 So, hello everybody. Welcome back to this new webinar session here in the Office of Webinars. So, this is the last webinar of the fourth season. So, we have been already 39 webinars. This is a record for us. And before to start with the webinar itself, I just remind you that you can make, you can follow us in YouTube or Twitter or WordPress. You just have to follow the links that is going to be in the description of this video. And also, all the questions to the speaker, to Tiantian. You have to make it via the YouTube chat of this. You're going to find this chat in the right part of the video. So, let's start then with the webinar itself. Today's speaker is Tiantian Yu. She's a postdoc at CERN. And before she did some postdoc in the CN Zhang Institute for Theoretical Physics in Estonic Brook University. And also she has been a Fermilab graduate student fellow. So, Tiantian, whenever you want to start, you are welcome. Great. Thanks for the invitation. Let me share this. Okay. So, I'll be talking today about some work that I've been doing over the last few years, primarily with Ruben Essig and Tomer Volanski, on different ways to look for sub-GEV dark matter through direct detection. So, as a kind of a way to start off to motivate, I'll talk a bit about the theory background. So, I'm primarily focused on this mass range of KV to TV WIMP dark matter. And so, in this mass range, there's a few ways that you can produce dark matter. The first one is maybe the most familiar one, and it's if dark matter is a thermal relic. The idea here is that, in very early times, the dark matter was in thermodynamic equilibrium with the thermal bath. So, you have this back and forth process between Kai Kai Bar, which is the dark matter, to the standard model. And so, as the number density starts to cool, they cool together the thermal bath and the dark matter. Until you get to a point where the dark matter does something called freezes out. And what this means is that the annihilation cross-section is the size such that the two dark matter particles cannot find each other. And so, you freeze out the number density of dark matter. This cross-section is kind of a nice theoretical target for a lot of dark matter models. And so, the reason why this is maybe the most familiar model for thermal relics, in particular, there's this paradigm called the WIMP. It's so popular. And so, WIMPs are for dark matter masses between GV up to the uniterity bound through 40 TV. The reason why the WIMP was so popular is we have something that's called the WIMP miracle, which is, you can decide for yourself whether you think it's a miracle or not. But the point here is that when you have a dark matter that has weak-skill masses and weak-skill couplings, you automatically get the correct relic abundance. So this is very nice. Another way of producing dark matter is through asymmetric means. And so, the basic idea here is that, so we know in the universe we have a baryon-acing truth because we exist. There's more matter than anti-matter. And we can ask, oh, what if the way to produce dark matter is related to this baryon in asymmetry? And so this is the mechanism in asymmetric dark matter. So the exact mass prediction depends on the way that this asymmetry is created. But roughly, this would predict masses between KV and a few GV. And the final way that I'll talk about that I'll mention later is something called freezing. And the way that freezing works is, in some sense, exactly opposite of how freeze-out works. And the idea here is you have dark matter that's very, very weakly coupled to the thermal bath and has a very low number density. And it slowly, slowly starts to get produced throughout of equilibrium scatterings. And so in this sense, the number density slowly increases as you go forward in time. So here are three different ways of producing dark matter in this mass range. And so how do we look for these dark matter candidates? Well, in the very low mass N on the KV scale, we have astrophysical probes. For example, the Lyman-Alpha force measurements are the ones that set this KV lower bound for a thermal dark matter. In this WIMP regime, in this weak scale regime, we have collider searches. So colliders like the LHC were created to look for new weak scale physics. And so in that sense, they can also look for a WIMP dark matter. These WIMPs can also be searched for indirect detection, which has been a very active field for the last couple of decades. And the current direct detection experiments are optimized for WIMPs. But you'll notice that there's this gap between this astrophysics detection methods and these direct detection methods that currently are unproved. So there hasn't been a lot of experimental work to look for dark matter in this mass range. So how do we solve this? Because I've shown that there's ways of producing dark matter. These dark matter models that live in this mass range that are well motivated. So we should try to look here. So in this talk, I want to claim that we can target this region with direct detection. So very quickly, what is direct detection? The basic idea with dark matter direct detection is you have some target material, which is this blue region that sits deep underground, usually, to shield it from cosmic rays, etc. Somebody is not muted anymore. Okay, you can continue just for a second. Okay, so we have this target material that's somewhere deep underground. And the idea is our galaxy is surrounded by a dark matter halo. So there's dark matter zipping through the earth at all times. And if you assume that this dark matter can have very small interactions with us, then you can say you can look for the scattering of dark matter off of one of the atoms in this target material. And so you can either scatter off the nucleus or the electron, and you look for some recoil of that. And so like I was saying, there's been a lot of progress in the last couple of decades in direct detection. And they've been primarily focused on dark matter nuclear scattering because this is a nice way to look for WIMP dark matter. So I'm showing here is sort of the current state of affairs for dark matter direct detection. Where on the x-axis, I'm showing the dark matter mass and gv, so it goes from roughly one gv to 10 tv. And on the y-axis is the cross section for WIMP nucleon scattering. The blue region is, I think right now, the current strongest bound. I think maybe there is one that's slightly stronger that got updated recently. But this is a bound from lux, which is a liquid xenon detector. And what this blue region means is that lux, because they have not seen any anomalous events, any extra events, that they rule out dark matter nucleon cross sections in this blue region and above. There's future projections from experiments like LZ, which is another liquid xenon detector that's going to come online in the next few years. And that would have a reach of this black dash line. So what this means is it would be sensitive to cross sections of where that black dash line reaches. And then super CDMS, a snow lab of this green line. And here they can go down to slightly lower masses. So they can go down to 400 MeV. The other thing that I'm showing in this plot is the salmon, this red salmon colored region, which I call the neutrino background. And so this is the cross sections where you would not be able to differentiate between a dark matter scattering and a neutrino scattering. And so in some sense, you can think of this as being the lowest you can go in dark matter direct detection if you want to discover dark matter. Otherwise, it's difficult to differentiate between the two types of events. So you can see that in this plot, we're really covering a lot of this parameter space. And so far we haven't seen very much. So in this gap region that I was showing earlier, this was at lower masses, where it was between MeV and GV. So you can ask the question, how do we get down to these masses? I want to go sub GV. And the other thing that you'll notice with Lux and LZ and even the super CDMS snow lab is that they have a lower mass limit. For example, Lux and LZ can only get down to a few GV. And super CDMS can only go down to 400 MeV. So for example, if you have a dark matter that's 100 MeV, then it would be invisible in all of these detectors. So in principle, you could have dark matter out there, but you would just not be able to see it with these experiments. So the question you can ask is how can we access this 100 MeV dark matter through direct detection? So the answer to why this Lux and LZ curve and also the super CDMS curves stop at a certain point is kinematics. So when you have dark matter nuclear scattering, the amount of recoil energy that you have available to detect goes roughly like the momentum transfer squared over twice the nucleus mass. And this goes roughly like 50 KV times the mass of the dark matter squared times over the nucleus mass. So if I take, for example, this energy that you have is available to be detected in a few ways, you can look for photons or electrons. So of course, the more energy that you have available, the more signal you get. So if I take a typical target like silicon, which is what super CDMS uses, the nucleus mass is 28 GV in the dark matter. When we take our typical WIMP dark matter of 100 GV, then we have 100 KV of energy available to detect. Now I go to my 100 MeV dark matter and the amount of recoil energy we have available now is 0.1 EV. So we've gone from 100 KV to 0.1 EV of energy. So the point here is that 0.1 EV is well below the thresholds of any of these direct detection experiments. So you would never be sensitive to recoil energies this small. So how do we get around this? So that was with dark matter nuclear scattering. But you can make the observation that inside an atom, you also have electrons. So instead of looking at dark matter scattering off the nucleus, you can look at dark matter scattering off of the electron. And in this case, the signal that you look for is the scattered electron or a few ionized electrons. If that electron is energetic enough, it'll ionize additional electrons. And in this case, the recoil energy goes roughly like half an EV times the dark matter mass in MeV. So I'll go back to the same example of dark matter scattering off of silicon, but this time it's setting off of the electron. And I take my 100 MeV dark matter and now I have 50 EV of recoil energy available to detect. And this is starting to get in the realm of possibilities of some of these experimental programs. Okay, so the next part of my talk is going to be a little bit more technical, but I'll talk about how you calculate the rate of dark matter electron scattering. So there's roughly three ingredients that go into this calculation. So the very first line I'm showing you the scattering rate or the scattering cross-section is the function of the energy. And so this thing that is in the blue box, this A to B min is where the astrophysics sits. So A to B min is known as the inverse mean speed and this tells you how the dark matter velocity distribution is in our galaxy. And usually we take this distribution to be Maxwell Boltzmann because we assume that the halo is virialized. And A to B min is this distribution over V integrated from a minimum velocity to the escape speed of your dark matter in the halo. What the minimum velocity is, it's the minimum velocity that your dark matter needs to have to scatter off of the electron and give you a certain amount of... So this depends on the momentum of the dark matter. The second ingredient is these things in the red boxes and this is where the particle physics lies. So this is where you parameterize how your dark matter and the electron talk to each other. And so in an effort to make this as model independent as possible, we parameterize it in terms of an object we call sigma E bar, which is a reference cross section for dark matter electron scattering, where we fix the momentum transfer to be alpha ME. And then you can pull out all of the momentum dependence of your scattering and put it into this FDM of Q. And in this way we can present our results in terms of the momentum dependence of the scattering. So for example, if my dark matter electron scattering is mediated by a heavy mediator, then this cross section is momentum independent and FDM equals 1. On the other hand, if it's mediated by an ultralight particle, then the cross section is going to go like 1 over Q squared. So FDM is 1 over Q squared. The last ingredient is this form factor, it's little f, which is a material dependent quantity. And what little f tells you is it's the wave function overlap between the initial and final electron states. So the way you can think about this is it tells you the probability of an electron going from some initial state I to some final state I prime. So with these three ingredients, we can wrap them up altogether. Then you can integrate over your energy threshold, multiply it by the local dark matter density divided by the dark matter mass, and multiply it by the number of target nuclei per unit mass. And now you have the rate for dark matter electron scattering. So this gives you the number of events you would expect to see per unit mass per unit time. So the first example I'll talk about is xenon, which is a noble liquid. And in this case, this form factor is given by this expression I have on the bottom of the slide. So it's a bit complicated. But the point here is that we have these R's are electronic wave functions calculated with Hartree-Fock methods for atoms. And the Hartree-Fock method tells you that you can think of each atom as being this isolated atom, and you can get these wave functions out of it. So for a hydrogen atom, this method is exact. We've done this in class before. And for more complicated atoms, you have to do some approximations, but it's fairly accurate. So with this form factor, I can now calculate the number of events I would expect in a xenon detector. So on the right hand side, I have a schematic of xenon. So xenon has atomic number 54. And the electron configuration for xenon I give down on the bottom right hand screen. On the left plot, I'm showing you a spectrum of the number of events you would expect to see and the function of the number of electrons that you get out of the process for a dark matter mass of 1gV and 1,000 kilogram years of exposure. And here in particular, I'm showing you the spectrum for the FDM equal to 1, so the heavy mediator case. And so the different colored lines tell you the contributions from the different shells of the electrons. So on the bottom right, I have the electron configuration. And so the different colors correspond to the electrons that live within those shells and how they show up in this spectrum. So you can see that at really low number of electrons, it's the outer more shells that contribute the 5p5s shells. And then as you go deeper and deeper into, or as you get higher and higher energy, the number of electrons corresponds to the energy, you start to probe the inner shells. And so the 4d turns on and the 4p turns on, 4s turns on. This black line is the total rate that you would, the total number of events you would expect to see. And this gray shaded band is this uncertainty from the secondary ionization. So what this means is you scatter off of one electron. If you have enough energy, if that electron has enough energy, it'll ionize secondary electrons. But this process is not known exactly. So this uncertainty is what's in the gray band. Okay, so now that I have a rate calculation for the dark matter electron scattering cross-section, or the number of events I would expect to see, I can compare with data. So I was saying before we have these bounds from LUX and the future LZ, which are xenon detectors. And some other examples of xenon detectors are xenon 10, xenon 100, xenon 1 time. So these detectors are called two-phase TPC, time projection chamber experiments. And they consist of a bulk of liquid xenon, which is this LXE, with a layer of gaseous xenon on top. And then on both ends, they're end capped with photomultiplier tubes. So for a WIMP search, what they do is they look for a direct scintillation signal. So this is this S1 where the WIMP scatters off of the nucleus and it produces a scintillation. The backgrounds for WIMP searches would only produce an S2, which is these secondary electrons that produce photo electrons that are then detected. And by looking at the ratio between S1 and S2, they discriminate between WIMP signals versus background. However, in the dark matter electron scattering case, you need an S2 only signal. What this means is you don't have this direct scintillation signal from the WIMP scattering off the nucleus because it's not scattering off the nucleus, it's scattering off of the electron. And the electron gets drifted up and you detect that electron itself through its S2 signal. And so here what the measurement is is photo electrons. So each electron would produce a certain amount of photo electrons. And so for example, for xenon 10, they've done an S2 only analysis. Let's release the data for that, which you can see on this PRL on the right-hand side. And so what I've taken here on the left-hand side is I take the xenon 10 S2 only data, which is the orange, these orange bars. It's the number of S that they see as a function of photo electrons. And so for xenon 10, one electron produces 27 photo electrons. So the inset shows you the binning in terms of number of electrons. On top of this, I've overlaid the spectrum for two different candidate dark matter events. So in blue is if the dark matter is 10 MeV. And you can see that it peaks at low electrons. So it mostly populates the one electron bin and populates a little bit in the two electron bin. The red spectrum is for a 1GV dark matter. And you can see here it gives a more even distribution across electrons. So it populates both the one electron bin all the way to the seven electron bin. And so what you can do here now is to set a limit on the cross-section. So you assume that all of the events that you see are dark matter. And you say, what is the cross-section that I need to explain these events that I see through dark matter? And so by asking this question, then you can set limits on the dark matter electron cross-section, which I'm showing on this slide. So on the left-hand side are the limits for a heavy mediator, FDM equal to 1. And the right-hand side are the limits for a light mediator, FDM equals 1 over Q squared. The black line is the total limit that you get. Whereas the different colored bands are the contributions from the individual bins. So before in this plot, you can see in the inset I have these different bins that are demarcated for one electron, two electron, three electron, etc. And so these bands roughly correspond to one electron threshold, two electron, three electron, etc. So you can see that on the left-hand side are low masses. It's the one electron bin that dominates. So this we saw in the spectrum that the 10 MeV1 really populates the low bins. And as you get up to higher masses, it's the higher bins that set the limit. On the right-hand side, for the ultralight mediator, we see that it's the one electron bin that sets the limit, no matter what. And the reason for this is because you have this 1 over Q squared suppression. And so, or you can think of as being you get an enhancement when you're at very low momentum. But when you're at low momentum, it means that you don't have very much recall energy available to detect. So you mostly populate this one electron bin. We can do the same exercise with xenon 100. So xenon 100 also had a S2 only analysis that they released last year with this spectrum on the right-hand side. And on the left-hand side, it's the same thing as the previous slide. But now for xenon 100. And xenon 100, one electron produces 20 photo electrons. So we can do the same exercise here. And the xenon 100 limits are the ones that you see in red or these red lines. So on the left-hand side, so the other point, sorry, I forgot to mention here is the xenon 100 data started at four electrons. So they didn't show any of the data below four electrons. So they have a threshold for electrons. And so you can see this in the effects of that threshold in these two plots. So on the left-hand side, you see it because xenon 100, it's not able to go down to as low of a mass as xenon 10. Well, it's on the right-hand side because you require at least four electrons. And I was saying for the light mediator case, the limit is set by the one electron bin. The xenon 100 is not competitive with the xenon 10 in this case. Okay, so I've showed you these limits without very much context. And I started off the talk with a discussion about different dark matter models. So we can now kind of put these limits in terms of a very specific model. And the model I have in mind is a model of a hidden photon. The way that the dark matter interacts with the electron is through a hidden photon. So on the left-hand side, I have this little diagram of a dark matter scaring off of an electron. The dark matter talks to what I call a hidden photon, which I denote by A prime. This hidden photon kinetically mixes with the regular photon, which is A, through a mixing epsilon, which is where this red X is. And the regular photon talks to electrons. And so I've shown here it's many equations, but it's the expression for sigma E bar and FDM in this very specific model. And so the pink to note here is on the bottom with this FDM. You can see that when you have a heavy mediator, this goes roughly like one. Whereas if you have a light meteor, so the hidden photon is much smaller than the momentum scales, it goes like one over two square. Okay, so in terms of this dark photon model, here where the xenon bounds sit. So in the gray I'm showing on both sides are limits on dark photon models from other experiments or other searches. So on the left-hand side, the lower masses are constrained by beam dump experiments, which look for dark photons directly. And on the right-hand side, the limits are set by current direct detection. So these are the nuclear recall experiments and collider. So the collider bound is primarily set by Babar, which is an E plus E minus collider that looks directly for dark photons. You can see that the xenon, 10 xenon, 100 bounds. It's hard to see in this plot, but around, let's see, 50, I think, 60 MAV. There's a little gap where the xenon bounds are in principle the strongest bounds that you have. So right-hand side, we have at low masses bounds from supernova cooling constraints, which constrain very light masses. And on the heavy mass side, you have the current direct detection constraints. But because, in this case, you have this one over Q squared suppression, you don't have bounds from colliders or these beam dump experiments. So there's this middle ground between a few MAV to a few tens of GV where there are no constraints at all. And the only constraints that you can set now are from these dark matter electron scattering direct detection experiments. So this model on the right-hand side is really where the strength of this technique comes in. In both of these plots, I'm also showing these kind of yellow, gold, orange lines. On the left-hand side, the yellow line is this freeze-out cross-section if you have a scalar dark matter. So earlier, I was saying one way to produce dark matter is through thermal freeze-out. And the cross-sections that you would need to get the observed relic abundance are at this yellow line. If you have an asymmetric model, then the cross-sections that you would need are this orange line. So in this case, I assume that my dark matter is a fermion. And you need to be above this line. So these are nice theoretical target regions for the heavy mediator case. On the right-hand side, I'm showing the line for a freeze-in model. So remember, this is where your dark matter is produced through freeze-in. And the cross-sections that you would need to produce the observed relic abundance are in this gold line. So these are, for this particular model, motivated regions that you want to be able to reach with these experiments. Because they're theoretically very interesting. So theoretically interesting targets. So when I did these in-on bounds, the thing that I assumed was that all of the observed events were signal. And so, okay, with this assumption, then you can start asking some more questions. Like, oh, how can I start to differentiate the signal? Can I start to look for interesting features in the signal if it's all dark matter? And one feature that you can look for is something called annual modulation. And so the basic idea with annual modulation is that it said that our galaxy is surrounded by a dark matter halo. Or it's enveloped in a dark matter halo. Whether dark matter is realized. The sun is going around the galaxy in some specific trajectory. And through the motion of the sun, you create an effective dark matter wind in the opposite direction of the sun. And our earth is going around the sun. And so depending on whether the earth is going in the same direction or the opposite direction of the sun, you either have a dark matter headwind or a tailwind. And the consequence of this is when you're going in the same direction, for example, in June, you would expect a slight increase in the rate of dark matter events because the flux is higher. Whereas in December, you would expect a small decrease in the rate. And so as a result, you would expect an annual modulation in your rate of dark matter events. So what are the sizes of these modulation? So in xenon for this dark matter electron scattering, I'm showing here it's the fractional modulation as a function of the number of electrons that you see. So this f-mod I define as the rate in June minus the rate in December divided by the mean. And we can see that we have modulation rates of a few percent up to a few tens of percent. So these are actually fairly sizable modulation signals. And so the light blue lines are for a 100 MeV dark matter and the black lines are for a 1 GeV dark matter. The dashed is for a light mediator and the solid is for a heavy mediator. So the other thing you'll notice here is especially for the dashed lines, as a whole the modulation is higher than for the solid lines. And this is because you have this 1 over Q squared dependence. And so you're sensitive to events that have low momentum transfer, which means that they need to have high velocities. You're sitting on the tails of the velocity distribution. So you're very sensitive to the velocity distribution of your dark matter. Likewise, as you increase the number of electrons that you see, you need to be at higher velocities because you have a larger amount of energy that is needed. So in this way also, this is why you see this increase in modulation as you go up in number of electrons. Okay, so now that we have this fractional modulation, we can do a annual modulation analysis. And the way that you do this is we quote a significance, which is roughly the modulation fraction times the number of signal events you see divided by the square root of signal plus background. And if we set this value to 1.645, we can set a limit at 90% covenants level. So we do this. So here I'm assuming that I have 1000 kilogram years of exposure. And I'm showing two different colored lines. So the blue line is for Xenon10 and red is for Xenon100. What I mean by Xenon10 and Xenon100 is I assume that I see the same rate that the Xenon10 or Xenon100 experiments see now and just scale it up to 1000 kilogram years. So this is my background, my B in the previous expression. And with this value, I can set these kinds of limits. So you can see with 1000 kilogram years, you can start to probe a lot of these theoretically interesting regions. So the point is because you'll have a lot of events, it's worthwhile to look at annual modulation in these cases. Okay. So I've pointed out, I keep pointing out these theoretically interesting target regions. And so you can ask, okay, how can we reach these for Xenon10? Okay, if we have 1000 kilogram years, you can start to reach them. But with the Xenon experiments also they curve up a few MEV. So if you want to go below a few MEV, you have to come up a new way. So what's limiting the reach of these Xenon experiments? One limiting factor is the electron energy. For example, in a noble gas, the minimum amount of energy you need to ionize one electron is roughly 10 EV. So for Xenon, it's 12 EV, it's ionization energy. So this sets the limit on the lower mass reach. So if you can decrease this energy requirement, you can start to reach much lower masses. And so in this case one alternative you can look at is semiconductors, which have bandgaps of one EV. And the bandgap is roughly equivalent to the ionization energy. The other thing that limits you is the number density. So Xenon was a liquid and it has this density that I have on the screen. Whereas a semiconductor like silicon is a solid, so it's much more dense. And so you have many more targets per volume to scatter off of. So this would allow you to go lower in cross section reach. So the point here now is, okay, we should start looking at other materials. And one nice material to look at is semiconductors. All right, so semiconductor targets was also very active or is still a very active field of research. And so I have a few references down here on the bottom. And so here's a picture of the energy band structure of silicon that we've calculated matches well with experiment. And the orange region is the field valence band. So these are the energy bands that contain electrons in them. There's four valence bands, there's four valence electrons. And then we have the bandgap. And then we have these empty conduction bands. So this is roughly what a semiconductor looks like. And so some rough numbers for the bandgap energies are for silicon. It's 1.1 EV. For a semiconductor like germanium, it's 0.67 EV. So even less than an EV. We also have, I also list gallium arsenide, which is another semiconductor, the bandgap of 1.5 EV. And some common scintillators like sodium iodide and caesium iodide have slightly larger bandgaps. But these are all smaller than the ionization energy needed for a silicon. And so in these semiconductor targets, what we have is, so we have our electron that lives in the valence band. We have our dark matter that comes in and scatters off of the electron and promotes it up to the conduction bands, and it leaves behind a hole. So once the electron is in the conduction band, you have a couple of options. One is you can apply an electric fuel to have some voltage and you extract the electron itself. And this is what I'll call an ionization signal. The other thing that can happen if you're in a scintillating material is the electron and the hole that it left behind recombine, and this produces a photon. And this is what I'll call a scintillation signal. And we have these two different paths depending on the material that you're scattering. And so for a semiconductor, which is a solid, the form factor, it turns out, is much more complicated to calculate than in the xenon case. And the reason for this is because the electrons in a solid are part of a complicated many-body system. And this means they feel the effects of all their neighbors. So we can't have this isolated atom picture, this Hartree-Fock method. It's not accurate for situations like this. Instead, we have to use some more complicated numerical techniques. And so what we did was we went down the hall, and this was when I was still at Stoenberg, and we found conventional condensed matter colleagues and asked them, so we have this problem that we're trying to calculate electrons in a solid. Can you help us? And they said, in fact, this is what people who do solid state do. And there's this code called quantum espresso, which is an open source code that calculates exactly this. It calculates the electronic structure in any material that you want, using something called density functional theory. So what I did with a graduate student, one of these condensed matter graduate students, was we wrote a module, which we call QE dark, which you can find at this website, which takes quantum espresso and calculates these form factors that you need for dark matter electron scattering. And so, okay, with this, then we have some results. So I'll show you the results for silicon in particular. So here is the spectrum, the expected rate that you would see for silicon. I've normalized the rate to one in the first bin. And I'm showing the rate for two different dark matter masses. So in black, I have one GV, and in blue is the 10 MeV. And so you can see that for the blue line, the lighter dark matter mass, the rate falls pretty rapidly as you increase the number of electrons or you increase the energy. Likewise, the different types of lines are for the different form factors, with the most shallow line being the solid one, which is the FDM equal to one case, and the steepest line being the dotted line, which is the one over Q squared case. So here you also see that as you start to increase the number of electrons you require, you're really penalized by this one over Q squared thing. Okay, so I have this spectrum. And then so when I start talking about different thresholds for experiments, what do I mean? So I mean is, for example, if I have a 10 electron threshold, it means you have access to the events living in this blue region. So you can see all events that have 10 electrons or more. If I have five electrons, then you can access more of this spectrum, and you can see more events. And then single electron means you can see all the scattering events that were created. Okay, so how does this look? So here is that same dark photon parameter space plot, which is the dark matter electron cross-section as a function of dark matter mass with the xenon balance. And now I'm showing on top of it are the reaches for a silicon detector with one kilogram year of exposure. And so the blue line is the reach that you would have if you have a 10 electron threshold. Red is if you have a five electron threshold, and green is if you have a one electron threshold. So you really see that as you decrease your threshold, you get huge gains in your reach. Orders of magnitude gains in reach. So currently super CDMS threshold is at 10 electrons. This is the lowest that they can go. So they can start to access some interesting parameter space, but it's still not reaching this theoretically interesting regions. So the question is, okay, can we go lower? Can we go down to single electron? Because if you get down to single electron, you cover basically all of interesting parameter space. The answer to that question is yes. And in fact, through this work, this motivated some of our experimental colleagues to look at this a bit further. And as a result, we now have a collaboration called Sensei. Sensei stands for sub electron noise skipper CCD experimental instrument. CCD somehow didn't make it into the acronym, but it's the most important part of the name. So Sensei is a silicon CCD detector using something called skipper technology, which allows it to have a single to a few electron sensitivity. So here's a list of the people. We're a combination of theorists and experimentalists. It will be at Fermilab. So Javier Tiffenberg was the main person who was really pushing for this. And he was able to fabricate one gram of a silicon skipper CCD. And the next step is so the sensei will be at Fermilab. So on the left is a picture of Fermilab. There's Wilson Hall. And the next step will be to put it inside the Minos Hall, which is about 100 meters underground next to the new me building. We're going to put this one gram there and start to take data. So this is in the next few months that this will happen. And so here's a, this is a very cool plot that Javier showed us. So this is when you take this one gram of skipper CCD and you just count the number of charges that you see in each pixel. And you can see that the, so here the number of entries is a function of the charge that you see. What the really notable thing about this plot is that you can really differentiate between the different peaks. What this means is you can count single electrons. Right. So you can really see the difference between having no, no, no charge, one electron, two electrons, et cetera. Unfortunately, the dark current, which is the thermal fluctuations limit your threshold to two electrons. But what we've demonstrated here is that you, you can get down to two electron. This is not a theoretical prediction or possibly we've demonstrated that you can get to two electron thresholds. So with this two electron threshold and sensei, and the goal is to get to 100 grams here, what, what you would expect to see. So on the left hand side, and this green dash line is if you had sensei with this two electron threshold and you let it run for one month, you would be able to beat the xenon balance and probe a lot of this interesting parameter space. On the right hand side, it's even more impressive because you turn sensing on for one minute. And you can beat the xenon 100 pounds. And if you let it go for one day, you could have the strongest balance for this ultra light mediator case. And then if we can go down to the full of a full year, then you start to probe almost all of this parameter space that is theoretically well motivated. This is sensei. And it's something that should be happening within the next year, year or two. We're applying for funding for this right now. So this is something to keep an eye out for. Okay, let's see how long we're on time. Okay, so in the last part, I'll talk about kind of a bonus, some work that we're still working on right now. And so with these form factors in these solid state crystals, so here is the expression for the form factor with the psi i star. psi i prime, sorry, is the electron wave function for the outgoing electron and psi i is the incoming electron. The point here is that there's directional dependence, right? We have the little vector arrows over our momentum of momentum factors. And so what this tells you is that you potentially could have some very powerful signal discrimination with these solid state crystals. And so one example is, here's a picture of gallium arsenide on the left hand side. This is one molecule of gallium arsenide with the different electrons sitting on it. And these colorful plots I'm showing are the form factors in the ZY plane for gallium arsenide for different values of qx. So you can start to see, so the red spots are where you have a high amount of overlap between the initial and final state electrons, whereas the blue is where there's no overlap. The point here is because the crystal has a fixed orientation that as you rotate it, you would expect a difference in the rate depending on which direction you're hitting the crystal. So here's a picture of gallium arsenide. It turns out gallium arsenide, even though it looks not very symmetric in this picture on the left, it's a bit too symmetric for our case. Instead, we're looking at something called gallium nitride instead, which has this, what's called a crystal worksite structure where you have a hexagon in one plane, and then rectangles in another plane with little pyramids stuck to them on the sides. And so on the right hand side, I'm showing these form factor plots and slices of y and z versus x and y. And you really see that there's a difference in the plots and the form factors depending which plane you're looking in. So how can we exploit this directionality of this crystal? So the idea that we have here is to use daily modulation to exploit this directionality. So here is a picture of the Earth, which is rotating. And we have the direct matter wind, which are these black arrows. And so for example, at 6 a.m., our detector is in this top red square and the wind is hitting the detector on the short side. Whereas at 6 p.m., where it's rotated down to the left hand side of the figure, the dark matter wind is hitting the detector on the long end, the long side. And so for gallium nitride, in this last slide that I showed, you could see that there really is a difference in the form factors depending on which plane you're hitting it in. So the modulations that you would expect for this. So for gallium arsenide, it's sub percent. So gallium arsenide is the blue, these blue curves. This is the modulation is a function of time of day. Whereas for gallium nitride, which is the green lines, we could get modulations of a few percent in principle. So this is for a 100 MeV dark matter mass. Of course, this is still preliminary work where we're still checking the code to make sure it's doing what we expect. But it's kind of a nice bonus of these solid state detectors that you could do. Okay, so I think I'll stop here. So I hope in this talk that I've shown you that dark matter electron scattering allows us to reach sub GV dark matter masses. And currently, the only constraints for this dark matter electron scattering come from the Xenon-10 and Xenon-100 S2 only analysis. But in the future, in the very new future, in fact, semiconductor targets like sensei will be able to push down these limits by orders of magnitude. Because you're sensitive to the velocity tail, because the dark matter electron scattering process is really sensitive to the velocity of the dark matter. And you have a much larger modulation rate than you do in nuclear scattering cases. And when you have a semiconductor target like sensei, or not sensei, but if you have a semiconductor target like with gallium nitride, because of the rigid structure of the crystal in principle, you could have some directional detection, which would be another very nice handle to discriminate between your dark matter signal and your background. That is it. So thank you very much, Xenon-10, for this very complete talk about the sub GV dark matter. And I guess we can start with a round of questions. So first of all, I want to remind the people that you can make all the questions that you want to Q&A via the YouTube chat. So now we can have some time to write questions, try to be precise and short, because of the time that we have for the webinar. And maybe we can start already with people from here from the session, please. The one that want to make a question, please. And you too, it's yourself and ask it. Okay, I have a question. Okay. So first, thanks to the webinar. So my question is about Xenon-10, Xenon-100. I was wondering why typical Xenon-10 gives stronger bounds than Xenon-100? So the main reason for that is because of the threshold. So Xenon-10 had data down to single, they had single electron, single two, three, four electron data, where Xenon-100 required at least four electrons. And so by requiring at least four electrons, the minimum amount of, basically you're saying the energy threshold is much higher. And so that limits you in both the mass and the cross-section limit. Okay, thanks. So I think in principle Xenon-100 has, they have single electron data, I think is what I've been told, but they didn't make it public yet. But if they did have it, it would be probably slightly stronger than the Xenon-10 bounds. So it's difficult for them to clean up the analyses that they haven't publicized yet. Okay. And I have another question. It's about the Trina background. So at the very beginning you show this Trina background starting from, I don't know, maybe one GV or something like this. But you know how does it behave when you go to the sub-GV region? So it's similar. This is actually something that I'm working on with a student right now. It's also preliminary. So I didn't show it. Turns out, so for one kilogram here, you won't reach the, its material dependency, of course. But for one kilogram here, you don't reach the neutrino background. But as you start increasing your exposure at some point, even like a 100 kilogram years, you would start to reach the neutrino background at the MEV masses, like the low end of the pots I was showing. It has a similar shape to the nuclear scattering neutrino background. But yeah, this is a good question because it's like, okay, you can keep pushing down the limit lower and lower, but then that, yeah, exactly. At some point you hit the neutrino background and you become a neutrino detector and on the dark matter detector. But in these cases, this is where it's useful to have like the annual modulation or the daily modulation signals. Because that could help you discriminate between the dark matter and the neutrinos. So it's not completely hopeless in those cases. Okay, thank you. Thanks. So somebody has more questions because I mean, for the moment I also have a couple of questions. The first one is when you were showing these plots like theoretical scenarios that are very interesting, how it behaves in the case of vectors in the sense that instead of scalars you have a vector. This, I didn't look at. I don't know if somebody has already worked out the freeze out cross sections needed for those. Yeah, I remember that for example, for direct attention like in the case of electron, usually this model was more constrained for LHC, I mean missing energy. You're talking about like spin dependent cross sections. Yeah, I don't know with the spin independent or it behaves exactly like a scalar, I don't know. Yeah, this is something we haven't looked at. This is like so we have a lot of things that we would like to do. One of the things is to look at more models. We just have these benchmark models. And so for the heavy meteor case, for example, we look at a very specific ratio. We assume the mediators three times the dark matter mass. But it's also interesting to look at different combinations. So this is something that we'd like to look at. Yeah, and another question is the, I mean, about regarding sensei is this, because you're putting one plot to your lines, your expected sensitivity is going to be for 300 grams. Oh, 100 grams. So my question was this type of detector is also scalable or you build one and upgrades are kind of, I mean, you can add more CCDs. Yeah, you could add more CCDs. And the really nice thing about the Skipper technology is there's only one place that you read out. So the detector itself can be much bigger. So this one gram versus 100 grams. It still only has one read out node node. And it's this read out that was in the past limited your sensitivity, your threshold, because there's noise that's involved in reading out your signal. And to avoid the noise, you usually have a much higher threshold. So if you only have one read out node, you can decrease. So yes, it is scalable. I think it's not 100 grams, I think was feasible. So just to give you some numbers for the 100 grams, like in our proposals, this would be like $1.2 million for 100 grams of the silicon CCD. So if you had more money, you could build something. Technically, it's cheaper than Xenon. Yeah, it's actually, I mean, I think it's pretty cheap. I don't really have a sense of. Yeah. No, of course, if someone Xenon can tell us how much it costs. But anyway, so. Yeah, I have these questions also. I don't know if there are more questions from the people here in this hangout session, because then we can pass to the question from the. From the. It's a question here. So when you show the discussion plots, you, you went till like no three GV or something like this. So you can, in principle, so go to higher masses, right? Okay, I know that you're not interesting. I mean, the most interesting part is the, the sub GV ballpark, but in principle you can go to to GV ish as well. Right. Yeah, you could go to 10 GV. So at some point. It's just, it goes like one over M. So you can just extend those lines. So you can go to higher, but once you get above. I think a few GV, then the nuclear scattering ones are so much stronger. That the dark matter electron scattering becomes very weak. In comparison. So you could do it at those, at those masses, but it's not going to give you the strongest points. Thanks. So you can, I mean, this region, you can test models that are leptophilic cases. Yeah. So yeah, I guess that's the other point. If you have a leptophobic model, then okay. You have to do it. I guess like Chris Covarez and Joseph Prather, we're doing with a Bram Strong. You need a different, a different technique. Yeah. So let's, let's pass. I don't know if, okay. If there's somebody in here in the session who wants to make a question, you can ask it. For the moment, we're going to pass with the question from the people following us in Judo. The first questions, but I already, I guess, Nicolas already did. What's your whole, John's was asking about the, this neutral of floor in this case. But I guess you already said about, no? Yeah. And this is something hopefully in the next few months, we can have a paper with a more quantitative number for that. Yeah. Now there is also there is a question. Miguel Angel is saying to you, red talk. And he's asking about the, I mean, he's, I'm going to, I'm going to read the kind of the context of the question. So it's like, it's like an S2 only analysis is quite interesting challenge. Set reconstruction is much worse without S1. You only have S2 with, and generally they are reconstruction gets worse to us. The S2 gets smaller. So hence you really want a special background model. You need a good treatment of the reconstruction and certainties and a believable spectrum of the low energy wall surface and maybe cut off events. Yeah. This is a great, a really great point. So with these S2 analysis, we don't assume. Like, we assume that all the events were a signal. And so this is a challenge with these dark matter electron scattering is, yeah, the backgrounds are not very well, well known. Partly because I think it was not the region of interest for these experiments in the past. So I mean, more effort was done for these wind, wind searches. But now with, because dark matter electron scattering is getting more interest on people are starting to look at these. The backgrounds in this master range or in this energy range. Some more, but it's like, it's something that requires more, a lot more careful, careful work. Yeah. Yeah, in fact, the question at the end was like, how much you can trust on this? Yes, it's the only but you're saying. So I think. So we've talked a lot with Peter Sorenson, who is on Lux and he's somebody who's very interested in these S2 only analysis. And in fact, I think the main, the main background that you have with these single, these S2 only searches is the fact that your electron can get stuck in the interface. So he claims that he thinks the main background for single electrons is after the scattering, the electron gets stuck in the liquid gas interface and then gets released at a later time. So this mimics a dark matter signal, but has nothing to do with with the dark matter. And he, he has some ideas of how to eliminate the signal. So he had a paper out maybe last month where he had proposed some ideas and he's trying to propose a small, a small mini, mini Xenon experiment to test this hypothesis and to do these S2 only analysis. So I guess. There is another question from Andres Perez. He's asking, let me see. The calculation you have done are for a scarlet matter only, right? Do you expect to have a, to have weaker constraint from spin dependence event? Oh, possibly we haven't, we haven't done, we haven't looked at the spin dependent. It's certainly worth, worth looking at. I'm trying to think of what would change. Yeah, because I guess in the nuclear scatter in case the spin dependent limits are much weaker than the spin independent. Yeah. That's a good question. We haven't looked, we haven't looked into that. Yeah, also gonna depend on the mediator that you put between how interactive that matter with your electrons. Yeah. So for right now we're assuming that the, we just categorize the interactions by the momentum dependence. And there's no talk about the spin dependence or anything. So these are all things you can add on onto it. To do list. Yeah. And now that all the talk that you were saying now with this question, I have another question that is about which other background you expect to interfere with this kind of signal, you expect kind of, I mean, in the case of Sensei, how do you have to shield Sensei to avoid the twins and other type of radioactive background? Putting it underground shields you from, from most of the backgrounds. In fact, Sensei, the primary background or the dark currents and the readout noise. So the dark currents is the thermal, thermal fluctuation set where an electron just thermally pops up to the conduction band and the readout noise is the noise that you get from reading the signal. And so the, with the Sensei, they, what they do is they're able to effectively eliminate the readout noise and the dark currents limit you to two electrons. But outside of that, it's effectively a background free experiment. So there are nine. So there's no, there's no, yeah, there's no neutrons or anything. It's really, it's really impressive. I think I didn't appreciate this until recently that it's really a background, that could be a background free experiment. This is hard to achieve in any experiment. Wow. It's really, it's very impressive. Yeah. So, okay. Ah, another question from, yeah, I mean, we were just because Bigelanger was asking if, doesn't Sensei have any intrinsic background, but yeah, but we were just talking about that, I guess. So if there are no more questions from the people in the live chat, we thank all the people that make questions in the live chat, of course. And I don't know if there are more questions here for the, for the present here in the session of Hangout. So if not, I guess we can close these low physics webinar that we just had. First of all, I want to acknowledge TNT for this very good webinar that she gave. And also to remind the people that don't forget to enter to our YouTube channel to subscribe to follow what we are activities we are going to try to complement with more topics to try to make these low physics webinar as much interesting as possible for all the public that is following us, for all PhD and postdoc students on any part of the work because you can access it in YouTube. So see you on the next time and goodbye. Bye bye.