 OK, I guess we can start now. So hello, everybody. My name is Roberto Lineros, and I'm going to be the host of this 14th webinar on this series of the Latin American Webinar for Physics. And today, we are going to have a very interesting talk that is relating to a testing fundamental symmetries like Lorentz and CPG. So before to start with this webinar, interesting webinar, first I have to remind you that you during the webinar, you can make questions that at the end of the webinar, we are going to answer, Jorge is going to answer, or guest. And you can do it via a Google Q&A system that you can see something around here with the Q&A, and also be a Twitter. You can see that. In any case, if you want to contact us or if you want to propose a webinar or a topic that we can do, so you can use Gmail to email and Twitter. So let's start now with the speaker. I'll have a little introduction about him. He is Jorge Diaz from the Cultural Institute of Technology in Germany, where he is a postdoc in this institution. So he obtained a PhD in the Indiana University in the United States. And he's also very known, because if he's part of a science blog called Connection Causal. So the title of his talk is the Searching for Violation of Law and CPT's Invariance with Entreat. So Jorge, if you want, now is the camera for you. OK, thank you. So thanks for working with that. Can you introduction? I will share my screen now. If you want, you can share your screen. Yeah, I'm trying to do that. It's frozen right now. And it looks like I'm trying it. OK, so is that working? Yes, you can see it. Great. Well, thanks again, Robert, for that kind introduction. I will start with just with a very short outline of the topics that I plan to describe today. First of all, for all of you who are not neutrino experts, I will give a very short introduction to neutrino, mostly neutrino solutions. And then I will describe the main topic, which is the search for Lorentz and CPT violation. And then I will combine the two and focus only on neutrinos. So mainly I will describe experimental searches for Lorentz and CPT invariance using neutrino solutions, also using high energy neutrinos. And at the low energy part of the spectrum, I will also describe data decays. So as I mentioned before, for all of you who are not expert neutrinos, this is all what you need to know. Well, first of all, they are fundamental particles on the standard model. So this famous table that we are used to see, these are the three neutrinos that we take in this description of fundamental particles. As their name indicates, these particles have no electric charge, which means they do not interact with the photon. They're neutral particles. They only interact via the weak interaction if we neglect gravity, of course. Experiments at CERN, which is shown in this figure here, show that there are only three flavors that we call active. That means flavors that interact via the weak interaction with the Z boson. And finally, which is also very important, is to emphasize that in the standard model of particle physics, neutrinos are massless. So let's imagine for a minute that neutrinos do not mix, which means that the flavor states that we observe in nature have well-defined energy. And also, let's suppose a neutrinos are in fact massless, as the standard model seems to be the way in which it was constructed. That would mean that in this very toy model of only two neutrinos, they both will have the same energy, and it's given by, well, the dispersion relation for a massless particle is given here. And the propagation of these states will be described by the Hamiltonian, which I described with a big H here. This, since there is no mixing of this completely diagonal, and what would happen is that you create a neutrino state, say, for instance, in a nuclear reaction, you create your neutrino state and you let this neutrino propagate, for which we use the basic quantum mechanics. So the evolution of the state is given by the time evolution operator in terms of the Hamiltonian. And then, after some distance, we can put a detector and ask ourselves what is the probability of measuring that initial state. And it's given by this expression here. So if these two assumptions are correct, means that a pure neutrino state will propagate and will not be affected by anything. Now, this picture has a few problems, because as there are even cold problems, the famous solar neutrino problem and atmospheric neutrino problem, they refer to the idea that the experimental value and the theoretical value do not agree. In the case of the solar case, only one third of the neutrinos seem to appear on at least on our planet. In the case of the atmospheric case, only 60% of the amount that we expected to see is being observed. So this was a big problem for some time. Now, if we assume that neutrinos do not satisfy the previous conditions, first of all, that they mix. So this is represented in this figure here. So we have the two mass eigenstates and we have the two flavor states and we assume that they are rotated with respect to each other by an angle theta that we call mixing angle. So that is that the electron and the muon in this example would be linear superpositions of the mass eigenstates. We now create a neutrino state. There will be a combination of these two mass eigenstates and we can let this state propagate. If we let it propagate, we have to use again the Hamiltonian, but now we have the evolution of two waves and these two waves can interfere if they have different frequencies and we will generate this phenomenon of quantum bits. So well-known phenomenon in acoustics, but for the particle point of view, this means that we start with an electron neutrino and after some distance this electron neutrino can evolve a muon component. So the probability of measuring the initial state is now given by this expression here. It's no longer one. It's one minus this expression. So this amplitude is given by the mixing angle and on the face of this probability is given by the energy difference of these two states. So here is a very important thing. For this probability to be different from one, we need a non-zero mixing angle, but we also need the two energies to be different. So if neutrinos are massless, this delta E is equal to zero. So the fact that we observe this agreement between theory and experiment that we can explain through these oscillations means that there is physics beyond the standard model and we understand it in the form of non-zero neutrinomass. And this exactly solves the two problems, the solar neutrino problem. Now we understand it as a bunch of electron neutrinos created at the solar core and when they propagate, they will also date into the other states and we only observe one third of the initial flux. This happens with the atmospheric neutrino case. So here's our detector. Neutrinos coming from above and the point of view from the detector are well in agreement, as the data shows here, but the ones produced on the other side of the earth in the atmosphere, but on the other side of the earth, they have enough time to also date into other flavors and that agrees perfectly with the oscillation prediction. So we solve the problem, the case is closed and as you will probably know, in a few weeks, Arthur McDonald and Takahaki Kajira, in fact, receiving the Nobel Prize for this. So we know the neutrino's oscillate. That is very important. That is one of the main results that I wanted to stress. We know that all these types of neutrinos actually do oscillate, observe like many of these experiments in the past 15 years. And as you also probably know, the main leaders of all these experiments receive another award a few weeks ago. So now I will switch gears. That's all you need to know about neutrinos and let me check now about Lorentz symmetry. So first of all, Lorentz invariance, I like to call it a cornerstone of modern physics. This is because Lorentz invariance is the symmetry that underlies a special relativity. It is remarkably simple in the statement. Lorentz invariance tells us that the laws of physics do not depend on the orientation of our physical apparatus or the relative speed at which this is moving. Now the other symmetry that I mentioned before, even in the title is CPT. So these two are closely linked and that is important in the context of properties of modern nantime matter. So that's why I also included it here. And one point which is very important to mention is that so far there is no competing evidence of any violation of this symmetry. So if that is the case, you can ask, so why do we bother on studying Lorentz invariance violation? The idea is actually really old. There is even a paper by Durak in the 50s in which he talks about Lorentz symmetry violation. But in the past 25 years mostly, there has been this really growing interest from the community. One of the reasons is that it was shown in the late 80s that some descriptions for quantum theories of gravity involved the breakdown of Lorentz symmetry. Not only the strength field theory, but also other candidates, such as loop quantum gravity or non-commutative geometries and many others, they all involved this possibility so that triggered the interest of many people. From a more experimental point of view, the fact that Lorentz symmetry is such an important ingredient of the most successful theories that we have, I mean general relativity and the standard model, this should be tested. And since today we have high precision experiments, we should go for it. So this is a cartoon, which is the way that I like to see, that I like to explain this idea, at least the way I like to visualize it. So right now we have two very successful theories. We have the standard model of particle physics and we have general relativity. We know that those two theories are not the final theory. They should be just a low energy limit of a more fundamental theory. We don't know what the theory is yet, but we expect these two descriptions of nature to merge at really high energies. So we hope to high energies, we hope that one day we'll have some quantum theory of gravity. I'm not gonna commit myself to any of these candidates. I will just call it quantum gravity for now. And as I mentioned before, many of these candidates involve the breakdown of Lorentz symmetry. So if we suppose that there is a breakdown down here in the fundamental theory, maybe some low energy signatures could propagate and could be observable in our experiments today at low energies. So this is a picture that I would like to pass to you. And the next step is to explain carefully what Lorentz symmetry and what Lorentz symmetry violation really is, because there are a lot of misconceptions at this point. So here we have two diagrams, the one on top and the one on below. At the bottom of the other slide I describe a very similar situation. So on the left, I have a physical system. In this example, I have a particle with some magnetic moment. It is important to emphasize that there are two ways to perform a Lorentz transformation. In the first one, we transform the coordinates. It means the labels that an observer uses to describe the physical system. So in this case, I'm only using a rotation. This can also be extended to boost, but it's a little bit more difficult to visualize, but the idea is exactly the same. So in this case, on the figure on top, I apply a rotation on the coordinates. It means only the labels, and we call this an observer Lorentz transformation. Textbooks call this a passive transformation. I'm not gonna use that name for a reason that will be clear in a second. The figure on the bottom is we start with the same situation, but instead of applying the transformation in this case, the rotation. To the coordinates, we're gonna transform the physical system in this case. I'm rotating the magnetic moment of this particle. I am doing this by, for instance, by rotating the experiment and rotating the table in which I have this system. We call this a particle Lorentz transformation because as the name indicates, it's a particle. It's a physical system, the one that is being transformed. Now, when there is no difference between the system before and after the transformation, we say we have a symmetry. Notice that the symmetry is associated to the particle transformation, not to the observer transformation. So let's now include a background field. And as an example, following the example of the magnetic moment, I'm including a magnetic field which is represented by the red arrows in the background. And one thing you can see is you can apply the same transformation. And of course, in this case, the observable quantity, for instance, the energy of the system doesn't change because when we apply this rotation to the coordinates, both the components of the system, in this case, a magnetic moment, and the components of the background field transform in opposite ways so that the interaction is completely invariant under this transformation. This is something we expect because this is just a coordinate transformation. Nature doesn't care about the coordinates we pick. However, if we apply now a particle transformation and we assume or we take the definition of background field, which means that it remains completely unchanged, of course, now we have a observable quantity that can distinguish the two systems. We say that we have a broken symmetry. This is something that should sound obvious to all of you. This is what we do, for instance, in quantum mechanics, basic quantum mechanics when we teach our students about, for instance, the Zeeman effect. We put a external magnetic field and we have an observable quantity or effect which is the spring of the spectral lines. Notice that the coordinate invariance remains, so the system remains invariant under this coordinate transformation, but if we can rotate, in this case, the system, say the electron, for instance, that I have here, we would distinguish the two systems. So we talk here about a broken symmetry. So this is the important key. The key point of this part is the symmetry that is broken, in this case, is invariance under rotations when we apply a particle transformation. That is a transformation that leads to a symmetry or to a broken symmetry, in this case. The coordinate invariance remains all the time. So once I say that, we can not extend all this, not only to rotations, but to all types of Lorentz transformations. And if we want to construct a very generic way to do this, we use what is called the standard model extension. This, or SME for short. This SME is a very genetic way to construct the most general theory that includes Lorentz symmetry violation. The way this is done is take the standard model of particle physics, if you want, you can couple this to general relativity and you add, at the action level, all the terms that will break Lorentz symmetry. Here I have an example, just to show how this is not only with words, here's an example, this is taken from the fermion sector, for instance. In parenthesis here, we have what we call the operator. The operator is constructed only using standard fields, so there are no new particles in this description. In front here, this little a mu quantity is what we call a coefficient for Lorentz violation. This is a controlling coefficient that basically controls the size of this violation and this little a will play the role of the magnetic field in the example of the previous slide. So it will be like the arrows in this cartoon here. In principle, this is a vector field where you can have any generic tensor field. Notice that the whole thing that we add to the Lagrangian is a observer scalar, which means it's invariant under coordinate transformation. This is sort of obvious by looking at the spacetime indices which are all properly contracted. And one very interesting feature of this is that every time you introduce operators with an odd number of spacetime indices, that you are basically introducing terms that break Lorentz symmetry, but also break CPT. So CPT is a subset of Lorentz, CPT violation is a subset of Lorentz violation and everything is already contained in this SME. I don't like to go through all this list just to show you how relevant this SME has been for studying CPT and Lorentz violation in many, many different kind of physical systems. It's a conference every three years that gathers mostly experimental, there's a lot of theories too, but mostly experimental results every three years. The next one will be next year. So now we'll move from the SME and I will only focus on neutrinos. So here is one of the not many equations that I plan to show. And this is how we describe neutrinos in the SME. So this is the Lagrangian. The first two terms are the conventional direct-looking terms for a fermion field and this Q hat here represents the Lorentz violation part. So this is the SME part that breaks Lorentz symmetry. The big sigh here is just a spinor that contains all the relevant neutrino fields. We have the three flavors. And although it's a little bit redundant, we have also included the charge conjugates of the fields. They both contain the secretary same information, but this kind of a structure is very useful because allows you to separate direct couplings from myeronic couplings. The Q hat part, this term, can be in general expanded as a series in terms of, in a basis of gamma matrices. So there is no surprise here. We have scalar, pseudo scalar vector, axial vector and tensor components. And just as an example, again, I don't want to show all these terms because there are many of them, but as an example, the vector part can be written in this way. This is in the minimal case. You can see the hat indicates that in principle, this can be operators, can be any number of derivatives there as long as you contract indices properly. Everything will be okay. So we take this Lagrangian and we go through many steps because we only want to extract the parts that is relevant for the physics, meaning we only want to have, for instance, left-handed neutrinos and right-handed anti-neutrinos and things like that. And once you do that, you can construct the Hamiltonian. You start the Hamiltonian and you get something like this. So since we are describing three flavors of neutrinos and three flavors of anti-neutrinos, the effective Hamiltonian takes the form of a six-by-six matrix. Here is separated into two parts. The first part is the conventional Hamiltonian. The first block is for neutrinos. The other block is for anti-neutrinos. And this is all the Lorentz-Baudetting part, where, again, we have the neutrinopart, the anti-neutrinopart. And there are also neutrinos and anti-neutrinomics in parts. This is a new part. And just to show you again, as an example, one of these terms, I will take the minimal neutrino three by three block. So I will take this block. By minimal, I mean that only operators of dimension three and four have been included, although, in principle, you can include any of them. Everything or no minimal terms can be found in this paper. So this is the Hamiltonian for a Lorentz-Baudetting neutrino in the SME. So the first two terms are the conventional terms that you get even in the absence of Lorentz-Baudetting. So the first is just a term proportional to the neutrino momentum. Then it's the mass term that produces oscillations. And then you have the new things. So the colorful terms are these coefficients, these sort of background fields. In blue, you have the ones that contain only one space-time index here. So these terms break both Lorentz symmetry and also CPT. The ones with even number of indices, the space-time indices break only Lorentz symmetry and they preserve CPT. The A and B are flavor indices for our electron neon-town neutrinos. And you notice that the Lorentz-Baudetting part introduces unconventional energy dependence, that means non-negative powers of the energy. There will be also some direction dependence. Notice that everything is contracted with this p-hat. P-hat tells you about the direction of which the neutrino is propagating. So this is telling you that the invariance on the rotation has been broken. There will be some effect called so ideal time dependence, which I will come back in a minute. And this happens only for experiments in which both the detector and the source of the neutrino are on the surface of the earth. There is CPT violation, as I mentioned, and as I also mentioned before, there's the possibility of neutrino to neutrino mixing due to this off-diagonal block, which is absent in the conventional case. So these are the effects that we get and now how we look for them. So one thing which is very important is that if we are really looking for something as important as the breakdown of Lorentz invariance, which I like to represent by this very nice cartoon from SMBC, so if I call this section here, this goal here to be Lorentz violation, if we're gonna look for that, especially if you're gonna ask our friends in the experimental community to look for this, we better have a plan. We want to know, how lecturers have some sort of systematic way to look for this. So this is exactly what is represented on the right. So this diagram here separates all the effects in the neutrino sector of the SME, depending on which kind of experimental signals you would expect. So the first separation has to do with whether or not they produce mixing. So the ones that produce flavor mixing will lead, of course, to neutrino solutions and we can look for this in different kind of experiments, which is exactly what I'm gonna describe right now. So this is related to one of the most studied kind of signatures of Lorentz violation and is what I mentioned before about this ideal time variation. So suppose you have your neutrino detector. This case, this looks suspiciously like the minus detector. You have your neutrino beam coming from your source. You, and here you're gonna hit the detector, you put your local coordinates, X, Y, and Z and you make a measurement in this frame, but if you really want to compare observations from different experiments, you have to do it in a regular way, in using a consistent reference frame. So for this, we use what is called a sun centered frame in which the Z axis points along the direction of the axis of rotation of the Earth. The X axis, big X, points in the direction of the vernal equinox. So we borrowed this from astronomy and the Y axis is, of course, we get it by a Z cross X. So this represents here the Earth, your experiment is somewhere, so here are your local coordinates, the one here, are now somewhere on the surface of the Earth at some collatitude, they call chi, and since the Earth is rotating at a given frequency, so this angle here is omega t, where omega is the cellular frequency of the Earth. We know exactly what the frequency is. That means that your lab is in fact rotating. So as I mentioned before, you would like to perform a particle Lorentz transformation. You would like to rotate your system. Now rotating a neutrino experiment is not an easy thing to do. However, the Earth does it for you for free. Since the Earth rotates, and we have these background fields that are feeling the universe, which are represented by these coefficients. So again, here an example, you're assuming like a vector field. If the Earth rotates from the point of view of the experiment is this arrows in the background which are rotating. And we can quantify the irrelevant observable in terms of harmonics of this frequency. So this expression down here represents the irrelevant observable for neutrino oscillation experiments which is the oscillation probability contains a constant part and then terms that go with harmonics of this quantity omega t. Where t is the time when you make the measurement and omega is the cellular frequency. It is not the solar frequency as we don't care about where the sun is unless you're playing with solar neutrinos. But for experiments on the Earth, we don't care about the solar frequency. This is the cellular frequency which is differs from the other by tiny fraction. The period is only a difference of four minutes. But it is very important. So here's an example. This is a paper that we wrote a few years ago in which we propose how to look for this effect using a beam experiment. So this is the, this is Fermilab, this is Fermilab campus. There's this main injector that accelerates protons. You hit a target, you produce a lot of particles which in turn produce a beam of neutrinos that go all the way to Minnesota. So they traveled 735 kilometers and since the direction is very well defined of this neutrino beam, we computed the probability which is given by the conventional probability of the aspect that has been measured very precisely but we were able to compute the modification that Lawrence Volition would introduce. And we did that and we're really excited to see that the Minos collaboration actually took our formula and did this analysis and they wrote this fantastic PRL in 2010. And unfortunately they didn't find any signal. So the figure down here shows the cellular local, the local cellular phase. And these are the number of events and it's completely a flat distribution. So they didn't find any significant deviation from the completely constant event rate. So they used that to put very tight constraints on many of these parameters. So this is how this business go. The business goes this way. We can also play another trick. This is another experiment. So this is a ton of show in France. So you can see in the background there are two nuclear reactors equaling towers. And this was also a very interesting experience to me because I got involved in this paper working with three experimentalists that were part of the show collaboration. And one day in a coffee break, Janet Conrad came to me and said, is there anything interesting we can do with this? And after a discussion during the coffee break, we came up with this idea of trying to test the possibility of anti-neutrino mixing using reactors. And this is expression. So this is the conventional probability that has been measured very precisely. And we computed this quantity and we look for it in the data. At two point out, this is a second order effect. So the equations are way more complicated and they're gonna show them. But we did this analysis. There's another view of the double check experiment. You can see the two reactors and the detector is about one kilometer away under this little mountain here. And well, unfortunately, we didn't find anything. We were able to put very tight bounds on all these coefficients that have never been measured before. So that was already exciting. And again, we look for these effects. We compute exactly how the effect would look like. We look for it in the experiment and if it's not there, we can put bounds, which is the game we are being playing so far. Now this is a list of many other experimental searches. I show you only two examples, but there are many others by different experiments and more are hopefully they're coming. This is another idea which doesn't involve metrenial oscillation experiments on Earth. This is an idea that was explored by Mauricio Gustamante, who gave us a webinar a few months ago with the Gauguin-Prinigarai. One thing that they described was the possibility of CPT violation in the flavor ratios. This means if we show you this figure on top, you have some event that produces neutrinos, some explosion or any astrophysical event that produces lots of neutrinos. Those neutrinos will be produced at a given rate, I mean a given ratio. For instance here, I'm using a one to two ratio which would be what you expect from pi on decay. And as they propagate from the source to the Earth, due to neutrinosolations, the flavors will mix. And we're not gonna see exactly the same rate on Earth. So in this case, we expect to see something like a one to one to one ratio. But they describe how CPT violation actually would produce that effect or would modify that effect. So how we can look for new physics using this. The fact that now we can do this, the Ascii experiment, for instance this figure was taken from this paper from the Ascii experiment, can actually measure the different flavors that arrived to Earth from astrophysical sources, allows us now to use this technique. Well, so far the contours are quite big, but they will decrease when more data comes. But at least this shows that this is possible. More recently, my friends actually, Carlos are well as and Tepicatori, they put this together in a very generic way they did not commit themselves only to Lorentz violation, they call it new physics in general, and they show that you can beat all many of the neutrinosolation experiments, all the bounds. If you happen to have very small regions that you can measure with ASCII, and depending on the initial flavor that you have, the flavor ratio that you have, you will end up in different sides of this triangle. And when you're doing this, you can actually get extremely tight constraints, several orders of magnitude better than the current bounds. So this is something that can be done in the near future. So that is about oscillations. I will go rapidly to the other part, which is the section that we call oscillation free. By oscillation free, we mean things that do not produce oscillations, that's sort of implicit in the name. And there are two things that could happen. D here represents the dimension of the operator, so you have dimension over three, I mean four or above. You will generate things like modified reactions that can be tested in astrophysical environments or time of flight experiments. So this is something that we did when ASCII announced the discovery of PV neutrinos, one reaction that could happen becomes allowed, is the possibility of tranquil radiation by a neutrino. So a neutrino can lose energy by producing a Z boson, which then decays into an electron-positron pair. The dispersion relation is modified, so that is what makes this process possible. So we can use the energy of this PV neutrinos to put constraints on this quantity called C. C is the name of the coefficient, OF means oscillation free, the little circle on top means that it's isotropic, so there is no direct independence, and the D is the dimension of the operator again. And this is the way we do it. The fact that we do observe neutrinos with a given energy, say a PV, means that as neutrinos come from really far, they will start losing energy in their path, and at some point they will fall, the energy will go below the energy threshold for this reaction to be allowed, and this threshold condition is given in this expression where it means the electron mass, and the fact that we do observe these neutrinos allows us to put constraints on these quantities, at least in the negative part of these quantities. And this is exactly why we did this in this work. When we were done with this paper actually, the ice cube experiment released more data now with several events distributed in the sky, and with this in mind, we describe a more generic search in which we include also the possibility of direction dependence. So this is, now the threshold becomes more complicated, but these are just the harmonical, spherical harmonics, J.M. are the conventional quantum numbers for to quantify the rotational properties, and by using several events distributed in the sky, we can put many, many constraints on the direction dependent effects. So finally, and this is the part that I've been working more recently, is what happens if D is equal to three, so why is D equal three so special? Well, it happens that D equal three allows the effects to be really hard to measure, at least in conventional experiments. We use the word counter-shadow, so the term, the expression actually, counter-shaded relativity violation was actually introduced by Kosoletsky and Tassin many years ago when they discovered that some effects of Lorentz violation could actually be large, and we don't see them only because they coupled to something very small, in the case of that paper at the time was coupled to gravitational field. So in our case, we also have a sort of counter-shaded effect. Counter-shaded for all of you who are not familiar with the word, actually it wasn't, it's a term borrowed from biology and refers to animals with some sort of camouflage, animals that have a very dark back and a very light belly, so they are really hard to detect for predators, it's a really good camouflage technique. So this has been found in many animals, you have example like a shark, a penguin, a squirrel, and a cat. So how do we look for this? We look for these effects in beta-DKs because in beta-DKs these terms actually show up. So for all of you who are ever in a study conventional beta-DK, I've probably seen this expression, it's called the Jackson decay rate, it's the same Jackson of the famous Jackson auto-dynamics. And so in this paper we describe all the details about Lorentz violating beta-DK, the neutrino spinards get modified which means they have to be solved carefully, the equation of motion has to be solved carefully, the phase space gets modified because non-neutrinos have a modified dispersion relation and there's only one coefficient but this coefficient has four components, these are the names. So it's A means that it's called an A type coefficient that means breaks both Lorentz and CPT environments. The three means that it's dimension three, OF again is oscillation free and the numbers here, the pair of numbers are the JM term so we are using an hysterical basis and A11 contains a real imaginary part. So there are four components, four numbers that control everything. This is how the decay rate looks like. In blue everything related to that through the electron, in red everything related to the anti-neutrino that is emitted in beta-DK and in green things related to the initial neutron in this case. And I should point out that when we did this there was an independent group who was working on a very similar idea but not in the neutrino sector but they were studying the W boson. So there's a remarkable list of papers that they have written in the Lorentz violation in beta-DKs and not also electron captures and things like that but the Lorentz violation effects in that case are in the W boson. In fact the most recent paper the one on top here appeared just this morning on the archive. So going back to the neutrino part there are two main effects. One is produced by this A which is a zero zero to the isotropic term that modifies the spectrum of beta-DK which is something that can be measured. The other three is a one zero and the real and imaginary parts of the A11 they modify the angular correlations and these are also some, these are parameters that can be measured in beta-DK experiment. The angular correlations refer to how many neutrinos or electrons are emitted in a given direction with respect to the other or with respect to the polarization of the initial neutron, et cetera. This effect can also be studied in Tritium-DK. Since I'm here in Calzburg from is very important to connect with the Catron experiment, the famous Catron experiment that will hopefully measure in the near future measure the neutrino mass by studying the endpoint of Tritium-Beta-DK and we have computed all the details for Catrin to be used and I'm already working with them for this possible measurement in the future. If we can do beta-DK, we can also do double beta-DK. This is way more complicated but we addressed the initial idea in the first paper and in a later paper I worked out all the expressions for the different kind of experiments. So there are two modes of beta-DK, one is called a two neutrino double beta-DK which you have four leptons in the final state and in the other case which is the one most people are interested in is called a neutrino less double beta-DK. This would give us an idea about the nature of the neutrino that are not semi-urana particle. But in both cases, Lorentz's violation can play a role. For the ones that I'm taking here at least the most relevant is for the two neutrino mode. And what happens in this two neutrino mode at least for experiments that cannot reconstruct the direction of the electrons that appear, neutrinos are not observed in this experiment, they just fly out. But these experiments can measure the energy of the two beta-electrons, that's why it's called double beta. And what happens is that since the the neutrinos satisfy a modified dispersion relation the energy conservation will get modified and therefore the shape of the spectrum can change. So here I have just an example using arbitrary units. And this is an effect that actually several experiments, I'm working with several experiments right now looking for this effect. So it should be some results hopefully soon. There's also an effect in a neutrino less double beta-DK and I'm not going to go into any of the details, but what happens in the double beta-DK case is that the parameter that controls the lifetime of double beta-DK gets modified. So the life, the one over the lifetime is given by this quantity GA, which is just a phase-space quantity for the electron. Z is the Z value of the nuclei that you case, Q is the Q value. This quantity here in green is the nuclear matrix element so that the term doesn't change. But the quantity here, which is called the effective Majorna mass square gets modified in this form. G is a quantity that involves many of these coefficients for Lorentz and CBT valuation. R is the radius of the nuclei that you case. So this shows actually in fact, neutrino less double beta-DK could even occur if there is no Majorna mass. Okay, so this takes me back to my summary, so I'm going to conclude here. The idea, I hope I can pass you the idea that the different tests of Lorentz invariance are now underway, they had been underway for more than 15 years actually, and they actually expand many, many different disciplines. I only took here about neutrinos, but there's a whole business there. In the photon sector, you can do it with quarks with oscillations of neutral mesons, neons, gravity tests, there are many, many of them. At least for the part that I described here, we have identified all the key experimental signatures. I'm interested on what can be measured, and we have identified all these key signatures in different kind of experiments in oscillations for astrophysical neutrinos, which are being extremely important these days, and for single and double-bitter decays, which is an extremely large amount of experiments looking for these effects right now. Many of these have not been explored, and that is very important, and it's also a motivation for these experiments to look for these signals. It's interesting that you can look for these effects, and you would expect only a really high energies, but also a low energies, a lot of that can be done, especially with these counter-shaded effects that you cannot study at high energies. And one thing that I personally find extremely, extremely important is that this is a very rich and active research topic in which there's a lot of collaboration between theory and experiment. So I will finish, just gonna leave you with that phrase that I quote from Feynman that I quite like. So I'm gonna stop right there. Thank you. Thank you very much, Jorge. It was very interesting, your talk, your seminar. So I guess now we can start with the round of questions. So but before I want to remind you that for all the people that is following this streaming in our Google Plus channel and in your YouTube channel, that you can make question via Twitter or using this Q&A system. So I leave you just the information here. So meanwhile, we can start with the question from the people that are here in this Hangout. So if someone has a question to do, this is the moment, I don't know, you can unmute yourself and make it to the forehead. So I don't know, since Nicolas, you want to make a question? No, if you don't know, we need to have a couple of questions. Okay. Hi, I can read my questions if you want. Okay, please. Okay, so let me see. I will just read them. As far as I know, the Lorentz violating coefficients in the neutrino sector of the standard model extension are independent of each other. However, is it possible to use the bounds that are on the coefficients from non-oscillation experiments to bound the ones relevant for oscillation experiments to translate the bounds from non-oscillation experiments to the bounds for oscillation experiments? Yeah, so this classification that I mentioned that I described at some point about oscillation-free and flavor-mixing coefficients, the idea that we did that is because the oscillation-free part cannot be observed in oscillations. So I can give you a very clear example, nothing to do with Lorentz violation. Think on the neutrino mass phases. Oscillation experiments only tell you about mass square differences, but they don't give you any information about the absolute mass scale. With that, you need to go to, like, treating decay experiments. So here is exactly the same idea. These oscillation-free effects can be visualized as a term which is proportional to the identity if you want in flavor space. So they affect the three neutrino flavors in the same way. So in any oscillation experiment, you will never see them, because in oscillations you only see transitions between different levels. But you cannot see them in... The oscillation-free part cannot be studied in oscillations. I see. All right. Should I ask my other question then? Yeah, sure. Okay. Again, I'm going to read it. The new Lorentz violation terms in the Hamiltonian are direction-dependent. So they depend on the three-dimensional P. Would they then affect the isotropy of the arrival directions of the high-energy neutrinos in myisocube or vice versa? Could the sky map of arrival directions that isocube sees be used to balance the coefficients? This is a really good question. This is something that has been... I personally have been discussing with people from another experiment. I shouldn't mention which one. But there is an idea of trying to, for instance, look for atmospheric neutrinos. They can sky-map of the atmospheric neutrinos. And in principle, in the isotropic case, you would expect a completely isotropic distribution. And maybe some of these coefficients could affect that isotropic. So yes, in principle, you could. I'm pretty sure that it's something that can be done there. It's probably not too complicated to do. So if you want to talk about it later, I'll be happy to discuss it. I have a few ideas, so yes. Okay. Cool. All right, thank you. Very good, very good. So is there any other question? Because also I have a couple of questions for Jorge. One, I mean... Not for me. Not for you. Okay, I'm gonna start with the one that looks like makes just a very short description that is... But you were explaining that in most of these cases, to analyze this effect of floating violation or CPT, you do this trick of rotate the experiment, let's say, in such a way, using that the earth is rotating on itself. So what about the other effects like, for instance, animal modulation, animal variations? Because since the earth is rotated around the sun and everything, it's like... A little bit just to finish the question is how it could be rated, for instance, with this experiment that are very sensitive for animal modulation, in the case of dark matter. Because these are also very sensitive apparatus for detecting. Yes, the idea of connecting this to direct dark matter is some sort of straightforward, because we are looking for a very similar kind of wind. You're looking for a wind of dark matter. We were looking for something that looks like a wind, which is sort of anisotropy in space, in this case. So the interest in to make that connection. Now, the animal effects would be there. Well, say for the neutrino experiments, for instance, they would be there. The fact that the earth is going around the sun, usually at a speed which is quite low, so the beta factor is about 10 to the minus four, if I remember correctly. They usually can suppress some of the effects. The other thing is that for most of the, at least terrestrial experiments, the data is collected in a given period of time of, say, weeks or maybe months. So the run periods are not too long. If you had an experiment that runs for 10 years and you want to do an analysis, you really need to be careful about the animal effects. But if you have an experiment, for instance, right now I'm working with the group of people describing a neutron decay in which you take data only for a few days, you don't need to worry about the effects due to animal variations. But yes, they in principle could be there. The serial effect will be way more easy to detect and will show up easier in your data. Okay, so yeah, okay, you need just to have long, long-run experiment to take into account this kind of effect. Yeah, and if you take a really long data-taking period, the serial effect since this frequency is way lower than the frequency of the earth going around the sun, this one will probably average away because it will be really fast compared to the other one. And you only would care about the animal, but the effect that you're trying to measure, I mean, this background field that you're really trying to measure is exactly the same. So you don't gain anything and it's way easier just to take data for several days and do the analysis. Because the time stamps are not easy to get in general. In some cases, cannot be very easy to get in the experiment because you need to know exactly the time at which the event occurs. So having a control experiment for a period of a few days is way easier than for several years. So also I have another question, but this is more, I don't know, because at the end, Lorentz violation and CPT are closely related with gravity. So do you expect or is it possible to observe some kind of effect related with the gravitational field in which these neutrinos are traveling across? I mean, for instance, a neutrino that pass close to the galactic center. So this gravitational field in that part is much stronger than in the outskirt of the Milky Way. Yeah, this is a really important point. Maybe I did not mention it or did not stress it enough, but all what I showed here is flat spacetime. So we have assumed that it's flat spacetime. As you say, what about gravity? Because I even mentioned that you can couple this SME, you can include the gravity sector. If you include gravity, things become more complicated, but people know how to do it. There are different groups working in the gravity, what we call the gravity sector of the SME. When you introduce gravity, you have to be more careful with things like the way, for instance, in which I introduce these terms in Lagrangian. I just put them there by hand. So what I'm doing here is a sort of explicit violation of Lorentz symmetry. It was shown in a paper in 2004 that if you do this in a curved spacetime, you're running into trouble. Basically, the Bianchi entities break down, so the geometry of the spacetime breaks down. So you cannot do this in a curved spacetime, unless you introduce the violation in a dynamic form. In other words, the breakdown is a spontaneous symmetry breaking, not a Hick's mechanism, but something like that. So these coefficients will be the backend expectation values of this dynamic field they have to introduce, and you need to introduce a particular potential and all the things that you know from a spontaneous symmetry breaking, and in that case, many interesting things happen. If you ask me what happened to a neutrino in this case, the answer is, I don't know, because nobody has studied, say, particles in this curved background. So most of the work in the gravity sector is done in two parts. One is called the pure gravity sector, which means there's gravity and nothing else, and you study what happens to, for instance, gravitational waves, or what happens to other kind of effects which actually can be measured with extremely high precision. For instance, with this lunar laser ranging, you can measure how far the moon is when it goes around the Earth, and different effects would make the moon go a little bit further away or closer or go faster, and all these effects can be measured. You can also do it with satellites, with a space station, and this is called the pure gravity sector. There's also a whole area which is called the matter gravity sector, which you couple a particle, say, an electron to the gravitational field, and that is something that has not been done for neutrinos, it's called an open thing to do. And in the matter gravity, you can test things like a Cubilins principle, you can drop an apple, an antenna apple, and see what happens. So this is the kind of things that people are doing in different experiments at CERN, like the alpha experiment or the aegis experiment in which they will test the gravitational of hydrogen and anti-hydrogen, and all these effects have been quantified within this SME. That's why this is such a huge, I call it a playground for both theories and experimentalists, because there's so much to explore, and that area at least is something that has been covered. I personally have not worked on the gravity sector, but see what happened to a very decent neutrino traveling through an important gravitational field would be interesting to see. I don't have the answer right now, but it would be interesting to check. Probably it's not easy, it's probably not an easy calculation. Of course, of course. Usually when gravity starts to mess up with the particles, it's a... Yeah, gravity is complicated. It's really, really complicated, yes. Yeah, in fact, you're showing one of your slides that the connection between the standard model and gravity and general relativity is not known. Yes. But you know what is the blue. I could mention now that you brought up the topic of gravity is that the people working on the gravity sector trying to introduce, to construct some sort of Hicks-like mechanism for this Lorentz violation, there are many questions that pop up. For instance, what happens, as you know, the Goulson theorem tells you that if you have a spontaneous symmetry breaking, of a continuous symmetry, you will have these Nambu-Golson modes, and you can ask what happened to them. And this is a very interesting area of research in which people have shown, for instance, if you use a vector field to break Lorentz symmetry, like this little A that I was putting there, they call it B for historical reason. What happens is that the massless modes that appeared due to this Goulson theorem look exactly like the photon. So this is not a claim that the photon exists because Lorentz symmetry is broken, but it's interesting to consider that that is a possibility. And the next step was sort of obvious, what if the Lorentz symmetry is not broken by a vector field, but a symmetric to tensor. And surprise, surprise, the Nambu-Golson, the massless modes, they satisfy Einstein equations. They behave just like the gravity. This is a very active topic of research, and I'm not personally involving to all, on all those details. I'm more interested on the phenomenology and the connection with experiments, but I think these are very interesting results that show that this area can be extended to all the topics too. Okay, just to, because we have now a question from the Q&A, but just to finish my random question, just what about analysis using photon itself, like the mass of the photon can Lorentz violation be tested also in studying just light? The studying light, this is actually one of the, you could go back to a hundred years ago or 110 years ago, and that is exactly what Michelson and Morley were doing, right? So they were looking for how a photon propagates in one direction and then in a different direction and see whether or not it wasn't, in that case, they were looking for, for a linear for us either. We're not looking for an ether, it's something that looks like it. So the photon sector is one of the most explored in this field. You can look for many, many effects. You can look for astrophysical effects in which you have access to really high energies like a gamma-ray astronomy. You can use cosmic rays actually too. This is a work that I did recently using cosmic rays from the PLJ observatory. You can put really, really tight constraints on the photon sector. You can also use a CMB because many of these effects grow with the distance. So the longer a photon propagates in this background field, the effect will basically, we will increase. The most recent photons we have access to are the ones coming from the CMB. They have really low energy, but there are effects which don't care about the energy just like these counter-shaded effects that are shown in the neutrino sector. There's something very similar in the photon sector where the energy is not that relevant. So the only thing that matters is how long they propagate and the CMB is one of the best laboratories which has a particular type of CPT violation and bounds there actually the best. They go to order 10 to the minus 43, something like that. It's crazy, crazy sensitive. But there would be some reason in, I mean, why in photos this effect doesn't seem to not appear, but in neutrino they could appear. Well, it's related that one is a vector field and the other is a... In principle, this effect would appear anywhere. It could appear in muons or towels or in the park sector. In principle, you can try to connect between them. This is something that has not been done. So for now, we treat them as completely independent. So the coefficients from the neutrino sector have nothing to do with the coefficients from the electron or for the gravity. They're completely independent. So from that point of view, we test them in a completely independent way. Okay, now you can say why photons or why neutrinos. I became interested in neutrinos. I always like neutrinos, but neutrinos are always give surprises. That's one of the reasons. There are many anomalies in neutrinos that we cannot understand. Actually during my thesis, I constructed models for neutrinosulations using Lorentz's violation that would feed the data way better than any other model. It's now excluded, but at the time it was one of the best models. And also oscillations. Neutronosulations are basically natural interferometers. And when you have an interferometer, you have access to really small effects. And now that we have ice cube in the future, we're gonna have other neutrino telescopes. High energies. That is exactly where we want to go. So neutrinos and photons are probably the two, are the two sectors in which actually I'm working on. And they offer really, really high sensitive, they can be high sensitive measurements. Okay. No, yeah. It's very interesting in fact the topic. So, but I have to go to the question from Arturo Samana that he's asking on a read. The main uncertainties in the double beta decay experiment are coming from different evaluation on the nuclear matrix element. It would be possible to estimate the percentage error in the double beta decay half lives with and without the neutrinos from the LB. Yeah. The Lorentz violation, sorry. Yeah. So the Lorentz violation doesn't modify the nuclear matrix elements. Or for anybody who's not familiar with this topic, the nuclear matrix elements are the parts that are really, really hard to calculate. So the uncertainties there could be, in some cases could be actually a killer in the sense that maybe we're not gonna be able to see the effect. Not because the experiment is not sensitive enough, but because the uncertainties in the nuclear matrix elements are too large. So then one thing that would be extremely useful would be in the future if, say, a neutrino less double beta decay is finally observed, the Lorentz violating effect depends on the radius of the size of the nuclei. So that means that different isotopes would look different if you have Lorentz violation. This is not the case for the conventional case because in the conventional Lorentz invariant theory, the neutrino less double beta decay only depends on both in different quantities, including the nuclear matrix elements, but also this Majorna effective mass, but nothing else. In our case, it would be perfect if tomorrow, say an experiment using xenon observes neutrino less double beta decay. So then we will rush immediately to try to see it with your menu because we would expect differences. And in that case, we could distinguish between the two. Interesting. So I guess this question is also answered. So I guess, I don't know if someone has another question for Jorge. I don't know, it seems not. So for the moment, so we can basically to thank Jorge and also if the people still want to make question, they can do it for the moment. Me, well, I'm gonna talk now. So, but I want to tell first of all to acknowledge Jorge for this very interesting webinar and the rest of the people that participated and to tell to the people that in two weeks more we are gonna have the next one of these Latin American webinars. And if there are no more questions, so I guess we can finish here. It was very nice to talk and I don't know, see you in the next season of the, in the next webinar of this Latin American webinar, South Physics.