 OK, I guess we can start. Welcome back to this low-physics webinar. My name is Roberto Lineros from the Instituto de Fisica Corpuscular. And today, we're going to have a very interesting webinar that is about ice cubes, neutrinos, and new physics. But first of all, for all the people that are following us, please, if you want to make questions to bodies, here is where you can make the questions in the YouTube live chat. Now, if you are watching this in YouTube in live. And if you want to see what is the program of the future webinars, you can enter to our WordPress page. So our speaker is Boris Panes. He got a PhD from the Catholic University in Chile. And after that, he did a postdoc in Hamburg. And nowadays, he's postdoc also in the University of Sao Paulo. So the talk of Boris, the title, how a nuclear and equal fluxes of highly astrophysical neutrinos and anti-neutrinos can fake new physics, very long title. But so Boris is going to explain us what is that. Please, Boris. OK. Can I start whenever? OK. Thank you very much for that introduction. So I suppose that I now have to move to the slides, right? Yes. First of all, I have to do this cherry and the screen. So let me know if you are seeing the slides correctly. Yeah, I can see it perfectly. You can. OK. Very good. So first of all, I would like to thank to Roberto and the organizer for giving me the opportunity to give this talk in this webinar serious. The title of the talk is how an equal fluxes of high energy astrophysical neutrinos and anti-neutrinos can fake new physics. This is a word in collaboration with Hiroshinonokawa and Renata Suganovic-Funkal. It has been accepted just a few weeks ago. I like to see that this word is done in the context of multi-messenger analysis, where you can analyze a correlation from different kind of cosmological signals like photos, neutrinos, cosmic rays, and even gravitational waves. But this is just a first attempt, or one of my first attempts on that direction. And here I am going to talk about just neutrinos, high-energy neutrinos. But in the future, I would like to put this word in context with other kind of detection to do more this kind of multi-messenger analysis. So during this talk, I am going to talk why I'm going to consider neutrinos and mostly the standard model physics. In order to show you that still we have to understand some things that are quite standard before going to be on the standard model physics. So you know the standard model of particle physics very well. So we have the quarks left on the forces and the hicks. And in particular, we are going to put our attention in the neutrinos. So these neutrinos are very small mass, neutral electric charge, very small cross sections that make them very challenging to detect. And most importantly, there are many properties or several properties of these neutrinos that need to be clarified. So it's always interesting to continue the study of these guys. So the three states that we are going to be worried about during this talks are production, propagation, and detection. For production, we have that they can be produced through electro-weight interaction. For example, from neutron decays, you can produce anti-electron neutrinos together with protons and electrons. But also you can have neutrinos from the interactions of protons and photons. That is one of the most studied sources of astrophysics and neutrinos. So we have cosmic rays in the form of protons and the magnetic fields or the cosmic microwave background that will be the photons. And then from the interaction of these two things, you can produce neutrinos. Then when the neutrinos are produced in these sources, like these astrophysical sources, they have to propagate. But because of the neutrinos, they have this really interesting property that they can oscillate between the flavors. You have to consider the possibility that an electron neutrino can travel and then compare it to a muon or tau neutrino. And the same happened for muon and tau. So from the source to the detection, you not always are going to have the same flavor that you produce. So this is well-known in neutrino physics. And it's something that you have to consider. And the formula, the general formula for the probability of transition is given in this study. And it depends on the European mathematics elements. The masses of the neutrinos, the difference of mass of neutrinos, and the energy of the neutrinos. Finally, when you want to detect these neutrinos, you can consider processes that are very similar to the previous ones. And for example, you can have the interaction of electron neutrinos and neutrons that produce protons and electrons. And then these electrons can be detected. Or you can have the interaction of electron neutrinos and protons that produce positrons, for instance. But also you could have the interaction of electron neutrinos and electrons and produce electrons or whatever you have there. OK, so these are the three stations that we are going to consider during this talk. But before that, I would like to show you what are the ubiquities of the neutrino in all the possible energies that we can measure them. So for example, we have that the energies of neutrinos can go from 10 to the minus 6 electron to 10 to 18 electron balls. So there you have 24 orders of magnets. Most of them can be already detected, but there are some of them that still need to be studied. For example, cosmological neutrinos, that these relic neutrinos from the very beginning of the evolution of the universe. But also we have very energetic neutrinos that are going to be the focus of our talk. These neutrinos for high energy, I mean neutrinos that have energies above the TV range going to PV or even more. But as you can see in the plot, as bigger is the energy of the neutrinos, smaller is the flux. And in fact, you can see that the flux can cover almost 50 orders of magnitude for this range of energy. It's for that reason that when you study very high energy neutrinos, you have to consider very huge detector like an ice cube, for instance. That is a 100 megatons detector. And this is basically because the number of neutrinos is proportional to the effective volume of the detector. So as bigger the volume, bigger the probability of detecting these neutrinos. So for that reason, people have built an ice cube and other kind of experiments that are huge neutrino detectors that can detect these really small fluxes. Ice cube in particular is a neutrino detector that is located at the south pole. And it's basically a 1 kilometer cube of ice that is instrumentalized that is able to detect the electrons, muons, and tau's that that produces from the interactions of neutrinos and the ice nuclei. One important thing that is important to record here is that ice cubes can detect at least, and for now, two different topologies that are the topologies showing here. We have a shower kind topologies and track light topologies. And these are two pictures or real events. These kind of topologies allow to ask you to kind of distinguish between the different flavors of neutrinos. For instance, it's expected that electron neutrinos and tan neutrinos produce showers like the first picture here. And these are spherically symmetric depositions of a sharing of light produced from the electrons and tau's from the interaction of electron neutrinos and tan neutrinos. On the other hand, you have this track light topology that is associated to muons. And the main advantage of that is that you can distinguish a muon neutrino as a source of this signal. So you can distinguish neutrinos and kind of the topology of the signal. So then maybe the most important results so far from ice cube summarizing in this slide. So here you have the flow that shows the events detected by ice cube during the first three years of data taking. And the range of energy goes from 10 TV to 10 PV. So we are in this very high-energy region of the spectrum. And here in this plot, you can see the data points with crosses here. And from this observation, they have obtained that there is no way to explain this observation with standard sources of neutrinos. And by standard, I mean neutrinos produced by the interaction of cosmic rays and the atmosphere. These are so-called atmospheric neutrinos the contribution of them are given in this blue, red, and purple line. The purple lines is like the sum of the contribution considering some errors. And you can see by eye that these contributions cannot explain the observation of these neutrinos here in the high-energy regime. The claim of ice cube, they have excluded the explanation from atmospheric neutrinos at 5.7 sigma level. So the impedance is quite high that we are already observing astrophysical neutrinos. And this has opened the research, so-called as a neutrino astronomy, at very high energies. So this is one of the very important results of ice cube after the first three years. Also, as I told you, ice cube is able to reconstruct the geometry of the position of energy emitted by the electrons. And especially, for example, for tracks, you can distinguish the direction of the neutrino that is colliding with the ice, right? And this can give you information about the direction of the neutrinos in the sky. So far, these results are given in this plot here in the right side of the slide. And the main result from these information, so from the location of the neutrinos in the sky, is that they are compatible with this tropic distribution of sources, let's say. And there are some of them that also come from the center of the galaxies, but still it is unknown how many of them come really from the center of the galaxies or from outside. The point is that they are consistent with an isotropic distribution. These are two kinds of information that you can get from an ice cube. Total flux and directions. But also, you can get this other information that I already told you that is about the flavor fractions. Why? Because you can distinguish between the different flavor to some point, right? You can distinguish between electron stars and muons. So you can play around and try to figure out how much is the contribution of each flavor, right? From the observation of these different topologies. And this is also what they have done. And in this slide, I am showing you the results of the analysis of these flavor ratios from the observation after three years of data taking. And here, in this triangle plot, they show the flavor fractions of neutrinos, electron, muon, and tauus. And they are normalized into one, so you can put them in this triangle plot. Also, there is a very strong assumption behind this kind of plot. And it's that here, for the feet of the data, they have considered that the fraction of neutrinos is equal to the fractions of anti-neutrinos, OK? And using that assumption, you just end with three fractions, right? Because in principle, you could have six fractions, neutrinos and anti-neutrinos. But you put them together by assuming that they are equal and you end with only three fractions that you normalize to one, OK? And for that reason, you can do this triangle plot. And here, the orange cross in the right border of the triangle show the best feet point of ice cube considering the current data. And this corresponds to 50% of electron neutrinos and 50% of muon neutrinos, OK? Also, you can see the one, two, three sigma confines level regions associated to this feet. And you can see that most of the triangle can be covered. But in the future generation of ice cube, you will expect that this sounds shrink. And you can see this expectation in these gray lines, OK? So this is the best feet point. And this is at the confidence level region. And also in this plot, you can see this figure here that contains these colors green, gray, green, purple, brown, and blue. Let us put attention in the gray region, right? The gray region is correspond to all three. What is the meaning of that? It's that you can assume that at the source, you produce any possible combination of fractions. So any possible famine of electron neutrinos, muon neutrinos, and tau neutrinos. And then you propagate them using the UPMNS metrics. And then you get at the air some set of flavor fractions. Because of the texture that we already know of the UPMNS metrics, we can predict what is the zone where you are going to get these fractions at the air. And this is the gray zone, OK? And as the gray zone includes all the possibilities, all the other situations live inside this zone. And these other regions, the green, the purple, the brown, and blue, are different possibilities considering particular sources, like sources that only contain photo disintegration interactions, or sources that only contain adrenic interactions. These are details that are not going to go further. The important things that is all of them predict that the fractions at air should be around the center of this triangle. And what you can see just from seeing these results is that you have a discrepancy from what you have observed and what you were expecting. So there have been some words about this, considering this discrepancy, claiming that this could be produced by new physics. But our approach in this world is the opposite, or maybe not the opposite, but different. And the idea of our world is to show that this kind of discrepancy can be explained by something that is more simple. You don't need new physics, but you need to consider very carefully one of your assumptions. And this assumption is that neutrinos and the neutrino fraction do not need to be the same at air. And this is kind of a hypothesis of our world. And in the next slide, I'm going to show you some evidence that can explain this situation using these purposes. So first of all, let me just repeat some assumptions and make it more clear before showing you the results of our analysis. So first of all, we need to compute the number of neutrinos. In order to do the analysis, we need to compute the number of neutrinos that you expect from every flavor, neutrinos and neutrinos, for the different topologies, like showers and tracks, and from the different channels that can be charged with current interaction, neutral current interaction, glacial resonance interaction, et cetera. These numbers are obtained from the convolution of different factors. For example, the time of the data collection, the flux of the neutrinos at air, air effects, like the regeneration and absorption, the cross sections between the neutrinos and the medium, that is in this case, is the ice, and also detector properties or detector effects, as for example, the resolution on the reconstruction of the energy of the neutrinos. All these effects have been considered in a previous paper from a group from Valencia, MENA, and company. And we have used this recipe in order to produce our kind of simulation of ice cube detector. Importantly here is that the flux of the neutrinos. Why? Because this is one kind of a strong assumption. We are assuming that the flux of the neutrinos for each flavor, neutrinos and neutrinos, follow the same power law, which means that we are using the same spectral power, spectral index for the flux of the neutrinos. And we only distinguish them from different flavors by the fraction that they contribute. So these numbers are completely free when we want to simulate the data, for instance. By the way, it is useful to recall that this kind of assumption is one that is doing a very good feed of the current data. So furthermore, when we are going to do the feed of ice cube, we are going to use the current approach that even the people from ice cube are using is that the fraction of neutrinos and the fraction of anti-neutrinos are equal. But this is only at the level of the feed. When we simulate data, we leave them free. So we can have different facts. But when we do the feed, we consider them equal. And because this is what we think could be the root of this discrepancy, or could produce this kind of discrepancy between what you observe and what you feed. So why we should think that the difference between neutrinos and anti-neutrinos fraction could produce this kind of misleading results can be motivated by this slide. Here, we show, for example, the distribution, the spectrum of showers as a function of the energy as observed by ice cube. So this is in terms of, OK, this is for showers. Here, we have the different contributions of neutrinos and anti-neutrinos in different colors. And for instance, here, you can see that the spectrum of neutrinos for these showers is different to the spectrum of electron anti-neutrinos. You see here a clear bump that distinguishes between them. And this bump is produced by the glacial resonance process that is the interaction of electron anti-neutrinos and the electrodes that are present in the ice nuclei. So this is very particular for electron anti-neutrinos. And you see that it can produce a very strong effect in the spectrum of showers, at least. So how this could produce some problems? Before going to the numerical results, I have a very simple example. For example, let's assume that what you observe at air, what is the fraction that you observe at air, do not contain any amount of electron anti-neutrinos. You don't receive any electron anti-neutrinos at air. So the spectrum of the shower will not present this bump in this region because you don't have this kind of interaction. OK, but then you try to do the feed of this data using the assumption that the fractions of neutrinos and fractions of anti-neutrinos are equal. But as you don't see the bump, the feed will require that the fraction of electron neutrinos must be equal to very similar to zero in order to avoid the presence of this bump. But in what you are observing, maybe contains some amount of electron neutrinos. So because of this assumption, you are saying that you don't need electron anti-neutrinos, but nature is saying that you could receive electron neutrinos. So there will be some discrepancy between your feed and what you have observed. And this, only because the assumption that the neutrino fractions are equal between neutrinos and anti-neutrinos. OK, now let me show you that there is some, why the assumption that the fractions could be different is not a very wide assumption. And this could be the normal situation. For instance, we can consider these two kind of scenarios that correspond to astrophysical sources of neutrinos that are produced, for example, from the interaction of protons and protons or from the interaction of protons and photons. In the first case, when you have protons and protons, you can produce in a similar way positive pions and negative pions. So you will observe at the end a similar fraction of neutrinos and anti-neutrinos. At first approximation, they are equal. And this can be seen in this line. Here, we put the fractions of neutrinos from this interaction turn out to be equal to the fractions of anti-neutrinos. And they respect this kind of distribution, 1, 6 to 6, 0. In this case, the fractions are equal. But if you consider the second case, that is also a possible scenario, that is photo disintegration, proton with photons. And for example, you can assume that these interactions is only affecting when you have the delta resonance as an intermediate state that produce only positive pions. These pions are going to decay to this kind of neutrinos. And here, for instance, you don't have electron anti-neutrinos. And you have equal numbers of mu-neutrinos. But the electron anti-neutrinos are alone here. You don't have electron anti-neutrinos. So here, the fractions of neutrinos and anti-neutrinos are not necessarily equal. And this is kind of very well studied scenario. In general, the situation can be much more complicated. But from this simple analysis, you can see that in the most simple scenario, you already see some discrepancy between the neutrinos and anti-neutrinos fractions. But this is a source. And we are interested in the fractions at air. In order to get the fractions at air, you have to apply the propagation effect that is dominated by the eupaminase matrix. But these propagation effects affect neutrinos and anti-neutrinos by separate. So if you have an asymmetry between neutrinos and anti-neutrinos at source, these mixings is not going to make them symmetric. What it's going to do, this mixing is going to distribute democratically between neutrinos here and between anti-neutrinos here. But the asymmetry between the two guys here, neutrinos and anti-neutrinos, is going to be there anyway. OK, for instance, let me show you now two particular scenarios where we have this asymmetry in opposite directions. For instance, we can consider the case A, where you start with the distribution of neutrinos as the previous case. So this is the photo disintegration scenario at source. Then you propagate them, and you consider the mixing between the different flavors, and you get these fractions at air. So you can see that the fractions of neutrinos have been distributed more or less democratically. The fractions of an anti-neutrinos are the same. But you still see some asymmetry between neutrinos and anti-neutrinos. And in particular, you can see that the fractions of neutrinos is much bigger than the fractions of anti-neutrinos. And this is similar to the example that I was trying to explain to you before when we had this spectrum of showers, OK? And there is also a case B that is kind of artificial. But in principle, you could reproduce it combining different kind of sources, like standard sources. But the details of this scenario can be found in the paper here. What is interesting is that starting with this kind of asymmetry distribution at source and using the UPMNS matrix to propagate this distribution to the air, you get an asymmetry distribution similar to the previous, but here the order is the opposite one. Here we have a very few amount of neutrinos and a big amount of anti-neutrinos, OK? Electron-antinotrinos in particular. So we are going to consider these two scenarios. And now we are going to, in order to simulate the mock data that you will expect at air for different luminosities. And then we are going to do the feed using the assumption that the fractions are equal. That is clearly in contradiction with what you are observing. But anyway, let's assume it and see what happens, OK? Before going to that result, just let me show you that the case is that the situation is quite general, in which sense. So here in these plots, we show the fractions of neutrinos and the fractions of anti-neutrinos at air. For these two scenarios, red and blue, A and B, but considering the potential uncertainties in the UPM-MS matrix. So before I show you very specific numbers after the propagation, but in general, you should consider that there are some uncertainties in the UPM-MS matrix still. So you need to see that you can see that what you observe at air can cover a zone in this triangle plot. But this source is always around the center, right? For neutrinos and for anti-neutrinos. And in the yellow region is when you leave all the sources at the fraction free at the source, but you fix the tau fraction to 0 at the source, OK? It's only to show you that the yellow zone covered the blue and the red that these are the expectation considering these two scenarios, OK? So if you sum both fractions, neutrinos and anti-neutrinos, you get the following plot. You sum these two plots and you get this plot here. And here you can see that the case is more extreme. For the sum of fractions that you have that the concentration is more, it's very close to the center of the triangle. But anyway, the yellow, what we're going to be more interested is about the yellow region, OK? So now let us remember this plot. The expectation for this kind of sources after considering the mixing of neutrinos is that the fractions there are around the center, OK? As is normally the case. So now we do the numerical computations of our feed. So here, we show the results of the following procedure. We simulate the mock data for the scenarios A and B for 10 times the luminosity at ice cube. And then we feed this pseudo data, this mock data, assuming that the fractions are equal. And then these fractions here in these triangles correspond to the sum of the fraction. That is basically two times of the fraction of the neutrino or the anti-neutrino, OK? And we do it for the both scenarios. And we include the 1, 2, 3 sigma region, OK? You can see that here, the best feed point, and this, for example, for the case E, is here. It's around here. And this is not in the yellow region, OK? So in principle, it could indicate that you are observing something unexpected, OK? You would have expected that the observation would have been around here in this region. But what you get from the feed is a point outside this yellow region, OK? But anyway, with this kind of luminosity, the 1, 2, 3 sigma regions are quite big. And you cannot say it's something very acute yet. But only from the best feed point, you see an effect that is misleading. Because you are analyzing the standard data only with a symmetric distribution of neutrinos and anti-neutrinos. And when you do the feed, you get something that is not in the standard region, OK? And the explanation is because of the glass of resonance, maybe. The situation is that, given that the glass of resonance has this particular spectrum, when you try to feed something that contains very few amount of anti-neutrino contribution, the feed tries to get a very small amount of neutrinos, of the electron neutrinos at all. So this is 10% of electron neutrinos. But these electron neutrinos are the sum of electron neutrinos and anti-neutrinos. But as the glass of resonance is very dominant when you do the feed, you get that this sum is very small. But this sum is very small, which is in disagreement with what you put in the beginning, that this person that's here, this is the sum of electron neutrinos and then electron anti-neutrinos from the mock data. But here, this is what you get from the feed, because it's mostly dominated by the fraction of electrons and neutrinos, OK? So this is a numerical explanation of the fact. What you get is different because there is a fissure in the spectrum of showers that is dominant and the feed tries to satisfy this fissure and therefore gives you results that are not in agreement with what you should expect, OK? Something similar happened in the case B, that the best feed point is outside of the central region. But here, the amount of electron neutrinos is much bigger than what you would expect because the same thing. Now, for this scenario, you can remember that the contribution of electrons and neutrinos is quite big, so you need to reproduce the pump in the spectrum. And for that reason, you predict a fraction that is quite similar to 0.656 that is different to what you would expect that is 0.34. So this discrepancy is only generated because of the assumption that the fractions are equal and the present of the relation. So the same exercise can be done with 10 times more statistics as before. And you see that if you continue with this assumption, at some point, you are going to be motivated to say that maybe there is some contribution to the propagation, to the production, or to the detection that put this best feed point outside of the yellow region. But I think that they are going to take into account this situation much before than when we get to this kind of luminosity. But the point here of this slide is just to say that at some point, this can be dangerous if you continue with the same assumption because you really can't say that one sigma level, or even a two sigma level, you are excluding the spectatory. And this takes me to the last slide of my talk that are the conclusions. So I have shown you that in this analysis, we have considered the results of ice cube that basically have taught us that there are estrophysical neutrinos that they are very energetic. And it is also possible to reconstruct some topologies that can give us information about the flavor of neutrinos that are colliding with the detector. Also, I have showed you that there is some kind of danger when you consider that the neutrino fractions are equal between neutrinos and neutrinos when you do the feed. Because a very simple reason that is that the features of neutrinos and anti-neutrinos can be different. And particularly for electron neutrinos and electron anti-neutrinos, this can produce even misleading results. So our suggestion is that the analysis of the flavor fraction should be extended to at least three flavors, electrons, muons, and electrons, anti-neutrinos. But maybe more because also you could have tau neutrinos that can produce kind of different signals. But this requires some energy of the incoming tau. But for instance, just considering until the PV region, couple of PV neutrinos with a couple of PV energy, you should at least try to consider these three flavors at least. But I suppose that this is also well known in the SQP collaboration. But this is in this paper, we only wanted to show it explicitly with the numerical analysis that's considered mock data and the regular feed that the people install. With this, I can conclude. So thank you very much. Thank you very much, Boris. It was a very interesting talk. Let me go back here. So first of all, before to start with the questions for Boris, we are going to remind the people that if they want to make questions to Boris, they can enter to here to the YouTube live chat. So if you are now following the webinar in YouTube, it's just a small window that appear in the right panel of the video, next to the video. And if you are watching now in YouTube, the recorded session, so you have to maybe contact Boris directly to make some questions to him. So for people in the future, you can do this. So we can maybe start before with the question from the people from the chat. We can start with the people that is here following the session in the Hangout. So anyone that they want to start, please free to ask to Boris. Maybe I need to have a question from Mauricio. OK. So that's interesting stuff. Thank you for presenting it. My knowledge, the ISD collaboration is now starting to actually consider in their next iteration of a global fit that neutrinos and antinutrinos might have different fractions. But they will not, as far as I know, consider individually flavor-dependent neutrino versus antinutrino fractions. They will just assume that this fraction is flavor universal. So they just have one new free parameter that will say what the fraction of neutrinos to antinutrinos is for electron, mu, and tau. So my question is, and they will also consider the antinutrinos that comes from a different analysis they're doing. So my question is, have you looked into how the regions that you just showed would vary if you had access to only one fraction of neutrinos versus antinutrinos? And that fraction would hold for the three flavors. OK. So let me understand the question. You're asking if you can get results that are more consistent with what you are simulating in this case, if you extend the fraction to just one extra fraction that distinguish between neutrinos and antinutrinos, right? Instead of five different fractions, right? Right, my question is, how would your plots look? We did this exercise when we were doing this research. And basically, when you have this mock data and you extend the domain of the fraction, you recover the results that are consistent with your observation. That is almost automatic, because there is nothing avoiding that possibility, right? And furthermore, you include more free parameters. So you are able to feed the data very well if you include more fractions. But the point is, it's interesting when you say, have you verified that only considering one extra fraction is still of the three antinutrino fractions, for instance, right? And this is what we have in tone. But as we say in the last slide, what we think that this will be the most economic approach to the feed of the data is just consider the electron antinutrino fraction, because this is the fraction. This is the spectrum that produces some difference. So if you see the spectrums like vectors like in different directions, this is really the new direction, right? The electron antinutrino spectrum is the new directions in the feed. So by including this new direction, you should, in principle, be able to get a more consistent results. That's a good point. Thank you. Yeah. Thank you. So I mean, just a small question about this point that you were talking with Mauricio. So only from the point of how this point, the best feed can move in the electron antinutrino direction, this is at the level of the assumption of for ice cube. But in principle, also, there is the mismatch between that ice cannot distinguish well between double neutrinos and electron neutrinos. Or in this case, it's just because of the pressure resonance that is making everything so variable in that direction only. Yeah, because I think that these are two different things. What happened now with the electron neutrinos and double neutrinos is that as they produce similar signals, the feed, the confidence level regions of the feed like a diagonal in that direction, right? You can have what you think is the sum of electron neutrinos and double neutrinos. Because if you body the different proportions of this sum, you get basically the same spectrum, right? So this is like the generacy in the parameters of your feed. Because you can distinguish just a few topologies. But what happened with the glacial resonance is that you're putting together two things that produce difference observable, right? And this is not what you should do when you do a feed. You should try to isolate the physical contributions that produce different results, right? And for that reason, you can get misleading results instead of big confidence level regions. Big confidence regions are not so dangerous because this is just the limitation of the experiment. But when you get a best feed point that is not inside of the expectation, you get that means lean message, right? I see that this is a kind of difference between these two situations. Yeah, yeah, I understand. Somebody has more questions for the hand called? Yes, I have one from him. Yes. Go ahead, Federico. Yeah, I mean, yeah. Hello. One question. You're assuming that you have a normal hierarchy or does it make a difference if you consider an inverted hierarchy? Yeah, in principle, I would say that doesn't make a difference because we are considering the just the effect of the UPMS matrix in the mixing of the nutrients and the mass here or the mass difference is not important. It's just the UPMS matrix. But now, right now, I don't remember if the UPMS matrix, the component of the UPMS matrix depends on the hierarchy. I wouldn't be able to say if this is really the case. But I would say that it's independent, OK? The UPMS matrix is independent. What we know about the UPMS matrix is independent of the hierarchy between the nutrients. But it's something that it should look. But in principle, in this case, I don't consider it. And we use just one version of the UPMS matrix. We consider it uncertainties also in the UPMS matrix, but nothing else. So there is a comment or more? Yeah, I have one small comment on that. So the PMMS matrix, its parametrication does not depend, of course, on the hierarchy. But when you fit to the experimental data to get the values of the angles and the delta m squares, you do assume one hierarchy usually. And the resulting values that you get in the confidence regions will depend on the assumed hierarchy. The differences in the confidence regions are small. So the results that were shown will not vary a lot if you use normal versus inverted hierarchy, unless there's an extra thing like neutrino decay, which is not the case now. So it's pretty much independent of neutrino hierarchy at this point. Thank you. So are there other questions? Because I have a couple that I want to say. Any last one to talk, please. So at the very end of the talk, Boris, in the conclusions, you were proposing to make a fit with the neutrino. I cannot hear you, Nicolas. It seems that Nicolas just got the connection, so we lost him. But anyway, I can make my questions. And now you're coming back. Nicolas, we couldn't hear anything. Can you hear me? Yeah, now we can hear you. OK, so at the very end, in the conclusions, Boris, you were proposing to make a fit with the electron neutrino, electron neutrino, and muon neutrino fraction, right? So why these three components and not the six? It's OK, because whenever you do a fit, you try to avoid, you try to be economic with the kind of, with the number of free parameters. This is a first thing. So the idea was try to find the most economic way in order to describe the data. And as I showed in the talk, what is producing the problem here is the contribution of the glacial resonance as a separate contribution to the fit. So this is the electron neutrino fraction. They have the electron neutrino. Why not tau neutrino? Because tau neutrinos produce similar spectrum, similar spectrums as electron neutrino. So you are not going to be able to break this degeneracy between electrons and tau neutrinos from current mesh. So the information is in the electron neutrinos and the confidence level regions will cover what you will expect for tau neutrinos. For muons, it's because they produce tracks. So these are the three distinguished signals that you will observe at that screw. Showers from electron neutrinos, tracks from muon neutrinos, and a bump from electron centenotrinos. So these are like the three distinct features. You could use all the fractions. But then it's not the most economic way because you are going to get always this degeneracy between electron neutrinos and tau neutrinos. So it doesn't add more information if you include all the fraction. Thank you. Thanks. So I don't know if somebody has other questions, but I have another one. So bodies, in the case of, for instance, the confidence region that ice cube presented. So how you could interpret this in terms of this asymmetry? I don't know if you try to reproduce the same best fit, but now to say, ah, this is 90% anti-electron neutrinos or 18% or I don't know. Just a question, just if you cannot get the same picture from the current assumption, I mean from the best fit of ice cube that they presented in XCRC. We did the case B of our. The case B is artificial, but with the idea of simulating the results of ice cube. This is because using these fractions and the same data obtained from them, when you do the fit, you get a best fit that is similar to the ice cube and the confidence-level regions are similar also to ice cube. Not the same because the analysis is not always the same. But the features are the same. And that is the idea of the case B, that is like the ice cube case. And the first case is photo disintegration that is kind of a standard scenario, but in a very basic situation. Just considering the resonance contribution. Yeah, right. So OK. So I understand. OK. So another question that I have is in the beginning, in the very beginning of your talk, you said that the gamma, the power index of your power law is going to be the same. But in principle, it could be different. I mean, it's a normal supposition that could be different. But do you have any possibility like how large could be the difference between the two? I mean, the simplest to say is the same. But it cannot be so different at the end because if the neutrino and the neutrinos came from a source that had this similar mechanism for production, we don't expect a large difference. But even though it could be, but I don't know if you know how large could be. Nothing on mind, but I know where you could go for that information. To some Binter, Walter Binter papers. He really does a kind of computation of the spectrum of neutrino for different scenarios. And on that paper, you can see that the situation can be much more complicated than this simple power law spectrum. So I will say that this is a well-motivated spectrum because of what we have from the data can be well fit with using this spectrum. But it's not realistic. And I will say that it's quite far from that. This is my impression. But to know the details of that, I will recommend to read this paper from Walter Binter. This is the paper that I am trying to follow to understand better this point in particular because it's my idea to consider more accurate or more realistic spectrum and see the effects. I don't know. That is the idea. So I don't know if there are other questions. Hi. Yeah, I have one. Please. So I was wondering, what are you doing with your systematics in the fit? Systematics, considering in which case, because, OK, let me see. Because we consider some systematic. For instance, when we use the fractions, it was OK. We fix the fractions for the source and we consider the fractions up there. But then we simulate the data. We consider the amount of neutrinos that have been observed. So in this amount of neutrinos, you have a different composition. You have atmospheric neutrinos and you have astrophysical neutrinos. And there is some error associated to these numbers. These errors are not considered in the plots that I showed in the talk. We didn't consider them in the paper, but after the suggestion of the referee, we did the computation considering these errors. And the main results are still the same, that the discrepancy between observed and the results of the fitting is still there. But the figures are not so nice, let's say. The confidence-level regions and the size of these confidence-level regions are not the same. They are bigger and the shape is not so elliptical. But the main conclusion is still the same. And this is the kind of error that we have considered. I don't know if that is the systematic error that we're thinking about. Yes, that's exactly the point. Because the issue came when you multiplied the luminosity. Because initially, it's one sigma, two sigma consistent, so you cannot really say anything. The point is when you increase luminosity that you get to exclude the real point. So my question was in that direction. If at some point the confidence region would be dominated by systematics instead of statistics, such that you, I mean, so that plot that you showed, that involved the systematics also? No, in that case, no. In that case, no. In that case, no. In that case, no. And in general, we didn't study so carefully when this could happen because we are really, we are completely sure that they are going to use the proper analysis as soon as they can or, I don't know, maybe in the next analysis. I don't think that it's really necessary to show them after 20 years of data taking, after you increase 10 times the volume, you are going to have this problem. And you can see that at the two sigma level, you are going to exclude the best fit point, the expected region. So for that reason, we didn't analyze too carefully that. But what you are saying is important, of course, that to say something at one sigma, two sigma, you should consider this kind of sources of errors, right? And this is one of the requirements of the referee also to get to this. But in general, the main result, the main message is unchanged. And the rest is a lot of extra information that can obscure that message. That's it. I see. I see. Thank you. Great. Thank you, too. So any other questions? I guess I have, from my side, I have just the very last, just to, because at the moment, you did all the analysis in the standard framework, in the sense there are no exotic sources. But your analysis also could be very important for people that consider exotic sources of production of neutrino. But you say exotic sources. That matter, decay. Even though it's going to produce it, but you'll have an extra component, or maybe you can manage in some way to have exotic source that really produce one type of neutrino and no anti-neutrino. So this analysis that you said that you have to distinguish both families, I mean, neutrino and neutrino by separately is very important at the end. Yeah, yeah, of course. OK, so it's like a message to take home for the people that produce new models and stuff like this for exotic flavors. Yeah, because if you are producing, but basically, a symmetric amount of neutrino. And for some reason, after the propagation, you are going to get this asymmetry also there. Even if this is new physics, you need to analyze it in the correct way. Because if not, you're not going to get the correct clue about your new physics scenario. This problem is more in the analysis stage. So it is kind of useful for other kind of studies that consider possible exotic sources, right? Yeah, exotic sources. So maybe now we can pass with the question from the chat. So we have only one that is from Nicolas that he was just asking maybe for the people to clarify a little bit better. I mean, why do you assume that the neutrino and the neutrino are really produced symmetrically at source? Maybe also for the people that are following the webinar, it's just to get a fresh idea. OK, I don't think that when they do the fit, assuming that the fractions of the neutrinos and the neutrinos are the same, they are sinking on sources that produce the same amount of neutrinos and the neutrinos. I think that because in general, this is not the case. So this is what you would expect, that the fractions are not equal. But the point is that what they have detected is still very few neutrinos. So in the confidence level regions, you are still covered the central region. So even if your assumption is not so well-motivated, basically you cannot say too much with the current data. So I think that this is what the data that we have. Let's assume this, but in general, this may not produce a big problem because, for instance, in ice cube papers, they do not claim that they are observing something exotic. They just put the base feed, and they put the confidence level regions, and everything is quite there, right? You're still compatible with the standard expectation. So I don't think that it's because of the sources, but I think that it's because of the low level of the statistic and the impact of that situation. OK, maybe Mauricio wanted to make a comment. He was telling me by inner chat. Yes. I don't know if my connection is OK right now, but I try. So as long as you are below the glacial resonance energy, which is 6.3 PV, you essentially have, in ice cube, no way of distinguishing neutrinos from anti-neutrinos. So you really don't lose anything at that point by assuming that you have a whatever mixture of neutrinos and anti-neutrinos getting into your detector. It could be equal. It could be more neutrinos and anti-neutrinos. It could be more neutrinos and anti-neutrinos, but you won't know. It's only when you get to a point where there's a signal that depends only on the anti-neutrino fraction, in this case, the anti-newe fraction, which is the amount of showers generated by the glacial resonance at 6.3 PV and energies close by, that you actually care about the difference between neutrinos and anti-neutrinos arriving at your detector. So assuming that the source produces, I mean, you correctly said, really, sources are not producing equal amounts of neutrinos and anti-neutrinos, but assuming that they do really doesn't hurt you unless you get to the glacial resonance energies, which actually you took into account your papers, so that's fine. That's all I wanted to say. Thank you. OK, thank you. I don't know if you probably want to say something, but. If I went to say something? Yeah. I mean, you already said something, but. OK, so because we don't have more questions, I guess the time is over. I mean, for all the people that are following the webinars, I guess they are. They like it a lot, but also it was one hour of submission. So we're going to finish this webinar of bodies about the ice cube and neutrinos and the new physics just to thank bodies, but also to thanks also Mauricio, that was all invited person here in the Hangout session to contribute with his knowledge and with neutrinos. So and then for the people that is following us and watching now the webinar, we can see the next time. It's going to be Pablo Roig from Simba Staff, Mexico. And it's going to be more or less in two weeks more. And for people that is following, watching this in a video in YouTube, you can see all our playlists with many interesting talks and webinars about very interesting hot topics. So for my side is everything that I want to say, so we can see again in the next session of these low-physics webinars. So see you everybody and take care.