 Okay. Hello, everyone. Welcome to our webinar, number 123. It's a pleasure to have today Professor Kate Lynch-Schutz. Professor Kate Lynch-Schutz got her PhD at the University of California at Berkeley after which she moved to Cambridge, Massachusetts, where she was a NASA Einstein Fellow and Papalardo Fellow at MIT. And now she's a professor at McGill University in Canada, and we are very delighted to have her today sharing with us some knowledge on Plasmon face-to-face amelie charge particles. Thank you, Kate. Absolutely. Before she starts, just a reminder to everyone that if you have any questions, please ask in the chat on YouTube. I will be happy to read these questions for the speaker at the end of the presentation. Again, thank you, Kate. All right, so let me share my screen. Okay. Okay, can you guys see my slides, all right? Yes. Okay, great. Thanks. Well, thanks so much for inviting me to give this talk. It's my pleasure to tell you about some work that I completed with my excellent collaborators, Chloride Vorkin and Tong Yanlin, as well as some work in progress. And the unifying theme of this work is that we're trying to use face-based signatures to figure out what's happening with hidden sector particles coming out of astrophysical plasmas, particularly the diagram that I have depicted here schematically in this little cartoon, which I'm going to refer to as Plasmon Decay, and we're going to see again and again through the talk. I want to talk about these topics. I want to just really quickly give an advertisement for some work that's actually going to be appearing on the archive tonight. So I'm giving you all a special preview of this work. It's not related at all to the main subject of my talk, but just the two slide version is that if dark matter is made of axions, axions can interact with light. So it's possible that any source of light, any astrophysical source could cause a stimulated decay of axions, and that's kind of what I'm depicting here schematically. You have these photons coming out of your source. They're hitting some little clump of dark matter over here, stimulating a decay, and we can potentially try to look for that on Earth. And we studied this effect. And in particular, when you're looking farther and farther away at clumps of dark matter that are farther and farther away from Earth, you're actually also looking back in time because of the finite speed of light. And so because of that fact, when you actually look at this clump of dark matter, you're seeing a reflection of what the source looked like a very long time ago. So for that reason, supernova remnants are ideal for being these sources of photons in this case, just because they're very bright today and radio waves and they were orders of magnitude brighter in the past. Okay, so here I'm showing just the key figure from our from our paper, where we show the projected reach with 100 hours of observing time on fast radio telescope in China. These different colors which we picked because it's Halloween is coming up so have some autumnal Halloween colors here, they correspond to different supernova remnants that we could try to look for these signals. The bands correspond to astrophysical uncertainties in the modeling of the supernova remnant evolution. But even in spite of these astrophysical uncertainties. We think it's still quite likely that we might be able to explore new parameter space. Okay, so again this is not related to the rest of my talk it's just a two slide summary of something you guys are getting a special preview. I also want to highlight that this work was led by MIT graduate student you can son. This was his first paper of graduate school and he's definitely I think someone to look out for in the future. Okay, so that was just the appetizer now on onto the main course main topic of my seminar today. I have a huge step backwards and trying to look at the big picture. This is how I like to think about the standard model so I've drawn it sort of as a Venn diagram of different particles according to which forces these particles feel. And the fact that gravity is the biggest bubble on this Venn diagram has been really useful. I've already alluded to it's allowed us to infer the presence of dark matter. So, you know we know dark matter sits inside of this biggest bubble of this Venn diagram, but we don't know what it is, and it doesn't appear to be consistent or to fit within the particles that we already know about within the framework of the standard model. So, given everything you see over here in the standard model. You know, most, most of the times we focus on the simplest dark matter theories but over here the standard model is clearly not very simple. So I think it's actually highly conceivable that this dark matter might come along with its own little bubble of it of the Venn diagram. It's possible that this new new stuff this dark matter feels its own forces, there might be auxiliary other particles in the spectrum of this theory that aren't necessarily the dark matter but just come along for the ride. And so then the question becomes, you know, are we in this situation where this new sector is a bubble on its own completely decoupled from the standard model. And in that case we have to only resort to using gravity to learn about it, or could it be possible that there is some, you know, direct overlap there's some. There's some intersection on this Venn diagram, where this new force is interacting with stuff in the standard model. It's actually a more, more optimistic, I would say outlook, if this is the scenario. And in particular, if you think about this from an effective field theory point of view, you can just very systematically enumerate and write down what are all the possible interactions that you can possibly have between this new sector and the standard that would be manifest at a wide range of energy scales. So if you if you do this, you can just be very systematic you can write down all of the kinds of interactions. They include things like a scalar Higgs portal where you have a singlet scalar that mixes with the Higgs, you have the vector portal, more on that because that's going to be a big focus of my talk. Neutrino portal, maybe the axion portal if you are lucky the dimension five operator but you might still have access to it at low energies. Okay, and so because it's a very short list of possibilities. You can just try to be very systematic about really exploring what all of the ramifications of this short list would be and really try to get as good of a handle on the phenomenology as you possibly can. And sort of spirit in mind. I'm going to be focusing today on a case where you have a new sector that's kinetically mixing with the standard model photon. And what we're going to see is that I've drawn this event diagram so it's just very barely overlapping with the standard model. So this is going to be, as we'll see a very very weak mixing with the standard model. And in many cases we're going to need to really have an additional, a little bit of additional sauce coming from gravity or coming from dense media which are going to help us enhance any signatures. Just to get a little bit more specific. The Lagrangian, if you're someone who yeah like likes to look at Lagrangians, if this is helpful. What we're looking at here is a Lagrangian that contains this kinetic mixing term where Kappa is some dimensionless quantity, which is mixing this f prime with the standard model f. The origins of that kinetic mixing can come from a wide range of possible UV origins, including loops of heavy particles or string theory compactifications. So this dark you won this a prime, a small Stuckelberg mass, which is a mass term which preserves gauge invariance and renormalizability, although not in a way that's obvious. And then finally I'm going to introduce a new fermion in the stark sector, and that is going to be a direct fermion and it's going to be charged under this new you won. So, over here when I was talking about the dark photon I mentioned it was a small a small Stuckelberg mass. Just how small are we talking. And here is just a quick plot showing the parameter space for for this dark photon I'm showing the coupling, can I mixing excuse me, Kappa here as a function of the dark photon mass. We can see already that there are some very strong constraints coming from a wide range of experimental and astrophysical signatures. So generally we're going to be living somewhere down here in this white space. Okay, so generally we're going to be very, very sub sub EV so small in fact that usually this Stuckelberg mass is not going to be a relevant scale and the problem from a dimensional analysis standpoint. Okay, so that's the parameter space we're dealing with for the dark photon. And now going back to this Lagrangian, in particular as we'll see today we're going to be working in various media. And so in a medium, basically the standard model photon acquires an effective mass. So what you do is you can put that in and you can rotate away this mixing term. You can put this Lagrangian Lagrangian in the so called interaction basis. And in this basis, the particle that's charged under this dark you one. It has its regular coupling, you know times cheek high this dark you engage coupling to the dark photon, but it also has this additional coupling to the standard model standard model photon which comes along with an additional factor of Kappa. So this new direct fermion appears to be charged under this new gauge group with an effective charge that's like the product of G chi times Kappa. This is called millicharge and this is I think a terrible misnomer that has persisted in the literature for many decades. There's nothing 10 to the minus three about this as we'll see so we're really going to be looking at charges that are much much smaller. Okay, so this is Lagrangian we're going to be working with primarily. There are also higher order terms, which scale like the dark photon mass over the in medium standard model photon mass to various powers. And these terms, in particular the dark photon, or excuse me, the standard model photon mass depends a lot on the kinematics of the situation and it depends on the properties of the medium. So this is for the purposes of this talk going to be in a regime where this is negligible. Okay. And so with this Lagrangian a key process that's going to give rise to these new direct fermions these new dark sector particles is plasma and decay as I depicted in the follow slide. Essentially the fact that in a medium photons have a non trivial dispersion relation means that they can decay to massive particles provide that those particles are sufficiently lights so that it's kinematically allowed and sufficiently controlled so that those particles in the final state aren't receiving a large thermal correction to their mass. And when I first learned about this it sounded super like exotic to me. I just thought like wow like how have I never heard about this before. It's kind of crazy. But then as I, you know, came to know this literature better and better I realized that this has actually been a well known phenomenon that's been studied for many decades in the context of stellar interiors and stellar systems. Just to give you a quick example of what I mean, I think this is, I think this is pretty cool. So if you look at populations of white dwarfs by basically studying their luminosity function so how many of these white dwarfs of a given given luminosity are there per volume. What you expect to see is basically this blue line. This is the outputs of a stellar evolution code, and you can see that matches the data these purple points quite well. And the physics interpretation of what's going on here is that white dwarfs are the simplest star to model in my opinion. They are just kind of born with some temperature and because they're not doing anything too complicated in their interior they're not doing nuclear fusion. They're just cooling down monotonically over time. And so they're born from the left side of the plot and they cool and they as they cool they move to the right side of this plot. The orange dashed line shows what you would expect if you had surface photons cooling down these white dwarfs, you can only cool down from photons emitted at the surface you can't cool from the interior, because the white dwarf is very thick and those photons from the interior get trapped so they're not good at cooling down these white dwarfs. So this is the prediction from this surface photon cooling channel and it agrees very well at this intermediate range of magnitudes, but there's a notable dip down here and what that's caused by is this plasma and decaying to a pair of neutrinos through an electron loop. So the fact that you have this additional channel to cool down means that particles evolve more quickly from the left hand side to the right hand side. And so you end up with fewer of them on the left hand side because the ones that would have been there, they've already moved on. Okay. So this is a really well studied process. We can also equally apply it not to just neutrino decay, we can also or excuse me decay to neutrinos, but we can also apply it to decay to these hidden sector military particles. Okay, so this is a very efficient process and I'm going to tell you about two applications of this process in my talk today. One of them is going to be a heloscope for looking for these particles that are gravitationally bound to the sun. And the second one is going to be a way of making dark matter into early universe and altering the standard cosmology. Okay, so I'm going to start with my first one, which is work in progress that should be coming out very soon with my collaborator Ashley Berlin, where we looked at basically gravitationally bound mille charge particles from the sun. So, going back to, you know, thinking about a star, as I mentioned before photons are not very efficient at leaving the interiors of stars because they get trapped very easily by the solar plasma, but particles that are weekly coupled, you can you can potentially just make them and then they stream out of the star and never really talk to the plasma of that star. So you can make them potentially very efficiently. And in particular, the typical scale for the plasma frequency and the temperature inside of the sun is of the order of a kev. So any mille charge particles that are, you know, lighter than this can be produced in the sun, fairly efficiently, even for very, very small values of their effective charge. Because basically, there's so much volume of the sun, and there's so much density in the sun that you can compensate for the rareness of the of that process the smallness of that coupling. And so this has been known for a really long time, you know, particles leaving various stellar interiors as a means of basically causing the stars to lose energy and affecting their behavior this has been known for many decades. But what wasn't realized until just last summer was realized in a paper by Ken van Tilburg that a very, very small fraction of these particles that you make are going to be produced at a velocity below the escape velocity. They are going to be gravitationally bound to the sun. And so here's a cartoon schematic showing that so here's the sun and here's the earth. You end up with this sort of halo of these particles that are gravitationally bound to the sun, and you're very face based pressed to make these particles because most of the particles that you make are going to be relativistic and so they're going to just leave the sun entirely, but a very small fraction of these particles that you make are going to be sitting over here their their velocity is going to be below the escape velocity of the sun which is roughly half a percent the speed of light. And the neat thing about these particles, even though they're very face based suppressed for the production side, the fact that they're gravitationally bound means that they stick around for longer. So you can think of them as accumulating. For that reason, Ken called this the solar basin, kind of like a basin like in your sink that you fill up with with tap water over time. So if you think about the mechanisms for producing these particles in the sun and you think about the fact that some of them are going to be gravitationally bound. You can actually compute what the profile the density profile is going to look like of these particles coming from the sun. If you go through outside the sun, the profile scales like r to the minus four, which is a fairly steep scaling for just purely geometric loss of particles like geometric flux, you would have r to the minus two. And this is even steeper than that, just because the fact that the sun is there and these are bound particles means that you get a big enhancement of particles closer to the sun because of its gravitational attraction. The intuition. So even though this is a really precipitously falling density profile. The density of particles can still actually be quite important at Earth. Now, in order for the density at Earth to be high, you have to meet a list of requirements or there's a few caveats. For instance, these particles that you make they can't be trapped in the sun by either scattering or by the sun's magnetic field. You can't have annihilation of the particles in the basin, because that would deplete the abundance. You can't have a lot of scattering between particles in the basin either because that would also effectively transport energy throughout the basin and it would distort the density profile. And finally, these particles need to be able to reach your experiment on Earth if you want to look for them. And so they have to be able to overcome any larger atmospheric voltages that may be present in the Earth's atmosphere. And I'm not going to go through these requirements. I'm just going to punt on this and claim that these requirements can be satisfied with massive dark photons and small couplings in a wide portion of the parameter space. So with that having been established, you can ask me about that later if you're curious, but with that being established, the density of particles at the Earth looks something like this as a function of their mass. So I'm comparing this density first of all to the dark matter density up here and you can see that for roughly like 100 EV particles, the density of particles from the basin is starting to approach the density of dark matter. And additionally, if you compare the basin density to the density of the unbound flux. So even though the unbound flux of relativistic particles is not face based suppressed. The basin density can still be greater than this unbound flux because of the fact that it's accumulating for a very long time. And so this actually tells us that it may it may be feasible to try to look for these particles on Earth in an experiment. Now, there's a complicating factor, which is that the phase space of these particles at Earth looks something like this. So two sort of things to note. First of all, the escape velocity at Earth is 10 to the minus four and basically the the velocity distribution in the direction coming from the sun is peaked very close to zero. So basically particles coming to the earth and being close to their apahilia. The other thing is that the distribution of particles coming from the sun is very collimated due to the fact that you had to make the particle in the sun in the first place, which means that they have very, very low angular momentum. So they're on nearly radial orbits going out and then back into the sun. So, as a caveat to this plot that I'm showing to you, gravitational interactions with things like the planets could potentially a satirized orbits on long time scales. But the jury is sort of still out on that question so we're going to, we're not going to deal with that for the rest of the talk. But the key point being is that you have this very coherent phase space it's very collimated and it's moving very, very slowly because of the escape velocity at Earth being so low. And that kind of poses a challenge to many traditional direct detection methods. Basically because in this situation we have particles with a conserved charge, which means that you can't do anything with them that doesn't conserve their charge so you can't have inelastic processes like absorption. You are actually restricted to only having elastic scattering, which is a problem because these particles, their kinetic energy is incredibly tiny. Okay, so any elastic single particle process is never going to be above any reasonable threshold of any reasonable direct detection experiment. This wasn't a problem by the way for previous studies looking at this basin. For example, and you know that initial paper from last summer by Ken, and then a follow up work by Robert Lazenby and Ken, they were looking at axioms and dark photons which are scalars. So you can actually just absorb them in your detector and all of the rest mass of those particles gets converted into energy deposition onto the target. So in those cases you are able to be above threshold, but in this case because we are restricted to elastic scattering. It's not going to be possible to be above threshold. We need to have some alternative strategy for looking for these particles, ideally something that's going to leverage some sort of collective effect, and that's not going to be penalized for the fact that the particles in this basin are moving quite slowly. And that's where this idea of direct deflection comes in. So direct deflection was an idea that my collaborator Asher Berlin and others at Slack, including people like Natalia Toro and others came up with a couple of years ago. Originally this was an idea to detect dark matter but as we'll see this is going to be very well suited to detecting the solar basin. But the way that it works is as follows so over here you have some wind of these particles coming in and it's moving through your, through your lab. There's this region over here where you have a shielded deflector, and it's grounded and you set up an oscillating electric field inside of that deflector. And then what happens is that as that wind of particles is blowing. If the E field is in a phase where it's pointing inwards, all of the positive charges are going to be concentrated inwards, and the negative charges are going to be deflected away from the away from the lab so they're going to move away. And we're going to be working in some quasi-static limits so the crossing time of these particles is very short compared to the oscillation time of this E field. So if I wait a little bit longer, then what happens is that now the E field is in the opposite phase. So now the negative charges are going to be concentrated towards the middle and positive charges are going to be deflected away from the lab. And then again if I wait a little bit longer, when the E field is pointing inward, the positive charges get deflected inward. And so while I've been deflecting these things, it's a wind so it's still continuing to move. This wind is blowing downstream. And what I've done here is I've set up this oscillating train, a wave train of particle charges. So what this shielded detector region sees is an oscillating charge density. And basically what I can do is use the fact that you see this oscillating charge density in here. I can try to pick that up with a resident RLC circuit. So the nice thing about this setup here is that this is not a single particle scattering type of event. This is actually inducing and deflecting a collective disturbance. And so there's no kinematic barrier. There's no real threshold here. And in fact, it's easier to deflect particles that are moving slowly. So you actually get a kind of an enhancement from the fact that the particles in the solar basin are moving fairly slowly. So if you just take the same idea, which again was developed for looking for dark matter, you just apply it to the situation of particles coming from the sun. In this case, you know, you actually really care about the getting the velocity distribution of particles right, because as I mentioned, the sensitivity that you have depends on that velocity distribution because it's easier to deflect particles that are moving slowly. So just to kind of see an example of that here I'm showing two two plots where I've assumed different phase space distributions on the left I've assumed a fairly narrow one where the dispersion in the transverse direction is less than the dispersion in the sort of longitudinal direction of this phase space. So here I've set them to be equal the two dispersions are equal. And you can see that you get different, different basically shapes to how the resulting charge distribution looks. And you also if you can read these little numbers here, you get actually a much bigger charge density in the wake of this deflector, when you have this more coherent velocity phase space. So that's actually something that's really helping us in the situation. So given some, you know, experimental parameters. This is the constraint that we are forecasting for the time being. So it's going, you know, as I said, I think the name Miller charge is a really big misconception or a misnomer, because now we're able to go all the way down to like 10 to the minus 15 times the charge of the electron. So let's look for really, really super weekly coupled particles with this method. And this, these are like the parameters that we're assuming for this experimental setup. One thing that's really nice about this signal is that it turns out it scales like charge to the eighth power. So just because, you know, so if it scales like charge to the power, any of the parameters in the experiment entering your prediction, you have to take the one eighth root of that expression. So you end up having charge sensitivity that scales like a bunch of stuff to these kind of funny powers over here. And the reason why I mentioned that is because the fact that you have this really weak scaling with these parameters means that, you know, we're really even if you make really conservative assumptions about what what experiments were able to build. You still get a pretty strong reach. Okay, so that's all I wanted to say on that topic. I'm not going to switch gears a little bit and talk about making dark matter in the early universe via this same sort of plasma and decay process. And this is an example of a thermal ish scenario called freezing, basically the opposite of freeze out, as we will see. It's similar to what I mentioned before, we're using the same plasma on process that we used in sun and in various stars. But now we're not dealing with a solar plasma or stellar plasma. Now we're actually dealing with the early universe plasma. And this is actually also a very efficient way of making dark matter in that plasma. What I wanted to talk about about this is that you often these days here about charge dark matter. It became very trendy to talk about charge dark matter in 2018 because of the edges anomaly. And, you know, people would always talk about it but not really talk about where this charge dark matter came from. In fact, this mechanism that I'm showing you right here is the simplest way of making charge dark matter, because the freeze out mechanism is excluded, because the coupling that you would need to make charge dark matter from freeze out is like, is really a true middle charges 10 to the minus three, and we've excluded that by many many orders of magnitude. Okay. So anyway before I get too ahead of myself, I want to just mention also the properties of this plasma are are different. The early universe plasma is a relativistic plasma with zero chemical potential. So if I plot the effective mass, it looks something like this, where because again it's a relativistic plasma the only really relevant scale in this plasma is the temperature. So you can see that the effective mass of these excitations is very comparable to the plasma frequency, and the plasma frequency has to be linear in the temperature just because like I said dimensional dimensional analysis reasons. And you can see here that the, this is a plotted at T of one MeV, the proportionality constant is roughly a factor of one tenth. Okay, and that's going to turn out to be quite important because that means that as the universe is expanding and it's cooling down, you're actually scanning through a range of different plasma masses. And so you're scanning through a wide range of different kinematic regimes. And it might just be explicit about what I mean. So in the case where your dark matter, let's say it's 400 kev. Okay, so in that case, here I'm on this plot I'm plotting the amount of dark matter in as a co moving quantity, relative to the amount that you would need to explain the dark matter of our universe as a function of temperature, and temperature is actually increasing to the left on this plot and so time is moving to the right on this plot. What you see here is that you have actually two contributions of making dark matter, you have this plasma process that I've mentioned, and you have also the E plus C minus and the E plus C minus is the same process but you just stick an E plus C minus onto the initial state. And what you see here is that they basically contribute at different times. Now what's setting the contribution from the plasma decay process is basically the point at which your plasma gets to the threshold. So the point at which the, the mass of the plasma is twice the dark matter mass. That's the point after which after the universe cools past that point you can't make dark matter anymore. It's not kinematically allowed. And so that's what shuts off that process. Meanwhile, because I chose a dark matter mass that's lighter than the electron mass. This process is always kinematically allowed the E plus C minus annihilation is always kinematically allowed. But it's just that at some point, these E plus C minus pairs start to leave the bath because once the thermal energy of the bath becomes comparable to their mass. They start to basically annihilate away. So that stops that basically depletes the number density and so this process stops when the temperature is similar to the electron mass. So that was 400 keV. If I make my dark matter even lighter than that. So let's say I make it 40 keV, then the electron story is still the same. But now this plasma story is such that you have to wait until even longer times before this process hits its kinematic threshold. And so for that reason, because this threshold is reached at a later time for this dark matter mass, you're actually able to make a lot more dark matter through this plasma decay process it's really efficient at making dark matter. So if it's active you have a factor of alpha basically additional additional strength compared to the E plus C minus channel. And so in this case you're actually making about 10 times more dark matter with this channel. So that's pretty neat. Another thing I want to know about the situation is, since we're now talking about sub MEV dark matter, you may be, you know, having alarm bells going off in your head, because the, you know, usual lore is that you can't have thermal dark matter below MEV. And the reason why is because if you think about freeze out for a minute. Then this is what I'm depicting here this purple line is freeze out. And I'm showing this for a dark matter mass of one MEV. And you can see that this this species is part of the bath has a has a thermal number density. And then it leaves the bath at a pretty low temperature over here. But in the meantime before that happens you have some very important things happening in the early universe you have a neutrino decoupling and you have deuterium forming. And this dark matter is leaving the bath after these really important things in the history of our universe. It's going to be injecting some sort of entropy over here into the visible sector somehow. And that injection of entropy when it leaves the bath is really, really bad from the point of view of these other early universe observables. You can mess up the neutrino to photon temperature ratio. And you can also potentially like photo dissociate light chemical elements that are trying to form. So for this reason, this dark matter freeze out scenario at this mass is excluded. In fact, depending on the spin of the dark matter particle, which tells you how much entropy it has, you can actually go up to potentially roughly 10 MEV and anything below that would be excluded. But note the whole time I've been plotting freeze in down here. The dark matter candidate contains very little entropy so it doesn't have a thermal abundance, unlike for the case of freeze out. So it doesn't actually mess up any of these other early universe observables because as it's being made it's just a very gentle process it's not heating up or cooling down anything. And so this means that this is sort of a unique loophole to the statement that you can't have thermal dark matter below an MEV. And then I would call freeze in the scenario I'm plotting here, thermal ish scenario because the dark matter is made from the thermal plasma, a thermal process in the thermal plasma. But the dark matter itself never thermalizes with that plasma. And so for that reason it's not going to have any of these weird entropy issues. Now, that might make you worry though because to say okay well I'm making this dark matter but I'm requiring that it needs to not thermalize, right. So that must mean that this dark matter is extremely weakly coupled. And that is true. However, you might still actually have a chance of detecting this thing, even though it's really weakly coupled, essentially because, you know, even if the coupling is really really small. So if you have this, if you have a light mediator, like what I what I've been talking about in this talk a dark photon that's much much lighter than an EV. Then any sort of scattering process that's mediated like by this mediator is going to have a velocity to the minus four enhancement to scattering. This is just like Rutherford scattering in the standard model. Basically just because the photon of the standard model is massless. So you get this V to the minus four scaling, which in the context of our galaxy is a really nice enhancement, because the typical speed of dark matter in our galaxy is 10 to the minus three times the speed of lights. So that's a 12 order of magnitude enhancement to this process relative to processes in the early universe where things are moving relativistically. So this actually is a scenario that in spite of the fact that it is very, very weakly coupled to the standard model, you can still potentially detect it in a lab. And it's so promising that this freezing sort of model, including this plasma and decay process that I talked about is actually one of the key targets for several proposed direct detection experiments. So here on this plot I'm showing already we have constraints coming from stellar emissions similar to what I was telling you about at the beginning of my talk, basically requiring that stars not lose energy too quickly. We also have this direct deflection, which is again similar to what I told you about before. This is an experiment that was originally proposed to look for dark matter and freezing is one of the key targets for that. And then we also have these other kinds of experiments over here, all of which are using novel properties of condensed matter systems so different materials that have a energy band gap that is similar and matches the kinematics of the dark matter in the galaxy. So yes, it's a it's very weakly coupled but it is very testable. And so for that reason I think this dark matter theory has a lot of really nice properties. As we saw the you're making more dark matter at late times. And so the relic abundance is independent of initial conditions, which is a really nice property to have you're not sensitive to things like, you know, what's happening at the time of, you know, reheating or anything like that. This is a unique kind of way of making dark matter that is thermal where you're making dark matter masses below an MEV and not messing up really universe observables. And finally, the relevant couplings can be experimentally propped in the lab. So I think this dark matter candidate has a lot of really nice properties. For the remainder of my talk, I want to discuss how to look for this dark matter candidate using cosmology. And that that's something that we're going to use to potentially constrain it all the way up to roughly 100 KV. Okay, and the key insight that we're going to be using to make these statements is that dark matter is in some sense born hot from freezing and the quotation marks are here, because as I've tried to emphasize the dark matter does not thermalize with the standard model. And in fact, it doesn't even necessarily possess a well defined notion of a temperature. And so you can't really say that it has, you know, it's hot or it's cold. But what I mean is just that because the dark matter because of how it's made, it's made out of the decays of these in medium photons and those are fundamentally relativistic particles. And so the dark matter is going to inherit some of the phase space of those particles. In particular, the phase space that you get from this process is kind of gnarly. We computed it in detail in our 2019 paper. But it looks like this in the end. So here I'm plotting the phase space density as a function of momentum. And here I'm plotting the momentum in units of the photons temperature. So both of these quantities the momentum and the temperatures redshift the same way in the universe. So this is actually a safe co moving quantity that's the same at all times. So one thing to immediately notice is that the dark matters phase space is sort of peaked at values of this dark matter momentum over the temperature that are of order unity. The dark matter momentum is of order the photon temperature in this distribution, which is kind of lending credence to what I said before, this dark matter is born going pretty fast. Okay. So that's one kind of key thing to note. The other thing to note is that this distribution this purple distribution looks really nothing like a thermal distribution. Okay the thermal one that would correspond to the same dark matter internal energy looks like this. Okay, so they don't look anything alike. The reason why is because when you make these particles here you get two contributions, one is from the plasma and decay process, which fundamentally is a decay. And as we know, because of special relativity, decay is preferred to happen in their own rest frame. If you're not in the rest frame of the decaying particle and there's going to be some big Lorentz time dilation factor which is going to affect your decay lifetime. And so that's what we see manifested here. Particle is trying to decay at rest. And so that means that it's decaying and imparting a very small velocity kick to the dark matter particles. At the same time though, you have this kind of fat tail, because as I mentioned earlier, as the universe is expanding and cooling you're scanning through a range of different of different plasma masses and so that's going to also impact the kinematics. So particles in this part of the tail are coming basically relics from a time when the plasma mass was higher. And so there, those particles are getting a little bit more of a kick in the final state. You also have this E plus E minus contribution which is giving you also kind of a fatter tail over here. So those are the two contributions. I want to note that ultimately it is possible at late times for the dark matter to thermalize in its own sector, if there are self interactions. That's going to be something that actually is a little bit model dependent and so we're going to leave that as an option but in what I'm about to show you we're going to be assuming these two phase based distributions all the time. So either the pristine one the purple one, or the fully thermalized one. In this case, those two distributions will have implications for cosmology. One of them being the effects of just their high speed their high velocity on clustering in a way that's very analogous to warm dark matter. So warm dark matter is another kind of interesting thermal relic that is inspired by neutrino decoupling. So if you have a species that decouples from the standard model while it's relativistic. The ultimate density that you get of that species looks like this. And so to get a fixed amount of dark matter that we know that we've measured, you have an inverse relationship between the mass and the temperature of these particles, in particular if you raise the mass you have to lower the temperature to get the same amount. Conversely, if you lower the mass you have to raise the temperature and that's actually very bad from point of view of structure formation because a typical velocity goes like the square root of T over M. So you have a high temperature and a low mass, then your velocity is very high. What that means is that the particles are not able to cluster together as effectively their velocity is just too high, and they're not able to be gravitationally captured. Another way of putting it is that the sort of nascent sort of cosmological structure that's trying to collapse and trying to form in the early universe has a very shallow and very delicate gravitational potential. So the escape velocity of those structures is not very high. So if dark matter is going too fast, it's just going to free stream and not be and not be affected by these potentials. And that's going to suppress their growth compared to the case where they do capture a lot of dark matter. So this is the sort of simulations showing this effect on the right hand side you have hotter dark matter, and it's fuzzing out it's smearing out structure, particularly on small scales which is a race. And we're very good at looking at this with cosmology. Another good example I think is the Lyman alpha forest, where we have some broadband spectrum of some high redshift quasar. And then as the light from that quasar is moving to our telescopes it's being absorbed by Lyman alpha absorbers so neutral gas and the high GM. Meanwhile, the whole universe is red shifting so this whole spectrum just moves to the right as the photons are traveling to our telescopes. Every time they find a new clump of neutral hydrogen gas, you impart more absorption lines on to this spectrum at the Lyman alpha wavelength corresponding to that transition. So ending up with at the end of the day is this. Again you see the envelope of this broadband spectrum but you also have this dense forest of spectral lines, which is telling you along the line of site, how many clumps of neutral hydrogen were there and what is their depth. So this is a way of having depth perception on to the clustering of matter in our universe. And this is one really helpful way of looking for the effects of fuzzy, or excuse me the effects of warm dark matter fuzzing out your distribution. There's also been a number of developments whoops, in recent years, where we've been able to look for low mass halos and subhalos, which would be erased, if the dark matter were very warm. I'm not going to have time to go into all of these but, for example we've been finding recently with, for example the dark energy survey we've been finding more and more of these very very faint dwarf galaxies that live inside of very very low mass dark matter halos. The fact that these dark matter halos even exist means that the dark matter can't have been too warm, otherwise they would have been erased and they would have never formed. For example this can be used to pretty much almost entirely rule out sterile neutrino warm dark matter if you assume a she fuller production mechanism. But you can also apply the same argument to this phase space that I showed you earlier. And I'm running low on time, okay, but essentially what this does, what this phase space over here does regardless of if the dark matter is thermal or not, is it keeps things pretty much the same on large scales, but on small scales, you start erasing power. So here I'm plotting the power spectrum and I'm normalizing it by the cold dark matter one. So you see everything looks the same over here for low values of k, large scales, but over here everything is suppressed. You can do a matching between warm dark matter constraints and freezing constraints. So we did that. And we found that with current data with, for example, the dark energy survey, you can actually rule out freezing below massive roughly 17 KV. The, the details depend a little bit on whether you've thermalized or not, but it's not too sensitive. Okay, finally, the fact that you made this dark matter from its interactions with the primordial plasma means that at some level you can drag that plasma, and you can potentially affect the dark matter, bury on sort of acoustic oscillations in the early universe which we see in the EMB. Just a quick cartoon picture. Usually if you have collisionless dark matter at the bottom of the gravitational potential well, that's weighing down the photon bury on fluid. So it's actually helping the photon bury on fluid to kind of cluster together. It can't actually cluster all the way because of radiation pressure which pushes it apart. So you have these competing effects between gravity and radiation pressure with the gravity part being helped out or being sourced largely by the collisionless dark matter, which doesn't feel the radiation pressure and is able to sit at the bottom of the gravitational potential. But if you start interacting, you if you start being able to have interactions between the dark matter and the burials, then every once in a while you can drag dark matter out of this potential. So in doing so you make it so that now gravity doesn't have as much of an advantage over radiation pressure. And so that's going to affect the nature of the acoustic peaks. I'm running pretty short on time so I can't actually go into this in too much detail but you can feel free to ask me about it in the Q&A. But essentially what this does is it damps out a lot of the acoustic peaks and the structures that we see in the CMB. So here I'm showing the change the CMB. And that level roughly as a function of multiple L. And using existing plank data, we can actually constrain freeze in masses below roughly 19 keV. Again, the details, you know, depend a little bit on the phase space but not too sensitive. With future probes like CMB Stage 4 for the CMB side as well as things like the Verrubin Observatory finding later and later halos, we can potentially actually start to probe dark matter freezing up to much higher masses. Just remind you very briefly this is also a key benchmark this whole parameter space is a key benchmark for direct detection. We're in a very nice situation because we have all of these different independent cosmological and astrophysical probes, all of which are kind of giving independent constraints because these are all different systems with their own systematics and different observations etc. And those are all kind of constrain this candidate from below. And then meanwhile in a few years time we're going to have terrestrial experiments constrain this from above and there's quite a lot of overlap here. Which means that there's going to be nowhere for this dark matter candidate to hide. And so we're either going to discover it or we're going to rule it out entirely either way I think that's interesting because I think this is a really kind of well motivated candidate like I mentioned before it has a lot of properties that are really nice. So that's all I wanted to say for today. Just to summarize, these military particles can be made from decaying plasmons and in many cases that's the simplest and easiest way to make these particles. You can have all sorts of you know non trivial phase space structure from these decays, which lead to interesting behavior in the lab and in the universe. And so these particles may be observed observable in the near future. Thank you. Thank you very much, Caitlin for this amazing talk. I'm going to open now the floor for any questions for the people who are in the, in the meeting, while we wait for questions on YouTube. Oh, okay, go first, go first. Thanks for the very nice thought. So just out of curiosity at some point you mentioned the fact of self interaction. What happened because I mean the charge is super small not can you really reach like chemical or equilibrium. Yeah, I think I have a backup slide on this maybe let me see if I can find it. Yes, good. So, yeah, so because you would scatter through self interactions where you don't have quite a small of a coupling. So in making the dark matter you have to look at the product of G chi times kappa, where kappa is again the kinetic mixing. But if you have dark matter self scattering, you don't have any factors of kappa. So parametrically, the self scattering can be a lot bigger than any sort of scattering off of particles in the standard model. Now, again, this is a process that's mediated by the dark photon which is very, very light. So it gets a velocity to the minus four enhancement. And so, similar to scattering in the lab. It's actually very enhanced, particularly at late times in the universe. So at early times of scattering is not is not very efficient. But if you wait long enough because velocities are Hubble damped over time. You wait long enough and the velocities go down, you start to be able to basically make up for the fact that the coupling is so small. So here at this plot that I'm showing is basically at what redshift is dark matter able to self thermalize as a function of mass. And here in this plot I'm showing two lines where I have fixed kappa the kinetic mixing, and based on the Boltzmann equations for making the dark matter that uniquely tells me as a function of mass, what does G chi have to be. And so if I know G chi, then I can figure out based on the density and based on the interaction cross section I can figure out at what redshift will this thermalize based on its velocity distribution at any given time. You know this to these two choices, small kappa and a bigger kappa were chosen just to show that you can thermalize before recombination or you can thermalize after recombination. In everything we were doing we weren't assuming one or the other we were just taking both both distributions and constraining them at face value. But the true reality is that the real truth is probably somewhere intermediate between the two cases that we were showing. I'll also quickly note that you can't actually thermalize too early. Again, because to compensate for the highest speeds, you have to have a higher coupling. And if you have too high of a coupling then you're going to ruin things like bullet cluster so SIDM constraints are going to be spoiled basically if your coupling is too high. So any any thermalization up here is actually ruled out. Okay, thank you. Yes. So I was trying to understand the role of the basin in the experiment that you're proposing. Because in principle, this dark matter coming out from the sun could be detected as solar neutrinos are detected. So what's the role of the basin? Yeah, yeah, so the role of the basin. Let me go back. Let's see. I think it's somewhere here. Yes. So the basin what it's doing for you is is essentially it's buying you a few orders of magnitude and density, because you have the unbound flux of particles just so just particles coming from the sun that are relatively relativistically. That makes up the majority of the of the phase space for this production. But because you have this basin and because you're able to accumulate these particles over time. So basically you're able to accumulate them over like five billion years because these particles are sticking around that really enhances your density. So that's what it's doing. I see. I see and come. So, so that would mean that okay we're building our own halo, right, like, yeah, there, and could that when I when I late. I could annihilate. Yes, it definitely could. And we did look at that basically setting requirements that the that for any given particle. So, yeah, this is actually a little bit tricky to figure out. We actually think there's going to have to be some follow up work looking at this in more detail. But basically we put a really conservative requirements on our situation and said, we need to make sure that the expected number of annihilations for any individual particle is much, much less than one throughout this whole five billion years that it's been in this basin. So that's the requirement that we put. It's probably a little bit too conservative. Because basically the, the rates for inter for annihilation depend on what part of the orbit you're in, when you're in the very inner part of the orbit where the density is higher than your likelihood to annihilate goes goes up. But for, for orbits they spend most of their time at the Apahilia. So the intrinsic spectrum of orbits tells you that there's going to be a spectrum of probabilities to annihilate. So what we did was likely too conservative. But yeah, it is something that we checked. Right. Okay, okay, now it's interesting because this would give given this, you wouldn't have an inhomogeneous like photon a flux arriving to the earth wouldn't be homogeneous. So, so my idea or my idea was okay maybe this could disturb the cosmic microwave backgrounders or something like this. Right. But, but no because given given this following orbits and the densities. It wouldn't be looking the same in all directions. Yeah, so it would definitely be highly anisotropic. Actually, so in addition to having the sun, you also have motion around the sun so that also kind of creates artificially a wind with particles. But yeah, because these particles to I mean just to go back or to go forward a few slides. So when we talk about our constraints or our predicted reach, we're going down to effective so these are charged particles in this basin and their effective charge 10 to the minus 15 times the charge of the electron. So they're extraordinarily weekly couple to photon, like so weekly couple to photons that they're passing through the solar plasma and never interacting with the solar plasma. So I think, I think these particles are very unlikely to affect the CMB photons. So it's so insanely weak that it's like almost, it's almost doing nothing. I see. Thank you. Nicholas. What, what happened there to 100. Like, like what's the range of masses that we did. Yes. Ah, yes, good. So on the high mass and it's basically just that you're hitting the threshold. So the at the core of the sun, the plasma masses around 0.3 KV. So particles have to be lighter than like 0.15 KV in order to be produced. So that's what's setting this line. And then over here, that's actually more of a theory cut that we put rather than a physical thing. So if I go back to this plot that I think I was just showing the density of these basin particles goes down at lower masses. And that's because as you go down to lower masses to be produced non relativistically is a bigger and bigger phase space suppression. So that's why there's less of them. And so at some point, this whole story that I told you about deflecting this wind of particles that sort of relies on a treatment where we're treating these particles as a continuum to something that we can continuously deflect and create densities. So if you start to get down to this region where you have very, very few particles, you can no longer treat them as a continuum you have to treat them on an individual particle by particle basis, and we don't have the machinery for that. So that's why we cut off. We cut off this plot basically when our deflector has fewer than 1000 particles in it. Okay. Yeah, so it's more of like a theory like we don't know how to treat this, rather than something physical. I do have a question. So the dark photo. So here, basically, in most of the of this work, the, the role is just to provide like the middle charge right but there is no. This guys are not around right I mean the, the, it's very unlikely that that matter even will create it just because a, there is no, no, no kinetic equilibrium or any sort of family collision for that matter once it's created right. Yeah, that's exactly right so it's really, it's really not possible to create a lot of these dark photons through something like yeah like scattering which creates bram or anything like that, of these dark photons. You also don't make that you don't populate the dark photons from the standard model side either, because of something that's actually a little bit subtle. Actually it goes back to one of my beginning slides early on where you have, you have terms that are higher order in MA prime over MA. And those are the terms that would lead to producing dark photons from the standard model. And so because we're always in a regime where this is really really tiny. You get additional suppression, even relative to just like factors of Kappa and G chi you get an additional plasma suppression of making dark photons from the standard model side. So yeah it is, it is pretty suppressed you don't make dark photons very much so you're not, you're not having them contribute to like an effective or anything like that. Thank you. Yeah, hi thanks. Thanks for the nice talk. I just have a very nice question and probably this makes no sense. So I was just trying to understand that how, how, how, I mean, there is essentially a difference between the phonons that you're talking about and and and the dark photon. So, what I understand the phonon is like a collective, you know, oscillation. Do you mean, do you mean plasma? Sorry, the plasmons. So the plasmons are somewhat like the phonons like the like a collective oscillation. So, so how physically like how their name different like what sort of difference is between a dark photon and the plasma like physically I'm saying. Yeah, so the plasma and is basically just, it's not really different from the standard model photon, it is the standard model photon just appropriately be like just modifying the behavior for the standard model photon to be appropriate to the in medium situation. So, yeah I think there's also some differences in nomenclature in the literature like some people only refer to the longitudinal mode of the photon as the plasma and but they keep calling the transverse mode the photon. It's a little confusing the terminology to be honest. But all the plasma is is it's just the regular photon of the standard model but it's in a medium. That means that it has an effective mass. So it doesn't have the vacuum dispersion relations it has a gap. And that means also that you now have the transverse mode, which you don't have in the vacuum because of gauge and variance. So that's, that's the difference there. The dark photon is its own. It's another it's a completely different particle. So that's a, that's like a separate gauge field, which, because it's not very strongly coupled to the medium. It does not receive thermal corrections to its mass. Okay. All right. So, thank you very much. Sorry, Roberto. Yeah, I have a very small question for Kathleen. First of all, very, very nice to talk. So I have a question in the sense of how this could change in the sense if your dark photon instead of a photon is a kind of dark z prime. And that if you allow the, the, that the your extra gauge, the field can interact with the with the neutrinos. Is it because you're now you're going to have an extra channel so I don't know if this could potentially open even more the parameter space or instead close the previous space space. Yeah, good question. I haven't thought about this too much. I know that there are pretty strong constraints on military neutrinos. I imagine that that would be very constraining, but I haven't looked at it in detail. Okay, thanks. Yeah. All right. So I think that this is a good time to stop since it's been already more than an hour. And we are very grateful, Kathleen, for sharing with you work with us. And this has been an amazing talk. And to all of you on the, on the transmission, we hope to see you in the next webinar. And thank you very much. Thank you.