 Hello, everyone, and welcome to our 72nd webinar on the Latin American Webinars in Physics. My name is Federico van der Palen from the Universidad Antioquia in Colombia, and I will be your host today. Our speaker is Natalia Tapia from the Universidad de Santiago de Chile, and she will speak about measuring the boiling point of the QED vacuum. So Natalia is currently a graduate student, a PhD graduate student at the Universidad de Chile, Santiago de Chile, but she's currently visiting the Universidad, University of Montreal, and she spent one year visiting as an internship at DELCI. And Natalia will speak about a very interesting subject because we usually hear about the QCD vacuum, and she will speak about the QED vacuum, and a work she's been doing with colleagues at DELCI. Well, let me remind you that you can be part of the discussion writing questions and comments via our YouTube live chat system. And I will hand you over now to Natalia. So Natalia, you can have now the board. You have to unmute yourself. OK. Can you listen to me? Yes, great. OK. Can you see my presentation now? Yes, perfect. OK, well, thank you very much again. And Natalia here. Thank you for letting me share my work with you. Today I will show you the results of my last paper in collaboration with Anthony Harting and Andrea Springbaugh at DELCI, where I spent 10 months doing an internship. The project involved a strong field QED and the measure of electron-positron per-production in this new experiment at DC, the Laxie experiment, very similar to the Slack experiment performed in the 90s. So we are all aware, we all know, of the successful of the QED theory. But there are some observables of the theory that are not possible to achieve by means of perturbation theory as the rates of spontaneous per-production. But there are some related processes that you can measure in non-linear experiments. So before I'll show you my results, I would like to talk a little bit of the history or the context of these kinds of experiments. So can you hear me? Yes, yes, don't worry, we can hear you. Okay, so can you see that I changed the slide? Yes, that's perfect. Okay, so the first attempt to measure a non-linear process was performed at the Slack experiment in the 90s. So this collaboration focused on extremely intense laser beam at a beam of high-energy electrons. This picture that you can see here appeared in the November 97 issue of Photonics Spectra. And you can find all these pictures, documents, news about the experiment, paper, pieces related to the experiment in the Slack repository. And in this experiment, it was the first time in history where per-production or light by light scattering was measured from real photons. So basically, in this experiment, they collided a high-energy electron beam with a laser, which at the focusing point had an intensity of around 0.5 times 10 to the 18 watt per centimeter square. So this number, you can think, is very high, but actually is below the non-perturbative regime, where you can somehow measure the critical field. So when the laser photons collided head on with the electrons from the electron beam, they got a huge energy bus, much like when you throw a ping-pong ball through a track in movement. So the ping-pong will get a lot of momentum from the track and will go away with a higher acceleration that it was in the beginning. So these high-energy photons that are produced when the electrons collide with the laser photons then can interact with the laser, with the laser incoming photons and producing electron-position pairs. These pairs are sometimes produced in accelerated experiments at high energies, but the photons involved in the process, at least one of them was a virtual photon. So this experiment marked the first time in history that real photons interacted to produce visible matter, electron-position pairs. So this old animation shows what is the experiment about. You have the electron beam in blue colliding with the laser. And in the same path of the laser, this high-energy photon in green produced from the previous collision will produce an electron-position pair. So around the 85, Kirt Magdana, one of the Spokesperson of the Slack experiment, established three different nonlinear processes that would be measured at this experiment. So by the time, the greatest acceleration that they could obtain in a laboratory was the one of an electron in a high-intensity laser beam. They were expecting to measure different nonlinear process with these highly-accelerated electrons. So they consider the case of a very unusual, strong electromagnetic field. So what are the kind of process that they were expecting to measure? For example, that always called the attention is Hawking radiation and Unruh radiation. In the case of Hawking radiation, you have an observer at rest near to a black hole. And due to the high acceleration produced for the very strong gravitational field around the black hole, this observer will be involved in a thermal bath. And it will scatter this thermal bath by means of emission of high-energy photons. A very similar process is the Unruh radiation in where a highly-accelerated particle, in this case an electron, will also fill a thermal bath around it. And it will scatter the thermal bath by emitting high-energy photons. So these high-energy photons would be measured by some observer in the laboratory. But this is still an experimental problem and how to measure this kind of radiation. And it has still not be solved. But it's always present in the propositions for this kind of experiments. So you could also measure various possible effects of vacuum polarization as light by light scattering or multiple benefits as spontaneous per production, stimulated per production. And you can also expect to see limits in the energy of the field due to the cascade process in which you will use energy of the laser in the focusing point. Due to, at some reference frame, the particles will have enough energy to produce electron-position pairs spontaneously. So that will be a limit to actually reach the critical field for QED. And by the time the most accessible process was a high-guer harmonic radiation of Thomson scattering. So just to see some numbers, for example, for light by light scattering, we know that this is a fourth order in perturbation theory, the interaction of two photon particles. And it happens by means of the virtual reproduction of electron-position pairs that then annihilate into two photons again. Related process is photon-photon scattering giving rise to electron-position pairs. So in this case, the cross-section goes as the fine structure constant to the fault power. And it will also depend on the energy of the photons involved in the process. So if you use the appropriate units in MEV, you will need 10 to the 15 photons of one MEV to be brought into collision to observe one pair. So usually, the laboratory beams around the MEV ranch have typically less than 10 to the 10 photons. That is why it's not possible to see this kind of process. So what they propose to observe nonlinear processes is the study of the scattering of 50 or around 50 GeV electrons and a laser with peak energy flux of 4 times 10 to the 18 watt per centimeter square. So there are two considerations in how to measure how strong is a field. One of it is when the electric field in the process is higher than the critical field. And this is quite difficult to achieve. The other way to measure that the field is strong is when this quantity is bigger than 1. When this quantity is bigger than 1, it's considered the static limit or the frequency is much smaller than all these other parameters. This parameter xi is also called the nonlinearity parameter, or the laser parameter. And it's strongly related with the nonperturbative limit. When this parameter is higher than 1, these fields are considered to be strong. The process is considered to be nonperturbative. And usually, it's also nonlinear. Due to the effect of the electron traveling in an electromagnetic wave, the mass of the electron will suffer some changes. Or seen from the outside, you will see an effective mass. The electron will move in a transverse way to the laser. So it will add momentum to the particle. And the electron will be heavier when you increase the intensity of the laser, for example. The parameter xi is also related to the intensity of the laser. So if you increase the intensities to see a higher nonlinearity process, the mass of the electron is going to be heavier. And that will be translated later in a higher number of photons involved in the process to see one pair production. So finally, what they observed in this experiment was nonlinear contents, electron positive jump nonlinear contents scattering and electron positive jump production for electrons around 50 GB. And the laser intensities peak were around 0.5 times 10 to the 18 watt per centimeter square, which corresponds to a laser parameter of around 0.4. As I said before, you need to be up one to see nonperturbative process. So all these measures that they get were not in the nonperturbative regime. However, these were the first laboratory evidence of inelastic light-by-light scattering involving only real photons. In the case of nonlinear contents scattering, they observed an absorption of up to four photons. That means that they observed nonlinear scattering for one to three and four photons in one process. The setup of the slack experiment was something like this. They had the electron beam here of around 50 GB colliding with the laser. And in the same spot of the laser, they will re-interact the high-energy photons produced for nonlinear contents scattering, for example, and then the electron positive jump pair production. And the particles that don't interact here will then be collected further. In our case, we propose something a little different. We propose first to obtain high-energy photons by means of ramstalling. So the beam of high-energy electrons, so it's going to be around 17.5 GB at the laxie experiment at DC, will hit a ramstalling converter foil, a thin foil, and they will produce high-energy photons here. So once they have the high-energy photons, they will collide them here with the laser at the focusing point. And here with these high-energy photons and a number N of laser optical photons, there will be pair production. So for the laxie experiment, it is expected the laser to be a one-perawatt laser system of around 35 m2 a bunch. And with a focal area of 10 micrometers squared. And with a peak intensity of around 10 to the 20 watt per centimeter squared. The electron beam is going to be of a size of 50 micrometers and with a repetition rate of 10 hertz. So as I said before, we consider this as one photon pair production. But this process is in the background of the laser. So this high-energy photon here has to interact with a N number of laser photons to produce these electron-position pairs. These particles are also called dress states because due to the laser or to be in the background of the laser, they will have different states. These are called bulk of states. And when you use them, you are already considered the nonlinear effects. So we are considered a rem shallowing spectrum to the pair production in the background of the laser. And these are the dress states that I named before. So the one photon pair production that we are considering is going to be a nonlinear process. And if we compare our rates later that we will obtain with the spontaneous pair production rate that you obtained from the Euler-Heisenberg Lagrangian, you obtained that the vacuum will decays in electron-positron pair production in this way. The dependency in the exponential here with the critical field also hides the dependency on the electric charge, that is the coupling constant of theory. So as you can see here, if the coupling constant goes to 0, the exponential diverges. And that means that you cannot obtain this result by means of perturbation theory. That is why it's considered to be non-preservative. So here you can see in the exponential, the dependency on the critical field that is around this value is expected to be 1.3 times 10 to the 18 volt per meter and the dependency on the coupling constant. So the bulk of states or dress states look like this. And from here you can see where this laser non-linearity factor comes from. This will affect the mass of the electron and you will have an effective mass that depends on the laser non-linearity parameter. So if you increase the intensity, the electron is going to be heavier. And that will mean it will need more and more photons to produce one pair. So other important parameters in these experiments, as I said before, the laser parameter are the photon and electron recoil parameter. This depends mainly on the kinematics of the process, on the energies of the photons involved, the mass of the electron, and the angle of collision. So this is the rate for electron position per production when you consider the bulk of states. So you can see here that it goes like some powers of vessel functions that depends on the set-up function. So you can see here that the argument of the vessel function depends also on the laser non-linearity parameter and the photon recoil parameter. So the threshold number of photons here needed to produce one pair is here. And you can see that also increase with the laser non-linearity parameter. So you will have higher orders and higher arguments for high intensity parameters. In this case, you can approximate in this range of parameters for psi much bigger than 1. And for photon recoil parameter less than 1, to this asymptotic expression, simplify from here when the argument and the order is high by the device asymptotic expression. So here we can see that the asymptotic rate goes as the exponential that also depends on the electric charge and the critical field here or here. So you can see here that the electron position per production rate from one photon, it also goes as the spontaneous per production in some extent. So these are the rates that we obtain with the function f that I showed you before here. So the full rates are the solid line here. The dot line is what you expect to be for a small laser parameter. This is the perturbative behavior. It means that it goes like psi squared for a process of two vertices. And for a high psi, for psi actually bigger than 1, you can see here the asymptotic result that actually fits very good for the case of psi bigger than 1. And for photon recoil parameter much less than 1. The other plots for different parameters are to compare the feet of the asymptotic result with the full rates. So you can see that indeed the best behavior is for the case for psi bigger than 1 and photon recoil parameter less than 1. So as we consider a Bremschalm spectrum, you can find, for example, in the review of particle physics, the rate for a Bremschalm spectrum and it goes like this. So we use this rate to integrate our rate of pair production and we integrate in terms of the photon recoil parameter between 0 and the electron recoil parameter. What we get for the asymptotic result is this analytical expression. In the case of the full rate, we obtain an numerical result that I will show you. So if we look to the Bremschalm pair production rate in terms of the critical field, you can see again the behavior very similar to the asymptotic result obtained for the pair production before the integration and in the spontaneous pair production rate. So here we recover the non-perturbative behavior. So that will mean that even after this Bremschalm spectrum, you will have non-perturbative behavior and this will be a way to measure the critical field in this experiment. So here I show you again in solid line, the full rate integrated and the dashed line is the asymptotic result integrated in the background of Bremschalm spectrum. So for different parameters, here we see again that the base behavior is for a small recoil parameter and for laser parameter bigger than one. You can see that the good behavior starts from psi equal one. And you can see here the rates produced of electron procedure pair production and you can see that these are very high numbers but actually the range of parameters for the Laxie experiment is around here, the corner, the right corner. So for the peak intensities, the rates are going to be around 10 to the four pairs. So in the case of the experiment, it's much easier to vary the intensity and the energy of the electrons. For example, if you want to keep the photon recoil parameter or the electron recoil parameter and vary the laser intensity or the laser parameter, it is much difficult because the recoil parameters depend on the laser parameters. So actually you will have to move the laser to change the angle for example and that is much difficult. So it's much easier to vary the intensity and the energy in this case. Here we can see that the laser non-linearity parameter around one, that is where you can see the non-perturbative behavior and the non-linearities, is going to be for an intensity around 10 to the 18. This is one of the reasons, even in the slack experiment, the energy of the electron beam was higher why they couldn't get a non-perturbative behavior because they were far less below this intensity. So here we see in terms of the intensity, the rates of per production. For the peak intensity, here we see that the rate production is going to be around 10 to the four, as I said before. Here the solid line is the complete rate integrated and the dashed line is the asymptotic result. So around one time 10 to the 18 watt per centimeter square, as I said before, is the laser parameter around one and the first pair is going to be produced around two times 10 to the 18 watt per centimeter square. That means that your first pair is going to be in the non-perturbative regime and is for a quite modest intensity. The dot line in blue here is for the case that the nominal value of the critical field is smaller. We wanted to get something like an error bar here. So if you have a 10% lower value of the nominal value expected for the critical field, you will have higher rates and this makes sense because if this kind of potential barrier to get per production is smaller, you will have more rates and if the value of the critical field is bigger, you will have less rates because it's more difficult to produce the pairs. So in this case for the experiment, the energy of the electron beam is going to be 17.5 GB with a bunch of six times 10 to the nine electrons per bunch with the remstallium foil thin in comparison with the radiation length of the material used under the laser shot of 50 femtoseconds an angle of P12 and the energy of the laser photons of 1.053 electron volts. In the case of the variation of the energy, the rates are going to be for an energy of around 14 GB. You will see a first pair for an intensity fix of three times 10 to the 19 watt per centimeter square. We know already that for this parameter, the behavior is non-perturbative. So you will have your first pair around 14 GB and you will see around 30 to 20 pairs for 17 GB, 17.5 GB for this fixed intensity. So in conclusion, we can see that the behavior of the electron positron per production will behave very similar to the spontaneous per production rates. Here we can see the similar behavior on the exponential dependency on the critical field that hides also the dependency on the electric charge that is the coupling constant of the theory. So even in this very restricted range of parameters that you need to get the asymptotic result where you have the non-perturbative limit, you will have the number of pairs high enough to see something in this kind of experiment. And it will be possible to measure the Schringer critical field for these modest intensities. Around two times 10 to the 19 watt per centimeter square, you should be able to see one pair in the non-perturbative regime. And with a 10% discrepancy with the nominal value of the electrocritical field, it's expected to see a high rate of electron positron per production. And these values around one order of magnitude for small intensities and for high-end intensities is affected because becomes less important. So, well, these are my reference. Thank you very much for your attention. Thank you, thank you, Natalia, for this very clear talk about the subject which is new to me, but I think I learned something. Now, let's pass, let's see if there are questions from the board or from the Q, Alberto? Yeah, I have a couple of questions for Natalia. First of all, Natalia, thank you very much. It was very interesting, in fact, your talk. So, I have one question that is more kind of a little bit naive, but in the sense that is it possible to observe this kind of process, the one that you were talking about, this boiling point in QED vacuum, but in some astrophysical environments, I don't know, pulsars physics, because also you have very intense electromagnetic field that could also bring electrons and all this stuff. Well, the Hacking Radiation is related with this process. And when you can have actually very intense electromagnetic field in astrophysical environment, so near a black hole, you will have, for example, a pair production and you will have a virtual pair. So it's thought that due to the very high gravitational field, one of the particles can fall inside the event horizons and you will have at least one real particle produced near to the black hole. So this particle can escape and you will have one particle produced and this particle will need some energy from somewhere, right? So the energy comes from the black hole. So this is translated as the Hacking Radiation, this loss of energy due to the pair production. So in this kind of process, you can see pair production. That is one way to think about it. Yeah, but in the sense of, yeah, I understand that with the Hacking Radiation, but do you think that it's possible to observe the effect in, I mean, I know that Hacking Radiation is super hard to observe nowadays with the technology that we have at the moment, but I don't know another type of gamma-ray burst that also there are very strong photons emitted and I don't know. No, it's just a question is, you know. Yeah, yeah, no, I understand, but I don't know if we are able to measure something like this. This process shouldn't happen in the universe, right? At some point of the history, but how we measure this is, I really haven't talked, think about it. It's actually difficult now to measure Hacking Radiation in a laboratory or UNRO radiation. So I hope maybe in the near future or not from here, it will be possible. Ah, yes. Okay, yeah, I have a nice question. Okay. Then you can have another question. And I was thinking, what do we learn with this experiment? I mean, do you expect to confirm QED or could you eventually find something new or new techniques in non-perturbative? Regimes of QED or even other models? Okay, so first, when I started my talk, I always like to talk a bit of the slack experiment at the Stanford Accelerator because I always think what they wanted to measure by that time. In that time, they wanted to measure non-linear QED and they measure it. Now the idea is to see the non-perturbative regime and indirectly measure the critical field. And if it's what it is expected, it will be a way to test QED and in a very extreme condition to test the theory. But there can be the case that you can find something different. So that means that you have to reformulate the theory and keep working. Right, so my question is, when do we know that we are within the range of errors or that we have to change the theory? I mean, my question leads to the following. If, I mean, QED is quite well established, but when you go into the non-perturbative regime, maybe you have, I mean, beyond the standard model of physics appearing or not. I don't know, do we have any possibility to measure something that goes beyond the standard model and what could it be? Right, I mean, the theory says that we should measure something with this behavior that I showed you and that would mean that, okay, the behavior is non-perturbative as it is expected by this result by Schringer, right? But if it's different, I think we are like, okay, what do we do now? Because there are not other ideas about it. We are expecting to prove the theory to be like this, right? So if we find something different, it would be also nice, right? Because then we find something funny, maybe, or something that we are not expecting. Okay, thanks. I mean, because in some theories, you expect something new, like flavor physics. Yeah. And in other cases, like, Schringer's traveling faster than light, you don't expect that. I mean, that's a result where you say that's probably wrong, the experiment, because it's so out of the way. So in this case, is it possible to find something different or would it be something like, you know, neutrinos faster than light, which are clearly not really wrong? I think that when they perform the experiment, they will measure this. There's no, like, I think that there's not like a big change of measure, something different, actually. Because QD, we know it's well-tested and it has worked until now, but it can happen that in some extreme range, it doesn't work. But there are no other ideas that I know, at least, how QD will behave in these extreme conditions. Okay, thanks. Roberto? Yeah, and in fact, there is also a question in YouTube, but then first I'm gonna do my question, then I'm gonna ask my question. Yeah, the other question that was, in fact, it's kind of related with the stuff that Federico was saying that because, in principle, in the context of the standard model, we know that QED, at some point, start to get mixed with weak forces. So to have the electro-weak processes that are very well-known, let's say, that also is well-tested. So do you expect also to more range in which range you start to have this correction due to the Z and W bosons or production, maybe, of neutrinos that would appear like kind of missing energy for your experiment or, I don't know, kind of? Because if you start to test QED in the non-linear regime, that means that your, in some sense, your energy in your processes start to be very high. So maybe in that sense also, you could start to perturbate the weak modes of the, because at the end, electrons also has a isospeed. So I don't know if you can understand what I'm saying, because I'm trying to... Yeah, I actually don't have any reference of how possible it would be to see something. I mean, in this kind of process, you could see spontaneous pair production, as I said before. This is a laser-assisted pair production because we produced the photons before. So you will have a spontaneous reproduction, but all non-linear QED process, actually. At this point, I think it's only QED. It's only QED, oh, okay. Yeah. Yeah, because the kind of the stuff that I was saying, Federico, in the sense that if you start to see a deviation with respect with QED, maybe it's not faster than light neutrino, but it's only, maybe it could be weak processes that start to perturbate your model. But yeah, but in this sense, yeah, makes sense. Okay, so now we have a question from Babesh Chauhan. I hope I pronounce his name correctly. So is it possible to also produce a muon pair? So what would be the expected rate? Okay, so first to see muon pre-production, you will need to have a muon accelerator to have the very high-grantu muons. Instead of an electron accelerator, right? But he is probably asking about the pair production which happens after the laser produced spontaneously. The process after you have the electron proceed on pair production. That's what I understand that his question is. Otherwise, he can reformulate it. Yes, because actually if you have an electron initially and photons you will, I mean, unless a left thumb number violation is considered, you will have electrons, right? I think you could produce muon pairs, but the problem is you need to have a mass of around 200 times larger than the electron. So you probably don't get to the energy. Yeah, that's one point also. But first you will need a muon beam to collate with the laser. And then you maybe will see electron muon pre-production but you will need much higher intensities to go above the energy that you need to produce one pair of muons, right? I don't know if Pavèche has something to say. I think that you don't need a muon beam. I mean, but okay, I don't know about the subject, but I think that once you have the photon, the very energetic photon, which by the way, what's the energy of those photons in a few GVs, I expect? Yeah, it's expected to be around the five and 15 GVs. Yeah, so once this photon, this is a virtual photon or a real photon, but which spontaneously interacts with some field and so produces a pair of, decays basically in an electron positron pair. So it can also decay to a pair of muon and muons. Yeah, I think there has to be some probability that this process happen, but probably at a higher intensities. Yeah, probably the rate, which was his question, is very small, but on the other case, this would be very nice event because it would be very clean. Yeah, probably around the peak intensities in the case of laxi experiment. Yeah, you will have maybe one in, I don't know, a very high numbers of electron pair production. Okay, let me see what he's saying that do we really need a muon B now? E was around 17 GV, the energy of the electron. I don't know, see why muons cannot be produced? I think this is what we discussed. Yeah, I mean, there has to be some, but what I'm trying to say is that I think if you are only considered electron beam to produce muon pairs later, the rates are going to be quite small. I don't think of this experiment as a way to produce pair production. I see that the other case would be maybe the right way to see. If you really want to see muon pair production, you have to do it in another way. All right, so okay, but in any case, I think it could be a simple exercise to change the mass instead of putting the mass of the electron, put the mass of a muon and see the rate. And who knows, I mean, sometimes naive questions are not so naive, I don't know, but are leads to something. So I have also another naive question. And basically a few years ago, we were discussing as an option for the linear collider, a few years at the beginning of this decade, a gamma-gamma collider option. But then they dropped that option, but some people continue to say we want to use these free electron lasers colliding with each other and producing gamma-gamma collisions. So these collisions come also in this regime, I mean colliding gamma-gammas basically, so having two lasers between each other. So would you go into this regime or would you get a higher energy regime? Okay, I've heard of this kind of experiment that is going to be performed in Shanghai. So there is people thinking about measuring these kinds of laser-laser interactions. But in this case, I'm not sure about the numbers because you will need very high energy for the laser to see some per-production. As I showed you before, we first produced the high energy photon in a previous process in order to get higher energies. Yeah, I mean, the point is that now when you two lasers collide, you are in an experiment where you can focus on the center of mass system. And so the energy, I mean, whereas in your case is an experiment where you hit a target. So the center of mass energy is not so high as the energy of the photons, right? Because you have a moving center of mass. And in this case, you can achieve a higher center of mass energy. And I don't know what the status is. I mean, 10 years, five years ago, people were still very excited. And then they decided to build a linear collider without the photon collider option. And then they stopped the linear collider optional together and so on. Okay. Yeah, I think it's an interesting case. Also, I haven't really checked the numbers of the rates, but it's also very interesting. And yeah, probably you will see at some point, some process, but I really, I'm not sure of the numbers. I will be, like. And another naive question. And basically, I mean, light by light scattering is very important. For instance, for radiative correction for g mu minus two corrections, for instance, where you have large uncertainties, but they are the uncertainties that are QCD and not QED. Does this relate to the Luxe experiment or not? I would say no. This is only QED processes. All right. So improving QED in extreme conditions. Thank you. Okay. So I mean, I asked more than what I was expecting from a subject where I learned something, but I didn't know anything. So I don't know. We don't have any more questions on YouTube. I have one more question. Nobody kind of also all the time thinking beyond standard model cases. So do you know, or maybe other people also try to do this? Because there are all these theories that propose that there is dark photons that are kind of similar to the photon, but just not as visible as the one that we know. So, or maybe other type of particles like albs, like action-like particles, even though they are not the action from QCD, but you can have some kind of action that couples to electrons. So is it possible, I'm not saying that in your theory to include this, but in the sense, is it possible to use the same experimental setup that you were explaining to detect this type of new particle? So it was kind of the experimental setup that you explained is only for testing QED processes to this number to routine regime or something like that. Okay. There were some ideas instead of using a thin foil. So you use a thicker foil and to have a laser before. So you will have something like light shining through the wall in the first process and then making this interact again with an electromagnetic field to measure something. There are some ideas for this experiment later, they prove the QED processes. Yes, there are some ideas that you can use later, they prove the QED processes. Yes, there are some, I know that there are some thoughts about measuring action-like particles with this. Okay. So yes. Ah, good, nice. Yes. And yeah, maybe later, this will go to something like hidden photons or something like that. Yeah. Ah, cool. Yeah. Okay, thank you. So if there are no more questions, we finish this very great talk and we'll meet in our next webinar. Okay, bye.