 Okay, I think we are live. Hello everybody, welcome back to these Latin American webinars of physics, law physics. Happy new year for those that we haven't seen since the last webinar and it's nice to be here again. So this time we have a very interesting webinar. The speaker is Bradley Cavanaugh from Grappa Institute in University of Netherlands. And first of all, he did the PhD in the University of Nottingham and after that he have done a post-doc in the L-P-T-A-H-E in Paris working with Marco Cirelli. So Bradley if you are there, you can go to your webinar. I remind to the people that is following the live streaming or in the future if you are watching the video that you can subscribe to our YouTube channel and also all the questions that you want to ask to Bradley at the end of the webinar you can write it in the chat that is available now in YouTube. So Bradley, the scenario is for you, the stage is for you. Thank you very much. Thank you, let's see if I can get this to work. Right, okay. First of all, thank you very much for the opportunity to talk. It's a real pleasure. This is my first webinar, so let's hope it goes okay. So I'm gonna talk about a project that I finished last year about in general it's about what information we can determine about dark matter from a future direct detection discovery. But in particular, I'm interested in whether or not we can find out if dark matter is myerana or Dirac or equivalently whether or not it's own antiparticle. Okay, so let's start on the very biggest scales. On cosmological scales we know dark matter has to be there to form the seeds for structure formation. This is the Planck temperature anisotropy spectrum. On intermediate scales, the scales of galaxy clusters the largest bound objects in the universe gravitationally bound objects in the universe. We know there's a huge mass to light ratio that's been observed. So there's a huge amount of missing mass which is attributed to dark matter. If we zoom in a little bit further we get down to galactic scales where rotation curves of galaxies have been known to flatten at large radii since the 1980s. And this again indicates that there's some missing mass component in the form of dark matter on galactic scales. There's one galaxy in particular that we're interested in and that's the Milky Way where we live. And so if we zoom all the way in to the earth you can ask how much dark matter is there near the earth near my house, near the room that you're sat in right now. You can look at the motions of nearby stars. You can model the total mass of the Milky Way and try and work out what that sort of, what that number is, how much dark matter there is. It turns out to be on the order of 0.5 GV per cubic centimeter. And what that means is that there's say one dark matter particle per pint all around you. And so you have hundreds of particles streaming through the room that you're in right now. And this is the principle behind the direct detection of dark matter. They dark matter particles which are GV scale in mass if they are GV scale in mass and they're traveling non-relativistically. So around 100 or 200 kilometers per second they pass into your detector and they hit a nucleus the target nucleus, one of the target nuclei in your detector. There's some kind of interaction although we don't know exactly what's going on inside that interaction and I'll talk a little bit more about that shortly. And then the nucleus recoils. And that recoil gives off energy into your detector which you can measure. You can measure charge or you can measure heat which is basically the crystal heats up. Or sometimes you can measure scintillation light from the energy that's released into the crystal. The hope is that you can measure the rate of these recoils and also that you can measure the energy of the recoils so that you can build up a spectrum for the recoil energy. If from this you should be able to reconstruct some of the properties of dark matter. Okay, before I go on I should certainly mention that this is a sort of theorists ideal view of the world and in reality there are lots of backgrounds that you have to worry about detection efficiencies just the everyday operation of a detector which is very, very hard and very important and we shouldn't neglect that in this whole discussion. But assuming that we could measure the rate of these recoils and their energies pretty well you can ask which properties of dark matter you might be able to extract. Okay, so from the slope of the recoil spectrum you should be able to extract the dark matter mass. This is just because the mass of the dark matter tells you the typical kinetic energy that each particle carries which tells you the typical recoil energy which your nucleus will carry away. Okay, and so different masses of dark matter particle here will have a different sort of characteristic recoil energy but it turns out that adding more and more experiments different nuclear targets allows you to pin down better and better the mass of the dark matter particle in the case of some future discovery. If you have multiple experiments and plenty of data you could imagine measuring not only the mass of the dark matter but also its speed distribution. Okay, in this case you don't know the kinetic energy of the dark matter particle both because you don't know its mass but also you don't know how quickly it's traveling. And so you can develop techniques for extracting both of those things at the same time. So here using a Zenon target argon and also Germanium you can try and measure the dark matter mass which is in this mock scenario you have a 50 GB dark matter particle which you can try and reconstruct. But then at the same time you try and reconstruct the shape of this speed distribution which is just the fraction of particles which have a particular speed. And it turns out that this is all stuff you can do. And it helps as it guides us into understanding which experiments should be built which experiments are the best to try and extract as much information as we can from the dark matter particle once it's discovered. So the other information that I'm gonna talk about today is not the mass of the particle or how quickly it's moving but whether or not it's a Dirac type or Myerana type particle. So if it's Myerana then it's its own antiparticle if it's Dirac then there are both dark matter particles and antiparticles streaming through your detector. And a couple of years ago, Farinaldo-Carros, Bernhard Rohde-Johann and Carlos Yaguna showed that the cross section for dark matter on nuclei should scale differently with the number of protons and neutrons depending on whether your dark matter is a Dirac particle or a Myerana particle. Okay, so I'll sort of revisit this argument and show you how it works. And then I'll look at some plausible experiments which are going to be up and running hopefully sort of between 2020 and 2025 and show you what chance we have of distinguishing between Dirac and Myerana dark matter. And this tells us something, I mean, this should help pin down sort of the theory of new physics where this dark matter particle is born. And so running through this whole talk is kind of a theme of asking which experiments we should be building and what we should be doing to get the most out of a dark matter discovery. So just in case the feed cuts out or people stop watching, here's three kind of highlights, three take home messages from the whole thing. Okay, so the first is that it turns out this is possible. You can distinguish dark matter as either Dirac or Myerana using upcoming, upcoming ton scale experiments, okay? And you need several of these different experiments to be able to do the job. And the second thing is that there are particular experiments which turn out to be really good for this, okay? And silicon detectors, as I'll show later on, because of the number of protons and neutrons they have, are a really nice detector to have, okay? And so this sort of is a motivation. It guides us in saying maybe we should be looking into planning for a large scale silicon detector if this is something we're interested in. And then the third thing is that everything that I'm presenting here should be 100% reproducible. Okay, so I'll share the links later on in the talk, but all the code is online, so you can check the code, you can make fun of how badly it's written, or if you find it useful, you can reuse it, okay? So they're the three key takeaway facts before I get down into the details. So Dirac versus Myerana dark matter. So we start off with the question of how does dark matter interact with nucleons? And as I alluded to earlier, we don't really know, but we can have a decent guess, okay? And so this is one of the ways you can do this is by writing down all of the possible interactions that you can imagine. Okay, so here I have some interaction Lagrangian between dark matter particle chi and nucleons N. Okay, and I'm just writing down possible terms that I can think of, and then this list carries on down off to infinity, lots of higher dimensional operators that we can think of writing. The point to notice is that some of these are typically sub-dominant. We don't always care about all of these interactions, even if they're there. So this term here, this axial vector interaction between dark matter and nucleons leads to a spin-dependent interaction. So a coupling between the spin of the dark matter and the spin of the nucleus. The spin of the nucleus, some nuclei don't have any spin. Typically, the spin of the nucleus is relatively small. It's order one or so. And so this tends to be sub-dominant compared to some other interactions, okay? And so we might be tempted to just forget about it all together. Interactions that we probably can neglect are what I've called velocity suppressed. And these two here, and many, many more below here, when you try and calculate the cross-section for these interactions, you find that you get some powers of the dark matter velocity appearing. Because the dark matter is traveling non-relativistically, these tend to be highly suppressed compared to sort of the leading order terms. Okay, and so if we neglected all of these interactions, we would just be left with these two guys up at the top. Okay, so let's do that. Let's assume that these two are the only interactions we have to worry about because the others are all suppressed in somewhere or another compared to these. And these, you might recognize as the standard spin-independent interactions, sort of scalar-scalar interaction and a vector-vector interaction. And each of these interactions just essentially counts the number of nucleons in the target. And so you get a coherent enhancement in the cross-section. So larger nuclei tend to give you a bigger cross-section, which I've sort of expressed here schematically. It's worth noting though that these two interactions act differently under the exchange of particles and antiparticles. Okay, so this term, it turns out, is even under that exchange. So this coupling has the same sign if we're interested in particles and antiparticles. This interaction here is odd. So if we exchange a particle for an antiparticle, then the sign of this term changes. Okay, and that's gonna become relevant shortly. So let's look at how these interactions look separately for Majorana dark matter and Dirac dark matter. So for Majorana dark matter, the case is reasonably straightforward because this interaction is not allowed. This vector current vanishes and all we have is this single interaction here. Okay, and then the cross-section for a Majorana dark matter particle acting on a nucleus A here, labeled it by its mass number, is just given by this formula here. It's just a coherent sum over all of the nucleons, all the protons and neutrons. This is the number of protons, this is the number of neutrons. Okay, how does the Dirac case compare? In this case, you have both interactions allowed. And as I said before, this lambda NO term is odd under the exchange of particles and antiparticles. Okay, so you have the same situation as you had before, except the couplings are slightly different, depending on whether you have a particle involved in the interaction or an antiparticle. Okay, so antiparticles have a minus sign here, particles have a plus. And you can see that I've rewritten things in terms of these two couplings, coupling to a Dirac particle and the coupling to a Dirac antiparticle and it's clear that because of the sign change, there should be two different couplings. And when you follow the same procedure through, you find that for a Dirac particle, for a Dirac dark matter, you have two contributions. You have the contribution from particles, dark matter particles and the contribution from dark matter antiparticles. Okay, and these couplings, these four different couplings here don't all have to be the same. I mean, they will be related in some way, but they don't necessarily have to be all the same. And then we get a factor of one half out the front here because in the case of symmetric dark matter, you expect half of the particles to be particles and half to be antiparticles. Okay, so it looks similar to the Majorana case, but slightly different, okay? And you can do a little bit of algebraic juggling to decide how different exactly it is. Okay, so the idea is to take your Dirac cross-section and try and get it into the same form as a Majorana cross-section to see where the difference lies. Okay, this is a reasonably straightforward sort of algebraic manipulation. We redefine some constants here and find that the Dirac cross-section can be written in this way. So you have this term in square brackets, which looks very much like your Majorana cross-section plus this extra term, which has a different dependence on the number of protons and neutrons, okay? And it's also controlled in some sense by this parameter F. F is just some combination of the coupling of the particle and antiparticle to protons and neutrons. Okay, so you might notice that if F equals one, this thing vanishes and your particle just looks like it's Majorana, okay? Because in that case, this vanishes and you just have this term. Similarly, if F is minus one, you get an overall minus sign here, which you can absorb into a minus sign here. And it turns out that also has the same form as the Majorana case. So you have to be a little bit careful because there are scenarios where you can't distinguish between the two just because the couplings are chosen in such a way that the scaling is the same. Okay, but assuming that this F takes sort of general values, what this means is that the cross-section for dark matter scattering on a nucleus scales differently as you change your detector, depending on whether or not you have direct dark matter or Majorana dark matter, okay? And so you can imagine building several detectors and measuring the cross-section in each and seeing whether you have a consistent picture. Okay, before I show you a sort of visual example of that, it's worth just discussing very briefly and with other spin, with dark matter, with other spins. So far, I've talked about fermions, I've talked about spin half dark matter, but it turns out that the whole discussion follows equally well for scalar dark matter or for vector dark matter. It turns out that in that case, you also have two spin independent operators, one which is even and one which is odd. And so much of the discussion that I'm talking about now follows over quite straightforwardly to a more general model where you have dark matter which is spin zero or spin one. Okay, so the question was, can we distinguish Majorana from direct dark matter? Okay, and so we imagine the following setup. This is a sort of illustration of how this would work before we get onto the sort of technical side of looking at real or proposed future experiments. So the idea is that you assume your dark matter is Dirac and you choose some couplings for it. These couplings look like they've been chosen at random, but it turns out these couplings give you a good chance of discriminating Dirac from Majorana. So you calculate your dark matter nucleus cross-section and then you assume that you've built a xenon experiment which measures that cross-section to about 20% precision. And then you attempt to fit that value of the cross-section assuming instead that you have a Majorana particle. And when you do that, you get two bands here, these two red bands, which are just the values of lambda P and lambda N, which give you the measured value of the cross-section. So now you, so all of these parameter values are consistent with the cross-section that you've measured. So then you go away and you build another experiment, you build an argon experiment. This has a different cross-section, which is measured. The slope of, so in this case, you can also ask, you know, what are the consistent values, what are the values of lambda P and lambda N, which fit the observed cross-section. And we get another set of bands in slope because the number of protons and neutrons in argon is different from xenon. And so what you see is that there are two regions now of this parameter space here and here, which are consistent with a Majorana interpretation of the data. And this is where we need a third experiment to see whether we can build a consistent picture. So now we add a silicon experiment. And again, you get a different set of bands. And what you notice is that there is no part of the parameter space where you can consistently explain each of the three cross-section measurements just in a simple Majorana interpretation. Okay, and so you would be led to conclude that your dark matter must be a direct particle. In this case, I've assumed that you measure the cross-section to the same precision in all three experiments. But, you know, things can really, really mess up this approach. This is a very simplified idea, for example. If my uncertainties on the cross-section measurement are much larger, then I start to notice areas where these three bands overlap. And so I could get a consistent picture here just because I don't have the necessary precision to measure the cross-section well enough. Okay, and we now have to worry about exactly how you would do this practically in an experiment. The best thing to do is not to measure the cross-section independently in three experiments and overlap these bands, although that's quite a nice visual interpretation which will help quite a bit. But instead, we want to do something slightly different. So let's look at future experiments. So we considered a number of different experiments which had been proposed, so xenon and ton, deep 50, Eureka. The idea is that all of these should be giving data between 2020 and 2025. Okay, and so we get a number of different target nuclei that we can look at, xenon, argon, germanium, calcium, tungstate. And what we also considered was silicon. Silicon is funny because no one is proposing a large-scale sort of few hundred kilogram silicon detector. But as we showed, it turns out to be really important in allowing us to discriminate Dirac from Majorana dark matter. And the reason for that is because silicon has the same number of protons and neutrons. Okay, so this ratio here, protons over neutrons is one, whereas for argon, it's something like 0.8 and xenon 0.7. And what that means is that the slopes of those bands that I was showing you earlier can be very different and that it turns out gives you a really good handle for discriminating between the two models. So we chose four different ensembles. We said we're probably going to have a large xenon and a large argon experiment in the future, but what's the best thing to supplement that to get the best discrimination possible? It turns out this ensemble D is the closest to sort of the truth, if you will. This is the xenon n-tun plus deep 50 plus Eureka has this combination of germanium and calcium tungstate. And so with this ensemble D, we're really asking if plans carry on as they are now, what are the chances of discriminating these two things? So before we get to the results, I have to tell you in a little bit more detail what we actually do. So the idea is that for a particular set of parameters, these couplings lambda p and lambda n, and this parameter f, you generate some mock data for your experiments. And then you calculate the likelihood, the maximum likelihood under two different hypotheses. One of those is that the dark matter is a Myrona particle, in which case you constrain f to be plus or minus one, which gives you the same cross section that we had before for Myrona particles. Or it's Dirac-like in which case you fit all of these parameters. And then you can calculate how well you can discriminate these two scenarios just by taking the log likelihood ratio. And then you repeat that 100 times and see what the median significance is. Okay, so that's how well do I expect to discriminate Dirac from Myrona dark matter in about 50% of cases. As I said, towards the start of the webinar, all of the code for this is all online. Won't go through the code right now. But I will just say that it was a great experience to put the code online. One of the reasons that we did it was because the techniques that we used to calculate these likelihoods was a little bit strange. We couldn't really describe it in enough detail in the paper. And so making the code public means that everyone can see exactly what we did. If anybody wants to reproduce what we did, it should be straightforward because it's all there. If people want to use this method to test their favorite model, they can do it using the code that we have rather than having to go away and redo the work. And finally, in preparing the code to be made public, we discovered actually a couple of mistakes. In commenting and explaining and checking the code, we discovered that there were some problems. And so actually making the code public made it better. So if you're interested, you can check out the code here and I would encourage people to try and make their code public so that everyone can see the whole part of the process. This webinar and the paper are essentially propaganda, whereas the code is the real work that went into it. Okay, that's enough for me on open science and reproducibility. Let's talk about some actual results. So each of these panels corresponds to a different dark matter mass. So we have 5300, 1000 GeV. And we're looking here at Ensemble A. So this was Xenon, Argonne, and Silicon. These contours correspond to the significance with which we can discriminate Dirac from Majorana dark matter. Okay, so the darker you get, the higher the significance. Okay, this black star is the point where you get the maximum significance. So you see that in each of these cases, different masses for this particular ensemble, you can get a reasonably good discrimination at least in some parts of the parameter space. So you can get four or five sigma discrimination. So you can really concretely say, this is definitely Dirac. If the particle parameters are just right. And the significance of this part of the parameter space that I'm showing you actually is for F very close to minus one. And the reason for that is that you only really get a good discrimination when there's some kind of cancellation in one of the cross sections or in multiple in some of the cross sections. Okay, so when this F is close to minus one, then you effectively get, you can bring this term inside the square brackets and you effectively get a minus sign here. And then also if you've tuned these lambda P and lambda N couplings correctly, then you can get an almost complete cancellation for one of the cross section of one of the new PI. Okay, so for example, these dashed lines show you where that cancellation occurs. So this line, in fact, this dashed line here is when this ratio of couplings is given is the same as this ratio of protons to neutrons for xenon. Okay, and so along that dashed line, close to minus one, the greatest cancellation in a xenon experiment. And why is a cancellation good or why do we expect to get a better discrimination when there's this kind of cancellation? Well, the best thing to do is again, to return to this visualization that we had. And it turns out that if you get a cancellation in your argon experiment, for example, it makes these bands narrower. Okay, so what it means is you observe fewer events than you would expect in your argon experiment makes these bands narrower. And the narrower the bands, the better chance you have of discriminating and determining whether or not there's any overlap between the bands. I expressed in a different way you could say, if I observe lots of events in one experiment and very few events in another, that gives me a better hint that something strange is going on, there's some strange scaling happening. Okay, so in this case, using these three detectors, you can get a reasonably good discrimination, at least in this region of the parameter space where there's some kind of cancellation. If we move on to a different ensemble, including germanium instead of silicon now, we seem to do much, much worse. Okay, we're limited to a very small region of the parameter space, very close to minus one. And also we never achieve anything more than about three sigma, even in the best case scenario. The way to see this is to notice that argon and germanium have similar ratios of protons to neutrons. What that means is that these bands more or less completely overlap. Okay, so adding a germanium experiment on top of an argon experiment doesn't really give you very much information. You want an experiment which has a very different number of protons and neutrons to try and discriminate as much as you can, to make sure that there's no overlap between these different bands. Okay, and we can carry on. This again is with xenon and argon plus a calcium tungstate detector. In this case, you do a little bit better than the previous case, and this is in part because calcium tungstate has multiple different nuclear targets. So you get a bit of improvement in the discrimination because you essentially have multiple bands running through that plot that I showed you earlier. Okay, and then we can move on to this final case which I said was closest to the truth, if you will. And in this case, we again can get up to four, perhaps five sigma in certain cases, but you'll notice that it's not nearly as wide a parameter space that we can explore with ensemble D compared to what we had with ensemble A. Okay, so if I go back and compare on the left-hand side, this ensemble with silicon, which had a very different number of protons to neutrons compared to xenon and argon, and on the right-hand side, I have quite a few different targets, but it turns out there's quite a lot of overlap in terms of how many protons and neutrons they have. Okay, and so in this first case, you can explore a much wider area of this parameter space compared to in the second case. You can quantify that a little bit better or a little differently by asking if I build a big xenon detector and a big argon detector, and then I want to know how big do I have to build my silicon detector or my germanium and calcium tungstate detector? How big do I have to build that to discriminate at the three sigma level or at the five sigma level? Okay, the particle, the coupling parameters that I've chosen here actually correspond to these two red squares. So you should expect to get a reasonably good discrimination in both cases, but this just sort of quantifies that in terms of how big a detector you need. So in some cases, you perhaps, to achieve the same significance, you might need a factor of two or three or four, larger germanium and calcium tungstate detector, whereas in other cases, you're talking about 10 or 20 times the exposure needed to achieve the same significance. So just by using a different target material, you can really gain a huge amount of information and you have a lot better chance of determining whether or not this thing is particle, antiparticle or whether there are no antiparticles. So I'm getting close to the end now. I should just probably mention something about fundamental couplings or at least the particle physics origin of some of these models, because I've been discussing mostly these sort of derived couplings, sort of called lambda N, lambda P, F, but I started off with these Lagrangian level couplings and it seems like I've completely forgotten those. Hey, but you can do this mapping. It's 10 or 20 slides back. You can perform this mapping and see what values of lambda N and lambda P give you a good discrimination, which is these are parameters I've chosen which give you a good discrimination in general. Okay, and so you see that looking at the values here, there's no great hierarchy in the couplings. Okay, so everything is order one. And so you don't need a huge amount of fine tuning. This isn't such a bizarre scenario. This bit of the parameter space we can probe is not so bizarre. What you do need is isospin violation. So you need to arrange the coupling to protons and neutrons in such a way that there is this cancellation. Okay, you can see that here in the fact that these points all follow, sorry, these points all follow a straight line. And so you need to arrange for your particle physics model to give you this isospin violation if you're going to be able to distinguish Dirac from Myron or Dark Matter. And it turns out that those models have been studied. There are a number around in the literature. For example, there are models introducing a new scalar mediator which mediates this interaction, as well as a new vector mediator mediating this interaction. And you can go through the whole procedure depending on what your favorite model is. So you need to start off at your high scale theory, calculate the coupling to quarks, embed those in the nucleons so that you can get these nucleon level couplings, and then map all the way down to these sort of phenomenological couplings that we've discussed. Okay, but you can go in and do that on a case-by-case basis. And before I finish, I'll sort of put this in a broader context. So I've been talking about whether or not we can distinguish Dirac and Myron or Dark Matter. I'm saying you can in certain cases. And I'm also saying that there are certain detectors which perform better for that particular purpose. And this is kind of happening within a wider universe of people doing lots of interesting things, trying to tease out what information you can get from Dark Matter once we discover it. So I discussed a little bit about measuring the mass and the local speed distribution, a couple of papers out in December about measuring the relic density, or maybe there are multiple Dark Matter particles contributing to the local density. And so I think it's very important to be thinking about these things so that we can come up with a theory motivation or a phenomenological guide for which detectors are the best to build, what kind of search strategies we should be exploring. So in conclusion, well, this is basically we can do this. This is a feasible thing to do. I showed that with upcoming detectors, so in the 2020 to 2025 era, you could perhaps distinguish Dirac from Myron of Dark Matter at the three to five sigma level. And I've summarized some of these maximum significances just here. It turns out that you need to set up a model with isospin violation to give you the cancellations needed to discriminate these, but they're not entirely implausible scenarios. There aren't any current plans for a silicon, a large-scale silicon detector as far as I know, if someone knows about one, then please let me know. But our recommendation is that that would be a great addition to future plans because it gives you a much greater handle on trying to discriminate Dirac from Myron of Dark Matter. And this whole analysis, as I said, is 100% reproducible, hopefully. So you can go look at what we did, check it, apply it to your favorite model and see whether or not you could distinguish Dirac from Myron in the near future. Thank you very much. Thank you very much, Bradley. It was very interesting your talk. Let me just adjust this to everybody can see us. Okay, now you can see us. So we're gonna start with the question round. So first of all, thank you again, Bradley. So for the people that is following the streaming of this webinar, please, you can write the questions in the chat. We're gonna be in meanwhile. We're gonna start with the question for the people that is present in this handout. And okay, the one that wants to start with the first question is free to unmute and go ahead. So, okay. Can you guys hear me? Yeah, we can hear you. Yeah, okay. So in the case of Dirac Dark Matter, sorry, you assume that there's no asymmetry between the particle and the antiparticle, right? Yeah. So what happened in the cable? Do you have a sizable asymmetry? So, well, that's a little, well, I think in that case you really don't have much control over the situation. I think you need to fix the ratio of particles to antiparticles, unless you have a model which gives you the size of that asymmetry, then it's hard to, I don't see how you would disentangle the two, if you had the size of that asymmetry as a free parameter. I mean, if you knew from your model here what the size of the asymmetry would be, then you could, I mean, you just need to change a few constants and then everything should work fine. Okay, thanks. Any other questions? I have a couple of questions. First, if, I mean, you mentioned the stuff that also you, you comment about, I mean, in the sense, can you comment about the cases of different spin? Because it could be very interesting to know if it is possible to check for entire scalar versus complex scalar Dark Matter. Well, let me, let me go to, let me go to the slides, perhaps. So I did have a very quick slide on that. Let's see, generalizing to all the spins. So essentially the same procedure just follows this. What I've written here would be the leading, in the same way that I did for, for fermionic Dark Matter, you can write down, you know, an effective field theory, essentially, of all the possible interactions that you might be interested in. And it turns out that when you do that for a scalar Dark Matter, these are the two leading order interactions which give you spin independent cross sections. And so essentially this becomes your scalar, scalar-scalar interaction and this is your vector-vector interaction. And actually it's surprisingly similar to the fermionic case. In the vector case, I believe it's a little more complicated just because there are some extra terms, some extra interactions involved, but I'm not 100% sure on that. So in principle, it's possible to analyze in the same way the cross section and to get something interesting, no? Yeah, yeah, so everything up to some constants, everything that I've said should also apply to a scalar Dark Matter. So, yeah, okay, very interesting. The another question that I have that is if you consider, for instance, the case of a light Dark Matter, I mean, sub-GV Dark Matter in the case of scattering with electrons, if this procedure can be also tried to address in, I mean, for sure it's not exactly the same because you don't have neutrons in the point of view of the electron clouds, but if some information can be extracted for the case of very light Dark Matter, I mean, sub-GV Dark Matter. Yeah, sub-GV Dark Matter scattering off electrons. Exactly. Now that I'm really not sure. Now I, the key, I mean, my initial thought is that the key here is that you have a setup where you have protons and neutrons and you have particles and antiparticles. And so each of the couplings between those four possible particles can be different for a direct particle, but there's some like correlation between them in the case of a Myrona particle. And so that's what gives you the handle which lets you discriminate. So I'm not sure how it would work if you just have one kind of particle, if you're just scattering off electrons. But it's an interesting thing to think about, basically thinking about which, in a similar way to here, thinking about which interactions are allowed if instead of nucleons you're thinking about electrons and it might be possible to come up with a similar sort of scheme. No, I think because, I mean, sometimes for the case of electron also, you have to consider the angular momentum of the cloud and other type of stuff that maybe could have a different signature for depending on the nature of the interaction of the type of interaction. But yeah, I think it's not straightforward answer in this type of... No, no, but it's an interesting, that would be an interesting thing because what I've talked about can only help you down to say one GV of dark matter particle. Whereas if you have a particle which is lighter, there's nothing you can, there's not a great deal you can do with standard nuclear scattering experiments. So maybe it's related with also with electron, but when you are saying about the silicon detector, are you thinking of CCD detector, do you think of electron experiment or other type of kind of crystal or something like that? I mean, so I was thinking more of a crystal detector. So I know the CDMS-1 and CDMS-2 experiments operated silicon detectors, which I think were just crystal detectors rather than CCD. And I think that's what I had in mind. As far as I understand the CCDs, I don't know if you can scale them up to a large enough mass. So I mean, CCDs are great for giving you, for collecting very small amounts of recall energy. But actually what you need here is not really a tiny amount of recall energy, it's a big exposure of your detector. And so in my head I'm thinking something similar to what a CDMS silicon had, like a few hundred gram crystal scaled up to a hundred kilogram or many of those, many of those smaller crystals multiplied lots of times. Yeah. Okay, so, okay. I guess we have some question from the chat that I don't know if somebody else want to make another question, but I mean, well, I don't know, there is nobody? Okay, anyway. So we have one question from Christian Rivera that he's asking if you can explain in more detail the assuming values for the Dirac-Tarpmatter coupling that you use in your example? Yeah, I can. Yes, let's see, share screen again. Okay, so, okay, so I had these values here, which I seemingly plucked out of thin air, but it turns out that these values I chose to give me a good cancellation in the argon detector. So essentially I think I chose this should give me, let's see if I just move forward a little bit. Sorry, yeah, so this, I think one of these parameter points is somewhere about here. Sorry, the parameters that I chose for that example were somewhere around here. So that kind of explains why the argon band is so narrow in that example. Basically I chose to illustrate using an example where this works very, very well. It turns out that if you pick other parameters, then you really struggle and these bands overlap quite easily. So, yeah, I understand. Another question, I don't know if maybe we have question for here, but I'm gonna, I guess maybe Christian can write in the chat if he agreed with your answer. If you think that his answer was answered. His question was answered. So, but in the meanwhile, we have another question from Ciaran O'Hare. Ciaran O'Hare. Ciaran O'Hare, yeah, sorry. Yeah, so he's asking about, if you assume the case of zero background experiment, then she said, I would anticipate that the neutrino background would complicate this a bit. She's asking about. Yeah, yeah, so, well, that's, yeah, the neutrino background would certainly complicate things. So, the case, well, the cases that I was looking at were mostly around, say, 50GV. If you go down to 10GV or so, or below, a little bit below that actually, then, yeah, the solar neutrino background starts to be important. Yeah, I really don't think, at that particular mass, I really don't think you would be able to, well, you can't detect dark matter anyway at that mass. Once you get down to 6GV and you don't have a way of discriminating, discriminating between dark matter and neutrino from the sun, then it's hard to make your discovery in the first place. At slightly higher masses, neutrinos from the sun shouldn't be a problem. And then, a diffuse supernova background, neutrinos also shouldn't be a problem. They appear at much, much lower cross sections, which we're not really close to probing at the minute. So, yeah, maybe you can say about this in the chat, if you think it's okay. So, but in fact, the stuff that you were saying now, I was thinking, what about complementarity with other type of experiments like accelerator physics? Is it possible to try to also pinpoint asymmetries between Dirac-Maiorana dark matter? I mean, because I think it kind of visualizing the point of view of the Feynman diagrams. If depending if it is Majorano Dirac, maybe you want to have different type of diagram for a particle that has the similar properties of it. Yeah. And so, so I haven't studied this, but as far as I understand, so in my case, I had this scalar interaction and a vector-vector interaction, which show up as, they show up the same in, they show up as identical in a direct detection experiment. Okay, they give you the same cross-section, it's hard to distinguish them. And that's kind of the whole point of what I've been talking about. Can you tell whether one of them is present and not both? Whereas in an accelerator, they should give you different signatures, these two different operators. And so actually that might be a good complimentary test if you have a hunch that you're seeing both of these operators in a direct detection experiment, then I think you should be able to disentangle them quite straight forwardly with an accelerator experiment. No, that's nice. So, I don't know, they are for the people that is asking questions in the chat, please write it as soon as possible, because, yeah, you know that there is some delay between the live streaming, I mean, what we are talking now and what is appearing in YouTube is only like five seconds. They have to consider that, because sometimes we have the stuff that happens that people ask after the webinar is finished. So, okay, you missed it, sorry. No, but anyway, people from the Hangout, do you have more, do you have questions for Bradley? I don't know if you can unmute yourself and ask for the moment. I was also thinking, I mean, in the, yeah, maybe it's not because of the same that you were telling me about the electrons, maybe it's not possible to have these kind of differences in the case of dark matter in the sun, like on the capture rays or something like that, because at the end it's gonna be all the time the scattering on problems only, you know? Yeah. You mean, the scenario that I've been considering with dark matter, nucleon scattering? Exactly, but in the sun. How it modified the capture rays? Because at the end it's, yeah, it's, I mean, in principle the, well, so if you have spin independent scattering, then you scatter off almost everything in the sun, like a little bit from protons, some iron contribution from everything that's heavy in the sun. And I guess it would be very difficult to disentangle. In the end, you would measure one flux coming from the sun and you would infer one capture rate and then I guess it would be very difficult to disentangle the contribution from all the different nuclei. And this is the, so in one of my examples, I had calcium tungstate, which is calcium oxygen and tungsten. And in principle, three, having three separate nuclei that you're scattering off could be great because you should be able to, it's essentially, each one is like a different set of lines in that plot. But when you observe the recoil, you can't always tell which nucleus is scattering. And so it's hard to actually, you can't really draw a distinct, three distinct bands in that plot. And I guess the same would hold for the sun. You know that there's an amount of total capture happening, but you don't know exactly which nucleus is doing most of the capturing. Yeah, no, it's a mess because you don't have control on the target. Yeah, I mean, it's possible that something, it's possible that something happens and, I mean, this would be a good complimentary test. You could, I mean, from, if you had three direct detection experiments, you could then say, I know exactly what the capture rate in the sun should be and then see how it is, but it's hard. Yeah, first of all, it's needed to pinpoint the mass of the dark matter before it goes. Yeah, yeah. But I mean, this is one of the, I think one of the nice things that we showed, and I actually, I didn't show this because it wasn't really the focus, but in each case, we actually fit the mass of the dark matter as well as these couplings. So in these illustrative examples that I showed, we were saying we know the mass of the dark matter in the first place. And one of the confounding factors is that you have to simultaneously fit the mass of the particle and all these couplings. And so we managed to show that that's possible and you get the correct value for that as well as extracting the couplings, which is nice. Okay, so it's very, and at the end it's very interesting. And it's one of kind of fundamental questions about the matter, if it is direct or my own particle or anti-particle. So I don't know if I'm taking now in the chat and it seems that there are no more questions. I don't know the last chance for the people in the hangout. If not, I think it's time to start to close this session of the law of physics. First of all, thank you very much, Bradley. It was very nice to talk. In fact, I was learning a lot about direct detection. No, thank you for the invitation. Thank you. Yeah, it was very nice. So for the people that is watching this video, please, if you think that we're doing a good job, you can leave comments in this video or in the rest of the videos that we have in the law of physics in order to channel. If you like, you can also subscribe. 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