 Hello everybody and welcome to the Latin American webinar of physics, all of physics for short, so welcome everybody for this very nice webinar that we are going to have today. Remember for all the people that is following us in the different social network that you can connect and subscribe to this YouTube channel and then you can see all the previous webinar and to keep updated with the latest things that are happening in physics about research and other topics like astro particles particles etc. So this time we have a very nice talk because Christoph Ternes, he is from the Instituto Nacionale Física Nucleare in Torino, the INFN Session in Torino. So he's going to talk about a phenomenology of astral neutrinos but before just a little bit presentation he obtained a PhD in the Institute of physical corpuscular in Valencia in Spain. And now he's postdoc in the INFN in Torino. So Christoph, welcome to physics and you can share the screen whenever you want. Okay, can you see my screen now? Yes, we can see it. Okay, good. So thank you Roberto for the introduction. So today I will talk about basically about neutrino oscillations and in particular about neutrino oscillations in presence of light and heavy sterile neutrinos. So neutrinos are produced at some source in charge current interactions as weak states like here. So they can be the weak states can be written as superpositions of mass eigenstates, which awaited with the entries of the leptomixing matrix here. So in the propagation, the mass states evolve in this form here. So from, from here we can trivially obtain the evolution of the flavor states by some just substituting new K of T here for new K. So this means that neutrino which is initially produced as new alpha will have some different composition after some time T. So then when arriving at detector, the neutrino which was initially alpha has a probability to be detected in a different flavor new beta. So the transition probability from new alpha to new beta. So the transition amplitude is given by by this quantity here. And from this we can obtain the oscillation probability by taking the absolute value squared of this. So in the standard case the mixing matrix here which characterizes the oscillations is written in terms of three rotations which are characterized by the by the three mixing angles here theta one two theta one three and theta two three. The one three or rotation here also has also has the Dirac CP phase associated with the mixing angle one three here. So basically there's a fourth matrix to the right here which contains two more CP phases, which are the Majorana phases. And I have not written them down here because they actually do not appear in the neutrino oscillation probability so oscillation experiments are blind to my run a CP phases. So we have three massive news Reynolds, which can be arranged in two different forms. So, in the first, in the first one here, we have new one, which is the neutrino with the largest Alex from content is the lightest neutrino followed by new one and new three and alternatively new three can be the lightest neutrino, followed by new one and then new two. So in the first case we talk about normal neutrino mass ordering and then the second case, we talk about inverted neutrino mass ordering. Now, in any case, oscillation experiments cannot measure directly the masses themselves, but only mass squared differences. So these are the deltas here. So delta m three one squared is m three squared minus m one squared. And so for the for the delta m to one squared. So you see that for normal ordering this quantity delta m three one squared is positive and for inverted ordering delta m three one squared is negative. Okay, so we have a total of six oscillation parameters so the two independent mass play things. And, and the four quantities here which define the left on mixing matrix you know over the last over the last 20 or more years. So all of these parameters have been measured more or less well. For example, the delta m two one squared. A mass splitting has been measured principally by the come along baseline reactor experiment. The other mass splitting or the absolute value of this mass splitting has been measured by long baseline accelerator experiments atmospheric experiments, and also reactor experiments, and so on here. So you see that any of the parameters is measured by at least one class of experiments sometimes even more classes of experiments. There's no parameter which is measured by only one experiment on their own except for the case of come land here for the first one. So this, this means that if we perform the combined analysis of all of the nutrient oscillation data, we will get more stringent resize on the, on the large ranges of the oscillation parameters, then from an analysis of the single experiment on their own. So this is the good motivation to perform the global analysis of nutrient oscillation data. So if we do this as we have done for example in this paper here. We get in the single analysis of experiments these regions here. So this is a bit simplified because many of the parameters measure more many of the experiments measure more than only two parameters. But so this is basically a recompilation of the data that we have included in this global fit. So for the react for the reactor experiments we use data from Renault and Diabae for the accelerator long baseline accelerator experiments we have mean or Canova, atmospheric experiments, ice cube deep core and supercaneopane and also data from the long baseline reactor experiment come land and all of the solar data, which has been collected so far. Now if you, if you combine all of all of these data sets you will eventually get some profiles like like these ones here. So essentially, as of now, the angle theta one two, the mass splitting delta and one squared, and the angle theta one three are measured very well for the remaining three here. We have, we have basically the last unknowns in the standard nutrient oscillation picture. For the atmospheric angle sine square theta two three, we don't know if the value is larger or smaller than 0.5 and this is sometimes referred to as atmospheric octant problem. So right now you see that the best fit is in the second octant, but first octant solutions still remain allowed at more or less to sigma confidence level. The other unknown is the value of the CP phase so you see we are obtaining this profile here, but actually there are only two measurements one from T2K and one from Nova, and they disagree. So the T2K best fit is actually like so close to 1.5 and the Nova best fit is somewhere here close to 0.8 and then in a combination they meet somewhere in the middle. We don't know what is going on here so the second unknown is the value of the CP phase. And the last unknown is the is the neutrino mass ordering. So here in these, in these plots in blue is the result for inverted ordering. And in magenta the result for inverted neutrino mass ordering. So you see it as always like 2.5 sigma above the normal order. So these 2.5 sigma actually do not come from a single measurement of an experiment on their own or so, but they come like from a series of tensions which are small or large in the determination of the remaining parameters. So we still don't know what what the real neutrino mass ordering if it is normal or inverted. So these profiles which I have here shown can also be translated into numbers. And from this table, you see that all of the parameters except for the CP phase currently it's below 5% precision level. Okay, so now all of these pictures seems very complete and to be functioning. There have been several observations which cannot be explained with three neutrino simulations. So first in this plot here we have what is known as the reactor neutrino anomaly. So we have plotted here the ratio of observed and the two calculated events. And you see that for most of the reactors, I indicated by the different points here, it is actually below one what you would expect. So the average of all of the measurements you see that you are actually around three sigma away from from unity. So this is a three sigma effect. And the second one is the gallium anomaly, which is depicted here and something very similar is happening here. And in the case of the reactor neutrinos. And the guy experiments were actually used to measure solar neutrinos but in the calibration phases, they were exposed to strong sources of electron neutrinos. But again, we have found that someone found that there was about three sigma deficit in the ratio of observed to calculated events. So this is a second three sigma effect here. And the last one was an excess of events in the LSMD experiment. So LSMD was looking for was using a new one neutrino beam, and they were expecting basically this background here on of electron neutrinos or anti neutrinos. And the dots here are what they actually observed. So you see that here they have a large excess actually at close to four sigma level, excess of anti neutrinos events. Okay, so they, these, these anomalies cannot be explained with these parameters which we had here, because you see that the mass split things which were obtained from this global analysis are at the order of 10 to the minus five and 20 to the minus three here. So if you calculate the oscillation lengths which are, which are corresponding to these, to these values, you see that one oscillations occur at about 50 kilometers for one electric for one mega electron volt. And the three one oscillations occur for about, or about one kilometer. So however, actually, here the gallium sources they were only about two meter from the sources. Because you see that this plotted here on the x axis, they, they go from like 10 to 100 or so. So also very short baselines are included here, and also the LSMD experiment had a baseline of about 30 meters. So if you take the L over E ratio, which is corresponding to these experiments, you actually need a new mass splitting, which is at the order of 0.1 electron volts squared. So, in order to accommodate this in the neutrino oscillation picture we, we need a fourth neutrino. So we can extend three by three neutrino oscillation, a leptomixing matrix to a four by four matrix. And now, so S stands for steroid, because the fourth neutrino cannot be an active neutrino so it means it can, it is steroid in the sense that it cannot participate in weak interactions. So now having this extended mixing matrix and to enter the new mass splitting, we will have new disappearance and new appearance channels. Our effective mixing angle, so the effective amplitude of our short baseline oscillations depends on one of the new U entries, while for the appearance channel the effective mixing angle depends on two of the U entries. Actually, you see that in the disappearance channel, the U entry is entering, so the U alpha four entry is entering linearly while here it is entering quadratically. So you assume that the appearance channel should be quadratically suppressed if you assume that your extended three plus one matrix is like an effective correction to the three by three matrix. Now the appearance channels are important for the LSD experiment that I have discussed before and also for experiments like Harman, Miniboon, Opera and others. While disappearance channel for PEE, we have the reactors and to guide your experiments and for atmospheric experiments and accelerators we have also can also look at the PMU channel. So now if we perform an analysis of the data from the Gallium Anomaly Reactor Anomaly LSD, you will see that indeed the preferred mass splittings are at the order of at least 10 to the 10 to the minus one electron volt squared. Okay. So here you see also that actually the mass splittings coincide for the for the Gallium and reactor anomalies. So now, this has been some time ago and the reactor neutrino had to be tested. The problem with the reactor is that it depends directly on the flux prediction from the nuclear reactor. And there are several models which can can differ differ a bit one from another. So depending on the model that you choose your reactor anti neutrino anomaly can also get modified. So in order to overcome overcome this this flaw from from the from the reactor anti neutrino anomaly, new experiments were designed, where instead of measuring the total rate, they measure the ratios with the sector put different distances from the source. For example, here we have a cartoon of dance experiment where the detector can be lifted to different positions. So then instead of taking the rates one position, they use the ratios. So actually in dance, it can be put to three different positions. So you can make three different ratios out of that. So the analysis is performed, taking the ratio of the sector to the respective positions. In this case, you basically cancel the effect from the your from your reactor flux model uncertainties. And indeed, when, when the combined analysis of dance and mirrors data was performed in 2018, there was a more than three sigma preference in favor of sterile oscillations as can be seen here in the left figure. So you see that both experiments had individual preferences or about three sigma level in favor of sterile oscillations and then when combining this was increased to two more than three sigma. So the mixing angle that they obtained here, it was a little bit smaller than the preferred angle from the reactor anti neutrino anomaly, but still at three sigma you see that there was complete overlap between both measurements. So, however, this was 2018 and then dance released new data in 2019. And this preference actually went down. So there was less agreement between the analysis in this new data set and you see now, there were no close three sigma regions anymore. So they're still at two, two sigma you had closed interval so the preference was above two sigma, but not not as large as it used to be in 2018. And now the dance collaboration has released also new resize and also some of the other experiments. And actually the picture has changed even more because using more recent data or most recent data. So you see that there is actually no preference anymore, not even, not even as to sigma. So you see that the, that this regions here in green. They go back to zero so they will have no close contrast anymore at two sigma, still at one sigma but the large preference that was observed in 2018 is mostly gone. So then the only way that there's only thing that can be done with this data is basically put up a limits on on the you for entry of the, of the extended mixing matrix. But of course, this was not including neutrino for data, because then we have this this very, let's say, large, huge. So this is the result where they actually say that they observe new sterile neutrino oscillations at more than three sigma confidence level on there. So without the need of combination with any other data sets or so. But the thing is that the mixing anger that they obtained. So you hear you see that the crosses in blue and black are the data and the red dots are the best fit prediction from the experiment. Even if you look only at the data, right. So the problem is that the mixing angle that they obtain is very large. It is actually so large that you could not even say anymore that you are three plus one case is just an effective correction to the tree neutrino oscillation. And also, they're mixing that they obtain this intention with with other data is for example indicated here with with solar experiments. So the neutrino for collaboration measures the ratios between 24 different distances so they take here 24 different distances and average them. And take the ratio to the average at all other distances. And also they use nine energy bins so they have basically 24 distance and nine magic bins. Now in order to create a figure like this here, they group all this this independent distance energy bins into bins in off L over E. Okay, so this is how you get from the independent distance and energy bins to bins in L over E. So this is this is basically what they observe and then you want to make the analysis. This is how you calculate the number of events for these ratios. Okay, so so basically you see that we have to take the average over the oscillating term here. Now this average is calculated in this form here. And I will not go into detail but this basically just contains several detector reactor effects and also and also an averaging over the distance of the of the reactor which is important for short baseline observations. And in particular, it contains the resolution function of the reactor. Using the information which was provided by the neutrino for collaboration in this paper here, we can actually extract the energy resolution function. And it is given in this form here so we zoom Gaussian energy smearing with with this resolution here. So if we perform the analysis then comparing power predicted events spectra with the with the observed events we get the we get the red magenta blue lines here. So you see that we actually obtain in our analysis and mix a value of the mixing angle, which is even larger than the one from the neutrino for collaboration. This is actually maximum. But on the other side, we obtain open three sigma bonds so we don't have a three sigma preference at this below three sigma but still above two sigma. And the only way that we were able to reproduce the results from the neutrino for collaboration was by ignoring the energy resolution of the detector. If we do this we get here the yellow green lines, which, which are in good agreement with with the resize officially resides from the collaboration. In any case, here we have still plotted also balance for example from Catherine from solar data and from other ratio experiments prospect and say, and stereo. So you see, even in the in the in the official results there in strong tension with the results from this other reactor experiments. So in this analysis here, we have used the standard Chi square analysis which does not take into account possible fluctuations in the data. Now, if we, if we, if we repeat basically this exercise but taking into account these fluctuations. The preference is is further decreased. So here we show now on the left side without energy resolution on the right side with energy resolution, how the preference goes further down so the dotted lines are the same as before. Now we go to the standard case square analysis, and now the solid lines are the result from this month, this Monte Carlo analysis taking into account statistical fluctuations. And you see, also in this case here without energy resolution, we have, we do not obtain close three sigma confidence regions anymore. So for the summary of this neutrino for analysis is basically that if you start without energy resolution and performing the standard case square analysis you obtain a preference at the 3.2 sigma level. However, after adding as should be done the energy resolution, and also performing the Monte Carlo analysis, the preference is reduced to only 2.2 sigma. So I have shown you correspond to this 500 kev data, but the neutrino for collaboration also presented different analysis using like an average of different data points, which I did not show you but essentially the analysis is the same so it goes from 2.7 to 2.2 final preference. Okay, so you see that in the other ratio analysis we we don't have a preference for sterile oscillations anymore. And for the neutrino for analysis we have a result which is, or they obtain a result which is rather doubtful. And we can also now see what what is going on in different oscillation channels. Sorry, no, so there's what was one more thing that I wanted to show you about neutrino for we have, we have created. So we have created at the order of 100,000. For like data sets without including oscillations and perform the oscillation analysis of this unassisted data. And here I have the best distribution obtained in these in these analysis. So you see that for a neutrino for life experiment. There is a large probability to find the best fit value with very large mixing, even in the absence of oscillations. Okay, so this is true for both places without the energy resolution and including energy resolution. And regarding the other channels then the electron neutrinos appearance there were also searches with with new on neutrinos. And there was no evidence found in favor of three plus one oscillations so you see that here on the left side. We have the exclusion calls from many experiments so basically everything which is on the right from Schlein is excluded at three Sigma confidence level. And from the combined analysis of all data we obtain the red line here. You see the driving force in in this determination here for you new for is basically me knows me knows plus which is the blue line here for low masses, while for large masses. And there are contributions for more experiments also important. Regarding the last of the of the sterile matrix elements you tell for actually the strongest bounds come from atmospheric data. Last year, there was also an update on this figure, because last year ice cube release this analysis here where they used eight days eight years of data. And you see that's now actually they obtain a closed region at 90% confidence level to see it is not it is not very significant. But still it is a closed region and interestingly it actually coincides exactly with the, with the mass range which is important for the reactant neutrino normally, or also experiments, such as neutrino for. So this this data here are not included in this figure because they have not been made public yet so once they are public we can also make the combined analysis to see how large this effect can be in comparison with the other experiments. So much for for disappearance experiments, but of course we observe appearance experiments. And especially there was, there was a large preference in favor of oscillations in LSD and minimum. And you see they are here painted in blue and red respectively, and although both of them prefer prefer have observed excess of of events. You see that they only partially agree with each other. So the interesting is that the most of the of the mini boom region is actually excluded by Icarus and opera, which are the vertical lines here. So it's the only the upper part of the region here survives. In the case of LSD, we have the lower region here and the large regions here so that the large region here is also there for mini boom but the larger confidence status. These regions are cut off by other experiments such as for example Carmen and Nomad. So if you perform the combined analysis of all of these data, you get again closed contours at three sigma confidence level. So this raises the question if a global fits in the three plus one picture is a sensitive thing to do. So you see that the disappearance experiments measure you for and you know for for electron neutrino experiments and you know three experiments respectively, while the appearance experiments from the last slide here. They measure the effective mixing which depends directly on both of these quantities. So if you combine the electron and the new one disappearance experiments you can also bound this mixing angle here. And, for example, this has been done here in 2017. In blue you have the appearance, the combined analysis of all appearance data and then read the combined analysis of all disappearance data and you see there was a nice overlap in this region here, roughly above one electron world squared. So if you combine closed regions, it's three sigma confidence. So, since then, many new data have appeared so if we make more or less to date version of this figure, it looks like this. So you see that the appearance and disappearance regions are fully disconnected. And the global three plus one neutrino oscillation pit is statistically not acceptable. So the goodness of it obtained here is at the level of 10 to minus 11. So you see the basically the message here is that we still don't know what is going on, because we have. We have a very large significant observation of excess and mini boom and LSD. We have the reactor anti neutrino anomaly which is still there. My racial anomaly is mostly gone but still we have the neutrino for data so basically this will probably remain a very active field of research in the next years. So let me tell you about lights that are neutrinos. Now, in the last part we go to heavy sterile neutrinos, which are predicted or required in type one CSO mechanisms. Okay, so in this case, our, our leptomixing matrix is extended into this form here so we, we have N, which is a three by three matrix, which is describing the. The leptomixing for the light neutrinos, but now we have also SV and T which, which contain the mixing between active and sterile neutrinos for SNV and the mixing between sterile neutrinos in the case of T. Okay, so this means that the sub matrix here which is describing neutrino mixing in the light sector is not unitary anymore. And it was shown that that convenient way to parameterize this matrix is by just taking the standard three by three matrix that we had before. We have the standard PMNS matrix and it is multiplied with with this triangular matrix, which basically contains the deviation from the unitary. So in this case we have nine new parameters in the three no oscillations because the diagonal parameters here are real, but the non diagonal parameters can can be complex. So you can see that we also are including here new sources of CP violation in neutrino mixing, which also can be, can be highly degenerated with the standard with the standard CP phase is as strong in this figure which I have taken from this picture. Okay. So if the new neutrinos, the heavy neutrinos, if they are very, very heavy, they are very, very strong bounds from electric measurements. So you see that then the bounds on the, on the alpha parameters are going to the 10 to the minus three level. If we have lighter neutrinos, these bounds are relaxed and then actually bounds can be derived from, from neutrino oscillation experiments. So we have a lighter here but I mean lighter with respect to the electric scale, they are they still have to be much large, much heavier than the lights that are neutrinos that we have discussed before. Okay, so in this case, neutrino oscillation probabilities are modified in this way. So for the P new new probability, we have the standard probability which is multiplied by by one of the alphas here. There are also new terms, which contain also the new, the new CP phases here. And also the appearance probability gets modified in this way. So you see that again the standards term gets this pre factor, while a new term appears containing both faces. And now we also have actually a zero distance effects terms here so you see that this last term, it does not depend on the energy or the base term anymore. So this means that the zero, zero distance flavor flavor transformation is possible in this scenario. So we have performed combined analysis of short and long baseline data using this one unitary parameterization of the mixing matrix. And we have used short baseline data from Nomad and new test experiments and long baseline experiments T2K and number one. Okay, so from our analysis of Nomad new test we can put rather strong bounds on the T new E oscillation probability here so this is the combination of these parameters at the level of like five or six times 10 to the minus four. So we will, we will combine this. This result here with the result from long baseline data, and we can do this by just transforming this guy square here into a guy square of alpha one one and and absolute value of alpha 21. So we can do this and project the result from all analysis into this plane where we have customized over all of the other parameters. So, all of the standard oscillation parameters and alpha one one. We obtain these contours here. And so you see that basically the bound on alpha 21 is more driven from the short baseline experiments and bound on alpha 22 is mostly coming from long baseline experiments. So the combination of T2K and short baseline data can put a much stronger bound on alpha 22 than the combination of Nova and short baseline data. And this is because the, because in the standard analysis T2K has has a better determination of the, of the mixing in data to three which is basically the principle factor in the standard oscillation probability. So you see it will be, it will be directly correlated with the new parameter alpha 22. So therefore a better, better determination of data to three translates on the better determination of alpha 22 in this scenario. So when we project this into the one dimensional plane we can obtain these bounds here on on the on the alpha parameters. Now these bounds can also be translated into bounds on the unitarity of the mixing matrix directly. So there, there are different parameterizations for, for this, for this three by three matrix. So we have used here this triangular, this triangular form of the, of the, of the my matrix which is multiplied on the standard matrix, but there are different parameterizations for example using Hermitian matrices so. So the idea of this is to translate the bounds of the alphas in the general bound which is not depending on the parameterization of the non-unitarity that has been chosen. So I have also said that there, that there are new sources of CP violation in, in this non-unitary scenario, and it would be good to see if they can ease the extension that I have talked about a little bit in the beginning between T2K and NOVA data. So basically these are these are the results from an analysis of T2K and NOVA data where you see that T2K prefers values of data close to 1.5 pi while NOVA is living here in the second reason so they basically perfectly disagree with each other. So the idea was to see, due to these new correlations, there can be some central value found for, for this, for the phases and that this tension might go away. But unfortunately, it does not go away because you see here in blue, the region obtained from the analysis of T2K data and in red the analysis for NOVA data and they perfectly disagree with each other again. So this is for, for the alpha parameters hold down at the best fit value that we have obtained, which is very close to unit, unitarity. But this remains true also if you allow values which are further away from the unitary point. So you see that here the NOVA region starts to close in the region around 1.5 pi and 1.15, 1.5 pi, but the T2K region starts to open up. So if you go to even larger values, they still avoid each other. And if you go even to revelage, maybe already the boundary of the allowed region values, this is still true. So you see that when including these new sources of CP violation, the T2K NOVA tension is not going away. So this brings me to the conclusions. So we have seen that some of the oscillation parameters, basically sine square theta 1, 2, sine square theta 1, 3 and delta M21 squared are rather well measured. But we still have open issues regarding CP violation, the octant of the atmospheric angle and the neutrino mass ordering in the case of standard nutrient oscillations. And for 3 plus 1 zinc, so light star and genus, we see that there is, there is no preference anymore in the ratio analysis of reactor experiments with the only exception of neutrino 4 where the result is more or less doubtful. We have also seen that the global fit to 3 plus 1 oscillation data is not possible at the moment due to this very strong tensions which appear between appearance and disappearance experiments. So what on the right side we have seen that neutrino oscillation experiments can be used to constrain heavy neutrino zinc, but unfortunately the CP tension observed in T2K and NOVA can not be resolved using these heavy neutrinos. Thanks. Thank you very much Christoph. It was very, very nice webinar about all the different features of sterile neutrinos. So just for the people that is following the live transmission don't forget to, if you like this webinar cycle you can subscribe to the YouTube channel, as well as you can check all social networks and maybe to also to subscribe to the mailing list in order to receive all the notifications and to be updated with all the activities that we are doing here in low physics. So let's start with some questions. Let me just check in the because for the people that is following us in in in YouTube, you can write the questions or your doubts or comment in the chat in the YouTube live in the chat in the YouTube transmissions. So maybe we can start with some questions here from the audience. Meanwhile, we give some time to the people to write questions there. So is there any somebody want to make a question for Christoph here in the audience. Okay, I have one question. I mean I have many questions but when when you were talking about the CP phase is usually as you I mean, is there any capability to physical implication for the CP phase in the sterile neutrinos sector. I mean with this fourth and three like, do you expect to have more phases than than the typical delta from the three neutrinos. So in the three plus one case you have actually you have actually also two more CP phases, but they are not relevant for for the reactor experiments. So they would only be relevant also for for experiments which measure the three neutrinos appearance at very large baselines and actually then you have, you can also have cancellations among the new phases, and the, and the standard phases. Okay. And, well, for the for the moment there is, there is a question from Joel that I'm going to ask you but before there is a greetings that Jorge Tirol he's saying nice talk Christoph. Thank you. Let's see, I mean, he sent a question via the chat because he has some connection issues, but he's asking on slide 29 you present an updated three plus one feet. What is points defeat one specific experiment, can it improve by removing something. Yes, it can be, it can be improved by removing many bone and lsnd because then you have no lower bound on. So you see that the only lower bound coming on on this quantity science where two times data me we are in you is from lsnd and many boom. If you remove these two, it can go back, it's kind of it can go to any value back to zero. So then you do this see this region here will extend also to zero and then you will have overlap in this region. But so in this 2017 18 fits, it was possible to very strongly improve the goodness of fit by removing, for example, only lsnd or mini boom. But this is not possible anymore so if you include either lsnd or if you exclude either lsnd or mini boom, it is still the goodness of it is still really bad mean better than he but still not good. So you have to exclude one full class of experiments. Okay, so it seems that there is a, I know he jolly saying, thanks. Okay, so there is a, maybe there are other questions here, or it seems then. Okay, I have one question that also I got a little bit confused now. There is a question from David Vanegas. He's asking, what is the future of the three plus one model. Can we say that it is ruled out by current data. No, so, you know, I mean, we can say that the comb that the combined explanation of lsnd mini boom, and reactant, you know, anomaly is very unlikely. But I mean the mini boom and lsnd are experiments which has an excess of four and five sigma confidence level right so this is something that cannot be ignored we just have probably this is not the right explanation or maybe not, but the excess is there. So it needs an explanation and we have not found it yet. And also, I have said that the, that the ratio analysis are now. From all experiments except for me to know for the ratio analysis are not preferring three plus one oscillations and more, but we still have the gallium and the, and the reactor. So they are not gone, they are still there as well. Okay, so there is another question via this time. Young is he's saying the he sent the answer the question. He's asking, are you saying that the neutrino for experiment is not suited for to do what they tried to do the plot with the assumption of no solution is basically saying that they can expect fake signals, but how it is not included in the experimental analysis by the collaboration. Yeah, so to, to basically include this one needs to make the Monte Carlo analysis, including the statistical fluctuations of the data, and this has not been done by the neutrino for collaboration yet. Okay, so maybe it is, I have another doubt. I mean, we can know I got a little bit confused. What is the different the, I mean, the essential difference between these two experiment that gives so different results. I mean, is the moon and Ellen Ellen Cindy is the technology that they used or the type of target or. No, the results from a lesson D and mini boom are more or less an agreement right so they both observe an excess in the electron appearance channels, or electric or anti neutrino electron appearance channels. So the problem is that the mixing anger that they need to explain this excess is very large you see so here to set the order of 10 to the minus two. But if you make down the combined analysis we have a bound on you meal on you for and then you meal for coming from the new one experiments and electron experiments. Now using the bound that you get from the reactors for example on this one and from ice to mean us etc. On this one, you can construct bound on the combination of these two. Okay, and so this is how you get the red line here. So the combination of the bound that is re bound is obtained, this is obtained by me knows me knows plus and the bond is obtained from you before are not compatible with the required large mix or rather relatively large distance more but relatively large mixing angle required to explain the LSD and mini bone signal here. Okay, I see. I see. So, let's check. No, okay, just to remind to the people in YouTube that you can, you can write more question for for Christophe. So, let's say history. Other question here in the in the audience, because I still have some questions. Anyway, I can get just a very another not. In the sense, usually most of the experiment is just taking different target like not target objective like neutrino or anti neutrino and then combining assuming that the two sectors are completely equal. And not sitting deep. I mean, separated analysis between the two. I mean that assuming that making out to do have to behave differently and then defeats and maybe not compatible because they have different mixing angle. Just a very naive question. So, you see that the reactor anomaly is using anti-neutrinos and the gallium anomaly is using neutrinos. So, you see that here, I mean, the best fits differ, but there is still a significant overlap. And for the, in the case of miniboon and LSD, LSD was using only anti-neutrinos, so this is coming from anti-neutrinos. And miniboon has made a combined analysis of neutrino and anti-neutrino data. And they see a large excess in the neutrino sample and a smaller excess, but there is still an excess in the anti-neutrino sample. And in the case of, in the case of, for example, for the, for these experiments here, so you see the most significant ones are probably the minos and ice cube. Minos was running most of the time in neutrino mode and minos plus was, and then the extension minos plus, if I remember correctly, was running only in neutrino mode. And for the, for the atmospheric neutrinos and ice cube, you cannot distinguish the neutrinos from anti-neutrinos. Okay. I see. I have, I haven't, I mean, there are other questions here from Martin and Joel. They're asking, okay, three plus one is not longer acceptable, but how does it compare with three plus zero or is there any hopes for three plus two? Okay, but this tension cannot go away with, if you just add more neutrinos, right? Because they are, they are requiring the same mass, the same mass difference, right? So if you had the preferred region, which was sitting here, and the preferred region, which was sitting, for example, up here, then you would need the three plus two model. But now adding to this here, three plus and a fifth neutrino would not, would not help. And what was the, what was the first part of the question, sorry? That is the three plus one is not longer acceptable. How does it, how does it compare with three plus zero? So which is, I guess, give a better fit, three plus one or three plus zero in the No, I mean, so three plus zero cannot fit the, the mini boon less and these things. And also in the case of three plus zero, this is where, where you have the anti-neutrino, I don't know if you know, so this is how we try to explain this. So three plus zero will not fit anything of, of, of a less and the mini boon or, or of the anomalies. So yeah, there is another comment that he said, saying, I mean, commenting also, but neither three plus one. So kind of if three plus zero and three plus one cannot fit the data. So there is a, both they have tensions in the, in their own way and their, their own strength, let's say, yes, kind of, yeah. So the, the question that, because you presented the beginning that every, everything was, I mean, is condensing in this global fit. So can you comment more or less the, the, how the global features are, are created like taking each experiment separated and then combine all the, you know, super major square or each. They, they are, they are. So in order to make this global fit, you first have to reproduce the, the official analysis from the experiments. So then you can, you can make chi-square calculations, combining them in terms of chi-square. So this, in this way, you take into account correlations, which can appear among different oscillation parameters. And so the, the data that the plot that I have shown here at the beginning is simplified, right? So because I have shown you here the projection, for example, of T2K and NOVA into this plane, but actually when we made analysis of T2K and NOVA, we also include data 1, 3, and here I didn't show you any plot of the CP phase. Okay. So actually the, the sectors here, they also, they talk to each other and this has to be taken into account when making the global fit. So, yeah, regarding this, this, all these experiments, which are then the, the, the future experiment that they can deal better with this anomaly, June is, for instance, better for, or it's going to be another, besides June. Yes. So basically the remaining unknowns that I was saying, like the octant mass ordering or, or the, or the CP phase, this will be, this will be addressed by the next generation of experiments. So I mean, right now we still have like a couple of years of T2K and NOVA running time now. NOVA will be running until June will take over. And T2K, I think it has been approved for an upgrade to this T2K2 or so. I don't remember exactly what the name, but, but yes. So the T2K and then the future upgrades of the T2K experiment, once HyperK is built, they will extract the value of the CP phase with, with a very good precision, if, if no new physics scenarios are present. They will also measure the neutrino mass ordering individually at five sigma confidence. I think the, even for the worst case scenario of oscillation parameters, the, the, since June expects to measure the mass ordering at five sigma confidence level after one year of data taking in the worst case scenario. But, but this will be like 2030, right? Yeah, there's gonna be a lot of time for the results. So, yeah, this is, yeah, now that you were telling me that, I, I also, I remembered one of the questions that I wanted to say in the beginning. What about in this, I mean, it's not part of the analysis or not the typical kind of hypothesis that is included for oscillation neutrinos with the sterile neutrino, but is there any, any hope to, I mean, or any way to alleviate this tension via non-standard interaction or, I don't know, sacred interaction in between the sterile neutrino sector and the active neutrino sector or something like that? I mean, I'm not sure because, I mean, probably, probably there should be some more, some, some way to do this, but you see that there's the bound on U4 here, that the most important contribution comes from Minos. And in the case of Minos, the matter effects are not so important. So the NSI have not a large effect in the Minos analysis. So you can probably alleviate the effect from ice cube or from the atmospheric experiments, but I don't know if you can get rich of Minos. So let's say that it's basically oscillation in vacuum, but I mean, the anomalies appear in oscillation in vacuum, let's say. I mean, it is not completely in vacuum because it's like 700 kilometer baseline, but the P mu mu channel is in general not so sensitive to matter effects as the P mu E channel would be. Ah, okay. Okay. I understand. I understood. Right. So let's see. Okay. No, in YouTube, we don't have any further questions. So I don't know if the very last question from the audience. Oh, okay. So the, no, it's just, even though this is not the, I mean, because I remember that there were some works in which they were including also the cosmological input from the neutrinos, kind of the from the early universe. And yes, but this doesn't modify anything of the of the tension. Yes. No, yeah. No, if you want to do nothing is allowed. So so if you, so if you look, the red lines here are once I showed you at the beginning from the combined analysis of Meos and Dansk when they were still preparing the three plus one mixing, right? But you see that actually in this case, they require a value of ineffective, which is, which is larger than 3.9. Yeah. Yeah. Okay. Okay. Yeah, because yeah, maybe, maybe there were some, I don't remember, well known, but it was related. Yeah, maybe with an ineffective, but these those are ineffective that are that principle kind of thermal ineffective because. So these are, these are, this is our assuming standard cosmology. You can, you can relax this by introducing secret interactions in your cosmology and then this bound is relaxed. But I am, I don't know how this works or how this, how much this improves the situation. Yeah. Right. Okay. So if there are no other questions, so we can, we can thank Christoph. It was very, very interesting and very, very, very nice to see all the improvement that the, the strain neutrino research area have, have arrived to this moment. So let's say, let's, for the other people that is following law physics, you can check all, all calendar of, of webinars that in more or less in two weeks more, we are going to have another webinar. And of course, thank Christoph for your nice webinar. And for all the people that is following law physics, we see each other in a next time. Bye.