 Good afternoon. It's a pleasure to introduce my colleague, Professor Aishwama Shankar. And it's a pleasure because just last month, actually in October, we had an announcement of the 2015 Nobel Prize, which was on neutrino oscillations. And Professor Umashankar has been working all his scientific career with neutrinos. And there cannot be a better person in the country than Professor Umashankar to talk about it. So we thought since we have a huge audience here, we invited him to talk to you on that. So, Professor Umashankar. I thank the organizers, especially Professor Deepan Ghosh for inviting me to give this talk. And neutrinos have been sort of puzzling us ever since I can't really say their discovery since before their discovery. So let us start with the story about 100 years ago. When radioactivity has been discovered and people started studying various aspects of radioactivity in particular beta decay. In beta decay, you have an electron which comes out of the nucleus. Question is, is the electron coming out with a constant energy or with different electrons are coming out with different energies? And if you apply the ideas of conservation of energy and momentum that says that the electron should have a fixed energy or you can consider the possibility that okay there are different nuclear states to which the initial nucleus can decay in which case the electron will have discrete energy states. It will come with say 1 MeV, 2 MeV, 3 MeV, not a continuous value. But James Chadwick who later became more famous for discovering a neutron, he showed with a set of very careful measurements that the electron spectrum is continuous that is electrons are coming with some minimum energy varying continuously all the way up to some maximum energy. This of course is in conflict with the concepts of energy conservation and momentum conservation. So what do we do? Do we give up on energy momentum conservation? Apparently Niels Bohr was willing to do so because one of the important quantum things in those days was that what holds classically at the quantum level is true for average properties not on a individual event by event process. So Niels Bohr's thought that maybe energy and momentum conservation hold on an ensemble over a average of all the beta decays not on a individual decay by decay process. However one can easily see that this idea will not work because if you believe this idea then some beta decay electrons should have energy greater than the upper limit imposed by energy conservation and some should have less. And if you see the graph on the screen you find that all the electrons that are observed have energy less than the upper limit. So certainly Niels Bohr idea that energy conservation holds on average that does not work. Now let us come to Pauli who is a junior contemporary of Niels Bohr and whose name I am sure all of you have heard in the context of Pauli's exclusion principle and Pauli is not willing to give up on energy conservation because of this theorem called Nodder's theorem. This Nodder's theorem states and it is a fairly simple theorem to show and most textbooks on classical mechanics for example the book by Goldstein proves this theorem which says that if there is a symmetry there is a conservation law and if there is a conservation law there is a symmetry. And in this case the symmetry that physical locks should be invariant under space translation that leads to momentum conservation and they should be invariant under time translation that leads to energy conservation. So if we give up on energy momentum conservation it means that we have to give up on the symmetries that physical loss should be invariant under space translations and time translations putting it in more ordinary language it means that two experiments done under identical conditions but at different places related to space translation or at different times related to time translation they need not have the same result. But whole of physics is dependent on reproducible experimental results. So if you give up on space translation and time translation you are essentially giving up on physics and obviously that is not acceptable to Pauli. So Pauli insisted that energy and momentum are conserved in beta decay and in order to conserve them Pauli postulated that there is a neutral spin half and nearly massless particle which is escaping detection. And if we impose energy conservation energy of electron plus energy of this new particle is equal to the difference in the masses of the mother nucleus and the daughter nucleus which is called the Q value of the nuclear decay. And so the fact that E is varying from minimum value up to maximum Q can be explained by saying that the remaining energy is being taken away by this neutrino. Of course this is a whenever we detect particles in an experiment it is usually through the interaction of the electric charge of the particle with the detector. You can say neutron does not have electric charge how do you detect neutron and of course detection of neutron was more difficult but on the other hand neutron is a very massive particle and when such a massive particle moving with some speed it can take away energy and you can sort of see the absence of energy of such a massive particle. Whereas this Pauli's particle it is neutral so it does not interact with the detector and it is nearly massless so it is a little difficult it is in fact not just a little difficult it is extremely difficult if not impossible to detect and in fact he was a bit ashamed to propose such a particle. So instead of writing his idea in a scientific paper he actually wrote a letter gave it to a friend and asked the friend to read it at a conference on radioactivity and in fact you can check in the internet that letter is available it starts with dear radioactive gentlemen ladies dear radioactive ladies and gentlemen dot, dot, dot it so happened that Pauli named his particle neutron but around the same time Chadwick discovered the massive neutron that we know of. So in order to resolve the confusion between the names for me called Pauli's particle neutrino meaning little neutral one in Fermi's mother tongue which is Italian and he also constructed a theory of beta decay which made a mathematical sense and out of Pauli's idea and you have been looking at quantum mechanics for the past couple of weeks I hope you have come across of this Fermi's golden rule which describes transitions from an initial state to a final state and the decay rate is given by the matrix element square times the energy conserving delta function multiplied by the possible number of final states that can be occupied by the neutrino and by the electron. Of course here we do not know what this transition matrix element is so Fermi made a simple assumption that it is a universal constant G and using that he was able to derive this formula the rate of decay per electron energy interval is G square times this function and the amazing thing is that all the beta decays that have been measured so far they all can be fit to this formula. There are some beta decays which have lifetimes of maybe milliseconds or even smaller and some beta decays which have lifetimes of thousands of years but all of them can be explained in terms of this single constant G and the variation in the lifetimes comes because this Q is different for different beta decays that is illustrated in the next slide. For example, neutron undergoes a beta decay and it has a Q value of about 0.8 MeV and a lifetime of 1000 seconds whereas tritium has a Q value of about 0.1 and it has a lifetime which is 10 power 5 times larger but this small this factor of about 8 in the Q value actually is leading to the factor 10 power 5 in the lifetimes and that can be explained based on this Fermi's formula with same G both for neutron decay as well as tritium decay. And another important advance that Fermi made is he in his construction he wrote this effective interaction by which a neutron decays and for those of you who have heard of this concept of second quantization in many body physics this is the first non-trivial use of second quantization that I know of. Now let us as I mentioned earlier Pauli was a little ashamed to predict neutrino because he felt it can never be detected and so people estimated what does it take to detect a neutrino and here we can do a simple dimensional calculation and that shows that cross section for an interaction of neutrino with a ordinary matter it will be this Fermi coupling constant square times the Q square where Q here is the energy of the neutrino which is typically a few MeV and if you substitute it in this formula you get a cross section of 10 power minus 46 meter square whereas you have just heard of Compton scattering today and the Compton scattering cross section is about 10 power minus 28 meters. So in order to detect the neutrino you need a source which is about 10 power 18 times more intense than let us say the X-ray source which we use for doing the Compton scattering experiment. So the situation is actually well summarized in this cartoon it is like we are being asked to accept on faith that neutrino exists but of course the important experimental confirmation is that every known beta decay follows this formula and this formula we can explain only if we assume that there is indeed a neutrino. Now of course second world war which is a very unfortunate thing but on the other hand it led to a few important scientific developments one of which is that it led to a nuclear reactor and in fact somebody at Los Alamos where the atom bomb was first designed wanted to set off an atom bomb which will release an Avogadro number of neutrinos and wanted to detect some of them but later people of course realized doing it in the neighborhood of a nuclear reactor is much more sensible and two experiments were done one is led by man called Ray Davis who tried to look for neutrino interacting with a chlorine 1337 nucleus and creating an organ and the other experiment look for this neutrino interacting with proton and producing a positron and a neutron and here one detects both the positron and the neutron and both experiments started taking data in 1953 and in 1956 the second experiment which detected the positrons and the neutrons they had 10 unambiguous events and apparently they spent a few million dollars to conduct this experiment. So the press report called the neutrino a million dollar particle course now we can buy get neutrinos a lot more cheaply now. So of the two experiments the second experiment detecting positrons and neutrons found events but the first experiment detecting organ atoms did not find any signal there were no organ atoms it shows the following it means that the reactors are emitting anti neutrinos point number 1 and it is anti neutrinos which carry which produce this reaction and create the signal and anti neutrinos do not produce this signal in order to produce this signal one needs neutrinos not anti neutrinos. So that was clarified and also it led to the concept of what is now called lepton number which is 1 for neutrinos and electrons and minus 1 for anti neutrinos and positrons. Of course here we have a picture of Ray Davis and understandably he got upset that his experiment did not see any signal but of course he understood why his experiment did not see any signal so he started looking for an intense source of neutrinos. And the most obvious such source is the sun because there are protons are getting fused into larger nuclei in producing energy in the sun and these reactions are producing so many neutrinos that a trillion that is about 10 power 12 are passing through our bodies every second even as we sit here and go through this. Unfortunately they all have rather small energy so they cannot drive the reaction that Ray Davis was looking for. A solar physicist named John Bacall he pointed out a way he said that there are additional nuclear reactions which are rare they occur only in about 1 in 10,000 but those nuclear reactions produce neutrinos with energy of almost 15 MeV and they can be used to detect the reaction that Davis was looking for. So in 1964 Davis built a 600 ton detector and size is chosen such that according to Bacall's calculation the detector should detect one organ atom per day. Mind you the detector contains something like 10 power 36 organ atoms so the job of Davis is to isolate one out of these 10 power 36. You hear people talking about separate looking for a needle in a haystack but imagine how much more difficult this is looking for one organ atom in 10 power 36 organ atoms. So Davis set up his experiment at this place called Homestake and as the experiment was running organ atoms were collected once a month and finally results were announced in 1968. There was some good news and some bad news. Good news is there were organ atoms so Davis's idea of detecting neutrinos was indeed correct. Bad news is only one third of the expected organ atoms were seen. So before we discuss the resolution to this puzzle we need to discuss some parallel developments and to discuss the parallel development we have to go back to 1938 where a some particle called Muon which is a heavier cousin of electron was discovered in 1938 when people were studying the cosmic ray interactions. Homi Bhava who founded the Tata Institute of Fundamental Research and also the Atomic Energy Commission in India he did some fundamental research on what was called the penetrating component of the cosmic rays and later it was identified that this Muon is actually that penetrating component of the cosmic rays and this Muon decays into an electron and two neutrinos. Question is what is the relation between these two neutrinos? Are they same or are they different? If they are the same then there is a single neutrino which interacts both with electron and with Muon and so sometimes when it interacts with matter sometimes it will produce an electron and sometimes it will produce a Muon. If they are different that means there is one neutrino which interacts only with electron and another neutrino which interacts only with Muon. So this was another puzzle that came up and this puzzle was solved by in an experiment that was took place in 1962 at Brookhaven lab. They succeeded in creating a what we now call a Muon neutrino beam through this reaction and so they had beam of neutrinos Muon neutrinos with energy 1 GeV and when this beam interacted with ordinary matter they found that only Muons were produced no electrons were produced. So this established that there is a second type of neutrino which we call Muon and the neutrino in beta decay is now called electron anti neutrino and there is a corresponding electron neutrino which occurs in other reactions. And previously I mentioned that a concept called leptor number was introduced but now we need to introduce two leptor numbers one for electron and its neutrino that is called le and a second leptor number l Mu for Muon and its neutrino and we make the hypothesis that le is conserved in all interactions and l Mu is conserved in all interactions. Now let us get back to home stake experiment of Ray Davis where as I mentioned they detected neutrinos coming from the sun but what they detected is only about one third of what was expected. So how do you resolve this discrepancy three possibilities maybe the expectation is wrong the theoretical calculation about 8 boron concentration in the sun is not correct because 8 boron occurs one in 10,000 times so it is the end product of a large number of nuclear reactions and it depends on the core temperature of the sun as p power 24. If we reduce the value of t by 5 percent then 8 boron concentration comes down by a factor of 3 that is one possibility and most people actually believed that is the case. Second possibility is something happened to neutrinos on their way from the sun third possibility is neutrinos are coming they are producing argon atoms but the procedure for collecting argon atoms is not working efficiently mind you you are trying to collect 30 argon atoms out of 10 power 36 chlorine atoms. So it is a very very complicated difficult process and maybe something is going wrong somewhere. So each of these possibilities was considered detector was calibrated using an intense radioactive source and it showed that efficiency of collection of argon atoms is as expected and people studied the sun more and more closely and they said you cannot reduce the temperature of the sun by 5 percent the temperature of sun has to be what the solar models indicate what they are. So 1 and 3 are ruled out so the only possibility we have left with is something happened to the neutrinos on their way from the sun. Mind you the Ray Davis's original experiment was in 68 and over the next 25 30 years other experiments also saw a deficit of solar neutrino signal and here three Japanese physicists made a proposal which could explain actually they made the proposal as a sort of bright idea in 1962 much before Ray Davis's experiment but this can provide a possible explanation of the deficit of Ray Davis. What they said is that if the neutrinos have a small mass and it has to be really small it should be about an electron volt or so to give a comparison electron which is the particle with the smallest known mass has a mass of about a million electron volts. So this is really really small then they can mix with one another and this mixing can lead to oscillation of one type of neutrino into another that is the electron neutrino emitted by the sun in principle can oscillate into a muon neutrino and Ray Davis's experiment is not capable of detecting muon neutrinos. However this idea was not taken seriously but then as I mentioned before other explanations for the deficit in Davis experiment are ruled out so people had to take this neutrinos oscillating into one another they people started trying to take it seriously and by the way here yet another interlude comes in in 1977 a third lepton that is yet heavier cousin of electron called tau was discovered and when you study its properties you find that it has its own associated neutrino which is called tau neutrino and just as we introduced two lepton numbers one for electron and one for muon we have to introduce a third lepton number here for tau and its neutrino and the tau neutrino indeed was rather difficult to detect and it was finally detected only about 15 years ago at an experiment in formula and here we have another important development this is theoretical development which took place a famous scientist called Wolfenstein who passed away recently he proposed that propagation of neutrinos in matter it gets modified by the propagation this effect is just like how we have refractive index for light in a dielectric medium so you have light in a dielectric medium and then there are electrons in the medium the light interacts with those electrons but most of it gets scattered in the forward direction and because of which there is a modification of the propagation of the light in the forward direction and that is what we see as refractive index and Wolfenstein applied exactly the same idea to neutrinos and claimed that propagation of neutrinos is modified when they pass through matter and two young Russian scientists use this idea to show that you with this idea one can actually enhance a neutrino mixing angle from a small value to a large value as the solar neutrino travels through dense matter in the sun and people were really enthusiastic about this idea and they worked out various possibilities one possibility is the mixing angle is small and there are various dramatic effects which actually take place other possibility is mixing angle itself is large but we have to do an experiment to distinguish between these two because both these solutions can account for the deficit seen in Ray Davis experiment so to do that this Sudbury neutrino observatory was set up and by the way before I discuss about this snow lab I should mention that after all this drama in neutrino physics finally in 2002 the Nobel committee awarded Nobel Prize to Ray Davis sort of which is a great which is a well deserved honor that Ray Davis got for do persisting with his experiment for more than 50 years. Now question that is posed to us is neutrinos are oscillating as they come from sun to earth are they really oscillating how do we test it in order to test it we should observe interactions of both electron neutrinos as well as muon neutrinos but it is difficult to observe the it is almost impossible to observe the interactions of muon neutrinos which have only low energy muon has a mass of 100 m e v so if you want to observe the interaction of a muon neutrino you have to produce a muon and to produce a muon you need an energy of 100 m e v but the neutrinos coming from the sun have energy of only a few m e v so how can you if they converted into muon neutrinos how do you tell whether they converted or not SNO experiment used heavy water which consists of deuteron and here neutrinos have two types of interactions one is what we call charge current interaction which is standard where neutrino comes interacts with the deuteron converts the neutron in the deuteron into a proton so I have two protons and an electron and here the electron is detected but there is another possibility which is called a neutral current interaction and in the neutral current interaction the neutrino simply breaks up the deuteron and getting a proton in the neutron and neutrino remains a neutrino and in this reaction the neutron is detected so that is what the Sudbury experiment tried to do it tried to detect the charge current interaction by detecting this electron and this neutral current interaction by detecting the neutron the important point here in the charge current interaction is that the electron neutrino is getting converted into an electron so only electron neutrinos can drive this reaction muon neutrinos cannot whereas here any neutrino can drive this reaction both electron and muon so if this hypothesis of neutrino oscillations is correct that is electron neutrinos are oscillating into muon neutrinos to be consistent with Ray Davis result this reaction should take place only about 35% or so of the expected rate whereas this reaction should take place at 100% of the expected rate because this reaction does not care whether there is an oscillation or not whereas this reaction cares whether there is an oscillation so that is what Sudbury experiment tried to do and here you see a electron neutrino coming from the sun hits a deuteron and converts it into two protons and an electron and this electron is detected and here the electron neutrino some of them got converted into muon neutrinos or tau neutrinos they come and hit the deuteron break it up and the detected and the emitted neutron is detected and the Sudbury experiment is led by this gentleman Art McDonald and as I explained before the charge current interaction that is the rate at which electrons are produced it is one third and the neutral current rate that is the rate at which the neutrons are produced is equal to the expectation and this is the sort of final smoking gun confirmation that two thirds of the neutrino submitted by the sun are converted into muon neutrinos and only one third are being are appearing as electron neutrinos so for resolving this long standing puzzle puzzle which sort of started in 1968 the Sudbury results first came out in 2002 so for resolution of this puzzle Art McDonald and the SNO lab the experiment have been given half the Nobel prize for 2015. Now let us go to the second half of the story in the earlier part I referred to and Riko for me he was the one who made up the theory of beta decay and he is known as the pope among his students in the Catholic religion there is a sort of understanding that pope knows everything about the religion and similarly for Fermi students he knows everything about physics which is why his students called him the pope and he once made a pope like statement that yesterday's discovery is today's calibration to which another great scientist Richard Feynman added it will become tomorrow's background that is it will become new sense in your experiments this problem called atmospheric neutrino problem is a really remarkable case where what was expected to be a new sense actually led to an important discovery and in fact led to two Nobel prizes but for which again we have to take a step back a little bit in during 50s and 60s an important theoretical principle was developed in particle physics it is called the gauge principle and based on this gauge principle people constructed theories for first electromagnetic interaction for which a Nobel prize in 65 was given later for weak interactions for which a Nobel prize in 79 was given and one of them was given to professor Abdus Salam from Pakistan and finally for constructing a gauge theory of strong interactions a Nobel prize was given in 2004 however having constructed these theories people became very bold these are three independent theories but based on the same theoretical idea right well why do we need three independent theories let us construct one single theory which was done and that was called grand unified theory in which the strong electromagnetic and weak interactions they are all different facets of the same interaction they begin to differ from each other at an energy scale of 10 power 16 GeV to give a idea of how high this is the large hadron collider where the Higgs boson was discovered a few years ago it has an energy of about 10,000 GeV so this is a trillion times larger not likely to be accessible in accelerators any time soon so we need other possible ways of testing this theory and one attractive possibility is to look for proton decay because according to grand unified theories protons are not stable but they will decay according to this reaction into lighter particles positron and pi0 so two experiments called nucleon decay experiments were set up and the grand unified theory is predicted that the lifetime of proton is about 10 power 30 years so test this you build a detector with 10 power 32 protons that is equivalent to a few thousand tons of mass wait for a year and see if you get about 100 decays so two such detectors were built and proton has a mass of about 1000 MeV so this E plus will have a mass of will have energy of 500 MeV and this pi0 will also will have energy of 500 MeV and so they will both travel with speed very close to speed of light and when they are produced in water because of that high speed speed close to the speed of light they produce what is called Cherenkov light and based on the pattern of the Cherenkov light one can actually identify whether it is an electron or a muon or a pi or whatever of course there can be other processes in particular cosmic ray interactions in the detector which can produce Cherenkov light and which can mimic proton decay so the experimenters had to worry about the cosmic ray interactions which can produce Cherenkov light in their detector and in particular they had to worry about neutrinos interacting in their detector there are cosmic rays are mostly protons they come and hit the nuclei in the atmosphere they produce lot of pions these pions decay first into muons muons will in general will then decay the end result is lots of neutrinos are produced and these neutrinos they can enter the detector and interact with them produce muons or electrons or positrons they will also be very traveling with speeds close to speed of light so they produce Cherenkov light and you can have a possible backgrounds backgrounds from neutrino interactions mimicking proton decay so these two detectors they needed to understand the neutrino interactions in their detectors completely here we have a picture of this how these neutrino interactions occur so this is earth and here is the detector because here it is shown sticking out of the earth but it is actually 1 kilometer below earth if a neutrino is coming above it essentially travels the thickness of the atmosphere which is maybe 10 to 20 kilometers but if the neutrino is coming from below it travels some 20 kilometers in the atmosphere here and then it travels anywhere between 5 to 10,000 kilometers of earth matter and remember neutrinos do not interact very often so very few of them will interact and most of them will come unscathed through all this earth matter and enter the detector and there maybe 1 in a billion or 1 in a billion will interact in the detector so if the neutrino is coming from below it has traveled tens of thousands of kilometers whereas if neutrino has come from above it traveled maybe 10 kilometers so these two experiments they did not find any proton decay at all and in fact they set a lower limit on proton lifetime of about 10 power 32 years they found that the rate of muon neutrino interactions is smaller than what is expected in particular they expected muon neutrino interaction rate to electron interaction neutrino rate they expected it to be 2 but measured value is only about 1.3 this is called atmospheric neutrino puzzle and this is where the background became the discovery the neutrino interactions are expected to be new sense for proton decay but there was no proton decay on the other hand the neutrino interactions provided a puzzle where they were expected to give a ratio of 2 but measured value turned out to be only 1.3 this is called the atmospheric neutrino puzzle and once again neutrino oscillations provide a solution to this puzzle three possibilities the original measurement only refer to the ratio that means muon neutrino rate is low electron neutrino rate is as expected or muon neutrino rate is low electron neutrino rate is high or muon neutrino rate is as expected and electron neutrino rate is high how to distinguish among these three possibilities to do that a experiment which is five times bigger than the previous experiments was set up and also the ability of this experiment to collect light the Charankov light is much much better compared to the previous experiments and the atmospheric neutrino group this experiment is called super cameo Kande it was set up at the location of one of the earlier experiments and of course super cameo Kande is a very big experiment with which did lot of studies but the atmospheric neutrino group of super cameo Kande experiment is headed by professor Takaki Kajita and he was involved in all aspects of this experiment including the calculation of how many neutrinos are coming what is expected to be their interaction and of course the construction of the experiment and data analysis and one important property super cameo Kande had is it could study electron neutrino interactions and muon neutrino interactions as a function of neutrino energy and neutrino direction in the previous experiments they just calculated the total rate all they could do was measure the total rate and that to take the ratio between muon rate and electron rate here they were able to make individual measurement electron neutrino interaction separately as a function of energy and direction muon neutrino interaction separately as a function of energy and direction and the results are summarized here. So they are energy wise they are divided into two bins energy less than 1 GeV energy more than 1 GeV and also electron like event separately and muon like event separately and you can see here the blue lines are the expectation and the dots are the data and you see that both for low energy electron like events and high energy electron like events the dots and the blue lines match exactly whereas both for low energy muons and for high energy muons there is a difference between the expectation and the dots here as well as here. Another important aspect especially in this multi GeV sample for cos theta minus values that is these are the neutrinos which are going in the upward direction and cos theta positive values these are neutrinos going in the downward direction. So these are neutrinos which are travelling thousands of kilometers whereas these are neutrinos travelling tens of kilometers and neutrinos travelling tens of kilometers they do not show any oscillation expectation matches data but neutrinos travelling thousands of kilometers there is a deficit the data points are well below the expectation and that is what that is precisely the signal that we expect from oscillations the neutrino which travels longer distance has a larger probability to oscillate compared to a neutrino which travels a shorter distance therefore we see more oscillation for upward going neutrinos and hardly any oscillation for the downward going neutrinos. So and here there is a sketch you have a downward going muon neutrino and you detect its direction you have an upward going muon neutrino you detect its direction and compare the two which was done in this graph and this graph shows that this deficit has the correct dependence on both energy as well as direction that we expect from oscillations. So this plot is the evidence that in atmosphere the electron neutrinos are not oscillating it is the muon neutrinos which are oscillating and they are oscillating into tau neutrinos. So for demonstrating this the atmospheric neutrino group of super comingoconde led by professor Kajita was given the second half of the Nobel Prize in 2050. Let me take just two minutes to discuss some first some later developments and some future mind you all the experiments that I have discussed so far they use what are called natural neutrinos that is neutrinos coming from the sun or neutrinos produced in the atmosphere. And what later experiments tried to do is to check the results of these experiments using what we call manmade sources one of them is called Kamla and experiment which has a nuclear reactor producing neutrinos electron anti-neutrinos. So this is a fancier version of the Coven-Reynes experiment except that the distance between the source and the detector is 180 kilometers and this confirmed that the solar neutrino oscillations are also occurring in reactor neutrinos. And there is accelerator experiment called minnows this is a fancier experiment compared to fancier version of the same experiment that was done in 1962 at Brookhaven. They produced a new mu beam and measured how many muons they get at a distance of 730 kilometers away and they found that they are indeed getting only about 50 percent or so of the muons. So it confirmed that there is a the deficit seen in atmospheric neutrinos occurs in accelerator neutrinos also and very recently an experiment in Japan called T2K it confirmed the results of minnows and for the first time we saw a muon neutrino oscillating into electron neutrino because all the other cases so far it is a deficit. You start with an electron neutrino source and you see a deficit of electron neutrinos. You start with a muon neutrino source and you see a deficit of muon neutrinos. So far we have not seen a actual muon neutrino going into an electron neutrino or an electron neutrino going into a muon neutrino about three years ago or two years ago for the first time T2K experiment has seen this explicit conversion. They started with a muon neutrino and they saw an electron neutrino. An experiment in US called NOVA is taking data and it also has seen this conversion. There are some outstanding problems still to be settled in neutrino physics. One of them is called establishing neutrino mass pattern, other one is called establishing CP violation in neutrinos and there is a chance mind you only a chance that NOVA and T2K together can establish CP violation. Let me take another couple of minutes to talk about future experiments. There is a plan to set up an experiment in India in Thaini district of Tamil Nadu. It will house a 50 kilo ton magnetized ion detector. This is a new technology which has not been tried so far under a mountain in the hills which sort of separate Tamil Nadu and Kerala. And this experiment can observe interactions of atmospheric neutrinos and they can do it much better than super kamyokande and it is capable of determining the mass pattern of neutrinos. There is a proposal in Japan called hyper kamyokande. This will be 10 times bigger than super kamyokande. It can function in two modes. In the beginning it will observe interactions of atmospheric neutrinos. Later they will have an accelerator 300 kilometers away which will shoot a neutrino beam towards this detector and then it can detect the accelerator neutrinos also. And this experiment hopes to determine both the pattern of neutrino masses as well as CP violation. Of course, as with INO the atmospheric neutrino data will determine the pattern of neutrino masses accelerator data will determine CP violation. And finally, there is a plan in the US. It is called DUNE, Deep Underground Neutrino Experiment. And this is being designed so that all the current questions regarding neutrino masses will definitely be answered. So, I will stop here and I thank you for your presence. Good afternoon sir. Good afternoon. My question is actually related with the experiments which are being performed in India. As you have mentioned in one of your slides, Henin Tamil Nadu. Actually, sir, why these neutrino detection experiments are being performed well deep inside the earth? Why? What are the reasons behind it? And people like what are the opportunity if I want to some work towards this direction? Okay. The neutrino experiments have to be underground at least a kilometer underground for the following reason. One thing which I have tried to emphasize throughout the talk is neutrinos interact very, very rarely. So, the number of signal events you get is very small. However, if you put the experiment on the surface, there are various cosmic rays which come and interact in your detector and that interaction rate is very high. It is like a few lakhs per day whereas neutrino interactions will be one or two per day. So, in order to suppress those cosmic ray interactions, you need to go underground. And in fact, not a few meters underground you need to go, I mean in this case of INO, you need to go roughly one kilometer underground. And INO project is being managed by people in TIFR and various details of INO are available on its website. And they have a graduate training program and students are welcome to write the test and attend the interviews for the INO graduate training program. And most certainly we welcome participation from a wider community. Hello, sir. Like electron has its antiparticle, electron has its antiparticle that is positron. Yeah. Proton has its antiparticle, antiproton. Right. As like that, neutrino has its antiparticle. Yes, there are, I mean mind you there are some complications here. I mean let me put it this way. We have seen interactions of neutrinos, we have seen interactions of anti-neutrinos and the two are very different. That is the important point. So, neutrinos are different from anti-neutrinos. However, there is a rather technical point about something called Majorana mass. It is a very, very technical point and I do not want to get into it now. But there are people who say that neutrinos can be their own antiparticles but I do not agree with that statement. We have seen neutrinos, we have seen anti-neutrinos. Reactions of neutrinos are different from reactions of anti-neutrinos. So, I would say neutrinos and anti-neutrinos are different particles. Sir, I have two questions. Yeah. Question number one. Why the neutrinos are emitted in beta decay? Question number two. Are the neutrinos exist in the nucleus before collision? Neutrinos are emitted in beta decay because I mean rather we talk about neutrinos from beta decay because that is the most copious source of neutrinos. There are other interactions in which neutrinos are emitted but those interactions are somewhat rare. Whereas, beta decay is the most copious source of neutrinos. So, whenever we talk about neutrinos, we talk about beta decay. But I mentioned in one of my slides that the best source of muon neutrinos is pion decay. So, in order to produce muon neutrinos, we produce a beam of pions, let them decay and then we get a beam of muon neutrinos. So, there are different sources of neutrinos but beta decay is the most prominent source for electron neutrinos and pion decay is the most prominent source for muon neutrinos. And to answer your question, neutrino was not present in the nucleus before beta decay. And I mentioned that for me made use of a non-trivial use of second quantization. This theoretical technique of second quantization precisely describes how a particle is spontaneously created at the time of decay. So, neutrino certainly neither neutrino nor beta decay electron were present in the nucleus before the decay. They are spontaneously created at the instant of the decay. Thank you, sir. Good afternoon, sir. My question is that, sir, gluons, photons and gravitons W plus or minus Z naught are the exchange particles. So, my question is that, sir, gluons, photons and gravitons doesn't has mass but W plus or minus and Z naught are having the mass. Why they have the mass? They have mass because they and, okay, this is what this whole Higgs mechanism is about. And that Higgs mechanism led to the prediction of that there should be something called Higgs boson which was discovered three years ago which showed that the whole idea is correct. So, its idea is somewhat like this. Imagine you try to shoot a photon through plasma and plasma is full of electric charge. So, the photon will find it very difficult to go through plasma and in fact, if you do some Google search, you can probably find this interesting quote. We get light from the sun and the light is produced in the core of the sun and sun has a radius of about a million kilometers. How long does it take? The photon produced at the core of the sun to come out of the sun travel a distance of a million kilometers. If you use C, you will say one second but somebody made an estimate that it will take 10 million years for the photon to come out of the sun. So, it is entirely possible that something has happened in the core of the sun and we will learn about it only 10 million years from now. So, if we have a background in which the force carrier interacts constantly, then the force carrier behaves as if it has mass. Now, the present belief is that the whole universe is filled with what is called a Higgs field and the force carriers W plus W minus and Z, they have a charge which corresponds to the same charge that the Higgs field has. So, this W plus W minus and Z, they keep interacting with the Higgs field as they propagate. So, that is why they appear massive to us whereas, photon, gluon, gravitan, they do not carry the charge. Therefore, they do not appear massive. I hope this conveyed some rough picture of what is happening. Thank you, sir. It was predicted by Pauli that the neutrino will be the for the particle as per the property of the charge, invented neutrino, neutron. Right, not invented, he discovered, he experimentally discovered it in the lab. And what was further prediction about the neutrino? Well, Pauli did not make any further prediction and later people thought that it was come, neutrino is a massless particle, but these neutrino oscillations show us that neutrino mass is nonzero. What it is? We do not know. So, there is an experiment. We only have an upper limit. We know that neutrino mass is less than 1 electron volt, that much we know. And there is an experiment in Germany called Cartrain which is trying to measure neutrino mass even if it is as small as 0.1 electron volt. So, that is the, I mean Pauli did not make any further predictions, but the neutrino oscillation experiments showed us that neutrino is massive, but do not tell us what the mass is. So, now there is an experiment being mounted, I mean in fact, it is running to measure what that neutrino mass is. There are other possible predictions, other predictions which are a little more complicated, but the simplest is about the neutrino mass. Yeah, go on. Sir, one is the only source of neutrino or any other source is possible? No, every star, every object in the universe where you have fusion taking place puts out neutrinos, but of course sun is much closer to us than any of the other star. And as I mentioned, cosmic rays when they come and hit the atmosphere, they produce neutrinos. And finally, we can produce neutrinos in lab by producing a beam of pions and letting them decay and then we get a beam of muon neutrinos. So, you have natural sources and you have manmade sources, both are possible. Sir, it is possible that in future we make any artificial source? I mean artificial source means first it has to be, there has to be some natural element because as of now we can produce neutrinos only through decays. So, in order for the decay to occur, we should have a source of pions or a source of radioactive nuclei. Thank you sir. We have three flavors of neutrinos. Do they combine among themselves to get the original particle back? Yeah, yeah. So, the oscillations mean first the three flavors have to combine for us to have oscillations. So, and we call it oscillations because the conversion probability has that sinusoidal form, it has that form sine squared of something, sine squared of L. So, first electron neutrino becomes muon neutrino and then it becomes electron neutrino back. So, yes, they mix among themselves and at regular intervals it gets back to its original state. Hello, good afternoon professor. Yeah, please go ahead with your question. My question is slightly offbeat but you were telling in your lecture that the lifetime or the decay time of the proton occurs in once in 32 years. If you consider the age of the universe, which is around 10 to the power 15 years, is it not contradictory? And also that if at all a proton decay is observed experimentally, will it not challenge the foundation of the Big Bang theory? No, proton decay does not challenge anything of the Big Bang theory. And here we are, the decay of proton we are counting according to the radioactive decay law, which says that enough the number of surviving protons is number of original protons times e power minus gamma t. So, I mean if I want to test proton decay at the level of proton lifetime of 10 power 30 years, all I need to do is to start with an initial sample of 10 power 32 protons and see if some of them decay, that is all. So, the fact that age of universe is only 10 power 15 years does not prevent me from measuring a possible lifetime, which is longer than age of universe. Because I am looking for only a few decays, I am not looking for the whole sample to decay. If I want to wait for roughly half the protons to decay, then I have to wait 10 power 32 years. But I am looking only for 10 protons to decay, not of the order of 10 power 32. So, I can measure lifetimes, which are much larger than the age of universe. As long as I accept this radioactive decay law and we do not see any problems with that in any experiment so far. Okay, this will be the last question. Sir, how the location of neutrino observatories were chosen, sir? Ah, how the location of? Oh, as you told, one kilometer depth is sufficient. Ah, sorry. As you told, one kilometer depth is sufficient to observe neutrinos. Right. So, but one kilometer depth is, I mean, for example, most of them are, most of neutrino experiments are located in mines and lot of mines are only about half kilometer deep and half kilometer is actually quite deep. In this particular case, this west body hill site is chosen because there is a mountain and if you make a one kilometer tunnel in the mountain, you will have a rock burden of one kilometer from all sides. But second important point, the neutrino experiments have to be very big because the neutrinos interact very rarely. I need a big detector so that I can observe maybe one event per day. So, this, I know it needs a cavern which is 100 meters long and a height of about 15 to 20 meters. So, I can have a tunnel one kilometer long which is only 3 meters high but if I want to have a 100 meter long cavern which is 15 to 20 meters high, I should be sure that there will be no cracks in the rock and the whole thing should not collapse on my head which means that the rock should be very strong and it should support such a cavern and all those studies have been done and only after approval by Geological Survey of India is this site in Thaini District of Tamil Nadu, it was chosen. Yeah, I think we see that questions are still coming up unfortunately because we are running short of time now. We have to close this session. I will request, please put up your questions on the Moodle. I will request Professor Umashankar to take his time off and answer the remaining questions that could not be taken up at this time. However, before we conclude this session, it is a pleasure to thank Professor Umashankar and looking at the amount of questions that have been already answered and coming up. I think now it was a big good decision to let him talk on the event that had a lot of significance this year and Professor Umashankar on behalf of all the participants and all of us here, a big thank you to you. Thank you very much. We assemble in about 15 minutes time.