 Okay, we are nerd. So hello everyone and welcome once again to the Latin American Webinars on Physics. I am Joel Jones from the PUCP in Peru and I'll be your host today. Well, you might have noticed that today is quite a special day. Besides having the webinar and getting a break from the World Cup, we're also celebrating the six-year anniversary of the discovery of the Higgs boson. So that means that if you need an excuse to make a birthday cake, now you've got it. Anyway, considering such a special occasion, it is very appropriate to have Juan Carlos Hello as our speaker today. Juan Carlos is a professor at the Universidad de la Serena in Chile. He did his PhD at the Universidad Federico Santa María in Valparaiso, also in Chile, and immediately became a junior professor afterwards. In 2016, he transferred to La Serena. He's a university which will acquire particular relevance once the Andes lab is finished. So, well, today Juan Carlos will talk about high-dimensional neutrino masks. This is webinar 66 in our series. So I'd like to remind you that if you want to be part of the discussion, you can write questions and comments via the YouTube live chat system. So, well, I think that's everything for the introduction. I will now hand you over to Juan Carlos. So here you go. We're all yours, man. Oh, sorry, we've muted you. Let's see. Okay, now you can speak. Okay. Yeah. Hello. First of all, I would like to thank you for the invitation to talk in the Latin American webinar from Physics. I'm very happy to do it. It's my first time. I'm going to share the screen. You can see the presentation, right? Everything good. Okay, perfect. So today we'll talk about neutrino mask models generated by high-dimensional operators. This talk is based on three papers I wrote in collaboration with Gaetana Namiti, Oscar Castillo, Renato Fonseca, Martin Hirsch, and Ricardo Cepedejo. Well, in the past 15 years, neutrino physics has revolutionized our understanding of particle physics. The discovery of neutrino oscillations implies that neutrinos have masses and missing shadow. This is the only particle, physics evidence of new physics beyond the standard model to date. The observed smallest of the neutrino masses is usually attributed to a large value of the scale of lepton number violation, typically of the order of 10 to 15 giga electron volts. This is the essence of the CISO mechanisms, in which with a large mass scale, we generate tiny neutrino masses. While this mechanism is simple and elegant, the larger mass scale involved in this argument makes the direct test of the classical CISO mechanism impossible. There exists, however, many possibilities to explain the smallest of neutrino masses with lower lepton number violating scales. In order to do this, it is necessary to have additional suppressions, such as neutrino masses generated by higher-dimensional operators, and or a different loop level. One can write, in general, minor neutrino masses in terms of the dimension of the operator D and the number of loops N as in equation one. Here V stands for the standard model vacuum expectation value. This equation can be used to estimate the typical lambda scale for which the observed neutrino masses could be explained for a given dimension D and loop number N. This figure illustrates this estimate. The energy range has been estimated using average yugawa couplings in the range of 10 to minus 2 to 1. For this figure, we can see that for dimension 5 operators at tree level, the typical scale goes from 10 to 10 to 10 to 15 giga-electron volts. These are the CISO mechanisms which correspond to the tree liberalization of dimension 5 operator. As the number of loops increases, the energy scale degrades. Same is true for high-dimensional operators from dimension 5 to dimension 13. In this figure, we also show the estimate reach for colliders. The left line is roughly 100 giga-electron volts after the negative surge performed at the left collider. The horizontal gray band indicates a very rough estimate of the reach of the LHC. The lower edge of the band corresponds to the per-production of sharp particles, while the upper edge is roughly the reach of the LHC for particles produced in its channel resonance. For dimension 9, enlarger, one expects that the LHC experiments will cover an important part of the available parameter space of these models. Thus, neutrino mass models generated at dimension 9 and higher should be testable in the near future. These arguments form the main motivation of our work in this presentation. The dimension 5 wind-up operator can be generated at tree level in exactly three different ways, which correspond to the three types of CISO mechanisms, type 1, type 2, and type 3. These three different models share the same diagram topology. So for dimension 5 operators, we have one possible topology and three different possible models, as discussed in this paper by Ernest Mann. Now, at dimension 7, one already finds four different topologies, which lead to several model realization, as we discussed in these papers. In order to make these dimension 7 tree level neutrino mass models to be interesting, it is necessary to forbid or suppress lower order contributions, which are in this case, the dimension 5 tree level CISO mechanisms. This can be done simply by the fact that the particle content does not allow lower order contributions or by imposing additional symmetries. In our work, we focus on the first possibility, models in which lower order contributions are absent only due to the particle content. It turns out that for the tree level dimension 7 neutrino mass models, there is only one model for which the dimension 5 tree levels CISO mechanisms are absent without the need of imposing any additional symmetries. This is the model shown in this figure. This model contains two new particles as shown in this figure. One, triplet fermion with the hypercharge 1, which is this particle over here, and one scalar which is quadruplet in S2 representation with the hypercharge 3 half. We call these type of models genuine, in the sense that the lower order contributions are absent without the need of imposing any additional symmetry. We analyze systematically all tree level the composition of the dimension 9, dimension 11, and dimension 13 neutrino mass operators, with the same logic that before, trying to find genuine models. The complete list of diagrams can be found at this link in the web page of Renato Fonseca. For dimension 9, we found 8 entopologies and 66 diagrams. However, among all these, there are only two genuine neutrino mass models which are showing these figures. These models are genuine, therefore the tree level dimension 5 or dimension 7 diagrams or the one loop dimension 5 diagrams are absent only due to the particle content. Imposing any discrete symmetry. Let us know that for these models, one Majorana fermion, which is akin to the necessary representations, appears. At dimension 11, there are 92 topologies plus 504 diagrams. The numbers start to increase very, very fast with the dimension of the operators. But again, there are only two genuine models. At dimension 11, genuine diagrams require at least four different Bayonne standard model particles and large SU2 representations. At least two different counterparts are needed and the model shown here in the right requires a second. Now in dimension 13, there are 576 topologies and 4199 diagrams. The numbers start to increase very fast, as I already said. But the numbers of genuine models still remain very small. Six genuine models. Here, we show the two, the six genuine models in a compact way. Let us know that they require to have Majorana fermions in the middle, which could be a keen to play or accepted. And for the diagram in the top, one can make an exchange of Higgs with Higgs-Dagak, replacing the quadruple fermion with hypercharge 3 half by a quadruple fermion with hypercharge 1 half. Changing one or both of these quadruple fermions, we get the six possible models. Let us know that for dimension 9 and dimension 13, there are genuine models with Majorana fermions in the middle of the diagram, which will lead to very interesting phenomenology, which we will analyze in future papers. Let us now discuss one liberalization of Newtonian mass models. The author of this paper systematically analyzed all one loop dimension 5 topologies. In total, they found that there are six topologies, but only two of them, which they call T1 and T3, can yield genuine models in our sense. These lead to four different diagrams shown in this figure. The well-known C model corresponds to T12, this one. An example for T3 is the scotogenic model, which has a right-handed neutrino and a doublet scalar in its particle content. The scotogenic model is not genuine in our sense because it requires an additional C2 symmetry in order to forbid the three-level dimension 5 scot-type 1 mechanism, which otherwise will be generated by the presence of the right-handed neutrino. In contrast to the three-level diagram for one loop diagram, the representation and the hypercharge of the internal particles are not uniquely fixed. This leads to a series of possible models at one loop, if one allows for larger S2 representations and hypercharges. We also, in our works, we analyze the dimension 7 one loop models in a systematic way. We found 48 topologies, from which, however, only eight can lead to genuine models. In total, there are 23 genuine diagrams. Among these genuine models, there is only one diagram in which the largest internal representation can be as small as a triplet, while there are a further 22 diagrams with at least one quadruplet. These figures are showing two example models, which contain triplets and quadruplets as the smallest representation. These two examples are one loop dimension 7 genuine neutrino mass models. This means that the three-level dimension 5, the three-level dimension 7 diagrams are absent only due to the particle content of these models without the need of imposing any additional symmetry. Again, as in the case of the dimension 5 one loop, one can build series of models allowing for a larger representation and or hypercharge for the particle in the loop. Here is the triplet model, the sampling that we analyzed in more detail, the Lagrangian of the model and the particle content. As we can see, it has a triplet fermion with hypercharge 1, a one doublet fermion with hypercharge 5 half, and three additional scalars doublets, two doublets, and one triplet. We studied the phenomenology of this triplet model and also the quadruplet model in detail. As you well know, experimental upper limits on leptom flavor violating decays provide important constraints on TBS scale detection of the standard model. In this figure, we show results for calculated branching ratios of mu going to e gamma, mu going to e e e, and mu e conversion for different choices of parameters as a function of one of the Yukawa couplings, in this case Y3. The horizontal full lines show current experimental limits and the horizontal dachet lines feature expected sensitivities. The non-observation of leptom flavor decays can be used to put upper bounds on the Yukawa couplings of our models. At the same time, the observed neutrino masses require lower bones on this Yukawa couplings and the combination of both constraints results in a very restrict range of allowed parameters. We also analyze constraints from LHC searchers. A number of different LHC searcher can be used to set limits on the various particles of our examples, models. The simplest search and currently the most stringent LHC limit for our models comes from a recent Atlas search for W charge particles that came to either ee or mu final states. Results of our calculations compared to the experimental limits are showing this figure for the mu final state. Here we have the cross-section of pre-production of a eta 1 W charge scalar that came into mu versus the mass of the W charge scalar. Scanning over the allowed neutrino parameters then leads to a variation of the branching ratios of eta 1 into different lepton generation. This explains the spread of the numerical calculation point in this figure. Combined with the experimental limits from Atlas, lower mass limits in the range of 600 and 80 GB result. I now turn the discussion to possible lepton number-violaton signals of the LHC. This table shows examples of different lepton number-violaton states from pre-production of scalars or fermions in the two models under consideration. The table gives in column 1 the multiplicity of the final states and in column 2 the lepton number-violaton signal. These final states are produced from the decays of the particles given in column 3. These particles can be produced in pre-production at the LHC and they can decay into the lepton number-violaton signals in the second column. Observation of this lepton number-violaton signal is only possible if both integrators have similar value. For instance, for this scalar, which is a four-charge scalar in the triplet model, can be produced in pre-production and can decay to four leptons with the same charge in one branch in the other branch to two leptons with two W's, generating a signal that dilates the lepton number by two units. If we want the lepton number-violaton signal to be possible, it's necessary that the branching ratio of these two possible channels to be of the similar order. Here in this plot, we show the ratio of this branching ratio as a function of the lambda-2 coupling of the triplet model for some fixes choice of the other parameters and different values of mu1. One can see from this figure that the equality of branching ratios is naturally possible for different choices of parameters. Without the need of any fine-tuning, same is true for the quadruple model, as shown in this other figure. Finally, the conclusions. In our work, we discussed the systematic reconstruction of dimension 9, dimension 11, and dimension 13, neutrino mass operators at three levels. From all the possible diagrams, we found only 10 genuine models, two models at dimension 9, two models at dimension 11, and six models at dimension 13. We also discussed neutrino mass models at one look dimension 7. We found 23 diagrams that lead to genuine models. Only one possible diagram for which the largest necessary representation is a triplet, and the remaining 22 diagrams with the largest representation being at least a quadruple. We study the two examples in detail, one triplet and one quadruple model. New left-to-number violating final states appears. In particular, final state with large multiplicities are predicted to occur. Thank you. Okay. Thank you very much. Let me get back. Okay. So thank you very much for the very nice webinar. So we are open to questions. So let's start with the audience. Right now. Have we lost Juan Carlos? I'm here. Here you are. Okay. Sorry. One question. I'm not here. Go ahead. Hi, Juan Carlos. What happened with the dark matter in the genuine model? Is there a dark matter candidate there, or are all the particles kind of stable? Yeah, that's a good question. In principle, for the one look dimension 7, genuine models could be a candidate of dark matter. In a similar way that I believe that you wrote a paper for dimension 5, right? With dark matter? Yes. So in principle, but we didn't analyze in detail those possibilities for the one look dimension 7. But in principle, you could have genuine models with dark matter in the particles in the loop. Yes. So that's an interesting direction to analyze. Okay. Any more questions over here? Okay. So I have a simple question. So when you talk about your genuine models, you said that no additional symmetries, all of the operators are generated by the introduction of new particles. So can you have two genuine models simultaneously giving you contributions to the same effective mass? Let's say the same, this equals seven months? That's a good question. For instance, and I'm going to share the screen again. Well, can you show one slide? Okay, go ahead. In this case, so I'm sharing the screen, right? Yes. So here you have two different genuine one look dimension 7 neutrino mass models. However, if they are together, you will get, you will have a diagram, which is dimension 7 at three level, which is actually this one, because this one has the quadruplet, a scalar with three half hypercharge, this one, and one fermion, which is a triplet with the hypercharge one, which is exactly what you have here and here. So if you have these two diatoms at the same time, they won't be genuine anymore, because you will generate the dimension 7, three level. Right. They will not be genuine one loop models. Yes, they won't be genuine. They won't be the leading order contribution anymore. I see, I see. Because it will have a lower order contribution, which is the three level, dimension 7. So also in this direction, so when one works with this TV scale, CISO models, one finds that there are, that the loop corrections for the neutrino masses can be important, right? So basically you have some other left on number violating parameters that don't appear at three levels, so they're not constrained by the neutrino masses, but they appear at loop level, so they can give large contributions to the neutrino masses. So that can constrain this TV scale CISO models. So I'm wondering if you have checked that this situation will not arise in this kind of models. Yeah, and I mean, we focus on the, I mean, in principle you can have, for instance, loop diagrams, which are more important than the three level diagrams at the same level operator, but you need to play with the couplings. If you put couplings very small for the two level, of course, the contribution will be very small. So we are not analyzing that situation, but that situation is also possible and also interesting. So we are not saying that all the other cases are not important. So we focus, we analyze one criteria, which is more or less saying that the couplings are of the same order, and under that criteria, we define this genuine condition. But in principle, yes, you can have situations when the loop is more important than the three level, only because some couplings you are putting very, very small in the three level, for instance. Fantastic. Thank you very much. I don't know if there are any more questions. Yeah, I have a very naive question. Juan Carlos, in the case of, one of these models can be compatible, for instance, with some realization for leptogenesis or something like that, in the sense that you need to, in the case maybe you have some scalars that one part get very heavy, the other light enough to contribute to the loop, not to Yeah, I have no thought in that direction, but maybe it's probably, but I have not analyzed that possibility at all. Okay, thank you. All right. Any more questions? Let me check the Oh, first question of Joel, do you mention that one could look the diagram dimension nine or or so was also generating a three level contribution at the end? How do you avoid the three level contribution? Sorry, can you repeat me the question again? In the slide that you're chatting now, the diagram of the left, in principle, has also one three level contribution? No, because of the presence of the quadruplet? No, no, in the left, you don't have a quadruplet. Oh, sorry, in the right, in the right. In the right, you don't have the triplet, let's say. So both separately, they don't have a three level contribution, not dimension seven, not dimension five. Could you remind me one, the three level contribution appears in the previous answer, how the three level contribution appears? Sorry? Do you mention before that with some combination of this diagram of the three level contribution reappears? Yes, yes. So the genuine three level dimension seven, which requires to have a quadruplet scalar with three half hyper charge, which is this one over here, and one triplet ferment with the hyper charge one, which is this one. Okay, so if you want to have these two diagrams at the same time, you will have also, unavoidably, at least you put an additional symmetry, of course, to level dimension seven. So those two diagrams won't be the leading order contribution anymore. However, if you analyze them separately, they will be the leading order contribution. By the way, in these kind of diagrams, the hyper charge of the multipliers seem to be very high, so it's in principle compatible with having a Darmator candidate. Do you have any example with something that can have one hyper charge compatible with some neutral Darmator light state? Yeah, as already said, I didn't analyze that in many detail, but you have some freedom in the loops, so you can change the hyper charge and also the S2 representation. So in principle, you can play around with these numbers in order to find this Darmator candidate. So in principle, you can play with that. We didn't do it, but in principle, it is possible. Okay. I have one very short question. Juan Carlos, in your analysis, let's say that you focus mostly in to generate the masses in the case of Majoran neutrinos. So have you considered, for instance, all the realization, maybe it's not for double beta decay or something like that, but in the case of direct neutrinos, if there is a kind of similar classification of... No, in principle, you can think in that direction too. Yeah, but we didn't do that. Okay. Just to know because in principle, with a direct neutrino, you have to add some symmetry in your model. So this is... I would say I don't know, but yeah, of course, in the case that you analyze, you didn't have any other extra symmetry for the reason. So analyze the analysis that you presented. Just a comment after the first word of Juan Carlos, there appears in fact, one paper about the Dimension 7 case of direct neutrinos. I don't remember now the specific reference, but there is some study already on this line. Okay. Good. Yeah. I think we could think it could be... So something analogous for the direct, but I haven't thought about it. Yeah. So you can send me the reference, Diego. Yes, of course. Hello. Can I ask a question? Yes. Maybe Naid, but in your case, you have Kaplan's order one, right? Or, I mean, not too small in masses, which are relatively light. So what about the Higgs Kaplan's? I mean, for instance, like the triple Higgs Kaplan would be probably quite... I mean, I expect to have changes on the Higgs Kaplan due to the new particles and charges, which are relatively large or not? Yeah. You mean, for instance, this one, the quadrant. Yeah. This is... Or this one. Two Higgs with two. Yeah, maybe a Naid question, right? I'm asking. No, no, no. It's a good question. I think here in this plot, this is for the triplet model. So mu one, this mu one, let me go up here. Mu one is the Kaplan among the two double scalars. I don't know. It's the Kaplan among these double scalars with the Higgs. It's mu one. And this mu one, here, we set it to be one TV for these triplets, for instance. And here, we play with this mu one from one giga-electron volts to 100 giga-electron volts. So basically, we give them some freedom from small values to larger values. Okay. So let me ask one question. So have you looked at tau mu gamma? Tau mu gamma is... Because I mean, usually one expects that mu e gamma, mu e conversion, will be dominant sources of constraints, right? Yes. That's why we didn't... I mean, we use a Spheno to calculate this. So in principle, Spheno gives you all with this flavor. So we had all the numbers, but the most stringent came from this C1. So that's why we... It's a shame, because with the Bell two experiments starting, you know, they will be putting new bounds in this leftover relating tau decays. But still, it seems that there are not many models around that I have seen, at least, that can use these bounds. Yes, too. Okay. I don't know if there's any other question. Okay. And then in the chat, okay, nothing in the chat. All right. So thank you very much, Juan Carlos, for the very nice talk. And let me remind you that in two weeks, we have Cosimo Bambi giving a talk. I'm not... I don't remember the topic, but it's probably something related to general relativity or gravity. Modified gravity, maybe. Anyway, so we'll see you then. Okay. So thank you for listening, and thank you, Juan Carlos, for the talk. Thank you for the invitation. I'm very happy to give it a talk. See you around. Bye-bye.