 OK, is this working? Can you hear me all the way in the back? OK. OK, so my job is to give you three lectures on the physics of neutrinos. And these lectures will probably be very different from the other two lectures you've seen so far. I will talk a lot about history of neutrino physics. I'll also talk about experiments a lot. So hopefully, you won't be too bored. And the most important thing to always remember with these lectures is if you do have questions, please ask questions. You may have noticed from almost all the lectures that we like to talk a lot, which is true. So if you don't ask questions, people will just keep on talking very, very quickly. So you don't want that. OK, so let's keep that in mind. And I'll mostly be showing slides, but I'll be writing a lot of stuff on the blackboard as well. So hopefully, this is going to work out. And it won't be too distracting. OK, so this is mostly what I'll try to tell you about. What I'll do mostly today is to give you a very condensed history of everything that we know about neutrinos until maybe about 20 years ago. Then I'll spend a reasonable amount of time reminding you or telling you, in case you don't follow this kind of physics, why neutrinos are so exciting today. They are among the most exciting things going on in particle physics today, if you ask me. Then I'll talk about the physics of neutrino oscillations, which is this new phenomenon that we learned. And I'll try to give you the big picture of where we stand with understanding neutrinos today. And I'll try to highlight what are the things about neutrinos that we haven't learned yet. And then towards the very end, I'll try to go into a little bit of detail about the physics of giving neutrinos a non-zero mass. And then I'll discuss some concrete ideas and so on. Since you're going to have access to these slides at some point, here's a very incomplete, very, very biased list of places you can learn more about neutrinos. I do want to highlight the very last one. This is a website kept by Carlo Giunti from Torino. And he has a lot of references on neutrino physics. He also has a book on neutrino physics. And you might want to check that one out as well. OK, so let's get started. So I want to give you a sense of a little bit of the history of particle physics, especially when it comes to understanding neutrino physics. Neutrino physics is a very old subject. It was always a very, very confusing subject. And I want to give you a sense that resolving certain problems in particle physics can take a very, very long time. And this is true even more than 100 years ago. So I do want you to keep that in mind for those of you that are very, very impatient and they want to find new physics tomorrow, like me. It's very important to keep in mind the history of particle physics and the fact that we learn something fundamentally new or very, very important every once in a while. But we don't get to do it on a yearly basis. So that's something I want to try to keep in mind. So I want to start this story in a place that, oh, and I should say the following, most everything that I will say today will be very, very basic. So don't be offended. If you feel like you know everything, on the flip side, people tend to be very happy when they hear about things that they already know because it makes you feel good. Oh, I already know this so I can pay attention. So but please ask questions. And if I say something that's wrong, which I will, you should correct me as well. So this is very important. So I want to start out in the beginning or in the end of the 19th century by the turn of the century, this is sort of when particle physics starts. If you want to identify when does something that smells like particle physics began, it's probably around those times. There's a very important date in 1897, which is when the first fundamental particle was identified. And that's when somebody figured out that electrons exist by doing an experiment, which is a really cool experiment, which I won't tell you about, but you should know about it. And if you don't know about it, you should look it up and that's when the electron was discovered and these experiments would cathode raise. It turns out that the year before, there's another very important discovery, which is a very weird phenomenon, which is a naturally occurring radioactivity. And this is where the history of neutrinos in some sense starts. So let me remind you of this story, which hopefully many of you learned in like high school or whatever the equivalent of high school is. And the idea is people were studying objects that emit radiation when you expose them to some source. So we're very familiar with this. We know that if you take like a piece of coal and you heat it up, it emits heat as well, which is nice. The other thing that happens is some materials will also emit some measurable energy when you expose them to light. So there's this phenomenon called a phosphorescence. And some things are phosphorescent, which means that you expose them to light and then they glow. So let's put it that way. So the story goes, and I'll tell you the story very quickly. So there's this French guy who lived in Paris and he was doing experiment with one of these phosphorescent materials. It's some compound that contains uranium. And the idea is a very simple experiment. So you take this uranium, you expose it to light, and then you bring it back to your office. They didn't have labs back then. They all have offices. So you bring it back to your office and he used to do experiments with photographic plates. One thing you might know is photographic plates already existed back then. This was a very, very big deal for science, it turns out. Both for things like astronomy because you could take a picture of a star instead of just looking at it, which is kind of a big deal. And you can also use that to study materials. And this is how you'd study these materials. You take your uranium, you would expose it to some photographic plate. You would leave it out in the sun, you would bring it back in, expose it to some photographic plate, and then you would measure how much it is irradiating something, some energy. So one day he was gonna do his experiment and the weather was bad. So he couldn't do the experiment and this happens a lot in Paris, so that's fine. So he went through his experiment, he came back into the lab, he actually had to go on a trip. So he put a sample inside of a drawer in his desk and then he went away for a couple of weeks. And then a very long time later, he remembered that he had left the sample inside of his drawer for a long time and then he found out that he had left his sample on top of a photographic plate. And he decided that he had left it there for a long time. He didn't know if the photographic plates were good or not, so he decided to develop them. And basically what he found out, and there's some pictures of this, so here's his little box, here's a photographic plate and the box was sitting right here. So when you develop the photographic plate, you see a signal of something, that this box of uranium was emitting some radiation and this was very puzzling because he hadn't left it out in the sun for it to do that. So basically the discovery that they made is that this piece of material was emitted radiation by itself. You didn't have to do anything, but somehow this piece of material was capable of emitting energy spontaneously without you doing anything. So this is a very, very big discovery. We had no idea that this could happen. Yeah, is it very? No, this is a, these are things you can find on the street. The harmful experiments happen later when people started to study what this does. So the next question you ask is, so what is going on here? And then you find out that there's something that's being emitted by this material. So now we wanna study this. So we wanna find out what it is that this material is doing and hopefully ultimately we wanna find out how it's doing that. And then what people did is, and they decided to study this in detail. And one thing which you must all know by now is that there are three kinds of radiation. And people figure this out experimentally. This is a completely experimental fact. And they found out that there are three kinds of radiation. They were given boring names. One is called the alpha radiation, beta radiation and gamma radiation for totally obvious reasons. And these things are classified in a couple of different ways. One is that you can take this radiation and you can place it in a magnetic field. So what you do is you take your little box of uranium, you surround it with something so that the radiation is forced to go in a fixed direction. Then you put a magnetic field somewhere like here and then you put the photographic plate over here and then you ask what does the radiation do? And you find out that there's one kind of radiation that does this, there's another kind that does this and then there's another kind that does that. And these are alpha, beta and gamma radiation. Now they actually figured out more stuff. One thing that they figured out of course is that alpha radiation was very, very easy to stop. So if you put a barrier here like a piece of paper, the alpha radiation stops before it makes it to the photographic plate. The other thing that they found out about the alpha radiation is that it would bend in the magnetic field but not by a huge lot and the interpretation we have for that is that whatever makes up that radiation is relatively heavy. Beta radiation on the other hand is a little bit harder to stop. It bends the opposite way of the alpha radiation and it's pretty light. So these are the things that we know. And finally there's gamma radiation. Gamma radiation is super hard to stop and it doesn't bend. This is what people knew and at the same time once you can make a measurement like this, you can also measure the energy of the radiation that's coming out. If you pretend that this radiation is made out of some object that has mass, you can calculate its kinetic energy and by doing that, people figured out that for example, almost all the alpha radiation that would come out of some material would have some characteristic energies. You know, it would like be a monochromatic radiation. All of the energies are the same. The same is also true of gamma radiation and beta radiation was more weird and it took people a very long time to figure out what was going on with beta radiation and that's the story that we wanna follow up by figuring out how did people study beta radiation. So again, this is in 1896. They identified all these different kinds of radiation very quickly. What they also decided to do was to figure out which materials were good at emitting radiation and that's where the very dangerous experiments started to happen because of course what you needed to do to study that is to get a lot of that material that emits radiation and then you wanna study it and sadly it turns out that the radiation is not good for you and people learn that over the next 40 years or so and some people learn that the hard way. Okay, so this is again in 1896. One challenge the people were facing was to understand the spectrum of beta radiation and again, the idea is very simple in terms of doing the experiment. Again, let's say that you have a source of beta radiation over here and then you wanna measure the energy that comes out and one question you wanna have is what kind of an energy spectrum do you have? Okay, so that's a simple question. So you wanna make a plot of, I don't know, number of events as a function of energy in some units as a function of energy and there are two qualitatively different things that can happen. One is that you're gonna get some lines and the other one is that you're gonna get something that looks like this. Okay, these are two qualitatively different things that can happen and one thing which is very important to know even if you know the story very well is that it took about 20 years to figure out what the spectrum looked like just from a measurement perspective. One thing is that these measurements are hard and the way you wanna imagine this is that you're really literally doing this on top of a photographic plate. So you have your sample here, you put a magnetic field so your electrons are gonna come in and beta radiation, by the way, are electrons. People figure that out quickly and the radiation is kind of doing that and it's hitting your photographic plate at different places and you need a lot of exposure to figure out if you have these sharp lines or if you have these continue as well. The other thing is a lot of the early measurements look like a continuum. That means that it looked like a continuous spectrum and people were very puzzled by that and it took again until 1914 until somebody did some very, very cute measurements and very clever experimental techniques to figure out and convince everybody that the spectrum of beta radiation was actually continuous. This is a difficult thing to do experimentally and people were very, very puzzled because all of this is going on in this first couple of decades in the 20th century where at the same time people were figuring out what quantum mechanics was. And the one thing that I wanna remind you of about quantum mechanics is the first bullet there at the bottom and quantum mechanics has started out from lots of different places. One place that you are probably familiar with is when people started measuring line spectra. So when material emits radiation and if you measure the frequency of the radiation that frequency is quantized. What that means is that you only get certain colors. And hopefully if you have seen experiments you can actually do the experiment of measuring the different frequencies of light that come out of the emission of anything. And you always get these very nice lines and that's part of the reason it's called quantum mechanics because you want to explain why certain energies are better than others let's say and materials can only emit in certain frequencies. And that was characteristic of atomic phenomena. And here was this other phenomenon which was beta radiation which was not quantized. It looked like you could get any kind of energy you wanted. Okay so this is problem number one. If you want this is a philosophical problem because if you see a new phenomenon that doesn't look like an old phenomenon it doesn't mean it's wrong it just means it's different. There's a much more complicated problem with beta radiation that everybody was also aware of early on was that if you looked at the kinematics of beta radiation it seemed to be violating energy momentum conservation by a lot. Okay so once you figure out what beta radiation is beta radiation is a physics process where you have a nucleus that converts into a different nucleus by emitting an electron. So the kinematics of this is very very simple and in reality if you knew everything very very well you could calculate the energy of the electron that comes out exactly. There's a little bit of a fudge factor because of the recoil of the nucleus. You can take that into account. So what you really expect out of your experiment if you did this measurement you would expect to see a very big peak right over here. So this is what your calculation tells you. It says that look the electron that comes out must have this energy and when you go out and you make the measurement the electron actually has all kinds of energies and they're all less than the energy that you expected. So this is kind of where people were and that's why it took them a very long time to believe that this was the right answer that this spectrum was the right answer. There are lots of things you can be suspicious of when you're making this measurement of beta radiation. The most obvious one it turns out is you know so I have some material here this electron wants to come out and you could postulate that maybe as the electron is leading your sample it's kind of hitting stuff around and then it's losing a little bit of energy that way. That sounds totally plausible. And that's what people suspected for a very long time and that's why it took people about 20 years to convince themselves that this wasn't happening. Now how do you do that? You have to be super clever. There are lots of things you can do you can change the size of your sample you can change the shape of your sample. If the electron were losing energy as it's coming out that energy has to be going somewhere so you know imagine that your sample would have to like heat up and maybe you can measure that. So people worked on that and and at the end of the day by the 1920s for sure they were very very sure that this beta radiation was very weird. By the time we're getting to like the 1930s that's when people were starting to take a serious stab at building a model for nuclei. And so I want to give you a primer of how nuclear physics look like by the 1920s. They were actually rather sophisticated they had a model that worked very well for many things and then they had some big problems. So I want to give you a sense of what the model was like. So people figured out that they could measure the masses of nuclei like hydrogen, helium, bralium, lithium, et cetera, et cetera. There's no periodic table in this room. There could be. So imagine there was one in your classroom there might be one. So you know all those nuclei. People figured out very quickly that the masses of those nuclei were almost in units of the proton mass, right? You know the helium has four units of the proton mass. So the mass model people had for the nucleus was to say that the nucleus was a collection of protons. And of course if you do that the charge doesn't work out. So even though helium has a mass which is a four times the proton mass it only has a charge which is twice the proton charge. So we can fix that by adding a couple of electrons inside of the nucleus as well. So basically nuclei were made out of protons and electrons. That was good because we knew that sometimes nuclei could spit electrons out. So that was the model. And this model would work very, very well for many things. So for example, so helium four was like a four protons and two electrons bound by some mysterious nuclear force we hadn't figured out yet. The problem is that you could take this further and then you could talk about other nuclei. So one other famous or infamous nucleus is like nitrogen 14. And nitrogen 14 would be made out of 14 protons and seven electrons. Now here's actually where people had a problem because if you look at 14 protons and seven electrons you can ask what kind of a particle is that? And the question means you can ask what's the spin of that? And we don't know but we're very, very sure that it's something plus a half, right? Because it has an odd number of fermions. So the total spin of that is a half integer spin which means for example that nitrogen 14 is a fermion. That's a prediction you can make. And sadly that's wrong. So nitrogen 14 is not a fermion, it's a boson. And people knew that, don't ask me how they knew that but they had information on that. The chemists know how to do stuff too so they knew that that was a boson. But that was one big problem is that nuclei as constructed that way seem to violate the spin statistics theorem. Which is not a small thing, it's a big deal. Another thing which is there's a problem with magnetic moments. We all know about magnetic moments. It's whatever happens to your spin when you place it in a magnetic field. It's how much energy you gain by aligning yourself with the magnetic field. And one thing that we knew by making measurements is that the magnetic moment of the proton is way smaller than the magnetic moment of the electron. That's a fact. And if you measure the magnetic moment of certain nuclei, those magnetic moments are of order the proton magnetic moment which is way smaller than the electron magnetic moment. So it was very hard to understand how can the nucleus have all of these electrons in it but somehow the contribution to the magnetic moment is a tiny from the electrons. So it was kind of weird. You always had to kind of convince yourself that the electrons had to align perfectly but then if you had a leftover electron it wouldn't work out. So it was not quantitatively working very well. So again, what's the solution to this very big problem? And the answer is people had absolutely no idea. One very popular solution which was a champion by people like Niels Bohr and other famous people at the time was that maybe when you have these bound electrons inside of a nucleus, they behave in a weird way. So bound electrons do not obey the same laws of physics as a free electrons. That was the model and that's a really, really crappy model. But that's what they could do. And one thing which I always like to remind people is even though I'm sure half of you must have heard versions of the story before and even though it sounds like a totally crazy idea to believe weird stuff, this is the best that people could do in the 1920s. And one thing which I always like to quote is at the very bottom of the slide there, there's a quote from George Gamov and basically he's talking about a bound electrons and he was talking about the beta spectrum and what he's saying is that in order to explain this spectrum here you have to violate the concentration of energy and momentum. And what he's saying is if you got to that part of the book and you've learned all the other weird things that bound electrons have to do which is they have to violate the spin statistics theorem and they have to have a very, very small magnetic moment it's not a surprise that they have to violate energy and momentum conservation because they do all kinds of wrong things anyway so they might as well this other one wrong thing as well. Now this is a quote by George Gamov who's a very famous physicist in the early 20th century he did lots of very important things. He was also known for being sort of a funny guy that told lots of jokes and but on the other hand this is from a textbook. It's not like he wrote this in an article or something like that. This was a nuclear physics textbook where people were really questioning whether nuclear physics was really strange. Okay so now I will tell you the solution to all of these problems that happened in the early 1930s and this is where neutrinos come in. So neutrinos were invented in 1930 in December to be more exact and they were invented to explain why these beta spectrum look like that and they were also invented to solve some of these other problems that people had with nuclear physics. Now the key thing is the neutrino was a theoretical idea by Pauli and basically what he did was in order to explain why the spectrum is continuous he invented a new particle. This is another very famous story that again I will make the assumption that at least half of you have heard this story before but I will just tell you the story very quickly. So again there was a nuclear physics convention in I always forget Zurich I think some place in Northern Europe and Pauli didn't go to the conference but he wrote a letter and he gave it to his friend so his friend would go in the conference and read the letter and that was his talk so it's a good talk. So he went up and he read Pauli's letter and I have an English translation of that here and it's a super famous letter the real letter is in German so I'm not gonna try to read that because I don't know any German. It is famous for lots and lots of things and a lot of it has to do with stuff that I've already told you so Pauli was also trying to be funny every once in a while so it starts with this via radioactive ladies and gentlemen. Basically what's happening here is that he's reminding people what the problems were. First of all he says he's come up with a desperate solution to the wrong statistics of Nitrogen-14 and Lithium-6 nuclei as well as the continuous beta spectrum so these are these two problems I've been telling you about one is that the spin statistics theorem doesn't work for nuclei and that beta radiation is continuous and also he wants to say in order to save the alternation law statistics and the energy law. So the energy law of course is energy momentum conservation and this alternation law statistics is of course the Pauli principle. Of course if you're Pauli you can't call it the Pauli principle it's not allowed so you have to give it some name. So basically what he's going to do is he's going to postulate that there's a new particle which also lives inside of the nucleus and that particle has no charge and again it's gonna live inside of the nucleus and it also has spin one half like the electron and the proton. So that way by adding some of these neutral particles inside of the nucleus that also have spin one half you can add the right amount in order to solve the suspense statistics theorem problem. That's good and that's his model. Now Pauli is a phenomenologist so he knows that he has to be in agreement with other experimental data so he's gonna use experimental data to constrain his new particle that he's just invented. One is this particle better not be super heavy because if it were heavy it would make the nuclei much heavier than they should be so they have to be lighter than something. So that's one constraint. Like I said it has to have spin one half and the other thing of course is that we haven't seen this particle do anything so it better not interact very much and if you keep reading the letter that's effectively what he's doing in the rest of the letter. He's basically saying this thing has to be light and it can't interact very much and he puts some very loose bounds on what things look like and one thing which is very important to also appreciate from a historical perspective that particle was called the neutron for completely obvious reasons. You had a proton, you had an electron so it had to end in on because it sounded Greek and it didn't have any charge so it was a neutron. So very simple. So this is what he's doing. He's doing lots of really cool phenomenology in that very first paragraph. So for example if you read the last sentence there it must have the penetrating power equal to 10 times larger than gamma radiation. Again that's to solve experimental issues because we've never seen one of these in quotes neutrons do anything. Okay so this is what Pauly was doing. So the last paragraph is a more philosophical paragraph and what he does in that paragraph is that first of all he's complaining that what he's doing feels like cheating because he's inventing a new particle to solve a problem and that sounded wrong and of course today we do that on a daily basis but that's a separate problem and then he has some more philosophical statements in the middle and then towards the end he tries to explain why he didn't get to go to the conference because he had to go to a party. There's a lot of debates about why Pauly didn't go to the meeting. Some people say he was kind of scared of making this bold presentation. I'm not sure if I buy that because he was Pauly and he was already famous at the time so I don't know if he was scared of that. But the one thing which I forgot to mention is the way that you solve this problem here is very simple. You have a nucleus that decays instead of this way it decays into a three-body final state and that solves the problem because now all of this energy here instead of being shot out with the electron it is split between the electron and the thing that we call the neutrino today. Okay so this is a very very simple kinematical solution to this problem and this is what Pauly came up with in December of 1930. So a lot of really cool things happen relatively quickly after that. A very interesting thing that happened was in 1932, Chadwick in Great Britain was doing more of these nuclear physics experiments and then he found a new particle which didn't have any charge and he called it the neutron and this was in 1932 and this is kind of a big deal and everybody learned about it very quickly and again the story goes and this may or may not be true but I think it's true was that a Fermi was giving a talk or he was giving an interview I don't remember if he was a talk on an interview and then somebody asked him hey Chadwick found this particle called the neutron and Pauly two years ago postulated there's a new particle called the neutron so did Chadwick discover Pauly's neutron and then Fermi said no, no, no the neutron that Chadwick discovered is actually quite heavy it weighs as much as a proton does the neutron that Pauly predicted is very, very light so it's not a neutron Pauly's neutron is a small neutron and he was giving the interview in Italian so in Italian if you wanna see a small neutron you say a neutrino it's a little neutron so if you know Latin languages it makes perfect sense so Fermi called it a neutrino and somehow the name stuck this is actually kinda cool because this INO suffix which in Italian means a small that got hijacked by physics and this INO started to become a fermion so you have things like a charginos and neutralinos and supersymmetric theories which are not small and not very light but they end in INO because they're fermions so this is what happened in 1932 in 1934 Fermi did something much more important than just calling the neutrino something he actually wrote down a theory for weak interactions so the first theory of weak interactions was written down by Fermi and it's a very, very crazy theory it's revolutionary and it's still the way in which we think about these processes today so again this is in the early 1930s people knew about electromagnetism very well we were starting to develop in a quantum electrodynamics and in particular, people knew how to describe say electromagnetic processes and there's a class or a large class of electromagnetic processes that you can describe by what are called the current-current interactions so hopefully that's vaguely familiar to people so Fermi said I want to describe these weak decay processes and I also want to use a current-current interaction language except that he invented what's called a charged current and basically he invented a physics process through which the nature of the particle could change with the physics process so basically the electromagnetism current that you know about is like an electron-electron current talking to another electron-electron current and we say that it works like that but effectively it's a current-current kind of interaction this electron current has a JMU nature to it this has another JMU nature to it and the coupling of that is the thing that you add in your perturbation theory so he wanted to do something similar except that he allowed for these currents to change the kind of particle and in particular he said that you know maybe there's a physics process that looks like this where a neutron magically converts into a proton and then it talks to another current that looks like this so again and we don't know what's going on here but this is what he postulated so the key thing was that he took this idea here and he generalized it in this really weird way where somehow one kind of a particle could disappear and then a different one would appear and you should be very impressed by this because this is very very non-trivial we were already accustomed with for example photons appearing out of nothing we knew that that could happen but again the photon is special it's a boson, it doesn't have any mass all kinds of interesting stuff are associated to photons we also grew accustomed with the idea that you could create a particle antiparticle pair out of the vacuum so again you could have a physics process where two things collide and then any plus any minus come out and we also grew accustomed to that idea but that's not too crazy because again we also know that a particle and antiparticle can annihilate into energy so again it just means that energy can transform itself into a particle and an antiparticle pair this is a qualitatively different idea but not super crazy idea but it just means that it is possible to destroy one kind of particle and create another kind of particle so this is what Fermi did so he wrote down a very very famous Hamiltonian which we still use today and this is again in 1934 we didn't know what kind of a current this was and this is another piece of history which took a very long time to figure out so again when I say kind of current this is a vector current people were smart enough they already knew you could have a vector current a pseudo scalar current an axial vector current, a tensor current they had classified all of those and we didn't know what kind of a current that was and curiously enough it took about 20 years to figure that out just because the measurements were hard to make so experimentally that was a big problem to solve but nonetheless what's really nice about the Fermi theory is it allows you to do calculations because now it's a theory so you can actually calculate stuff and in particular since you can describe beta decay and you can do a calculation of that you can also calculate other things and in particular you could calculate let's say this physics process here and you could calculate the cross section for that or what's the likelihood that a neutrino will hit something produce a positron and a neutron and we'll come back to that reaction in just a second but the first thing that happens is if you calculate the cross section for that which is the likelihood that this will happen the cross section is laughably small it's super, super tiny so what people said at the time was that okay good, the cross section for this is so small we'll never, ever, ever get to measure this, ever there's a lot of stories about that one is the first estimates were a little bit wrong the cross section was maybe an order of magnitude bigger which is still very small the other thing that happened is there's a story that Pauli made a bet that nobody would ever see the neutrino that he had invented he lost the bet but he almost won and it's very important to keep this in mind you know the neutrino is invented in 1930 the first time somebody saw a neutrino do something was in the mid 1950s which is 25 years later this was almost as long as we had to wait to discover the Higgs boson okay just something to keep in mind anyway so that's what was going on there and I want to mention a couple of other things that were happening at the same time because this will be important for us in a second one is this is in 1930 oh I forgot to say by the mid 1930s we had given up the nuclear physics model from the 1920s and we had a much better model which was to say that nuclear made out of protons and neutrons and then the neutron would decay in that way so that would explain the beta radiation without you having to put a bunch of electrons inside of the nucleus as well and that model works much much better so we even believe that that's true today the nuclei are mostly made out of protons and neutrons and of course once you postulate that the next step is to understand how the protons and neutrons talk to each other to stay bound inside of a nucleus and that's what people were working on and of course we knew about electromagnetism and you probably have noticed by now if you keep studying particle physics is that everything kind of looks like electromagnetism right because that worked so well it must be true for everything else so that's what our people were working on let's postulate that there is a force between protons and neutrons which is kind of like electromagnetism except that it is very very strong at very short distances because it has to be stronger than electromagnetism to allow the protons to bind together because the protons like to repel but of course we know that if you take one proton and you shoot another proton at it whatever this force is for the most part it doesn't do anything because the protons are so far away so if two protons are very far away they will talk to each other via electromagnetism they will not talk to each other via this strong force unless they come close together so there is this very very famous theory by a guy named Yukawa in Japan where he postulated that you had something like a Coulomb potential that explains how protons and neutrons bind together except that that interaction has a short range so instead of having a regular Coulomb one over R potential you have a one over R potential multiplied by an exponential and you could guess the strength of the exponential by the range of this nuclear force and by looking at the range of the nuclear force you would get a number out of that and that number can be associated with the mass of whatever particle it is just like the photon that mediates electromagnetism there would be a new particle that mediates this nuclear force and the mass of that is proportional to the range of the nuclear force so what Yukawa did in 1935 was to postulate or to estimate what's the mass of this new particle and the mass was pretty heavy but not too heavy it was about 100 MeV you can get that just by measurements of the nuclear force and that particle with a mass of about 100 MeV was called a meson so do people know why a meson is called a meson? do you know what mesons are? because people are too young nowadays so you've heard the word meson so why is it called a meson? yeah what's that? yeah so the mesons have a mass which is in between the proton mass and the electron mass it's kind of in the middle so it's called a meson it's a really stupid name it's also stuck and we use that so Yukawa postulated that and the thing which is very amazing and amusing is that one year later people actually discovered a new particle doing cosmic ray experiments and the mass of that particle is 100 MeV which is absolutely amazing so imagine that you're Yukawa and you postulate a new particle that weighs 100 MeV and then the year next year somebody discovers a new particle that weighs 100 MeV which is really cool except that people are very confused because that particle didn't do the right thing so that particle was discovered in cosmic rays and you can actually measure that particle here or by the ocean which is more pleasant you can do the experiment there and you see those particles there and people figured out that those things were produced in the atmosphere about 50 kilometers above us and that was very strange because that particle really liked to talk to nucleons to protons and neutrons and nuclei in general because it was the mediator of this nuclear force so how can those things get all the way from the upper atmosphere down here people had no idea how that happened it was very strange because that particle you actually got the right amount of those particles by any estimates that you can make but somehow that particle wasn't behaving properly after it was produced so this is very very strange and it was a mystery for about a decade and the solution to that is a very strange solution which is to say that the cosmic rays are coming from somewhere they hit the atmosphere they produce the eukala meson but somehow the eukala meson decays really quickly into a new particle so this is the model so the eukala meson is now these called the pion and then the pion would decay into a new particle and it turns out it's a two-body decay it looks like that so this was the hypothesis that was put forward again it's a really really stupid hypothesis because it's very simple it's also right so this at the time was called the two meson hypothesis so the new particle that people had actually measured was a muon not the pion which is the eukala meson so it's kind of a weird story it took about a decade to figure this out and the way that this was resolved by the way was also experimentally so again the idea is a theoretical idea this was resolved by experiments and the way that you do that is that you go high up in the atmosphere and then you could see the pions directly from cosmic rays so this is kind of what happened and then of course what people did is that they discovered the muon then they started measuring the properties of the muon the muon was not a strongly interacting particle it only interacted via electromagnetism so as everybody knows the muon is more like an electron than a pion and then people figured out that the muon also decayed and it decays in this way and I'm always using this modern notation but we'll come back to this again the muon it turns out has a decay that looks a lot like beta decay so the muon would decay this way they also figured out that the pion decayed that way which is also kind of like a beta decay it's a two-body final state beta decay but these are all different manifestations of the strong interactions the weak interactions and the other thing that people figured out was that all of these different processes could be explained by the equivalent of a Fermi's theory up to order one factors that we only figured out a very long time after that but that was also a big deal because it gave some universality nature to this weak interactions so it's not like there's one kind of weak interactions for pion decay one kind of weak interactions for beta decay and one kind of weak interactions for muon decay but these are all manifestations of the same interaction okay so again this is what was going on in the 1940s and there are a couple of things so let's go back to talking about neutrinos and the pions are going to be important for something else and remember we got over here to the mid-1930s we could calculate the cross-section for a reaction that looked like that and we figured out that the cross-section was super small so people said okay we'll never be able to detect this and then something happened so we're getting to the 1940s and as we are very well aware something very special happened in the 1940s in the early 1940s and the big thing that happened was we had a big war there was a world war that was going on and that turned out to be very important for neutrino physics because what happened was even though this cross-section was super small if you had a powerful enough source of neutrinos you could make up for that and that's kind of what happened so I'm skipping this so there was a serious campaign to try to observe the neutrinos directly again using that reaction over there and the motivation for that was that people had figured out ways of getting very very intense sources of neutrinos so this is the thing which is qualitatively different and neutrinos was first discovered in 1956 and by the people associated to that Rhinus and Kaun they actually got the Nobel Prize for discovering the electron neutrino and neutrinos are ultimately discovered in a reactor experiment and again reactors are a side effect of the Second World War basically a reactor is a place where you put a lot of radioactive material and they just do what they're supposed to do and of course we use them to get energy out I do want to say that the first proposal that Rhinus and Kaun made was using a different kind of neutrino source and this was only a proposal it's a really cool proposal and what was also going on at the time sadly was that people were getting good at building nuclear weapons and it turns out that the explosion of a nuclear bomb is an amazing source of neutrinos so if you want to get a lot of neutrinos you should go right next to a nuclear explosion to do your experiment this is the idea this by the way was from a proposal at Los Alamos and the proposal was encouraged but never funded because it had some problems but that's the idea so on top of that tower there's a nuclear bomb that's going off at the time the United States was doing a lot of tests so there were these explosions going on in the desert somewhere and the idea is you place your detector relatively close to the explosion because the neutrino flux is very large so that's the main idea now the technical problem is you need to make this measurement while there's a big explosion going on which makes it for a very very difficult measurement to make so they had a really good idea which they never tried out is that in order for you to avoid the explosion you wanted to have your detector in free fall which is a good idea because you have to figure imagine that your detector is falling the ground is shaking and all kinds of bad things are happening but your detector is just falling so it doesn't sense all of that shaking that's going on at the same time and then of course you make it land somewhere nice these feathers and foam rubber and hopefully your experiment will survive so they never got to do this experiment by the way nobody ever did as far as I know get to measure the neutrino flux from nuclear bomb which is probably a good thing so instead they did the experiment with a nuclear reactor and a nuclear reactor is like a really inefficient nuclear bomb that just blows up very very very slowly so it's almost as good you get a very large flux of neutrinos coming from the nuclear reactor and the neutrinos were actually measured using this reaction here and I want to talk about that for just a minute because we still measure neutrinos this way today measuring neutrinos is still very hard so this reaction is a very famous reaction where the neutrino comes in it hits something so whatever that something is it has lots of protons in it so that part is easy we can get lots of protons in lots of different ways and then it converts the proton into a neutron and you get a positron so it's kind of the inverse of this reaction here this is sometimes called the inverse beta decay because you're converting protons into neutrons and from an experimental point of view your signal is a positron that's what you see positrons are nice because they will annihilate with some electron in the medium and they will give you some gamma rays and you can measure the energies of the gamma rays the big challenge for this is even though your nuclear reactor is a good source of neutrinos you still need a gigantic detector to measure this so you need a really big detector that sits there close to your nuclear reactor and the problem is at the same time there's all kinds of other junk going on that will look like a positron and remember the positron is not really a positron it's just some electromagnetic energy that's detected in your detector so basically it's like a blip it's like a count in your detector of electromagnetic radiation so lots of things look like that for example gamma radiation from nuclear decays looks exactly like this all kinds of junk look exactly like that so the question is how do we get around this in order to detect that this is the reaction that's going on and not just some slow gamma decay process there's no slow... so nuclear physics processes that will mess this up the solution turns out to be the neutron so this process here gives you a positron and a free neutron and what people figured out is that the free neutron will move around in your detector until it gets absorbed by some nucleus and then the nucleus will be in some excited state and then it will emit some gamma radiation and what's really nice is that the neutron has a characteristic time that it takes to be captured by the medium that's easy to understand the neutrons that come out of this are relatively hot meaning they have a lot of energy that means they have to move around a little bit to lose energy until they get captured by some nucleus so there's a characteristic time associated to that so you basically get this really nice signal which is you see a signal from the positron you wait a fixed amount of time and then you should see the signal from the neutron being captured and then giving you gamma radiation so this is what's called a coincidence signal which means that not only do you see this but a little bit afterwards you have to see that and nuclear physics processes in general don't look like that so by looking at this coincidence here you could get rid of your nuclear physics backgrounds and then you could discover the neutrino and this is what they did in the 1950s I forgot to mention this I guess I didn't write it on the slide if you want to learn more about this there was a first measurement in one nuclear reactor that they weren't very sure about then they moved to this other nuclear reactor in Savannah River and that's where they made the discovery this whole enterprise is called the Project Poltergeist so you can look that up it's a really cool little history there and they wanted to see something that was impossible to see and by the late 1950s Pauly had lost his bet I think he paid like a bottle of champagne or a case of champagne to somebody I'm sure he didn't mind so that was it okay so continuing the story there's something interesting that happens in the late 1950s as well is that people managed to measure the spin of the neutrinos and they also managed to measure what's called the Helicity of the neutrino and I'm not going to talk about this very much this is in 1958 there's a very clever nuclear physics experiment where you have this nucleus called the Europium it undergoes weak electron capture that means it captures an electron converts into another weird nucleus like samarium and emits a neutrino and the samarium immediately decays into a photon so if you look on the left hand side you have electron going into samarium plus a photon and because we can measure the photon polarization and because I wrote something wrong the ground state of samarium has no spin by measuring the polarization of the photon you could infer the polarization of the neutrino that's being emitted as well and the only reason I'm talking about this is that people figured out that neutrinos not only had spin one half but in reactions where neutrinos are produced the neutrinos are always 100% polarized so the neutrinos are always left-handed anti-neutrinos are always right-handed in those experiments it's always a charge current interaction is there in general a possibility to measure the helicity of a neutrino in neutral current? that's a very good question yes we can we try to do that and it's very difficult it has to also come from neutrino scattering and we can do neutrino scattering via so let me qualify that a little bit better so it's very very difficult to measure the helicity of the neutrino from a neutral current interaction for the following reason if you want to do a neutrino scattering experiment the neutrinos are always produced by charge current interactions which means that your beam is going to be 100% polarized so if you have 100% polarized beam even if you do a neutron scattering experiment afterwards your beam is in quotes polluted because it's 100% polarized but we can still measure that so we can measure the strength of left-handed neutrino scattering on for example an electron so let's say you do new mu scattering on an electron that's a purely neutral current process so if you do this process here that's a purely neutral current process and people have measured this as well as they can there's a couple of experiments there's a charm 2 experiment that did a pretty good job of that so you have a 100% polarized new mu beam and you can measure the strength of this it doesn't tell you about the helicity of the neutrino because you have a 100% polarized beam however we can then measure for example z decay and from z decay we can also measure the strength of the coupling of the neutrino to the z boson that measurement doesn't know that the neutrino is left-handed they could have been 100% right-handed but if you compare this with the z decay for example and you compare the strengths of that the strength of the z decay is as strong as the strength of this purely left-handed new mu scattering process so you can infer relatively indirectly that the neutral current is also purely left-handed but it's very difficult to get good information on that because the neutrinos are always 100% polarized in the initial state and we have a couple of other handles but that's the answer to that very good, that's a great question and we'll come back and talk about this more so again this is 1958 then in the 1960s people came back to looking at the muon this is another great story which is very very important to know which is again I said the muon was discovered in the 1930s there's a big gap in particle physics again because of the Second World War when people were busy doing other stuff and then when they came back by studying properties of the muon first of all they figured out that the muon decayed this way and they also figured out that the muon really did look like a heavy electron so the muon was the first second generation particle to be discovered there are lots and lots of stories associated with the muon the most interesting one that you want to remember is when people figured out that the muon was a heavy electron there's a very famous quote that says who ordered that which is the interpretation is what are muons good for why would anybody invent this we still don't know what the answer is but that's to a quote and the key thing about muons is if the muon really is like an electron but heavier the first thing that people thought when they were trying to understand what a muon was was to say that maybe the electron is kind of like a nucleus and maybe the muon is an excited state of that nucleus that makes up the electron so the question that people thought was so why doesn't the muon undergo gamma radiation so why doesn't it do that it's a fair question to ask nuclei know how to do this so why doesn't the muon do that and people started looking for this decay the muon going to an electron in a photon and they never saw it so they put a bound on the likelihood that this happens and let's say that they got to like 10-2 a percent 0.1 percent and they say okay so this model is not a good model but now let's go back to how the muon decays this way and we can draw a Feynman diagram for that it's a diagram that looks like this and it goes like that so people said okay so the muon decays this way and it's certainly not going to undergo gamma radiation kind of decay but one thing I can do is here's a neutrino, here's an anti-neutrino I can close a loop here that goes like that and then I can attach a photon somewhere and then I get to do this decay okay I can do this calculation and people did that and the branching ratio that you estimate just by knowing about regular muon decay was a branching ratio of about 10 to the minus 4 which is small and people kept doing experiments with muons and they figured out that this did not happen at the 10 to the minus 4 level and just as a spoiler alert we keep looking for this if you don't follow this literature we know that this doesn't happen at the 10 to the minus 12 level which is super small okay and we have never seen this happen before so the puzzle at the time was why doesn't this happen? I mean it has to happen right you know that's a it's a simple thing that you can do in a Feynman diagram calculation and in order for this not to happen people invented what's called the two neutrino hypothesis and the idea was to invent a new quantum number so you basically look at this reaction and you say okay this never happens there must be a reason for this so you invent two new quantum numbers one is called the muon number the other one is called the electron number so the muon has muon number 1 the electron has muon number 0 the electron has electron number 1 and the muon has muon electron number 0 so this is forbidden by electron number conservation and muon number conservation of course the muon has to decay this way which means that the two neutrinos that come out have to carry different quantum numbers so this one has electron number and this one has muon number that's why they get these indices like that and that explains how the muon can decay and the price you pay for this is that now you have two different kinds of neutrinos the electron neutrino and the muon neutrino so that's the two neutrino hypothesis it was invented or people came up with that to explain why mutoid gamma doesn't happen that was the reason for that and how do you test this experimentally the idea is relatively simple as I am sure everybody knows the pion really likes to decay this way and it never decays to electrons so the pion decays this way into a muon and the neutrino because of this muon number conservation this neutrino hears the muon neutrino so if I could do an experiment with this guy so imagine that this guy comes in and it hits something if it does that it has to produce a muon and it never produces a positron so this is the experiment you want to do you want to make a beam of these neutrinos this is what's written over here so you shoot protons on a target oh this is wrong you shoot protons on a target you get a bunch of pions the pions decay and then the muon hits something and then you ask what happens at the end do you only produce muons or do you actually produce electrons the answer is people did this experiment in the early 1960s and they figured out that you never ever produce an electron you always produce a muon and one thing you want to keep in mind is of course the electron is lighter than the muon so if the reaction on the bottom could happen it would happen more frequently so that means that by doing this experiment you actually convinced yourself that the muon neutrino and the electron neutrino are different particles this is another Nobel Prize winning experiment by Letterman, Steinberg and Schwartz and I wrote Schwartz wrong it ends with a Z for obvious reasons it was done at Brookhaven and I am told that Schwartz was the guy who did the whole work who did all the work he was also a graduate student so keep that in mind and this experiment is famous for lots of different things the most important thing is that they invented a neutrino beam so this is a beam of neutrinos that all go in the same direction more or less and we still produce neutrino beams exactly this way and that's probably the main reason they got the Nobel Prize other than convincing everybody that there are two kinds of neutrinos there's a joke people like to tell which is the Nobel Prize for the muon neutrino came before the Nobel Prize for the electron neutrino which means that the second neutrino got the Nobel Prize before the first neutrino did finally to end this part of the story what happens in the 1970s is that we discovered a whole bunch of new particles in particular we discovered the tau lepton the tau lepton is like the muon and the electron but it's heavier and immediately people postulated that there must be a third kind of neutrino called the tau neutrino and the tau neutrino must also be able to interact with stuff and produce a tau lepton and this was discovered only in 2001 so this is also something to keep in mind so direct evidence for tau leptons only showed for tau neutrinos only happened this century not last century and I always like to say this is seven years after the top quark was discovered so the last fermion to be discovered was the tau neutrino not the top quark by a lot this was actually discovered at Fermilab the idea is very very similar you want to produce a bunch of these tau neutrinos and you want to see them producing a tau lepton studying tau neutrinos is very very hard one thing which I want to say is if we look at the world's neutrino data today or up to today and we ask how many tau neutrinos we have ever seen do this hard core evidence that this is what was going on the answer is we've seen about 10 of those ever okay we have a lot of indirect evidence for tau neutrinos but to identify a tau neutrino event one by one I think we've seen about 10 of those so keep that in mind it's not the particle we know the best and these are really cool experiments so I want to say something about those that's not it this is how you look for tau leptons the idea is really nice because what happens is you have a you have a tau neutrino comes in it hits something and it produces a tau now what happens with the tau is the tau lifetime is long enough that it can actually propagate a little bit before it decays and one of the tau decay modes is into a muon so the tau goes this way just like the muon does so you see the tau it propagates a little bit and then it decays into a muon and what's nice is you get something that's good to look for which is a signal that looks like this so a neutrino is coming in from over here nothing happens it hits something produces a tau and then the tau moves a little bit and then it decays this way and this is the muon so here's a tau here's a muon and all the neutrinos are invisible and this is the experiment that you want to do and of course this is one event this is another event again the tau is moving over here it decays into a muon and some neutrinos that you don't see there's another one over here then there's another one over here and this is almost all the events of the donut experiment that's it that's all the events one thing that you want to appreciate is that your detections are actually these are red points and the green points so you have to reconstruct these trajectories to identify these kinks and what makes these experiments super hard is in order to have this tau neutrino beam you're basically doing something very similar to this experiment you're shooting protons on a target you're producing a lot of junk and in order to produce a tau neutrino you need to produce something that decays into tau and the first thing that does that is a strange charm quark it's called a d sub s so the d sub s likes to go into tau and a new tau so that's how you produce your new tau beam sadly when you do that you also produce a whole lot of pions and kaons and the pions and kaons still decay and they decay mostly into muon neutrinos and some electron neutrinos so basically in order to produce a new tau beam even if you're super clever the fraction of the neutrinos that are actually going to be of the type that you're looking for is less than a percent so most of the neutrinos are going to be muon neutrinos and the muon neutrinos are very very similar to this event except that they don't have the kink instead of producing a tau and a muon they just produce a muon directly so that's how you distinguish your events and that's why this is a big deal I do like to show this picture because this is how your experiment really looks like this is a photographic experiment what this means is you don't see this in an event by event basis your tracks actually leave a mark in your experiment so every time there's a track you get a mark in your experiment so things literally look like this and the claim is that there's one of these interesting events there so the challenge is how do you find it and that's where the art of the experiment goes is how do you identify out of all of these tracks the track that you're looking for so there's this very complex process of cleaning out your this is an emotion detector which I forgot to say emotion is a technology that was used to discover the pion and cosmic rays and people got better at it but it's still the same technology it's still the same scientific plate this is the discovery of the tau neutrino okay and that's the end of this part of the story and now I want to summarize where we were with neutrinos and then I want to start talking about weird stuff that was going on in terms of data and of course I won't be able to finish that but just to summarize this is everything we knew about neutrinos by the end of the last century more or less if you open like a peskens book that's how neutrinos are discussed for the most part if you open an older quantum filtering book that's also how neutrinos are going to be discovered they're very easy one thing is they only interact via the weak interactions that means that they only talk to the W and the Z as far as we know and this is something that I already alluded to and there's even a question all of the neutrinos that are ever produced are left-handed all of the anti-neutrinos that are ever produced are right-handed now this is a side effect of the maximally parity violating nature of the weak interactions which you have heard about it's the V-A character of the current and there's nothing we can do about that but we can exploit it of course the neutrinos come in three different flavors the electron neutrino the muon neutrino and the tau neutrino are characterized by whom they talk to when they undergo a charge-current interaction so the electron neutrino talks to electrons the muon neutrino talks to muons the tau neutrino talks to tau's and so this is this piece here this is this other piece here the thing I want to come back to and talk about a lot is until very very recently we thought that neutrino masses were exactly zero and I'll come back to explain that probably by Friday and like I said all of the neutrinos are left-handed all of the anti-neutrinos are right-handed and finally the last thing which I'll also come back to is like I said the electron muon and tau neutrinos carry these conserved quantum numbers muon number, electron number and tau number and they also carry what's called a total lepton number and the idea is that neutrinos have lepton number plus charge leptons have lepton number plus they're antiparticles of lepton number minus and as far as we can tell this is also a conserved law of nature and I'll come back to this as well okay so for the last 10 minutes I want to start talking about what happened so and I won't have time to finish talking about this at all but what happened is starting out in the 1960s neutrinos started to do weird things so they were not obeying the laws that I was or the properties that I was describing in the last slide and this is a problem that did start out in the 1960s people didn't believe it for a very long time and it was only definitively confirmed in the early 2000s and it was a 50 year old problem that took a lot of convincing for people to believe that those experiments were actually correct okay and the evidence that we have is if you look at this picture here we found out that it's possible to produce an electron neutrino or a muon neutrino somewhere and when those neutrinos get detected they actually behave like a different kind of neutrino so we have evidence that muon neutrinos sometimes behave like tau neutrinos electron neutrinos behave like other kinds of neutrinos electron antinutrinos behave like something else and muon neutrinos also behave like something else if you allow them to propagate long enough so that was the caveat to the story is that if you do the experiment right away the neutrinos behave like they should but if you wait long enough they have this non-zero probability of behaving as a different flavor this flavor transition capabilities depend on the neutrino energy and they also depend on how much time you wait or how far away the source and the detector are so this is what we discovered and I want to start out by telling you about the oldest problem which is kind of a fun problem and that's probably where I'll stop today it's called the solar neutrino problem this is a very very old story it's a really cool story and it goes back to a very old physics problem that people had been pondering about for a very long time like you know hundreds of years ever since like Newton and the question is how does the sun work because the sun is a very very efficient source of energy right so somehow there's a lot of energy coming from the sun and the question is where is that energy coming from we believe in conservation of energy so whatever that energy is coming from we have to see it and one estimate that people did for a long time is they calculated for example the gravitational energy that's contained in the sun just by binding it and then they ask you know maybe that's the source of the power that's coming from the sun and that turns out to be totally wrong it doesn't work at all it's a very very tiny amount of energy so the answer to this problem only happened in the 20th century because of nuclear physics so nuclear physics allows us to convert mass into energy very very efficiently so the sun is basically killing itself by converting its mass into electromagnetic radiation and that's how the sun works and it's so efficient that the sun has a really long lifetime even though it's destroying itself it'll take a long time for that to happen so we all know about this it took people a long time to figure out how does this happen in detail and the model that won is this thing called the proton fusion so the interior of the sun is very very dense and what happens there is that two protons can fuse into deuteron a weak process by the way so you get a deuteron you get a positron and an electron neutrino other stuff happens at the end of the day you end up producing a helium-4 plus electromagnetic radiation that's most of what's going on in the sun if you want to think about it four protons come together then fuse into helium-4 two positrons and two neutrinos and a lot of electromagnetic radiation now the thing that's really important is that you get these neutrinos and the neutrinos come out because they don't interact very much so that means that at the same time that you're producing this electromagnetic radiation you're also producing neutrinos by the way other stuff also happens you don't just produce helium-4 you produce other elements as well and in all of these processes here you're producing electron neutrinos so if this model is correct the sun is producing a whole lot of electron neutrinos along with the radiation so if you wanted to test this you should try to measure these electron neutrinos coming from the sun that was the idea so the question is how do we do that the answer is it's super hard because the flux of electron neutrinos is not huge it's large but it's not gigantic and the neutrinos are neutrinos and the neutrinos are neutrinos so that's the other part of the problem there are lots of stories associated to this which I won't get into the details but we can we're very predictive on this and this is a calculation of the differential flux of neutrinos coming from the sun and oh this button is weird and this is the this is the neutrinos that come out for the most part this is a lot of neutrinos but they're very very low energy neutrinos and these are all the different kinds of neutrinos that come out these neutrinos all get names and they have to do with what's the physics process that's going on inside of the sun that leads to these neutrinos and the key thing we want to remember is that the energies are below about 10 MeV and most of them are super low energy what this thing here also contains is different kinds of experiments that people constructed in order to measure the flux of neutrinos from the sun and these experiments use different techniques and the way that the earlier experiments worked was that you wanted to detect neutrinos by beta decay so remember this is beta decay so you want to do inverse beta decay which is a process that looks like this so this is what you want to look for this is a prime so it's one nucleus that gets converted into another nucleus so that's what you want to measure now this is a very hard experiment for lots of reasons one reason is your signal is an electron which is a really horrible signal you don't look for that in all different kinds of experiments some of the experiments look for this this nucleus that's appearing inside of your experiment and the very first experiment was done with chlorine and the experiment is very simple it's a very very very big tank of chlorine now chlorine is very easy to get you can go to the supermarket and buy chlorine that's your experiment so you take a gigantic volume out of chlorine you build a very big tank inside of a mine that was done in South Dakota and the United States it was a gold mine at the time so you build this gigantic tank that's the size of a very big swimming pool you fill it up with chlorine you can't do pure chlorine it's some chlorine mixed with hydrogen and other stuff and then the neutrinos come in they hit the chlorine and they convert it into argon which is good argon is a noble gas that means when the argon is produced inside of your chlorine tank it just kind of sits there so you then filter out the chlorine and then you get the argon atoms out the other thing that's very very nice is that the argon that you produce is a radioactive kind of argon which means it decays after a certain amount of time that means that you basically have this big tank you produce a argon inside of the big tank and you filter it you get the argon gas out and then the argons decay and then they let you know that they're there and that's nice so this is the experiment that started off in the 1960s and the key thing you want to remember and that's the last thing I'll say is that they did this experiment and this is a really really crazy experiment because they would filter and make measurements let's say once a month and out of this big swimming pool of chlorine they would get that's it, that's your signal so it's 10 atoms per month out of a swimming pool of chlorine they actually did the experiment they did get a signal and this is also a Nobel Prize winning experiment by the way and this is the first measurement of neutrinos from the sun and the thing that's very important to remember and that's where I'll start tomorrow is even though they made this measurement the number of events that they get was about a third of the number of events that they expected so they see a lot fewer neutrinos from the sun than they expected so the good news are they actually see neutrinos coming from the sun which is an amazing measurement by itself the bad news are that they don't see as many as they expected and then what we're going to do is to talk about what does that mean starting next time and I think that's exactly time so good