotenzial is given by this expression. The leading order tens generate this 2, 3 block. This term here will generate these entries. This term here, these other entries. And the last one, the 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3. Again, the power of the epsilon and epsilon prime tell us the number of labor insertion. So if we think in the diagram that I have shown you before, just using this expression, we can compute the pre-factors from the trilinears. The trilinear will keep the same structure that the yukavas with these proportionality factors in front. And now we can do the same for the color. We consider all the particles that we have in our model. We compute the possible operators present for related to the left-handed field and right-handed field and we write our color. For the left-handed color, we'll have this expression while for the right-handed color, we'll have this other expression. Now you can observe that these operators within principle will be always here, contribute to the two three and three two n three, which is much less dangerous than the previous one. Now this term here is the one that contributes to the one two to one in the present of additional symmetries we could add new symmetries and trying to avoid it if the terms of the model will be fine with this. From this structure here and with the expression that we have used before and we have obtained it, we can compute the left-handed and right-handed matrices, soft matrices with the corresponding pre-factors and we will have these results. And now this will be our result. Again, we go to the canonical basis where the color are the identity. We go to the mass basis where the yukavas are the diagonal and again, all these rotations only change or they're one coefficient that we have obtained here in these expressions. We represent the same in zero versus in one half and we obtain again these typical shapes that we have set are the expected one in the present of left-left mass insertion. And now for current bounds, we'll have these two shapes Tanyen beta five and Tanyen beta 20. And for future bound, we have these exclusion contours for Tanyen beta five and Tanyen beta 20. The last comment that I wanted to make here is about reducible bounds in the same that I have said before. In principle, now this operator that is the one contributing to the one two entries in the code and therefore in the soft masses for like hundred fields could be somehow avoided and probably these constraints will decrease. The last model that I want to show you in which we have performed this type of analysis is a Delta 27 model, including quarks and leptons. This model is from Evo, Prahan-Ross and Jim Talbert. And in principle, they use a triplet representation for all the standard model fermions. This will be the flavors. We transform like antitriplets. This is the usual heats and another colors. In this model, the depth of the Delta three give us the Yuccava of the third generation. So from this term in the superpotential will generate the Yuccava, the entry in the 33, the 33 element of the Yuccava. The other information that we have here is just related to the ratio of the other babes with this one. We have these two relations, theta one, theta two, three squared sigma over the theta three babes and theta two, three, theta one, three S over the theta three give us this epsilon power. Considering for instance that the mediators have all the same masses, we can unfixing this, we could infer the size of the bed of this theta two, three, that will be epsilon. I'm putting this here still we see that we have some freedom in the bed assignment for theta one, three and S. So to be general, we have studied this model assigning epsilon F2 alpha where alpha is a parameter that can go from zero to one, and the corresponding one to S. So right in the superpotential, we see that this term goes here, this term here generate the two, three block and this term generate this element in the Yuccava matrix. And considering all the contributions, in principle we can keep this universal texture zero which is characteristic of this model. To compute the tri-linear from these structures, we just have to see how many flagon insertion we have for each operator and computing the proportionality factor with this expression and put it here. For instance, here we have a two-flagon insertion which means a pre-factor five here and the other tens that have always three insertion means a pre-factor seven in the rest of the elements. As we have done before, you can compute now the color for left-handed fields and right-handed fields. Here, a characteristic of this model also arise because in principle, in order to have different expansion parameter, you see that we have put here epsilon F. It means that we need two expansion parameter for the down-core sector and the up-core sector and that can be achieved considering that left-handed mediators are much heavier than the right-handed ones. So in principle, corrections to the left-handed color will be negligible and we will have that it is already the identity matrix and we will compute all the correction for right-handed mediator that will enter in the color for right-handed fields. We write again all possible operators and we see how it goes in the color metric. From here, we can compute the corresponding soft masses. Again, only for right-handed fields because in principle, the left-handed field will be just the identity for this M0 square and looking at the number of flavoring insertion, we can compute the proportionality factor. Here, we have always two flavoring insertion. Therefore, the proportionality factor will be two. While here, for instance, we have three insertion which means two fields entering one leaving, which means two here, one here and that gives me a proportionality factor of four. With this, again, we go to the canonical basis. We go to the mass basis. We, in this case, where we have also the course, we have to reface the CKM to the standard model convention and we have a plot of this type. First, I have selected these two plots in order to show you some characteristics of the model. I will show you afterwards the complete result which are all these plots. So first of all, I have selected these two plots for tangent beta-5 and tangent beta-8, 20. You remember that we have some freedom in the alpha, in the beta assignment, for the phi one, two, three here. We have this alpha. In this plot, this plot corresponds to alpha equal to one half, which is like the, it could go from zero to one, so the intermediate possibility. And now, the shape that we observe for mutoid transition, instead of being like before this rounded shape, have this like butterfly shape. And this is a characteristic behavior expected for, in the case of right-handed, right-right mass insertion. Now, the left-left insertion are absent because we don't have, or we don't consider the left-handed mediators because they are much more heavy than the right-handed one. And we obtain, and for right-right mass insertion, this is a typical cancellation that arrives from, when we observe the destructive interference between the contributions coming from the vino and that coming from the vino-hixino exchange. About from here, okay. This is to command the shapes. Now, the most important process to constrain from currents bound is coming again from mu i gamma. And now also, we have epsilon k. We have epsilon k as a very important constraint because we are introducing these complex phases. For future bounds, the most important or the most constraining processes are mu i conversion which is given by the yellow shape and mu triple i, which is given by this red shape. Now, the plots that I have shown you before will correspond to these two plots. But in fact, we could have alpha equal to one in the BEP assignment for the phi one, two, three flavor. And this will be the constraint for tangent beta five and tangent beta 20. And we could also have alpha equal to zero, for instance. And this will be the constraint for tangent beta five and this for tangent beta 20 principle. The model prefers higher values of tangent beta and smaller values of alpha. So they will go to this direction, but in order to be general, we wanted to study more cases. And another interesting, and this is just the last part, another interesting thing that we can study with this analysis are correlation among observables. We have seen that in the color metric and then this is translated to the soft masses, the entries in the matrix are related because they are given always for the same parameter, for this epsilon parameter. So if we represent the branching ratio for processes like for instance tau mu or tau mu gamma, we could relate this type of processes with mu and gamma, for instance. So this white window will be the window for current bounce from mu and gamma to future bounce and we can see the predictions for the rest of processes. So if at some point we measure one value of mu and gamma, we could predict the value for all these other processes and with this I arrive to my conclusions. The flavor sector is still one of the most extreme legacies of the standard model. We have analyzed the effects of study of flavor symmetry in super symmetry and we have seen that even in ultraviolet universal models, the soft terms introduce non-universal effects. We have compute the coefficients, the structures for tri-linear groups, soft masses, something good. And finally, let me see, okay, here. And finally, I would like to point out that these results are generically valid for any supersymmetric model where the scale of susie-breaking transmission is about the scale of the flavor. Symmetry is broken. We have studied some symmetries for the leptonic sector and for quark and leptons. We are working now in another symmetry and we are seeing under which condition we can relate the neutrinos with char-leptons observable and for future work is implement this type of analysis in other extension of the standard model which has not to be supersymmetric. Thank you. Thank you very much. So time for questions. Okay, I'll start with them. Federico has a question. Oh, Federico. I'm sorry. I thought I was... No, that's fine. I was wondering in the leptonic sector at least, you need complex couplings. And in fact, I think in one of the last models you had the Dirac phase, I think. But I was wondering what about EDM constraints? Well, in principle, we take that into account when we study all the phenomenology of the model. But the most important constraint related to CP phases was coming from this epsilon k. In principle, for this delta-27 model, we didn't find important contributions to EDMs. Okay, thank you. And what about EDMs in the quark sector? Yeah, it's still needed for the quark. The most important constraint was coming from this epsilon k. Yeah, here I haven't put all the least of flavor observable, but in principle, for all models, we consider all possible processes. We did all the running of the extractor and computation of the constraint with Esfino and Sara, and we check all the flavor processes, but only the ones that we have put in the plots were the important ones, or the more constraining ones. But in the case of the EDMs, I think that I remember fine. We don't find important constraints from that. Okay, thanks. Thank you. Any other questions? Yeah, I have a small question. First of all, thank you, Maria Luisa, for the talk. Very interesting. I was wondering, is there any connection with, for instance, with bilinear parity violation? Is it possible to map your constraint on these kind of models that are not effective theory? They generate flavor changes in the case of bilinear in the leptonic sector. Can you repeat? I think that I don't... Bilinear parity violation. Ah, bilinear parity. We haven't considered anything with parity violation, but I don't know. I don't know. Which is exactly bilinear parity violation? It's when you add to the superpotential a term that is proportional to the... It's an L-hicks term. Okay, no. We haven't considered any parity violation, but it can be interesting, I don't know, to extend the work in this type of non-minimal Susy model. Yeah, and the sense that if I don't remember, if I remember well, is I guess there were some works doing something in this aspect from Abelino Vicente that he was using discrete symmetries in the bilinear sector. I mean, in the parity broken sector. Something like that, but I don't remember well the... Okay. On what type of server, or maybe also play with this constraint that you were using, but there was something like this. I don't know if you ever considered or something like that, or what's my question. Yeah, okay. Okay, this is my... That was my question. Okay, anybody else? Okay, I have a question which is related to a question that we have on the YouTube channel. So we are being asked on page 29 of your presentation, there is a factor that has a proportionality factor, no? Yes, a 2n plus 1 instead of 2n minus 1. Okay, I can show you this. These are the diagrams. This is the diagram that give us the Yuccava elements. And I have to compute the trilinear test from this previous diagram attaching the expirium field in all possible vertex. So if I have... When I put 2n plus 1, the n is giving me the number of flagon insertion. So for each flagon insertion, I have one, two possibilities, no? One, two, one, two. And the last one, the last possibility is the Higgs. So in principle, 2n plus 1. This is where the proportionality factor comes from. I think I hope it's clear, no? I guess we'll see if he answers later. So my question regarding that topic also is at each point where the expirium field couples, shouldn't there be different couplings? You're assuming that it's the same coupling at each point, right? I'm assuming that because I want to be conservative. Because in the case that I have different couplings, I will have already, like, flavor violation. I mean, I will have already, like, different factor in each element, no? Or in the different situation. I'm trying to be as conservative as possible. So I consider just one choice of the sucy breaking and the difference among the element in the matrix just come from the different possibilities which I can attach the spurion field to the diagram. Okay, okay. So that's clear. Well, it seems that there's a lot happening on the YouTube channel. But let me go for one final question from me which is in your plots of M0 and M1-1-1-2. What is the reach of the LHC in those plots? Exactly. We say the dark shape where put atlas bound will be the direct bound atlas 4 and sura model. But they are the stronger one, no? So those are the current bounds? Yes. But, well, in principle, the absolute bound doesn't have to be much more. At this point, I guess, I shouldn't change much. Okay. I guess. But so from your point of view in this kind of models, it would let's say that it seems that most of the flavor observables already said that the LHC was not going to see in these kinds of models. Right? You see the epsilon k, the region that is rolled out and the gamma. Exactly. The only way of exploring the parameter space would be through indirect processes like the flavor processes. If we see one thing, some of these processes we could interpret it in the flavor model. And what we could do is through these type of diagrams to see which are the predictions for all the purchases. Okay. Cool. So let me go back to YouTube. So we have another question asking if it is possible to link the textures of quarks with the textures of the neutrinos? Well, in fact, this model does it. In this model, I have put here only the yukabas. Well, I have referred here only to the yukabas for quarks and leptons. So these are the observables that we, the processes that we can check. But for the neutrinos, the details are in this reference. But for the neutrinos, they have the same structure at the end. So they use CISO mechanism. And at the end, let me check. And at the end, they have the same final structure. Yeah, I think it's like this. Yes. In the paper, they can check all the details of the model. And they use the same symmetry for neutrinos and for charts, fermions. Right. And what about the other models that you looked before? Because the other ones were only for leptons, right? I don't know if they... Well, the S3 also, I think that they say something about quarks. But the previous one, the first day for model was just for the leptonic sector. Okay. Any other questions from the audience? It seems not. Let's check the YouTube channel. Ah, okay. We've had a lot of... So the previous person asking the question is thanking you. And we've had a lot of comments from our PhD father, Oscar, who's saying that, yeah, regarding flavor symmetries and our parity, there were some works of Herbie Dreiner. Okay. He's also saying that with different couplings, it would be even more non-universal. Yeah. So there we go. Thank you. Thank you, Oscar. Okay, so I think this is it. No more questions from the audience. Okay, so before we log out, I would like to make some advertising for a conference. We are organizing here in Lima. It's the Latin American Symposium of High Energy Physics. Let me share my screen. I cannot do this. I cannot share my screen. I wanted to, okay, let me share my entire screen. And then you should be able to see. This is the webpage that we have prepared. So this will be happening between the 26th and 30th of November this year. And it's a big event for Latin America. So if you're watching us and you haven't got anything to do on those days, well, please sign up because it'll be a very, very interesting conference. Okay, so let me stop sharing. Okay, so that is all. Thank you very much, Marisa, for the very, very interesting and very pedagogical talk. And we'll be seeing each other in two weeks where the speaker I think will be Ramiz, which will be talking about cosmic acceleration and bulk flow. So it'll be until then. Thanks for watching and we'll be seeing you in two weeks.