Okay, welcome back. So we have the fourth lecture about dark matter by Tracy's laser Okay, much better. Just the check again. Can people at the back here me? Okay. Okay, great Alright, so welcome to the last of my four lectures on dark matter in this lecture I'm going to mostly focus on terrestrial searches Whereas in the previous lecture I talked about Searches that you can do using telescopes say I'm mostly going to talk about searches that you can do in the in the lab I will however sneak in a couple of cosmological searches cause I like them and so So what I want to focus on so most of this lecture what I want to focus on is the WIMP direct detection program This doesn't strictly only apply to WIMPs, but that's its main focus It's a big active experimental program with many experiments with competing techniques I want to talk you through the basic mechanics of how those experiments You know how they work what they're expecting to see Kind of signatures you can look for then I want to talk more briefly about the collider searches for dark matter currently ongoing and Of these searches for axioms which again in the last couple of years has become a particularly rich field with many ideas For how to go after the axiom dark matter, but when we get to that I want to finish up what I was taught what I promised to tell you about yesterday, which is the indirect indirect detection ways in which the annihilation or decay products of dark matter could potentially affect the Cosmological history that you've been hearing about in Barbara's lectures Okay, so you're now all experts on this so I don't need to spend very much time on it But between around well, this is redshift 30 to a thousand, but that's even a bit of an overestimate between the epochs of recombination and reionization The universe was extremely close to neutral The residual ionization fraction turns out I mean you can work it out It's not zero, but it's a few times ten to the minus four So only a few hydrogen atoms in every ten thousand are ionized now We can measure that low level of ionization very sensitively using the cosmic microwave background Idiation which you've heard a bit about from me and Barbara and you're going to hear more about Over the next week and a half We now have fantastically precise measurements of the cosmic microwave background Idiation if you add any more free electrons between us and the surface of last scattering those free like Transactors a screen to the CMB so by measuring the CMB anisotropies we can put pretty strong constraints on them So there's a constraint that you can set on dark matter annihilation or decay just by saying well Would it ionize the universe too much at early times now by early times here during the cosmic dark ages? We said you know the temperature of the universe at the surface of last scattering is about 2700 Kelvin That translates into an energy scale of about 1 e v the CMB So I told you back in the first lecture that dark matter thermal dark matter typically freezes out when the temperature of the universe is about 20th of the dark matter mass so if we're talking about 100 gv dark matter freeze out happens long long before any of the times That I'm talking about here. So you might still write well the annihilation is frozen out So there's no annihilation happening anymore, right? So how can this be a big effect? The point is that even long after freeze out freeze out just means that dark matter annihilation is no longer Significantly depleting the amount of dark matter in the universe, but it's still ongoing There's still this slow trickle of production of high-energy particles if dark matter annihilates everywhere in the universe and at all times And we could do a back of the envelope calculation to understand what this might do in terms of ionization Point here is basically that if you can convert all your and all your mass into energy that corresponds to a lot of hydrogen Ionizations suppose just to make the numbers easy. Let's say we were talking about 5 gv dark matter So that means since the mass density of dark matter is about five times the mass density of protons and neutrons That means that there's about one dark matter particle for every barrier in the universe if this was our mass scale a single dark matter annihilation will give you 10 gv of energy Approximating 13.6 ev is about 10 ev that means that for every annihilation I can ionize 10 to the 9 Hydrogen atoms so if one dark matter particle in 10 to the 9 were to annihilate the same time That's enough power to ionize every hydrogen atom in the universe Okay, so even though The fraction of dark matter annihilating can be absolutely minuscule. This is way after freeze out is not affecting the abundance of dark matter There's so much energy locked up in the dark matter that even a tiny fraction of it can have very substantial effects now This did not happen We would be able to tell if the universe of being completely ionized during the cosmic dark ages because we wouldn't see the CMB But that means that we can use this to set this argument to set constraints on dark matter annihilation Now so the physical process here is that if dark matter annihilates and Produces standard model particles so long as they're not neutrinos then when they decay they'll make protons and electrons and positrons Those photons electrons and positrons can in principle put energy into ionization now. There is some Astrophysics cosmology in this step because you need to understand the efficiency of this process If I just give you a 5gb photon and put it into the universe at redshift a thousand its ionization cross-station is absolutely tiny It doesn't actually look like it's a very efficient ionizer, but these particles they'll scatter off the CMB They'll scatter off the gas they cool down they lose their energy They partition their energy into many lower energy particles and those particles can be efficient ionizers Once we have once we know how the ionization history is modified There are publicly available tools like the class code or the cam code To understand how that translates into a perturbation to the CMB and isotropies The essential physics is just we have extra electrons those extra electrons scatter the CMB photons Okay So I'm going to summarize a lot of this calculation because it's just you know a lot of numerics But it basically just involves numerically simulating the cooling of these processes in the early universe It turns out that That essentially you can boil all this down to just one number some efficiency factor for each dark matter model It tells you about how well it how well it ionizes the universe that efficiency factor comes mostly From just understanding what fraction of the power goes into photons electrons and positrons versus neutrinos If a lot of power goes in neutrinos, you don't see much of a signal But it also depends somewhat on the energy of those particles that you produce this is the Dependence on energy of this efficiency factor. So this is based on again in numerical calculation simulation that cooling. This is for I Think this is for photons. This is for electron positron pairs You see that this number sort of varies over about an order of magnitude between about 0.1 and 1 this efficiency factor So it's an order one factor now Okay, so I so I'll show you in a moment what constraints we get from using the cosmic microwave background To look at this, but first I just want to tell you briefly about another Excessing in direct detection that got a lot of attention a couple of years ago and is still quite interesting at the moment so so moving away from the early universe back to the present day there are There are Experiments called Pamela and AMSO2 that measure the cosmic rays in the neighborhood of the earth and what the Pamela experiment found Back in 2008 was that if you look at this ratio of positrons to electrons in these cosmic rays Then it falls as a function of energy up to some point But then around 10 gv this trend turns around and it starts going up That's a little bit unexpected from standard cosmic ray Propagation models just because the positrons are mostly produced as secondaries from protons hitting the gas the electrons are primary particles You naively expect there to be more high energy electrons than high energy positrons That said there are possibilities for explaining this that have nothing to do with dark matter and adjusts Well cosmic ray propagation is modified somehow or there's some additional astrophysical source of positrons But one possible explanation for this would be that dark matter particles are annihilating since dark matter is neutral It produces positrons and electrons in equal quantities. You can see this ratio is You know, there are still a lot more there are a lot more Electrons than positrons even though there are more positrons than you might have expected so if you had a big source of that was 50% positrons and electrons it could have this observed effect and This was later confirmed by the AMSO2 experiment a couple of years ago now with Extremely now with pretty small error bars and they see this extends up to about 500 gv So this would need to be TV scale or heavier dark matter To work you also it also needs to have a very large annihilation cross-section much larger than the much larger than the thermorellic Cross-section by typically two to three orders of magnitude That can be explained if dark matter has the kind of physics that we talked about in the context of self interaction on Monday that it is coupled to some light mediator that enhances its annihilation This plot on the right is showing the fit for various dark matter models that have been fed into the data So it can do a reasonable job, but then you can ask the question Okay, suppose I take these electrons and positrons and I just transpose them into the early universe say that whatever There's a dark matter annihilation process that is making electrons and positrons that generate this signal If I were to inject at the same rate those electrons and positrons into the early universe What would that do to the CMB? so So it turns out that that distortion effect is actually at least in in this naive translation Appears to be already ruled out by the Planck experiment So this plot on the left the y-axis is this efficiency factor I mentioned that describes the efficiency by which the dark matter annihilation gets converted into ionization power times the cross-section on The on the x-axis. This is the mass of the dark matter in GV And as you might have guessed from our sort of initial first order of magnitude estimate This is a very strong constraint for light dark matter for few d GV dark matter. So everything above this blue line is ruled out This red band is roughly for you know range of FF between about think about point two and point seven or eight Which is most of the standard model channels This is where the thermal. This is what F effective times Sigma V would be for a thermo relic particle So underlying annihilation cross-section two or three times ten to the minus twenty six centimeters per second And then you multiply by a reasonable efficiency factor So what this tells you is that this appears to just pretty much rule out for most channels annihilating dark matter below with masses below about 20 GV Unless unless it annihilates mostly to neutrinos At the high mass end these gray dots are models that have been tuned to fit the Pamela and AMS or two excesses And you can see that they're above this blue line Incidentally these gray stars down here which are all below the lion are models which fit which fit the GV excess With dark matter annihilation so you can't quite reach those with this kind of probe This plot on the right actually puts in the F effective values for various standard model annihilation channels These red lines are annihilation straight to photons or electrons and positrons This band of densely clustered lines here is all the other standard model possible standard model final states except neutrinos So one of the nice things about this constraint about the solar universe limit. You don't care about dark matter structure formation It's all coming from times when the universe was neutral when Structure formation was linear when perturbations had not gotten very big yet And it's also almost independent of the annihilation channel You can apply anything above this band is ruled out regardless of whether you're annihilating to W bosons or quarks or Some combination or some combination of the two or three body final states. They're all in this band This are bad this brown band up here is actually the limit for neutrinos The reason you have a limit for neutrinos at all is because if you produce sufficiently high-energy neutrinos They can radiate electro wheat gauge bosons and when those particles decay they produce photons and positrons It's kind of amusing that this bound is actually pretty comparable to the limits that the ice cube neutrino experiment sets from looking Directly at galaxy clusters in the present day So we can get comparable constraints by on one hand Using neutrino telescopes and on the other hand just saying well if we had high-energy neutrinos There have to be other high-energy particles with them and those high-energy particles would have ionized the universe too much at early times I think this is a really neat demonstration of just how good our understanding of the early universe has become and on this plot these dots Again represent models that fit that Pamela and AMS or to excess with annihilation You should compare the red dots to the red lines and this gray region and yellow region to this band and you see again They appear to be pretty cleanly ruled out You can avoid these CMB constraints if the dark matter annihilation rate is really suppressed at low velocities You can avoid but then it's hard to generate the positron signal you can avoid the conclusion that the positron signal is ruled out if we're sitting close to a big lump of dark matter and that's Enhancing the local rate for positrons, but wouldn't enhance the annihilation rate in the CMB But if you don't make assumptions like that, then this is a pretty clean way of disfavoring The dark matter explanation for that access. Okay, so that's all I wanted to say about that The point I want to make is just if dark matter annihilates or decays it provides a source of heating and ionization That occurs everywhere in the universe over the whole age of the universe And that's one example of how it can have interesting effects It could also modify nuclear synthesis modify reionization It could play a role in most of the special epochs that you heard about in the cosmology talks So there belatedly is my summary of yesterday's lecture, which is essentially that Santa model particles produced by dark matter interactions could give you a wide range of observable signals They could modify the cosmic history in interesting ways There are a couple of current possible signals that have caused a lot of excitement in the field I argue to you that this first one is probably telling us about a new point source population rather than dark matter annihilation And the second one well will we will see hopefully we can get more Experimental information on that in the near future Okay, so now so now let's move on so okay first ask if people have questions about this Then we'll talk about earth-based experiments Okay, I'm good with indirect detection. Okay, so let me talk about so now let me talk about terrestrial searches for dark matter and Earth-based experiments. Okay, so what's the basic idea of direct detection? Well, so this is the summary plot for direct detection This is the current status of the field most of what we do for the next How far or so is going to be understanding Understanding this plot and exactly what it's telling us The basic idea is that what you want to look for is nuclei jumping or re-coiling with no apparent cause so Visible particles moving in a way that doesn't appear to conserve energy and momentum Because in that case you can infer that they had they just struck something invisible Something invisible such as dark matter So the strategy for this is you take a large volume of matter you put very sensitive detectors around that large volume Typically you choose a material such that the nuclear recoil has some visible effect It might produce low energy scintillation photons It might produce ionization in the material and might produce phonons for example You bury your detector underground to get it away from cosmic ray backgrounds because you don't want your nuclei to recoil due to anything other than dark matter hitting them and And then you sit there and then you sit there and wait Now it's worth noticing that what I've described you could also be used as a way to detect the cosmic neutrino background We know there are we know that there are weakly interacting particles out there that can't be shielded out And there is in fact a point of which these experiments will run into the point where their major background is cosmic neutrinos We're not there yet, but we will get there in the next few years So when you run these experiments and you see no signal you get a lima plot that looks something like this so again here there's the dark matter mass in Dark matter mass on the x-axis in GV on the y-axis is a measure of the scattering cross it was called the WIMP nuclear on the scattering cross-section So this is the in third cross-section For scattering between the WIMP and a proton or an individual proton or a neutron There are some assumptions that go into this number. We'll work it out But what I want you to notice here is that so this black line is the current bound for is the current best limit from the Locke's experiment And we'll understand the shape of this plot and why the constraint just come so if you see a few things One you can see that this constraint gets much much much weaker below about 5 GV Simple reason for that. We'll understand it on the next couple of slides but at higher masses this can this is an extraordinary constraint the minimum of this curve is Constraining cross-sections, you know several times 10 to the minus 46 square centimeters I said There's that back on Monday when we talked about self interaction cross-sections This is we talked about the kinds of cross-sections that you would need to have observable impacts on the bullet cluster to change the nature of dwarf Galaxies those cross-sections are 20 orders of magnitude bigger than this if the dark matter Interacted just through exchange of a zebo's on it if it interacted naively like You know like in utrino we would have seen that Years we would have seen that years ago That we've been past that point for a long time This is cutting deep into the parameter space of weak scale interactions So so that's so why are these direct detection experiments so very sensitive? Okay So let's go through the math. So direct detection. It's nice and simple.  So your observable is how many scatterings do you have with a given recoil energy for the nucleus? So let's work out the classical kinematics in this frame We can write down our equations for conservation of energy and momentum Doing the lab frame first. So we'll say the nucleus is at rest to start off with we're interested in what it's But and what is energy is after it recoils? Then we can just write down how everything's non-relativistic here the dark matters Dark matter in our halo. We believe is going at about 200 kilometers per second So it's about 10 of the minus 3 times C. So it's fine to ignore relativistic effects Nucleus is suddenly not an relativistic So if we just write down our energy and momentum equations and then manipulate it as I'm sure you've all done in undergrad then we've end up finding that the and that the recoil energy is given by The reduced mass of the system squared the velocity of the incoming particle squared an angular factor And it's also determined by the mass of the of the nucleus So we can see a couple of things from this already So that tells us that For a given dark map for a given velocity of a dark matter particle We should see some spectrum of recoils extending from zero energy up to this maximum recoil energy So we can another way to say this is that if I fix the recoil energy Then only dark matter particles with a velocity higher than some minimum velocity can contribute Now there does come a point if you push the recoil energy high enough Where there's a cutoff because that minimum velocity is higher than the escape velocity of particles from the Milky Way So anything that was high that was high energy any dark matter particle that had a high enough velocity to give you a Very high recoil energy would already have escaped But but let's but let's just do some quick but let's just do some quick estimates here of what kind of recoil Energies that we're talking about So let's suppose I mean you saw on that plot our best constraints was sort of a 10 GB and up So let's imagine that our So let's imagine. Well, okay. Let's not even specify the dark matter mass yet when we're talking about the target nucleus we Have many options for target nuclear eye But most of the but the order of magnitude of the total of the atomic mass is going to be somewhere around the range of 10 to 100 there may be a couple of hundred it's going to be somewhere in that ballpark So let's let's suppose first that the dark matter is of a similar mass or heavier To that term to the target nucleus in that case the reduced mass is set mostly by the mass of the target nucleus So we'll just approximate this reduced mass is about M n Show me the nucleus mass as I said previously the velocity dispersion of dark matter locally It's just set by our galactic potential you can read it off from the rotation curves and we estimate that it's about 10 to the minus 3 So that means that the typical recoil energies Adjust of order v squared times what we're setting mu equal to m n so it's just like the nuclear mass times v squared So that corresponds so that's about 10 to the minus 6 times the nuclear mass So we're looking at sort of 10 to a hundred KV recoil energies So if you design an experiment like this you need to be able to see Recoils at that at that scale. This is your basic requirement for dark matter direction experiment And no matter how heavy you make your dark matter You're just not going to get recoil energies much bigger than that on the other hand We assumed here that the dark matter was heavier than the target nucleus If you go the other direction if you make the dark matter very light relative to the nucleus Now the now the reduced mass is going to be set by the dark matter mass So compared to what we had before you're going to get a suppression Which is like the dark matter mass divided by the nucleus square So if we say that okay, we had a nuclear we had a target which was a hundred GV in mass so Nucleus that has an atomic mass of a hundred or so Then if we were looking for one GV dark matter scattering this three coal energy that we were looking at would only be 0.01 KV That's extremely hard to see 10 to 100 KV is doable much lower than that gets gets very difficult So if we want to go after light DM then we preferentially want light targets and And extremely low energy thresholds So this behavior is why that limit plot that I showed you has that very very sharp cut-off at energies below At energies below about 10 GV that was in that limit comes from locks Which is a xenon based experiment which has an atomic mass of about a hundred once the dark matter mass gets too far Below that scale the limit just dies The recoil energy that you need is just too low to be observable by locks which has a threshold of several KV Okay, any questions about these parametrics before we move on Okay, good. I hope that means that everyone is comfortable with classical energy and momentum conservation as opposed to Everyone is confused and or didn't get enough coffee. Okay, so like it's okay So that gives us our general picture our spectrum is going to extend up to a few tens or a hundred KV But what will that spectrum look like? I mean, this is what we actually want to look for as an observable So what ingredients go into this before we actually go ahead and calculate it? Well, first we need to know how does dark matter scatter on individual nucleons So there's some particle physics in this, you know What is the fundamental coupling of the dark matter to the particles present in a nucleus to the quarks to the gluons? But there's also a nuclear physics element, which is okay If I tell you that my dark matter couples in some way to the up and down as strange quarks You know, we we say the protons and neutrons are Up up down or whatever But in reality the quark content of the nucleon is a bit more complicated than that They behave as if they have some significant command of strange quarks for example So you need to know that and there's actually been some interesting progress in QCD and lattice Calculations over the last year is improving these estimates of the quark cannon of the nucleon when I wrote a paper on this That which was the very first paper of my PhD About eight years ago the error bars on these parameters were sort of order one But my understanding is they've gotten much better since then Okay, so once you know that you know how if I've scattered my dark matter particle of a proton how it would behave But then I need to translate this into scattering off a collection of protons and neutrons that are bound together There's some particle physics in this question again one of those questions is okay. How do these amplitudes add? When I put them together. What do they depend on are they all just identical? Do they just add together coherently? That's the situation that you classically have with spin with spin independent scattering But you can have situations where the scattering amplitude Depends on the spin of the nucleon you're hearing spins for nucleons occur in in pairs As you may remember from your quantum mechanics classes So then in that case most of the contributions from most of the nucleons actually cancel out and you get a much smaller Cross-section that is just determined on the unpaired spins Likewise that you have a question. Well is is this scattering cross is this amplitude? Is it approximately the same for protons and neutrons some dark matter particles will only couple to protons the only couple to charge? There's a That there's a flavor of dark matter in the literature that was designed to try to explain why Some other experiments were seeing hints of signal and the xenon experiments weren't seeing anything which was dubbed xenophobic dark matter With the idea being that if you tune the couplings to protons and neutrons correctly and they have the opposite sign You can cause it to hate scattering on xenon and love scattering on everything else which is Advantages in a way because our most sensitive experiments are made with xenon It would just be a really unfortunate coincidence if the universe worked like this But but in principle you can have those kinds of cancellations where the contributions from protons and neutrons actually interfere with each other There's again some nuclear physics at this step The so-called nuclear form factor which basically accounts for the fact that the nucleus is not a point particle It has a finite size the protons and neutrons bound in it have some individual momentum of their own This suppresses scatterings where the momentum transfer is much larger than the characteristic momentum scale of the nucleus Okay Okay, and we'll we'll talk a bit more about the approximation of that later and then lastly To convert this in rules of all quantity we need to say okay I've got my I know if I had an individual dark matter particle and I scattered off this nucleus What would happen, but then I need to understand how does that translate into a rate so to do that? I need to know about how many dark matter particles are passing through my detector at any given time and With what velocities because you just saw the spectrum of recall energies is going to depend on the velocity of the dark matter particles So we also so this kind so just predicting what you'll see in this area Detection experiment relies on on both having a particle physics model, but also on understanding the nuclear physics and understanding the dark matter astrophysics Now the way that this is traditionally done and the way that we make limit plots like the one on the earlier slide is to make a Whole bunch of simplifying assumptions Now the main thing that I just wanted to establish here is these are all assumptions. They're not necessarily true They allow you to write down a simple constraint on the scattering cross-section but many of the sort of Modifications to dark matter models or novel dark matter models that people have come up with in the last few years are Essentially just going back to this list of assumptions and saying what if this assumption was wrong, okay? So the usual assumptions are first you say all right. We're going to assume that this scattering whatever it is It doesn't scatter the scattering amplitude itself doesn't depend on the velocity the particles are going out It doesn't depend on the momentum transfer. It doesn't depend on the scattering angle. It's just some simple isotropic contact interaction We also often further assume that the Coupling to neutrons and the coupling to protons are just completely identical dark matter doesn't care about whether you're interacting with something charged or not Of course, this is an assumption We usually separate out these two cases of spin independent or spin dependent Interactions just because the constraints are very very different the two cases In the case of spin independent interactions all the contributions from different nucleons add coherently So if this assumption is true if you transfer protons contribute equally then the overall rate scales is the square of the atomic mass The spin dependent interactions the overall rate just scales as the net spin of the nuclear squared, which is much smaller For the form factor This is what I said earlier. This is what it does Typically for most studies people just use a simple analytic parameterization called the Helm form factor To do this more carefully you want to actually take results based on You want to probably take numerical fits to nuclear scattering data but low energies and Lastly for the dark matter velocity distribution to make these plots people typically just assume that the dark matter is Insult that the dark matter speed follows some Maxwellian distribution isotropic in the frame of the galaxy with some characteristic velocity which is typically taken to be about 220 kilometers per second, okay now any Now pretty much any of these assumptions could be wrong and some of them are just Approximations which are definitely wrong at some level like these last two So many non-standard dark matter models work just by changing one or more of these assumptions And the reason that this is important is when you're comparing for example a constraint from a xenon experiment To something that you think might be a signal in a sodium iodide experiment It can make it can make a big difference what you assume for this if experiments have different numbers of protons and neutrons Then it matters what their relative proton-neutron couplings are if Experiments have different target masses then it matters what you think the velocity of the particles in the halo is because the translation between between The the the recoil energy spectrum depends on both the mass and the velocity of the particles in the halo Okay, but let's but With all those caveats, let's go ahead and do the standard calculation because it's good to see it and understand where it comes from Okay, so first this is sort of the easiest simplest ingredient. This is so this is the so-called form factor This is a plot of the home form factor for a equals a hundred and thirty. So this is a numerical fit to some data You don't need to memorize this. We're not all write it down We're not going to use that as just so you can see in this is basically like a Bessel function This is just this is just not even a best function. This is just a simple trig function This is so this plot you can see this form factor is one zero momentum transfer so the x-axis here is describing the momentum transfer in the In the interaction It starts to become it starts to diverge significantly from one when you got up to momentum transfer scales that correspond to about One femtometer that corresponds to a transfer of momentum around about a hundred MEV now the Now that we said earlier this momentum transfer is Some is typical so the scale of this momentum transfer is about the dark matter mass times the velocity We know the velocity is about ten of the minus three So this becomes a pretty important effect for heavy dark matter matter above about a hundred TV The light dark matter you can essentially ignore the form factor for heavy and including the uncertainties in the form factor For heavy dark matter. It's important because you start getting these significant suppressions in the rain We'll use that later. Okay, so let's do the standard calculation again We're going to do standard classical scattering theory this time We're going to switch to the center of mass frame rather than the lab frame The reason for that is that when I say all right I want my scattering to be my scattering matrix element to be simple and isotropic It only really makes sense to demand that it be isotropic in the center of momentum frame The fundamental particle physics doesn't know which frame is your lab frame, but it does know what the center of momentum frame is Okay so So this is so this is our configuration particles some come in with some equal and opposite three momentum p after scattering They have some equal and opposite three momentum k The momentum transfer, which is just the momentum of an individual the difference between the momentum of one of these particles before and after the Scattering is given by this vector quantity We can write in in terms of the reduced mass of the system and the relative velocity Between the two particles and the scattering angle theta Okay Now we can now remember our observable quantity was the recoil energy in the lab frame Okay, our experiment is in the lab frame our new glaze at rest is initially at rest in the lab frame That's where we're going to measure the recoil energy. Okay, so that's related to the momentum transfer By this by this relationship So you can check just by um as I mean this is as you can check just by going back to the lab frame So if I want to write my observable lab frame recoil energy in terms of the center of mass frame The center of momentum frame scattering angle I can write down this equation So when I want to ask what is the number of events at a given recoil energy in my lab frame I can recast it as just the differential rate by scattering angle in the center of momentum frame With this pre-factor that depends on the reduced mass of the system their relative velocity of the particles and the target mass Okay, we good Okay, so let's I'm just going to do this for spin independent scattering the spin dependent scattering case is Pretty similar. It's just that you need to keep track of the fact that most of the contributions cancel out So the overall rate is much smaller So let's just do spin dependent scattering So then let's say okay, let's write down. Let's parameterize our scattering amplitude for scattering on the nucleus as This is out. This is our form factor This is our factor that's going to describe the finite size of the nucleus and its function of the momentum transfer And then we're going to get a contribution from the protons which all I'd coherently from each proton We get a contribution of fp and z is the atomic number number of protons And then we get a contribution from the neutrons and there are a minus z neutrons where a is the atomic mass Z is the atomic number Okay, so Then now if we say, okay, this is our matrix element. Let's work out our differential cross-section Some of you who've done much scattering theory. You can just work out the math. I should say here. I mean I'm saying this is the contribution from each nucleon But it's still possible at this stage that these contributions could depend on the mass of the whole nucleus for example It's just a parameterization Okay, so I so I can write down I can write down this expression haven't justified this expression But it's a standard scattering theory calculation Okay, so now so now I have my differential cross-section by angle But what I want is my differential rate of events by angle But you could but my scattering rate is just going to be the number density of the dark matter particles okay times the Velocity of which the dark matter particles are hitting the target So this is a um, so this is essentially so this n and v factors essentially the flux of dark matter particles onto the target That's the rate to hit a single target atom That's the rate at which dark matter particles will encounter a single target nucleus So then we need to multiply by what I'm calling NT here the number of target nuclei in your sample If I were to multiply by number density here This would be a rate per unit volume, but I'm actually just interested in total in total rate here Okay, so I'm just multiplying by the total number of targets not the number density So then if we just put all these factors together Plug them into this equation and do a little bit of algebra Then we end up with an expression like this for our observable quantity. So um Because this d omega is just d cos theta times d d phi I can write down an expression for my observable quantity in terms of these f coefficients which describe the particle physics coupling between the nucleons and And the dark matter any questions at this stage Okay So then so okay, but you still have this question. Okay. Here's here's my spectrum And I couldn't I mean this is this is a useful formula. I could go ahead compute these These coefficients from my particle physics theory go ahead and work out the spectrum But you might still ask well, okay, but how does this translate to this? Nucleon dark matter cross-section that we appear to be constraining on the first page So that's just a definition. Let's call this the effective cross-section for scattering on a single nucleon we'll say that if We'll caught so we'll call this sigma chi lowercase n where lowercase n means nucleon uppercase n means nucleus So we'll take this to be the scattering cross-section on the nucleus on the whole thing Where we had if we had zero momentum transfer and so we didn't have to worry about the form factor Okay, so we're just basically throwing out the form factor from this calculation We saw here that this cross-section is proportional to the reduced mass squared of the nuclear of the system of the nucleus dark matter system So we're going to divide out by that reduced mass Squared multiply by the reduced mass squared that you would have if you only had a dark matter nucleon system and Then divide out by this factor of one over a squared Which would map onto the factor that you'd get here if you said okay? Well, let's um Well, let's assume that fp is equal to fn Then this factor here would just be a times fn Which would appear it which would appear as a square in the cross-section So you will get dependence on a squared times fn square So this is just a definition it may or may not have in a given model. It may or may not have any direct physical meaning Essentially a sort of average over all the nucleons in the nucleus of what their contributions to the cross-section is That is the quantity that is being bounded when we write those limit plots is this conventionally defined Nucleon cross-section Nucleon dark matter scattering cross-section and The reason that we do it this way is that it allows you to make sensible comparisons between Experiments that have very different numbers of nucleons because this usually does map to something that is almost a That is almost independent of the number of nucleons in your target nucleus So if we make this replacement then we can write down our observable spectrum in this form This is just a substitution from the equation that we had on the previous page since we can write the momentum transfer totally in terms of the Energy recoil I've just written the form factor as a function of the energy recoil here not the momentum transfer So then we have this expression and that is the express so this is now the expression so this sigma This is what's being plotted is what we constrain This is how we constrain it this a cross-section of a given size leads directly to this observable spectrum Okay, but we we should pause for a moment because here I've been treating the Velocity of the dark the relative velocity of the dark matter and the And the nucleus as though it was just something I knew just one number You know, I've measured the velocity of the dark matter coming in I've said it's you know 300 kilometers per second Okay, now we can go ahead and work out the cross-section, but in reality, of course, this isn't true. I I Mean I'm never going to know the velocity of a given dark matter particle All I can hope to do is say there's some distribution for the incoming dark matter part for the velocities of the incoming dark matter particles and Then I need to integrate over this distribution to get my total rate so Then so then we can rewrite so then we can rewrite this expression this dr dr We can write what I previously was just a factor of 1 over v as an integral Over a probability distribution for the dark matter for the relative speed between the dark matter particle and the nucleus So this f is just a probability distribution for that speed has to integrate to one Okay, so now this is a convenient form for the cross-section because we've really Separated off the different uncertainties this piece So we have this first piece here this depends on the massive on the atomic mass of the target nucleus Depends on yeah. Well, so this is really another factor of a This is it depends on the number of target nuclei you have so how big your system is this combination Mn times Nt is basically your total mass in the target and And it depends on the form factor Which again depends on the new on the properties of the nucleus that you're dealing with on how big a nucleus it is So these all tell you these are all things that in principle you could know perfectly if you understand your target well enough Then we have these terms So this is the cross-section that we want to constrain the nucleon dark matter cross-section and You also see here the dark matter mass and the reduced mass of the dark matter Nucleon system These if we understood given a dark matter model I know these things perfectly given a model for the dark matter particle physics and then lastly we have the astrophysics We have the overall density of dark matter Which tells you about the um, you know, which tells you about the flux of incoming particles And we have this integral over the velocity distribution So this allows us to sort of factor the uncertainties into these three parts So that makes sense to anyone any questions about this Okay, good. Good But I'm not sure if it's no one if it's Insufficient questions or people are insufficiently caffeinated or I'm just going too slow Okay, I'll continue. Okay So now we so now we have this expression So where in this so we'd like to know what the shape of this spectrum is what in it? What recall energy should we look we be looking at we said 10 to 100 KV Where should we focus our efforts low energies at high energies? What will that? How will this spectrum look we know that this form factor will suppress the spectrum at sufficiently high recoil energies low recoil energies That's essentially just a factor of one So what's the other energy recoil dependence? It's a little non-obvious, but it actually shows up in this integral because you'll recall as we said earlier What are the limits of integration on this integral there from some minimum velocity to some maximum velocity? The maximum velocity is set just by the maximum velocity of the particles in our halo. They're going above a certain speed They're not sticking around in the milky way The minimum velocity is this expression that we wrote down earlier And it's just a function of three and it's just a function of the recoil energy These are these are the slowest moving particles that can give you recoils at a given energy in your detector Now there's another point that I've been glossing over a bit here when I when I wrote down this expression And that is that when I write down this velocity distribution if I want a simple isotropic Maxwellian velocity distribution It only really makes sense to talk about that in the rest frame of our galaxy There's no reason that the dark matter velocities should all be isotropic in the frame of the earth I mean the earth is going around the Sun the Sun is moving around the center of our galaxy There's no reason to think that dark matter should be coming equally from all directions on the earth, right? So that means that in reality when we write down this distribution so this should be the distribution of velocities as Seen by an observer on the earth. That's what we've assumed it to be that means it's going to be an isotropic By an amount that depends on how fast the Sun is moving through the galaxy and how fast the earth is moving around the Sun And it's also going to be time-dependent Because that's not a constant relative velocity. The earth is orbiting around the Sun its velocity relative to the Galactic frame changes over the course of a year however Those are both relatively small effects. So at first order I'm going to ignore them and I just show you what happens when we ignore them and then we'll talk about what happens when you include them Okay, so for the moment, let's ignore escape velocity. Let's treat V max is infinite Let's assume that f of v is isotropic in the frame of the earth just because it'll make the integral very easy So then so when I say a max well in distribution, this is what I mean for the distribution for a speed So it's essentially so it's a Gaussian distribution with some appropriate with some Characteristic velocity which is about 220 kilometers per second in the local halo Then when we do this integral you can do this integral yourself or plug it into whatever program you like We get this expression so this is where most of the end of the energy of the recoil energy dependence comes from there's this Exponential suppression of the recoil energy With this characteristic scale which is the same scale that we talked about as the typical scale for equal energies Back in the earliest line So what we expect to see from dark matter is a smooth exponentially falling spectrum Which then gets multiplied by the form factor squared This is from a talk by a representative of the xenon collaboration The dark matter meeting a couple of months ago So this is showing as you change the dark matter mass What does the spectrum of electron recalls look like you can see as you go from light dark matter to heavier dark matter The scale for the recoil energy becomes larger and larger So you see broader and broader distributions and eventually for this heavy dark matter where the rate goes to zero down here That's the form factor kicking in okay so a Point to take away from this is low energy sensitivity is really important It's especially important for light wimps where there's just no signal above 10 KV or so But for all wimps the spectrum is exponentially falling Often you'll get the best sensitivity from the lowest end use the problem Of course is that if you're looking at very low energy recalls. There's a lot of background and They're just hard to see in the first place Okay, so that's our observable We know how to relate so we've written down our Our spectrum in terms of this Sigma we can go ahead and ask You know, okay, that's our spectrum. What about the total rate? How many scatters do we actually need to see in these experiments? This is the calculation that was sort of done back at the beginning of the direct detection era So let's just do this back of the envelope estimate ourselves So if we integrate again ignoring the form factor and we just just said the form factor to one And we integrate over the whole spectrum we get this expression for the final rate So let's imagine that we have a hundred kilograms of xenon to be our detector That's about the scale of the current best xenon based experiments And we're going to approximate the atomic mass of xenon, you know, it's a hundred and thirty-two there and there around that There's ever isotopes, but we're just approximated as a hundred because we just need not our magnitude estimate Okay, so the question is what when you click on cross-section would you need to have in order to see one event per year? For a hundred GV WIMP because if you're much lower than that then well It's it's hard to get funding to run your experiment for 20 years on the basis that you might see one event Okay, so this is going to be our our possible reach So what are the ingredients that go into this? Well, so our number of target nuclei This is Avogadro's number. Well one mole of xenon is about a hundred grams here We have a hundred kilos of it. So that's a thousand times as much So a number of targets is going to be Avogadro's number times a thousand. It's about six times ten to the twenty-six This is the first factor that gives you that allows you to do such sensitive searches with these direct detection experiments We were talking about annihilation. We were talking about dark matter particles scattering with other particles Those are both very low density objects here on the earth We can make enormous over densities of matter if we want we can cram ten to the twenty-six Target particles into a reasonably sized space So that's part of why dairy detection allows you to probe cross sections that are just vastly smaller than anything that you can do With astrophysics. Okay. What are the other parameters in this expression? We've got the reduced mass Well here we're saying that the target and the dark matter are about the same mass So the reduced mass is half of that it's about 50 gv The reduced mass of the nucleon dark matter system is well They're reduced mass when one mass is much smaller than the others through a juice masses the smaller of the two So it's going to be about one gv The dark matter local density there are estimates of this it comes out to about point three or point four gv per cubic centimeter So we'll use point four That's for definiteness and I told you the typical the venor at the characteristic velocity of this distribution is about 200 kilometers per second That's a so we can convert this into units of centimeters in years Since what I want is the rate per year And we get this number just as a just as a handy mnemonic that's useful a year is about pi times ten to the seven seconds It's not exactly of course, but it's three point one four times ten to the seven seconds, so Okay, so we put all these numbers together The view with a bit of paper and a pencil can do the estimate yourself and please do check me on this because I did this Quite early in the morning this morning So it's possible that I have lost some important factors, but this is what I got when I did it You just put in all these numbers you put them together and the number that you end up getting is about for the rate is about sigma Divided by ten to the minus forty six square centimeters per year So we would predict that if I had a cross section of ten to the minus forty five Square centimeters, I would see about ten events per year That's not actual that and that's not actually about estimate We saw on that first page that our current limits from the xenon experiments are in that ballpark. Yeah, sorry Yeah, so the question was what about the spin dependent case? Yes, this is the rate for the spin in this is the rate for the spin independent case And you'll note that we're benefiting in this spin independent case from the fact that we have this a squared Factor out the front. This is coming from the fact that it's been independent and everything adds coherently And it's giving us four orders of magnitude here. Okay So, yeah, so so the spin The spin D so xenon's not the best Target for spin dependent searches. I think precisely because it doesn't have It doesn't have much overall spin Yeah, I mean I can I don't actually have that Plot on my slides. I think although we it might be peripherally there in the LHC constraints because the LHC often Actually does better than direct detection a constraining models which have spin dependent scattering So, yeah, this is this is the best case for direct detection If you look at spin dependent bounds, they will usually be quite a few orders of magnitude weaker Because we'd essentially be replacing this a squared with With something, you know, we'd only be getting contributions from the unpaired new plans Okay, but these are the basic parametrics of why dark matter it could be so my dark matter Derek detection can be so sensitive you can have many targets and You can have a you can have a fairly high flux Because they're going so fast. All right, so I just said I said, okay We're going to make all these approximations about the signal being time Independent, so let's go back and just briefly revisit those I'm not going to do go through the whole integral because the analytic form of that integral is not super enlightening But but we can understand what's going to happen So first this finite escape velocity that 500 or 600 kilometers per second is going to impose an Additional cutoff on this spectrum at high recoil energies when the minimum velocity Just becomes larger than the escape velocity then the rates actually going to go to zero Rather than just being rather than just being exponentially suppressed Second though this time dependence is going to induce an approximately sinusoidal and your modulation in the rate You can understand this just because this total rate You see has a dependence has an approximate dependence on the not here if you change the typical velocity between the earth and The dark matter particles then you will um that then you will change then you'll change the overall rate This is just a sketch The Sun is moving relative to what we believe to be the approximate rest stream of the galactic halo at about 230 kilometers per second in a direction that we know the earth's orbital velocity around the Sun is about 30 kilometers per second So depending on where the earth is in its orbit It's its velocity relative to that overall halo varies from like 200 typical velocity relative to that overall halo varies from like 200 kilometers per second To 260 kilometers per second That's not a very big effect and what it leads to is a is a modulation of a few percent in the annual rate It also shifts the spectrum somewhat. So this is a plot of log of the rate versus e-recoil and This is the difference between December. This is the difference between December and June So it tilts so the effect of taking into account this time dependence is a small few percent level Change in the overall date and it's a tilt in the and something of a tilt in the spectrum. So this is okay So suppose I want to go look for this signal. What do I need to do? So I Want so in this kind of spin independent search. I want high a okay I want high mass nuclei unless I'm looking for very light dark matter in which case the advantage of having high a is Destroyed by the fact that my recoil energies are really really really low and really hard to see I Want large volumes. I want to raise that NT factor up as much as I possibly can Signal just scales directly with the number of target nuclei that I can apply and I want to reduce my backgrounds as much as possible especially at low energies the kinds of backgrounds that you get in these searches you Can have neutrons scattering off the materials. They're neutral particles Some ways like dark matter, but since neutrons interact much more strongly than dark matter They they can be they can be shielded against they don't go very far Now you could also have scatters of Photons and electrons that make their way into the detector somehow One challenge in these experiments is making sure that your detection material has extremely low levels of radioactivity Because else, you know if it has some level of radioactivity you can't shield out decays that happen inside your detector there's it's a Neat anecdote that I was told a few years ago. You also have to worry about radioactivity from the shielding itself In you typically have some swell fraction of radioisotopes in lead for example And so you put all this later and your detector to try to block out cosmic rays But then the letters itself radioactive and gives you a background So what they use Sometimes to shield these detectors is lead from ancient shipwrecks That has been sitting on the bottom of the ocean and thus has been shielded from cosmic rays for a couple of centuries So, you know, there is there is a market for Retrieving lead from ships that sank hundreds of years ago so that you can use it as a low-radio activity shield For a dark matter detection experiment She sort of wonder what the sailors in those times would have thought if they had known what the eventual outcome of their Of their shipwrecks was going to be So in the future so these photon electron scatters are less problematic than neutron scatters Because they're in general because those particles are very light or massless They're mostly scattered off the electrons present in the medium not off the nuclei so The current flagship experiments have ways to try to distinguish between the backgrounds coming from of these electron Recoils and actual nuclear recoils in the future as I said earlier We're also going to have to worry about the cosmic neutrino background, which are you know and That is going to be a problem is sometimes called the neutrino floor. It's going to be We're at the moment in the happy case of having essentially zero background So if we double our volume we can double our sensitivity in terms of significant Spot once you have backgrounds to deal with if you can remove them at all your signal to background ratio I'll signal over square root background ratio will be scaling like square root time not time So things will slow down when we hit that point The current flagship experiments in the US at least there are really two major directions One is experiments like Lux and Xenon. These use large quantities of liquid Xenon Liquid Xenon is a scintillator material nuclear recoils produce low-energy photons They also produce an ionization signal and you can look for both the ratio of Ionization to scintillation is quite different for nuclear recalls and electronic recalls and I'll show you a plot of this on the next page So you can use this to reject those electron recall backgrounds The other kind of flagship approach is the super CDMS experiment Which uses silicon germanium super semiconductors in that case and you clearly call causes ionization It also produces phonons Did me okay that says ionization plus photons is should say it phonons that may be an autocorrect problem Super CDMS is great advantage is that it can go down to lower mass scales than Xenon. So Xenon is the high a Maximized volume strategy super CDMS is the reduced background reduced energy threshold try to probe the low mass and Strategy and also reduce a There are many other experiments using a range of different materials and techniques these experiments are currently leading in the search to push down that those constraints, but There's there are there are a number of other contenders in the field often using very clever expert very clever experimental methods at the moment the only experiment that has a substantive that has a Claim a strong claim of a detection is the Dharma Libra experiment which actually claimed its detection back in the 1990s So it's been around for quite it's been around for quite a long time What they do this experiment doesn't try to remove the backgrounds It doesn't try to take these two approaches to try to separate electronic recalls from nuclear e-coils What they do do is look just directly for this modulation signal this few percent seasonal effect and they indeed see a rate of Scatters that modulate that appears to modulate sinusoidally over the course of it with a period of one year and A phase which is about what you would expect from that matter. I think it's off by about a month Which is about one sigma and this signal is extremely significant like the galactic center access that we talked about yesterday This is about a 10 or 12 sigma signal. So they certainly appear to be seeing something modulate but The field is the reason that the field as a whole isn't super excited about this result is that In the absence of background rejection You can imagine that there might be other quantities that modulate with a period of a year over the course of a year So the I mean the obvious thing is temperature for example Now the Dama Libre experiment the Dama Libre team has done various things to try to exclude many of these seasonal effects, but it's Yeah, but but it's it's hard to completely prove a negative that there is no background that it could possibly be There there are currently Experiments being planned in the southern hemisphere in Australia at the South Pole to try to reproduce the Dama Libre Experiment in the South because the seasons are reversed there But the cosmology of how is the earth moving relative to the dark matter halo that doesn't change So you would hope so if it really is dark matter You would expect to see the same modulation signal with the same phase Showing up in the southern hemisphere if it does that will be a game changer and I may come back in a few years And be like I'm sorry guys Dama was right all along but I think most people are expecting them to either see nothing or to see a modulation with the opposite phase But we'll we'll test it out and see what happens The other reason that people are skeptical about Dama is as we'll see in a slide or two It's actually very difficult to reconcile this result with the limits from the other experiments somebody else should have seen it by now All right, so just to illustrate a couple of things that I said on this that last slide This is an example of how Lux does their background ejection So this is a plot of what they call S1 versus S2 where S1 is amount of Sintolation light and S2 is amount of photo ionization and each amount of ionization and each of these black dots on here is an event now these blue lines from here to here show the sort of 10% to 90% confidence bands for Electronary coils, so this is what we expect the ratio between S1 and S2 to be for electron recalls This red band shows what we expect for nuclear recoils for Wimplike recoils You can see that they're reasonably well separated You can see that there are a ton of events in this electron recall band and Enough that you can estimate what the leakage should be into this red band And you can see that there are very few events in this red band and in particular there are no events in this bottom half of This of this red nuclear recoil band where you would expect the electron recall contribution to be small So this is the kind of thing that allows Lux to set the strong limit that it does Okay, so where is direct detection going? So this is from a talk late last year by On behalf of the xenon-1-tonne collaboration. So the liquid xenon experiments they already have order 100 kilo Experiments they're pushing forward to the ton scale so this Green line, I think is the Lux limit that we just saw this is an estimate of Xenon-1-tonne which is currently in progress and this is hope to say something in 2017 So in the fairly near future this orange Dashline is the neutrino floor that I told you about when neutrinos will actually start to become a significant background For these experiments you can see that it's a couple of orders of magnitude below this Next year experiment I think it's quite possible that we will start to be pushing on that neutrino floor in the next several years Now as well as pushing down in sensitivity There's also a lot of active work at the moment on pushing to this side of the plot to follow this TV scale now As we've just worked out this nuclear recoil technique is not very effective at probing masses below the GV scale I Don't really have a ton of time to talk about this. So I'm just going to I'm just going to point you to these references and Yeah, that you can look at dark matter electron scattering very clever tricks involving superconductors and superfluous to try to pull out The scattering of very light. Okay So now at the end. I just want to say some brief things about collider searches and axion searches But any questions about the direct detection side of things though? Yeah, okay, so the question is is there a good explanation for the Dharma signal other than dark matter Well, is there an explanation I added the good part There's not a clean it There's not an explanation that is good enough that everyone has said. Oh, okay. This is clearly what's going on where we're done There are several ideas involving things like annual modulations in the muon flux at a grand Sasso But yeah, that there's no there's no explanation which clearly explains the data It remains a bit of a mystery So hopefully the confirmatory experiments in the southern hemisphere will tell us something about what's going on There is something going on so collider searches in a nutshell so In a collider search what we're trying to do is collide standard model particles together and produce dark matter particles So in a sense This is like the inverse of the annihilation process in the early universe The problem with this is that if it was literally this process then all that we would see is You put a beam into the collider and Nothing came out which is not a very interesting signal because of course, you know all the particles that didn't do this Are still going to come out. So this is hard to find What you can do though is look for the signatures of production of these black matter particles as missing Energy and momentum the way that we typically see particles in the collider is that they decay and then we look at the decay products But that's not going to happen for dark matter cause it's stable on cosmological time scale So it's certainly stable and the time it takes to get out of the LHC The searches that people mostly talk about the dark matter at the LHC The four mono X searches by which we just mean you look for a visible particle That appears to be moving in a way that doesn't conserve energy and momentum So it seems to be recoiling off an invisible partner These could be like mono Higgs where the visible thing you look for is the Higgs Mono jets where the visible thing you look for is a QCD jet or mono photons where the thing that you look for is a Photon it doesn't fundamentally have to be mono. You can have more than one visible particle or jet in the event as well Okay, so at the LHC we can potentially produce dark matter particles if it's below about the TV Mass scale if we can produce dark matter under these control conditions It would allow us to probe the interactions between the dark matter in the standard model in depth But yeah, this is what I just said the LHC Experiments are beautiful. They're very sophisticated. They do not include dark matter spotting modules The kinds of processes that you can that can give you dark matter particles You should think of this as essentially just a left to right plot You're gonna have to standard model one is you can have standard model particles come in one of them radiates off a Particle which is a photon as part of this interaction Then you pair produce the dark matter But the kinematics of this final dark matter state is affected by the fact that there's this photon here And the photon kinematics are affected by the fact that oh look I produced two heavy dark matter particles You could also have processes like this where to standard model particles produce other Intermediate particles and they decay into dark matter and something else There are two broad models for looking for dark matter for trying to set dark matter constraints based on the LHC One is to say yeah question Yeah, okay, so the question is are there standard model particles that can decay directly to dark matter? It's possible that the There could be dark matter hiding in the invisible decays of the Higgs for example We don't know the Higgs decays as well as we know a lot of other So if the dark matter is pretty light then standard model particles could potentially decay and produce dark matter particles in their decays Sorry, so Yeah, so if dark I mean you might yeah, so right the Higgs field could mix with another scalar field it could also have It it if you're talking about Susie dark matter will often naturally have some couplings the Higgs or the other standard model gauge bosons Depending on depending on them if the dark matters So if the dark matters light enough then it could appear in the decay chains You can actually set some pretty interesting constraints on light like tens of GB dark matter by saying well, okay We have some limits on the invisible width of the Higgs Yeah Yeah, so the question is do we have the estimates on the missing momentum from dark matter versus the missing momentum from neutrinos I Mean you can predict given a model you can predict what the distribution of met should look like the dark matter particles You can predict what it should look like the neutrinos from the standard model processes These are not background free searches I mean you like you will have standard model events that have the same kind of behavior as dark matter events So what you're always looking for is some deviation in the distribution of events from the standard model Okay, so two broad approaches for these dark matter searches one is to say all right I'm going to build a detailed top-down model and then I'm going to search for the signatures of that model as a whole Now this can have very striking effects These models typically contain many particles that are not dark matter in something like a Susie model All are any superpartner that you produce ever will have a decay chain that eventually ends in the LSP the light of supersymmetric particle As well as other particles so you can see so you can look for your complicated cascade final states Which have large amounts of missing energy due to the presence of the dark matter particle The downside of this approach is you can say constraints on your one specific model And then if you want to try to constrain a different model you have to do the whole calculation over again So it can be harder to generalize and if you use these kinds of models to guide the kind of searches you do You worry that maybe you're going to miss a signal because it's not in the set of models that you were looking at So the LHC experiments have I think increasingly be moving towards using this framework of simplified models Where they just include a few ingredients and use that to develop generic searches The upside of this is that these constraints are easy to translate to many models The downside is that well sometimes those extra ingredients in your model are important And there's no guarantee that the simplified model you write down could be embedded into a reasonable high energy theory like just as an example Other particles in your model might significantly affect their electricity of the dark matter So so in general these approaches are complementary So I just want to show you this is an example of the kinds of constraints that you can set with the LHC Using one of these simplified models. So this is a picture where you just say, okay Let's suppose dark matter couples to some mediator in this case. They're treating it as an axial vector mediator let's look for Signatures of this form and then let's try to exclude parts of the parameter space that are so this is the mediator mass on the x axis and The dark matter max on the y-axis and the regions inside this region here between these blue lines here and between these purple lines You're abounded by these different searches and the scales here are both TV So you see that I mean where the LHC is good. It can be very good It can potentially rule out dark matter and couplings to dark matter and particles coupled to dark matter That are right up at the TV or two TV scale can be very sensitive However, this tends to depend fairly strongly on the properties of this mediator whether it's a vector an axial vector a Scaler or a pseudo-scaler If we want to combine if we want to ask the question of which does better the LHC or direct detection or indirect detection That's an extremely model dependent statement So this is an example for a set of models taken from what's called the phenomenological MSSM Where MSSM means minimal super symmetric standard model So this is already a simplified Susie model these different colored dots show it so this is a parameter space of a Scattering cross-section times the versus the dark matter mass You see that Above this black line which is sort of the locks bound from direct detection most models are ruled out So green means ruled out by direct detection red means ruled out by both direct detection and in direct detection Below this line direct detection can't do much purple means you can rule out model those models with the LHC But not with direct detection or indirect detection And you see that over this hall mass range and sort of the hundred GB scale up to the few hundred GB scale Grey points of models that aren't ruled out at all The LHC can eliminate a lot of models in this range But there are those that survive in direct detection for this particular set of parameters becomes particularly strong at higher masses Where the LHC can't really go because there's just not enough center of mass energy But we can use experiments like Hess and CTA as we talked about earlier to probe And look at gamma rays from those models to probe this high mass range so blue means Excluded by indirect detection, but not but not anything else Okay, so it's pretty much lunchtime So I'm just going to say super quickly and give you some references for axion searches So the axion searches in a nutshell slide third in a nutshell slide There's a really good review of this by Peter Graham and his collaborators So if you're interested in axion searches, this is a good place to start But the basic framework of most axion searches is just that in the presence of a magnetic field The axion can convert into a photon. This has a couple of implications It means that actually it means the photons can travel through regions That should be opaque to them by converting into axions and then back into photons And it means that it might be possible to catch the cosmological dark matter axions using magnetic fields by converting them into photons or equivalently into electromagnetic fields Axions have some other interesting effects because at least the QCD axion The parameter that we started this off by saying well Let's replace the parameter that controls a neutron electric dipole moment with the axion field So axions can induce nuclear electric dipole moments. You can look for these with NMR You know originally developed for medical applications They can also mess up the proton-neutron mass splitting if you remember our discussion in nuclear synthesis earlier that helium abundance Actually depended fairly sensitively on the proton-neutron mass splitting so you can use that kind of thing to set cosmological constraints on axions But if we just focus on these two topics, there's again, there's a range of possibilities here High-energy photons traveling to us from high red shifts can actually which would normally be absorbed by the Extragalactic background light if they can convert into an axion for part of their journey They could still get to us. So if we see very high energy photons from very high red shifts That might point to a cosmological role for axions You can do experiments light shining through a wall where which is just what it sounds like you would try to get the Photon to convert into an axion so that it can go through the wall In white dwarfs axions can have a significant effect on stellar cooling Photons that convert into axions can escape when they would otherwise not be able to escape and you can set lit and there There's actually all that there are some claims that there's maybe a slight discrepancy in white dwarf cooling That could be alleviated by axions Right at the level of the bound on the second front I'll talk briefly about the admx experiment because this is this field's current flagship experiment But you also have the CERN axion solar telescope Which tries to do this conversion of cosmological axions and look at the resulting photons using the magnetic field of the Sun and There's an experiment which I just have to advertise because it's by my colleagues at MIT and it has a great acronym Which is abracadabra Which where the idea is to have a toroidal configuration with an oscillating Magnetic field and devia undergrad electromagnetism the presence of an axion induces a slight extra current which you can look for Okay, this is after your time Let me just give you one slide summary of the axion dark matter experiment So the idea here is you build a resident magnetic a resident microwave cavity containing a strong magnetic field So it's like your microwave at home except quite a lot more powerful And what you look at is you look at the output power from this cavity Now in this case the axion photon conversion will occur at the largest rate if the frequency of the magnetic field is a close mass Match to the axion energy if we're talking about cold dark matter axions here, then they're very very non-relativistic So this is basically saying when the frequency of your cavity is equal to the axion mass Then you will then you will convert axions into photons and you can see those photons in your cavity The background here is that we're talking about very low-energy photons here if you're talking about milli e v axions, then you're also talking about You know photons around the same scale So there are backgrounds, but this is a bump pump The idea is that you change the frequency of your cavity and as you vary the frequency of your cavity Then as you pass through this resonance you will see a bump So if we were to take something here We would also automatically have a measurement of the axion mass and if it's the QCD axion that automatically tells us about its couplings this is the So this is a from an idiom X paper their sensitivity So this is the axion mass on the x-axis This is axion coupling the photons which is mostly controlled by the FA parameter that we were talking about two days ago this is their preferred region for axion cold dark matter and Blue is the current limits you will note that they managed to exactly miss the region of interest for cold dark matter searches But there is a funded upgrade to idiom X currently in progress which hopes to cut into this region Now it's worth noting a caveat when idiom X people show these plots This side of the plot where they have marked too much dark matter That's assuming that the misalignment angle is order one If the misalignment angle is very small then there could actually be cold dark matter axions down in this region as well And some of the other experiments that I mentioned briefly and posted references to which you can look up If you're interested are going to carve into that regime and That's just what I was talking about earlier with the high energy With the high energy gamma is making their way to the earth okay, so Thank you very much for saying I'll let you guys go to lunch So just to summarize we can prove the properties of dark matter particles with terrestrial experiments I've talked about a range of such searches something. I didn't talk about was the dark photon searches, which are also pretty neat But We have done enough time so to conclude this whole sequence of four dark matter lectures our basic problem We know the dark matter is 80% the universe's matter. We don't know what it is We don't know quite a bit about dark matter though We have a wide range of gravitational probes that tell us about its properties We have no shortage of ideas for dark for particle dark matter candidates. They fit fairly neatly into a range of expanded models There are several completely independent possibilities for matching the observations that we currently see I Hope that I've given you a flavor of what's going on in this field and at least pointed you to some useful tools For understanding it. Thanks very much for listening. Thanks very much for the great questions. Have a great time with the rest of the workshop Thank you