 There are many subtle points, but again I insist that there is no conceptual problems and the picture I have presented here is kind of the most economical way to describe oscillations without facing any conceptual problems. Well I can add a little bit more confusion saying that even energy momentum are not conserved in this picture and sometimes you need to take into account this and the point is we have this kind of situation when we have localization right we have localization of the sources and also localization of the detector. When you do localization which means that you create something quantum system which should have some kind of finite size which means that you face here uncertainty relation immediately. Of course energy and momentum are conserved if you consider all the system all through the walls or something which produces localization. In all the system energy momentum are conserved however if you turn key description saying okay now I'm just focused on neutrinos only or probably some particles which are accompanying neutrinos then sometime you may take into account also uncertainty principle and energy momentum violation related to finite size of the production region. So now let's back to my lecture and yesterday it was some question probably it has some interest to others. I have shown this summary of the results on solar neutrinos and the question was how we determine mass square difference and mixing angles from here. Remember we discussed how we determined this from a selectory picture. So here you see theoretical curves to which correspond to two different delta m square. So you see here we have sensitivity to delta m square and if you change delta m square this curve moves. So this is the way how we are fixing delta m square or extracting delta m square from a solar neutrino data. The probability here just corresponds to sine square theta 1 2. So if you are measuring this asymptotic value immediately determine this one to mixing. And also the probability here is given essentially to vacuum oscillations and the formula is 1 minus this one half sine square to theta. By the way it was always question that if you take into account three neutrinos right so here is just two neutrino problem. If you also include the third neutrino in analysis then the change is very little. So you should just add to this probability two factors cosine 1 3 to the fourth power then this probability which we are discussing here p2 actually this is which takes into account also this 1 3 mixing plus sine 1 3 to the fourth. So this is very close to 1 this is very small and usually can be neglected and this is how we connect the probability in three neutrino case with the probability of two neutrino oscillations. So there's no problem to include immediately 1 3 mixed. So in some slides before and what you will see next I will also mention two different mass hierarchies. So when we are saying about two different mass hierarchies we mean the following. This type of the spectrum I have already described before and this refers to normal mass hierarchy case and actually the states can be enumerated by amount of electron flavor in a given state. So let us call the state number one the one which has the biggest amount of electron flavor. Second state has intermediate one and the third state is the one which has the smallest amount of electron flavor right. So there is no kind of ambiguity what to call neutrino 1, neutrino 2, neutrino 3. Now inverted mass hierarchy case corresponds when the third neutrino is the lightest one and two others with a big amount of electron flavor are the bigger mass. Again from oscillations immediately we are extracting mass square difference. Remember this? Now it's not complete permutation of this picture because the ordering of the first state and the second state is the same as here and actually this ordering is determined or fixed by solar neutrinos. If you would have opposite then you would not have resonance or abioticity conversion which I have discussed before and suppression would be much weaker than you saw in the previous slide where suppression is something like one-third at high energies. So hierarchy of elements one and two is fixed by solar neutrino data. So we actually now consider it one-two-sector and one-two-sector sometime is referred as a solar neutrino. So this how delta m square one-two and sine square theta one-two are fixed from solar neutrino data and from Camland. So these two experiments allow us to extract these two parameters. So let's go to atmospheric neutrinos. Atmospheric neutrinos are produced in interactions of cosmic rays with a nuclei in atmosphere. So in these interactions many secondary particles are produced and in particular pi mesons, k mesons, charm mesons and others depending on energy. Then pines decay into muon and muon neutrino and muon in turn decays into electron, muon neutrino and electron neutrino. In this chain we produce two muon neutrinos and one electron neutrino and the ratio of fluxes at least at low energies where these processes dominate is two. So the number of muon neutrinos is two times bigger than the number of electron neutrinos. Actually this is a very important quantity and many observations actually can be explained taking into account this ratio. At higher energies also these processes actually even at not very high but the higher energies these processes become more also important. At very high energies the production of charm mesons and their decays into neutrinos gives some contribution. Till now we haven't observed though in atmospheric neutrino these decays. They should actually give probably even dominant flux in atmospheric neutrino at very high energies like in PEV range, the range where we are observing cosmic neutrinos now. So at high energies at least this cosmic rays produce isotropic essentially flux of muon neutrinos which actually comes from different directions and so if your detector is here you detect neutrinos from everywhere. So it's from from all all the directions and in some cases neutrino crosses the core of the earth in some cases it's just atmospheric neutrino. Now these are fluxes of atmospheric neutrinos. This is the energy scale that the flux multiplied by energy cube. So in fact if you just show the fluxes they have maximum somewhere here near 1 GeV and then very fast decrease of the fluxes essentially like energy into fifth power. You see the dominant components especially for at high energies are muon neutrinos and muon anti neutrinos and much lower flux of electron neutrinos and electron anti neutrinos and the point is this electron neutrinos are produced in decay of muons and so muon have five times which is two orders of magnitude bigger than pine right and so pine has enough time to decay and muon especially at high energies they have no time to decay they just heat the surface of the earth and so do not produce neutrinos. So they degrade energy degrades they produce neutrinos however the energy is much lower. This is the the so-called flavor ratio and you see we are producing all four neutrinos species actually at very very high energies also town neutrinos should be produced in the origin. So this is what we have and these are the ratio of different fluxes so the fluxes around two of muon and electron neutrinos and then this flux increases this ratio increases. Now atmospheric neutrinos have very enormous physics potential because the energy range is huge say from point zero one GeV up to ten to the five ten to the six GeVs. The baselines we are studying is just comparable with diameter of the earth is one certain thousand kilometers. Matter effect is present and actually these neutrinos feel all these profile and features of density profile of the earth. So we have a neutrinos of all neutrinos of all the types electron muon and also we have neutrinos and anti-neutrinos and town neutrinos are produced copiously through oscillations. So achievements you know that the first discovery of oscillations has taken into account in atmospheric neutrinos. The first statement that we see oscillations was done studying atmospheric neutrinos and then atmospheric neutrinos allowed us to measure two three mixing and two three mass splitting and nowadays and even in early days we are using atmospheric neutrinos to search for new physics beyond the standard model and the program is to search for sterile neutrinos and there are a number of bounds obtained on the properties of sterile neutrinos to search for non-standard interactions, violation of fundamental symmetries like CPT or Lorentz invariance. Now this just to show the quality of the data on atmospheric neutrinos what has been observed it was observed the deficit of muon neutrino flux and no deficit of electron neutrino flux and you see here zenith angle distributions of different type of the events. For instance this is events in sub GV range so these are zenith angle distribution of events in different energy regions. So here is a low energy new mu like events and you see this is what is predicted and that was observed and blue line corresponds to the best feed point when you use certain values of parameters so you extract from here two three mixing angle and two three mass split. So you see here the deficit this is also some other type of the events and the difference is here when the biggest one when neutrinos are coming from down so they have big baseline. Here close to vertical direction the effect is very small because the distance from the point when neutrinos are produced something like 10 20 kilometers and there from downstairs it's something like 13,000 kilometers and you see this kind of very profound effect of oscillation. This is for higher energy events and again so this is what is expected without oscillations and this is what you observe in the experiments. So the data are dominated by super Kamiakanta so these are the data from super Kamiakanta. So these are even higher energy mu on mu like events as we are saying again there is a deficit and certain change with energy range at the type of events so this is for instance partially contained mu on events which means that something is produced but go out of the detector and so you do not see all the track and that corresponds to higher energies. In contrast to E-like events like here for instance there is a good agreement so it looks like electron neutrinos are not the subject of oscillation they do not participate in oscillations in contrast to mu on events and the interpretation was that this deficit is because of oscillations of mu on neutrinos into tau neutrinos so that's interpretation and we extract from here experimental results a values of mixing angles and mass square differences. Apart from super Kamiakanta now this type new type of the experiments provides with very nice experimental data so you see here the ice cube detector and I will speak about this detector also a bit later so what is this this is in Antarctica and you see here there's the surface the ice and this is the ice the ice has the width something like three kilometers in some places in Antarctica and here you see strings and the strings to strings the so-called digital optical models are attached essentially these are kind of PMT multipliers in the sphere with some electronics inside so it's already sends to the surface elaborated signal. There are 86 strings here and the total volume is one kilometer so you can see here two refilled. Each of these strings contain something like 60 models. This is ice cube detector now inside ice cube detector there's a deep core and deep core detector is just more strings so you have you have higher density of automultipliers. When you have higher density of automultipliers you reduce the threshold so if ice cube can detect events above 100 GEVs the energy release the deep core can detect events down to 10 to 15 GEVs and now we are discussing even more dense array Pingu to determine the mass hierarchy of neutrinos which will have the energy threshold 3 GEVs and this Pingu detector I will speak a little bit more later we'll have even denser array of the strings and automultipliers something like 40 strings more in the smaller volume of this type and about 96 sorry 86 automultipliers or 96 each string yeah yes yeah so one inside actually the Pingu will probably will take approximately the same volume as this near part of lower part of deep core actually this this layer has no automultipliers because of dust actually interesting geological studies and the ice was accumulated and you see some layers with dust when it was a book of you know volcanic activity and so there's a dust related to this activity now this is the result which deep core released quite recently and so it was end of last year and they see also oscillation so what they detect they detect mules produced by muon neutrinos charge current interactions so muon neutrinos atmospheric interact in the in the detector produce mules and these mules are detected by a deep core okay so here you see number of events at the function of reconstructed energy in say this is L over E L over E is just the factor which enters the face the face is proportion to this and so you expect oscillatory picture and this precisely what they see so this is what is expected without oscillations and this is with oscillations of course you are not covering many periods it just one period essentially of the oscillations and this is the ratio of what is what is observed to what is expected and you see here clear with high sensitivity the deficit of the signal here just because of muon neutrinos partially are transformed to tau neutrinos and tau neutrinos produce signal but not what you expect here so here is determination of parameters delta m square 3 2 and this is sine square theta 2 3 and you see results from different experiments these are more or less the data which we are getting so delta m square is something like 2.5 I mean if you add some other experiment this is 2.7 comes from this experiment but you see the accuracy of of deep core is comparable with accuracy of other experiments I think this one is from t2k this is a accelerator experiment and this one from super kamiakanda detector and this is from minos see here so there's a good agreement of all the data and what they show is that the mixing 2 3 mixing is close to maximum remember we had already in the picture before the mixing is close to maximum although some kind of steel wide range allowed now what are problems and what is the future of these studies first of all nowadays we are going to very precise measurements in atmospheric neutrinos and remember this is a cheap signal no need to produce accelerators which now it's very costly so this is you know the nature gift for us but the problem is that we need to understand these fluxes very well and now for future experiments we need to have to have a knowledge of these fluxes with say one two percent level accuracy if you want to determine mass hierarchy and CP violation which I will speak about so this is serious issue because it looks that everything is known of course you don't know where you precisely the cosmic ray fluxes but it low energies you know you even can measure this these fluxes but then you need to develop to develop your algorithm to compute cascades because you have actually not most fear the cascades and to compute these fluxes then things becomes not so trivial but anyway so now this is one of the important activities to make really very precise predictions of the fluxes this is kind of next step in in this business because if you have just say want to have 10 20 percent accuracy this is one story but if you want to go to say one percent level two percent you need to take into account various effects new ones and processes etc. Now what we expect from from this usage of atmospheric neutrinos determination of mass hierarchy measurements of CP phase and search for new physics which I have already mentioned and what are experiments super case still continue to operate now deep core we release more data and ice cube actually ice cube measures this atmospheric neutrino fluxes at higher energies even so up to this pv range where cosmic neutrinos already appeared so the flux of electron and muon neutrinos is now measured up to this very high energies oscillations effects actually show up at lower energies there is no big oscillation effect that high energies except for if there are sterile neutrinos if there are sterile neutrinos say in the range of one electron volt mass then they should show up at this experiment in ice cube at energies few TVs and so we are expecting analysis from ice cube now which will put so I hope very stringent bound on this sterile neutrinos you may ask me I can elaborate on this more so then pingoo and orca these are kind of experiments which are quite similar orcish probably will be in Mediterranean here so this one as I explained already in Antarctica and so the aim is to determine mass hierarchy using atmospheric neutrino so you need to create just detector good detector and have good prediction for atmospheric neutrino fluxes although here in the case of hierarchy you may not need to have very precise flux knowledge then hyper kamiakanda this is next project after super kamiakanda which may probably start to operate in 10 years and they will have bigger volume I also have very nice capacities to have flavor identification measurements of energy and so they will of course contribute then the very you know future projects are like mica or super pingoo to major CP violation and this one again in Antarctica to have very low threshold to be sensitive to supernova neutrinos and he wants to solar accelerator neutrinos so this is actually nice it went in in super cave now it's a really kind of artistic you know also this is techniques of detection but pictures are really amazing the colors actually they show the timing so that the signal probably started from here and then developed in the green and these are the later times and so you see here these dots these are photomultipliers which detect this event and this is high energy when I think now what are the sources of neutrinos accelerators is you usually have proton nucleon collision again in which you are producing fine k mesons also charm mesons and so then you create the fluxes of neutrinos mostly neutrinos but also electron neutrinos and now you can separate neutrinos and anti-neutrinos by just using magnetic field so you can say remove pi plus and then you have the case of pi minus or vice versa so accelerator neutrinos fluxes are considered the fluxes which you can manage you know it's not like atmospheric it's given that's it you cannot do anything but here we can play with this important thing with what you can do with with accelerator fluxes you can change even the energy range or the spectrum but first of all the energy spectrum is determined by the original protons right if you have initially very high energy protons they will produce higher energy pines and neutrinos not only this now you can use the following actually produce pines and pines decay and the beam when it propagates long distance becomes very wide right so actually transverse momentum is determined by the mass of the pie because everything else is just in this from direct but even if you take this momentum of energy which transverse from the pie and decay which is something like 30 NEVs at the distance of say 10 kilometers or 100 kilometers the beam becomes very big it's just kilometer size you can put your detector not in the center but off axis and that actually changes the spectrum and you see here the spectrum of neutrinos produced at different angles from precise direction to the to the source so we can produce narrow beam being not being out of axis of course you are losing somehow sensitivity to some extent but you can play with this if you need really to have this this type of the spectrum here you see typical spectrum energy spectrum actually this is from T2K of different neutrinos species so this what you are producing and you see the average energy is somehow 0.6 GEVs now present day operating experiments are T2K and this is long baseline experiment with distance 295 kilometers the neutrino beam is produced at J Park complex accelerator complex so here are the some rings and then also there is a front detector and in all these experiments usually they have near detector front detector so that you measure the flux and the properties of the flux close to production when you can neglect oscillation effects and so these studies of oscillations are usually based on comparison of the signal signal in far detector and close detector in this way you are removing a lot of a systematics and other uncertainties so neutrinos are detected in cameo command and this is this is super cameo counter detector I don't remember I probably I said already this is 50 kilo ton water cherry and cold detector it's a big cylinder of the size and on 40 meters height and something like 40 meters in diameter it's nice acoustic in this and before you know this detector was filled by by water you know they organize some concerts and people are saying it's just amazing especially you have this photo multiplies this kind of eyes glasses it and so then public said why not to continue with this is maybe this neutrinos come just go ahead with concert probably they would be very profitable I don't know let's think about this so these are some parameters you see the original protons have energy something like 50 30 g e v's this is average energy of neutrinos and so this kind of configuration is kind of fitted in such a way that you are sitting in the first oscillation maximum to maximize oscillation effect the second running experiment is Minos plus before it was Minos experiment which was using a narrow beam now they're using quite wide it's from 4 to 10 g e v's this is the distance between the source and the detector it's from Fermilab to Minnesota and nowadays this experiment is aimed at searches for non-standard in physics and they also made the measurements of 2 3 mixing and delta m squared 2 3 so you saw some results from Minos in the previous slide so that was previous Minos experiment actually this is the detector now opera experiment they essentially finished and now just analyzing data and just recently it was announcement that they observed the fifth tau neutrino event this experiment is aimed at searches for tau neutrinos produced in oscillations of my own neutrinos so my own neutrinos were produced at CERN and so they propagated from CERN to Gran Sasso laboratory here to Italy and in Gran Sasso laboratory there is this opera experiment and it's very difficult because they want to explicitly see tau neutrino for instance Minos experiment and super kamyakana they see disappearance of me on neutrinos opera as aimed to see appearance of tau neutrinos and so you need to see some signal and identify that you really see tau neutrinos interactions production of tau leptin and then the result of decay of tau leptin so for a number of years they see just five events so unfortunately it doesn't contribute much to global feet and global picture but it's important at some point to see that that the tau neutrinos really appear mini boon experiment this one which produced anomaly and I will tell you about this later so this is this oscillation probabilities in t2k experiment this is new mu to new mu this what you are expecting at the function of energy and this is new mu to new e so that's that's dependence and so essentially what this t2k observes is this interval and the next slide I will show you how it looks like this is for probabilities and this how the events look like this is new mu disappearance exploration number of events at the function of reconstructed energy this what you are expecting without oscillations and that what you see due to oscillations so the signals really very strongly suppressed you see it's it's not a joke I mean it's not like neutrinos something career somewhere this is this way now here you see the ratio of oscillation to knows no oscillation then you see here the deep experiment was planning to a large extent to discovery 1 3 mixing through the appearance of electron neutrinos so accelerator produces the flux of muon neutrinos and then what was expected that this muon neutrinos are oscillating into electron neutrinos due to 1 3 mixing so when experiment was planned we didn't know what is the size of this 1 3 mixing so here you see the signal of this electron neutrinos appearance as the function of gain of reconstruction energy and now this is something like 27 events so of this which actually gives very important very important result for for our analysis they actually give 1 3 mixing which is bigger than the 1 3 mixing extracted from reactor experiments and this is interesting because this is something which testify probably from certain for certain value of CP violation phase now these are results from t2k for two different mass hierarchies to some extent you saw already this picture and also this is for inverted mass hierarchy mixing is close to maximal though minors probably the only experiment which indicates substantial deviation of some deviation from maximal mixing so that may be something like 0.4 and also here the best feed point is somewhere here and so the mass square differences is here now this is important result from t2k which is the value of sine square t the 1 3 remember this was small red part in the third state which I showed you before something like 2% as a function of phase delta so this is phase delta CP violation phase and this is sine square t the 1 3 and there is a this is a vaguely form here because in the first approximation the result just determined by this is probability appearance probability new mu go to new e and it is proportional to sine square t2 3 multiplied by sine square 2 t1 3 multiplied by phase factor sine square f 1 3 over 2 with some corrections but there are interference terms here which depend on phase delta so the first term doesn't depend and there are some interference terms which depend on cosine delta and also on sine delta and it is due to this interference term you have this wiggly wiggly form I'll come to this picture later also now no experiment is working now and we are expecting the first results by the end of this year so this is experiment in US the beam is at Fermil up and then to assure you with the distance 810 kilometers this is long baseline experiment it's a 14 kilotone experiment this are kind of scintillator and the average energies so the energy interval is from one to three gvt the aim of this experiment to detect and to study oscillations of muon neutrinos to electron neutrinos with the aim again to measure 1 3 mixing to probably determine mass hierarchy this is big distance so you may have a still some matter effect is actually can help you to identify mass hierarchy and hopefully to contribute somehow to CP violation measurements now reactor experiments this is kind of historical experiments and neutrinos are produced in atomic reactors uranium torium chains of the decay which produce anti-neutrinos the flux of neutrinos is very small we know that such as beta decays and and electron anti-neutrinos appears in such a decay the detection method is this is inverse beta decay when electron neutrinos are absorbed produced positron and neutron and both products are detected so to detect this in many experiments people are using also gadolinium which is very good capture of neutrons so gadolinium captures neutron go to excited state then there's a de-excitation the photons are emitted and you detect this meet these photons actually you see this blue light what is this who knows so this is one of the detectors surrounded by what this is actually sharing co-fragmentation now there are three experiments reactor experiments which delivered recently the data on measurements of one three mixing actually again reactor experiments have long story history and in the last period they mainly are focused to major one three mixing and all these experiments are have the distances or baselines to have a better sensitivity to one three mixing and to delta m square which is this 2.5 10 to the minus 3 electron walls which is the biggest now three experiments are diabetes Reno in Korea this is in China and this is double shoes experiment in in France and you see here the detectors so sorry these are reactor com these are reactors in China so and they have three regions of detection close to the detectors again to better control the flux and the remote one and the distance is typically two kilometers this is oscillation links for typical energy of neutrinos from atomic reactors now Reno has six reactors and one that that I don't hear or there so double shoes has here has reactors here and two detectors one is a remote here something like this one almost 2,000 meters and the close one 280 meters these detectors started to operate just recently at the end of last year and so unfortunately they the first analysis is based on just not comparison of near and far detector results but on studies of energy spectrum of events the biggest detector is this one they have the the most power total power of reactors and therefore the flux of anti-neutrinos is the biggest one and they have also the biggest volume of of the detector so they produce the most precise result and you see here is out from Diabae that is the spectrum without oscillations see this is the spectrum which is produced by by by reactor and this what is the effect of oscillations the experimental errors are quite small and so this is the ratio of no oscillation to oscillation result and you clearly see kind of oscillatory curves also just one of this the first minimum oscillation and here is again dependence L over E and the literally the points very nicely are you know match with this oscillatory curve so no doubt that we see and we have discovered oscillations right this is determination of parameters the most precise measurements of one three mixing and science here is sine square 2 theta it's something like a close to point a nine and sine square theta without two is something like point zero twenty five and they also have major delta m squared because then you have this access to the period of oscillation this is the summary of all the data this is from deep core unfortunately this result without this a near detector and therefore there are bars are quite big this is from rena experiment and this is Diabae and this is global feet of the data so here we have for sine square theta one three multiplied by hundred so it's close to say 2.2 so sine square to theta is 2.2 10 to the minus 2 2% which I mentioned before questions yeah sorry so in the beginning of today's lecture you mentioned about the sine determination of m one two square from solar and nutrient experiment the fact that the MSW resonance occurs gives us the opportunity to measure the sign but if you if I remember the expression correctly the in one side there was m one two square times a cosine factor so by knowing the sign of the potential I can be sure of the sign of m one two square times the cosine so I miss the point how that sign of this cosine factor was determined so that I can unambiguously in this experiment in reactor or in solar in solar in solar you see in solar neutrinos solar neutrinos one three mixing enters as it is written here and you can imagine what is this since this is say 0.02 square and this is one minus 0.02 square is close to one and so actually solar neutrinos are not very much sensitive to one three mixing at all so there is still some indication that they see some effect but this is less than one sigma so essentially one three mixing is not entering here now for for this it is different story because here different delta m square enters in this business so for solar neutrinos delta m square to one is important which is which is very small and therefore oscillations are at very big distances they have big oscillation lengths now one two mixing and delta m square to one also affect this but very little because the typical oscillation lengths due to this one two delta m square is something like 60 kilometers or even more it's half 60 kilometers these experiments are organized in such a way that the distance between the source and detector is two kilometers so here this again the situation when to a large extent your problem is reduced to three in a problem so in the first approximation you can just neglect this solar sector analyzing these results sorry I'm just curious how do you actually feel a cylinder with 50 kilotons of water how I feel cylinder so the first of all this is not super k so yeah I'm asking for super k super k so I know even more how they clean this not only they feel it's slow and there are some plots from from down somewhere yeah I don't know precisely where water comes I don't along the wall but a nice nice nice pictures when you know some guys are just you know have the boat and they're going by the boat and cleaning some multipliers from down but what they are doing actually they're cycling this water because I need to clean this again sorry I don't know this details and my other question is why do they actually use in Nova exactly gadolinium why they're using Nova why do they use gadolinium in Nova gadolinium is he gadolinium is in this reactor experiments sorry anyway I mean I'm curious why do they use exactly this gadolinium because this is very nice neutron capture so this is nuclear which capture neutrons this is starting from from Ryan's experiment so you have in the final state positron and neutron so what you have usually this annihilates and then produce some flash of the light right very fast now neutron still kind of travels in your detector scatters and then he meets this nuclear of gadolinium then this guy go to excited state and then it emits a number of photons and so you have two flashes one photons or gammas from positron annihilation and then from a decay from the excitation of gadolinium so this is in this experiments actually in the future Juno experiment they will use another way they will use capture of neutron on proton with production of neutron plus gamma so they will detect this gamma it's not not everything all the experiments with this gadolinium thank you hey so reactors reactor experiments actually produced to some extent this reactor anomaly not even probably experiments but theoreticians I made this confusion because they made some new computations of the fluxes of of reactor neutrinos and the latest computations of the fluxes give something like three to six percent lower value of fluxes no higher higher amount of fluxes increase of the fluxes by three to six percent so before it was nice agreement of data with predictions now third distance I said no the fluxes are six percent higher and therefore you have deficit and so that actually what is called reactor anomaly and so one of the explanation maybe there are these sterile neutrinos again and what is interesting that these three neutrinos may be the same which are needed to explain gallium anomaly I mentioned so this is a big activity here to figure out what's going on new computations of the of the of fluxes then it was realized that there are some features which people never realized before that there were actually even observed so if you are interested I can elaborate more so global feed we have a lot of data from all this experiment the solar neutrino calm and atmospheric double shoes die by minors Rena Antares deep core t2k we use essentially to process oscillations and adiabatic conversion to extract delta m2 and teta so you saw already this picture this is the summary of the results from this type of the analysis two spectra but this small one for anti-neutrinos they can be slightly different because of CP violation phase if it is non-zero then I said already before that borders can be a slightly moved you see some certain symmetry which I a little bit explained before and here you see one of the global analysis actually there are three groups in the world which are producing this all analysis of all the data all oscillation data I know very well Mikhail Maltoni he's one of the authors of this and he for instance spent one year just to adjust atmospheric neutrino section in this global analysis but then they put everything so it's kind of hard work you need to take into account and you need to understand experiments and experimentalists are not keen to give you the data so what they are doing they're trying you know to cheat a little bit so they think okay so let us make some assumptions but then using this assumptions we will feed the data in such a way that they have some agreement with what these variations are giving actually only few open all the results and so because you need to take into account not only statistical it's clear but also systematics and then correlations between different systematic errors and this is really huge business to do these things so this is the result of global feed they didn't do analysis of data including the latest so it's the end of last year and you see here one to mixing which we have to discuss something sine square theta point three this is delta m square 7.5 10 to the minus 5 this is theta 2 3 and there are two possibilities depending on mass hierarchy actually because here red is for normal hierarchy and blue for inverted you see there are some changes here however this is not statistically significant one sigma is one two sigma is four so there's differences within kind of small small variations what else here this is one three mixing which is close to what diabetes is giving because this is kind of dominant experiment they have the best accuracy and this is interesting because they see some hint for CP violation phase and again not very significant you know it's not even to see from zero so zero is here zero phase that's something here and the strongest is for inverted hierarchy however they kind of exclude some region when this phase is pi over two something like a game 2.5 sigma disfavor in this way it doesn't mean yet anything so about masses using constellation data using delta m square actually we can put this very interesting bound m2 over m3 if you take normal mass hierarchy is should be bigger than square root of this delta m square 2 1 and delta m square 3 2 and this is the quality is when m1 is zero so it's clear then you get this if m1 is non-zero then it should be bigger so this ratio actually gives you something like point 18 and this means that neutrinos if they have hierarchy it may still happen that neutrinos are quasi degenerate all three neutrinos are close to each other but at least you can claim that the hierarchy of neutrino masses is the weakest one among all other thermals so this is for top quarks this is for down quarks this is for charge left and this is what you have for neutrinos so this state is either here or even closer and the last the lightest state may be even 0 and so what's next next is to major identify mass hierarchy to determine CPU violating phase to major very precisely deviation of two three mixing from maximum and this is very important measurement because if it is maximum that certainly testify for the symmetry behind this picture and also it's important to compare for instance this deviation of two three mixing from maximum with one three mixing because things may be connected especially if you are in working some symmetry to explain this data so it's important to have very precise measurements of deviation if it exists of two three mixing from maximum then of course we need still to know what is identify what is the mass hierarchy what is the type of the mass spectrum so the spectrum still can be very hierarchical or it may be quasi degenerate so that all three states are around say 0.2 electron volts with small relative split then absolute scale of neutrino mass nature of neutrino mass are neutrinos Dirac and Majorana remember I never mentioned before if neutrinos I'm speaking are Majorana or Dirac not it's not accidental because all this pattern which I have discussed before is the same for Majorana and Dirac neutrinos the same and this is due to alter relativistic neutrinos and the character of neutrinos in all these experiments and because of in this oscillation process there is no change of chirality or helicity so essentially neutrinos like a bosonic particle superiority so there's no kind of sensitivity to the nature of neutrino mass yeah so I will discuss this so the question is how we distinguish Majorana and Dirac so it's different type of the experiments it's double beta decay experiment which is sensitive to the nature of neutrino mass now this related question is left and number violation because if neutrinos are Majorana then you expect violation of left and number and in particular by two units so that's what we can search for the question about existence of new neutrinos states because you saw that there are some indications that maybe we need to to consider some more neutrino speech is to explain the data the open question if there is some symmetry or no symmetry behind this pattern of neutrino mixing so it's nice it so when you see this you actually immediately recognize there's something interesting right some very symmetric in this pattern I didn't set much about neutrino interaction so mostly we have discussed neutrino propagation but of course there is a lot of activity in studies of neutrino interactions this is also important for even oscillation experiments and at high energies you have deep and elastic scattering at low energies quasi-elastic scattering but there's intermediate range where still there are big uncertainties that so called resonance region or one pine production etc so there is a big activity in several experiments aimed at very precise measurements of cross sections of you don't learn much about neutrinos from these studies you more learn about hydrons and interactions with hydrons but these are important experiments which and the results will be used in future oscillation studies now some exotic interactions again so we discussed a little bit non-standard neutrino interactions only in this respect but it doesn't seem that there's any deviation from the standard model so for time being it's more like hydron physics which is involved here and it to be clarified so probably this will be the last topic of my lectures and I will discuss a race for hierarchy and CP violation but before I start this if you have some questions okay so what is this mass hierarchy you saw these two pictures and actually differ by the change of the sign of the square if you change the sign of this delta m square then the resonance due to one three splitting will be in uterine or in anti-neutrino channel so these are two spectra and what are the properties this type of the spectrum normal mass hierarchy with all the white mild hierarchy resembles what we have in quark sector and in charge left so it's quite similar if this is realized then that may be kind of indication that we deal with a seesaw mechanism quark left and symmetry and some unification so this type of course there's no proof that if you see normal mass hierarchy this is the evidence for unification of quark and left but still kind of indication this is probably when more interesting situation because in the case of inverted mass hierarchy the split is here in delta m square is the same but relative delta m or m is something like 10 to the minus 2 so these two states are really degenerate and certainly some symmetry should be behind this one what's the reason that two states are very close to each other so it may happen that then neutrino mass spectrum is organized like one pseudo dirac neutrino and one Majorana neutrino and then you have some small split here in this state it may testify for flavor symmetries and often people use this l e minus l mu minus l tau symmetry to explain this type of the spectrum now raised for mass hierarchy there are different experiments and phenomenology for neutrino mass hierarchy is very rich actually many things depend on the type of mass hierarchy and you see here that you can major neutrino mass hierarchy using matter effect on one three mixing so depending on hierarchy you have resonance in neutrino run to neutrino channel so for this you can use atmospheric neutrinos experiments like ping work I know you can use long baseline experiments accelerator experiments on also supernova neutrinos to identify mass hierarchy let me tell you so there's a this big deal with mass hierarchy but if tomorrow neutrino burst will arrive from supernova I think probably in three days I will tell you what is the mass hierarchy of neutrinos so you know it's kind of interesting situation and already more than 20 neutrino burst are approaching us neutrino burst from galactic supernova what we have detected in 87 a was not supernova in our galaxy it was in large Magellanic cloud the distance was big so we are expecting that if next supernova will be from our galaxy number of events will be big maybe very big even and so using this number of events and making analysis you can extract information about mass hierarchy just seeing where Earth's matter effect is in neutrino or in 19th year channel now another method to determine mass hierarchies to major delta m2 at reactors another proposal then cosmology cosmology gives bound on the sum of neutrino masses and therefore you can distinguish mass hierarchy if you know your sensitivity to this some will be less than point one because in the case of normal mass hierarchy you expect that the sum of neutrino masses will be point zero five electron volt something like this which is the mass of the heaviest neutrino and two others are light right if the hierarchy is inverted then you expect two neutrinos with this mass and so you expect that the sum of neutrino masses will be point one so if cosmology would be sensitive to this sum of neutrino masses and the present bounds are around say point two point say five electron volts silver big uncertainty but they promise that they do much better work maybe even in five ten years and so they may be sensitive or to give some kind of serious indication toward the mass hierarchy and also double beta decay neutrino less double beta decay is sensitive to the mass hierarchy and I will show you this if I have time so why it is important as I said the rich phenomenology of course it is important for theoretical implications and it is also important for further measurements of CP violation because various uncertainties disappear if you know precisely what is the mass hierarchy for measurements of CP violation phase so the idea is that probably first we will measure mass hierarchy established and then we'll go for for for CP although some experiments are planned to do both things simultaneously so tell me how much humanity will pay for identification of mass hierarchy can you have some idea and to CP violation so tell me what do you think so the cost of the experiments I was saying this record experiments I say 20 40 60 millions now super K cost more of course then so now that nowadays experiments are already hundred millions what do you think how much we should pay for for mass hierarchy and for CP let me tell you for about CP one of the experiments which people are now promote very strongly is in the United States is Dune experiment I will show you some picture that kind of Dune experiment and J what is this LBNF Dune LBNF a long baseline neutrino facility so which means the beam will be from Fermilab and then it will be to home stake that will cost at least one billion I don't know Michael maybe no precisely so Dune how much it will cost Dune experiment at well it's already so two billions right I think okay so how about mass hierarchy so what is two billion you know approach to some rich guy say look we named by your name this kind of we'll call you know this hierarchy and this will be forever no so anyway let me speak a little bit about supernova neutrinos and you know what I will do so of course I have a lot of material you understand that I'm trying to adjust my my lectures to the audience what I will do I will just you know stop in ten minutes where I stopped you know but then I will do the phone I will flash many many hundred slides and if you find something interesting you okay stop please tell me what what what is that so chairman don't worry so supernova had no time to speak on this they're beautiful effects collective effect which is very interesting you know supernova neutrinos are produced when we have collapse of the star gravitational one so you may have the collapse to neutron star or to black hole and that produces actually neutrinos huge fluxes of neutrinos and essentially all the energy which is released gravitational when you do this when these collapse occurs essentially is released in the form of neutrinos and so all types of neutrinos are emitted the first half new EPIC this is so-called neutronization picking the early time but then you produce the spectra of all three new of all neutrinos species and anti-neutrinos so you have something like this for neutrinos if this is energy this is something for anti-neutrinos and then you have the fluxes of new mule new tau and corresponding anti-neutrinos and they are the largest so these neutrinos are something like from say essentially from zero to 20 mv's this is slightly higher and that can be up to 40 mv's with maximum somewhere say 20 mv's here probably less something like 16 mv's this is even less 15 mv's so this is the spectrum which is produced by neutrinos now what happens with these neutrinos what happens is the following the flux of these neutrinos in the central part is so high that you should take into account neutrinos-neutrinos scattering and then the problem becomes extremely complicated I mean some if someone to you know break his mind one can work on this the point is that the problem becomes non-linear and then you need to take into account all these kind of transformations and so non-linear problem is often very very complicated so interesting effect is that you will have even matter effects which are off-diagonal so matter effects in off diagonal elements of the of the Hamiltonian so it's extremely interesting very complicated and still we don't know what is the outcome I was working on this spending a couple of years and we have found that it may be kind of a fact of spectral split so suddenly due to this collective effect and some range of energies for instance like this the spectrum of different neutrino types just flip electron neutrinos become millon neutrinos millon neutrinos become electron neutrinos and in contrast of MSW effect it's just in very sharp range here curves it's not clear because there are some instabilities and people see more and more effects if these collective effects are really realized or not anyway so there's some uncertainties here then there is a region of MSW effects when the density is relatively low it's below 10 to the 4 gram per cubic centimeter and the picture of transformations is here very clear so very clear now we had already observation of one supernova as I said supernova 87a unfortunately we have just 19 events and it's difficult to extract any information if oscillations occur or not and the point is that oscillation effect is always proportional to difference of the fluxes if you have oscillations of electron neutrino to muon neutrino then eventually effect is proportional to difference of these fluxes because if fluxes are the same you do not see any oscillation effect right so unfortunately here for anti neutrinos this difference of the fluxes electron anti neutrinos and muon anti neutrinos for instance is something like 10% and of course how can you extract something useful if you have effect which is below 10% and you have just 19 events so again we are expecting new supernova galactic one and so hopefully we will see many interesting things from that so these neutrinos have this undergo adiabatic conversion and with this big one pre-mixing everything is very adiabatic so just we know these results what happens there with very high accuracy apart from the fact that it may be shockwave propagating from inner part to outer and then it breaks adiabaticity you may even observe effect of shockwave on studying spectrum in time but also in energy so it happens that shockwave will reflect modification of the spectrum at different energies and the energy where the effect becomes important changes with time so you can see some interesting effect that you have spectrum the text spectrum of events and then it changes same from low energies to high energy so you can even trace shock wave propagating inside the supernova so then neutrinos arrive at the surface of the earth as the solar neutrinos they split and start to oscillate inside the earth and this can be used to identify mask hierarchy so I will skip many slides because that's details and if you ask me what was going on here you see two resonances which are involved and you can use adiabaticity and to trace immediately what happens for instance here electric neutrinos are just be transformed to new three now you expect effects like permutation of the spectrum so support this is a regional spectrum then after crossing MSW region you will get this exchange of the flavor and now let me comment on on hierarchy in fact there are many effects not just one estimate effect but many effects which can be the consequences of different mask hierarchies but let me just to discuss this earth matter effect because it's easy you have to detect us in different places and you measure the same spectrum they see some difference then you conclude that there's a certain matter effect or oscillations produce some kind of weekly distortion of the spectrum and you expect to observe something like that so this is without us matter effect it just nutrients arriving during the day so the fact is small but if your detector is shielded by the earth then you would expect to see something like this and even using just one detector and observing this type of weekly behavior you can conclude that that there's a matter effect in one channel or another but what is interesting that it depends on mask hierarchy and if the earth matter effect is observed in anti-neutrino channel only then that is proof of a normal mask hierarchy so if you ask me I can elaborate this later more if it is in neutrino channel then it is inverted mask hierarchy so there is another suggestion to use reactor neutrinos to identify mask hierarchy so you see what happens the depths of oscillations between state 3 and 1 is two times smaller than the depths of oscillation between so it's two times bigger than the depths of oscillation between 3 and 2 because the depths of oscillation suppose we consider the oscillations between this state and that one is proportional to the product of this red part and this red part okay because if there's no red part here then there's no oscillations of electron neutrino now here amount of electron neutrino is two times bigger and therefore the depths of oscillation between this and that will be two times bigger than between this and this so you have these depths of 3 1 is approximately 2 depths of 3 2 okay now in the case of normal mask hierarchy the split 1 3 is bigger than the split then 2 3 okay and therefore the frequency of 3 1 should be bigger than frequency than 3 2 the frequency is inversely proportional to the split now oh it's proportional to the split sorry so in the case of inverted hierarchy you have in opposite situation that because here the state 1 and this split is smaller than a split between 2 and 3 so suppose you use reactor experiment and you see some big picture and then you do Fourier analysis and you do Fourier analysis and in the case of normal mask hierarchy and this is the frequency you expect the situation that the peak here is smaller than the peak there because of this inequality and the opposite situation in the case of inverted mask hierarchy so think about this it's easy understand just knowing such a situation and they still so just to see where the big peak is and very small one you cannot identify mask hierarchy now to do this new experiment even several experiments actually are planned and one is this Juno which is Chinese experiment and this year it was kind of a serious breakthrough because so essentially this experiment is approved so you expect to observe this type of the pattern and the red is for normal so blue is for normal and red is for for inverted mask hierarchy and you need to distinguish these two curves essentially so that's that's the problem now the experiment will have it's or will be organized in in the mind something like 700 meters depths it will have distance from complex of reactors something like 53 kilometers so you're sitting essentially in the first oscillation minimum due to one to oscillations huge power of reactors and they will use 20 kilotons scintillator detector which is shown here so you need really to figure out what's going on the biggest problem is that you really need to have very good energy resolution right because you need to essentially be sensitive to this small weekly curves and one needs to achieve something like 3% energy resolution at one MVV here it's 3% energy this is the big challenge of this experiment if they manage then they will manage so the experiment is planned to start something in 2020 there's another experiment also planned in Korea which is Reno 50 kind of continuation of the experiments they had already now now in other ways to and probably I will stop this is final what I want to say is to use atmospheric neutrinos and propagation inside the inside the inside the earth so here you see the probabilities in different channels this is what they see I have so this is px and x can be mu and some and to going to mew this is also x to mew this is for neutrinos and this is for nutrients for anti-neutrion so you see here the difference between hierarchy is a normal is solid and inverted is dashed and here one sees some enhancement of oscillations in one channel and here's in another channel so this is for anti-neutrinos and this is for neutrinos sorry this is for for neutrinos this is for anti-neutrinos so this is MSW resonance this is enhancement due to MSW resonance and depending on mass hierarchy this enhancement occurs in neutrino anti-neutrino channel so essentially going from one hierarchy to another you permute neutrino and anti neutrino channels that what do you expect for oscillations of new ego to new e so this is the peak that what you expect if you have normal mass hierarchy and if it is inverted mass hierarchy then you expect such a pattern again this is energy of neutrino zenith angle energies are 2 3 4 20 g e these actually you know this line you saw this already in before this corresponds to the border between core of the earth and the mantle of the earth and these are due to parametric resonance different channel new ego to new mu this what you expect in the case of normal mass hierarchy this in the case of inverted mass hierarchy so you need just to distinguish this picture this is for new mu to new mu and for this you need to have measurements of atmospheric neutrino flux with energies at least below than 6 gv right because all these kind of patterns are around 6 gv 6 5 gv unfortunately you cannot do this with deep core because deep core has energy threshold say 10 10 gv 10 20 gv and because of these there is a new plan to have ping experiment which is more dense array of auto multipliers with lower threshold around say 1 3 gv's and then what this experiment can observe is the following so this is this is let me say this is not this is the quantity which we call distinguish ability between two mass hierarchies so this is the difference of number of events in different beans for normal and inverted hierarchy and you see the maximal effect is around say 10 to 14 gv's and in this range of the angles this is for two different resolutions actually these plots have been obtained from the nice plots I have shown you before with these kind of images of the earth and of course cheating was because that where the plots in terms of neutrino energies and neutrino direction however in the experiment we are not measuring neutrino energies at moment we are measuring something which is secondary this what neutrinos are produced so these plots are smearing plots out of what you saw before but still you see some effect here so literally what is shown here is a number of events in each of the being for inverted hierarchy minus normal hierarchy over square root of normal mass hierarchy this is kind of statistical significance in each of these things concluding let me say that Pingu experiment I probably have shown some pictures of this so so that's Pingu will be will be here they will observe 10 to the 5 events every year 10 to the 5 events so to some extent statistic is not a big deal so the most important is to understand our systematics and the procedure of reconstruction of the plants so I think I stop at this point that big discussions of CP violation and this what I told you before so please ask me the questions and then you'll just you know you will see how many other slides and if you select something interesting you can so questions to this part so a question of technical nature you said that if tomorrow there is a supernova explosion you can say in three days that the hierarchy is one or the other my one objection would be aren't most of these things which off at the moment and wasn't is the same case in 1987 and shouldn't there be some sort of coordination that would be disaster so there's kind of a warning procedures and you see unfortunately you will see the light later and the point is that you see the light from this supernova course you can see this it unless there is a dust because neutrons are coming immediately from from the central parts and the light appears when you have expansion of envelope enough so it maybe it takes some some hours so there's a warning system at least if one detector sees something that others can they inform each other that would be disaster of course waiting for for so many years actually we had no supernova here 50 years or so already 50 years of observation and that would be just really but super case able to detect so they are operating then some small detectors even small detectors like like June will produce a lot of stuff relatively small it's not very small right now hopefully SNO plus will just start to operate and they will see some signal also so not many so that's kind of a dangerous face actually ice cube can see the signal but they will see not individual neutrinos they will just see because the flux is so big and some neutrinos will be interacting very close to these PMTs and they will produce observable signal so so they will see kind of a flash of the light in the detector detector will shine this kilometer cube stuff so I have a quick question about the collider neutrino experiments you said that they're they shoot them off beam or off the beam axis yeah are they just going to fix these at one angle and leave it there are they able to actually go down and hit there unfortunately you cannot do this unless you move the tech right well over those distances I mean a little bit of kilometers the distance is not it's not a joke yeah it's a it's probably you can in some cases we go to change a little bit beam yeah that you can go so if a few days is the minimum time scale where we might know what the mass hierarchy is what is the maximum time scale at which full will find out no it's like a more you see again so experimentalist will release data and if I see some weekly distortion in say in spectrum of anti-neutrinos then I make this conclusion so it's I'm not going to even probably even to analyze I just ask experimentally give me the energy spectrum of neutrinos and anti-neutrinos unfortunately for new anti-neutrinos it's easy for neutrinos it's difficult usual number of nutrient events is less because it's more difficult to detect neutrinos so I mean if there is no supernova then obviously there are experiments to try to measure the mass hierarchy which hierarchy inverted on normal ordering what is the longest time scale okay we can go without knowing so that's that's important this is important question actually this is serious even political question let me say I mean scientific politics so you see the there's a competition now there are two major methods one is to use a reactor neutrinos Juno will start to work in 2020 they need something like six years if everything is okay so using Juno experiment Reno will be a little bit late saying the middle of 2020s you may know now the story with Spingo and Orca maybe faster but you know it also depends on the time scale of funding of this experiment they aim to start to build experiment in not build I mean to go to this Pingo proposal in 2018 1 8 and they need two seasons to put these additional strings so this procedure is you know there are some equipments in Antarctica they melt the the eyes and the put the strings and this present kind of speed of this putting they need to two seasons to summers Antarctica says so this means that they also can start in 2020 now they may need even less time if everything is okay they may produce already some actually I have seen even dependence on time here so that's how Pingo is going to to measure this is confidence level and this number of years so in two years they may have already for Sigma result in two years and this is a competition I mean people are nervous you know it's now next what what's next next is if accelerator experiments you see the accelerate accelerator experiments nova plus plus t2k they are struggling they still trying to collect some sigmas they may have some some indication already there are some differences you saw these results for normal and inverted hierarchy but it will not be statistically significant they may come up with a to Sigma at most I think in in in maybe five six years no will start really to release data now then joint analysis may produce something now dedicated experiments like this dune so and this LDNF dune experiment which is kind of the main major experiment I mean Americans community is kind of big one is built around this they may release results in can you guess when 2035 if everything is okay no they will start early yeah no I mean to release results so the point is that they still need to have some time to operate and even in 1993 or more so how many of you will be you know so I don't know I will be around but so that's that's yeah sorry yeah people like this idea to be kind to be sure in your career you know so yeah you mentioned a few slides before that this tool kind of a neutrino mass hierarchy can be a hint for instance the the normal hierarchy can be a clue for the CISO mechanism can you explain that more little bit because I still don't quite see that there's no kind of of course firm you can get even if you have CISO mechanism you have inverted mass hierarchy also according to the CISO mechanism the mass of neutrino is say M Dirac square over some Majorana masses and in three neutrino case you need to have these matrices right you have matrices this one over M so what is important that if you have grant unification which is actually CISO mechanism indicate to work grant unification is also together with grant unification then these Dirac mass matrices of neutrinos they are somehow related to Dirac mass matrices of other fermions for instance you quarks then what you have is the following so let me write it in this way md transponent and here is in denominator so this is very hierarchical and this is very hierarchical so you actually expect quite hierarchical mass matrix of neutrinos unless you do something crazy with this structure of this Majorana mass matrix you typically get quite strong mass hierarchy normal mass hierarchy of neutrinos just because this is inherited from quarks and lapons charged lapons so if the neutrinos flux is equal from all sides why do we have one water detectors in the form of a cylinder and others like as you know in the form of a sphere I didn't catch your question so what so in this in the case when we have a cylinder with water to detect neutrinos when they come from the side they travel less in the water than if they come from above and on the other hand we also have the S&O detector which is spherical so why do we have two different shapes of detectors what's the benefits in frankly you know you may have even water detectors so I don't know actually precise the region a reason for this probably for for water chain coffe and the bigger bigger volume probably this cylinder is more preferable actually hyper k will also have some kind of cylindric form hyper k this is future that they will have even two cylinders of this type so all these types so the answer that I have no answer good answer to your question I may guess but I don't want to do this it's more symmetric of course this you know cylinder and maybe to some extent easy to analyze I don't know maybe Michael know this answer I think it's just purely technical it's easier to hang photo multipliers on a vertical wall than on a sphere no this I don't know why and the sphere is this kind of also trivial they have this in S&O plus they had this in Borek see you know they had this in no there's a specific reason why it's a sphere which which is that they had heavy water yeah there's a bag of heavy water but that's also insulators yeah if I remember correctly sits in the middle of a cylindrical container of ordinary water right S&O yes I don't remember actually there's some actually serve this even bigger volume which is filled by usual water that's right I don't know maybe there are some constructions but I don't think that there is any water kind of for at least for this so it may be somehow related what also Michael said that it's in one case we are using water maybe it's water is easy and of course if you have cylinder it's easy to analyze result maybe but it's not a big deal really so I think you briefly mentioned that with new three no less you can also be sensitive to the hierarchy problem can you comment on that yeah so now I start you know to already to let me let me do this and then it was this is the topic with a CP violation how CP violation interference effect occurs here some information about CP violation now how to major CP violation and you see different experiments now even present data said already give some indication for CP violation and this is what we obtained from from T2K remember this is a sine square T213 and this what we get from reactor experiments determination of one three mixing reactors do not depend on CP phase and you see the overlap is here and here and the overlap is when the phase is minus five or two so let me go further because there is somewhere so that's how CP is determined presently this is the picture of all these kind of experiments ice cube deep core pingu super pingu orca and mica with different threshold so that I have shown this is how CP should be determined so these are pictures for different CP phases now let's go further so this is due an experiment I mentioned right so this is in US long baseline experiment with the aim to detect CP violation phase and also mask hierarchy this is what will be in 2000 producing results in 2035 so these are hyper kamiak and you see the two cylinders are aligned in this way Nova and this is I know which I haven't discussed here but if you ask this is how to major absolute scale of neutrino mass and this spectrometer will start to operate hopefully next year I mean there's so big delay and they will have sensitivity to neutrino mass point to electron walls they can put this bound there's also another projects to major neutrino mass so this is Catherine will be sensitive to this cosmological bounds now this is physics related to dirac in my run I you can ask me and so this is double beta decay so double beta decay major so-called effective mass of electron neutrinos and so let me just show you the picture and then if you ask more questions I can explain these are the bands which actually obtained using oscillation data information from oscillation data for this effective my run a mass and neutrino less double beta decay is proportional probability is proportional square of this mass as a function of the lightest mass of neutrino so these two bands corresponds to inverted mass hierarchy and these two normal mass hierarchy and so if a future neutrino less double beta decay for instance put the bound at this level they will exclude inverted mass hierarchy now if you want to listen more than than I can explore say more because I know it's time by the way so I will be here next week and so if you want to discuss more and the chairman say no I will not give you to speak more to give more lectures so that yeah so let me let me continue and you will see so this is this are some experiments on double beta decay Gerda then core X so so this experiment will be very sensitive now that's some explanation and this are sterile neutrinos with some anomalies many bone this is the scheme and you know why have I just skip this I always had kind of temptation you know to include more material but then I said so if I believe that that say after a few years this will be still you know existing anomaly or things disappeared and why I should teach you know to spend my time and your time on something which is not existing can you know disappear in a few years or so so I made kind of selection of this type I discussed mostly existing and solid result so just not to you know to take your time for various speculations I mostly didn't discuss any kind of the theories as you as you observe so this is again about this anomaly I had some slides about cosmic neutrinos which is kind of interesting and also neutrinos and LHC and I skip this because I'm not sure that we will see something which is related to neutrinos at LHC although there is a huge activity in this field but if you ask me I can explain you and one can see some other things here let me see how many many things you can see in principle and there's a lot of speculations on this and some mechanisms of neutrinos mass generation if you want oh this is very interesting that you can see probably some same sign leptons which will indicate then this is famous new MSM model which is the economical one let's see what else parameters of this model and then some theories some funny things and things which I have already shown you and I'll stop completely at this point thank you very much