Signals of Dark Matter - Neal Weiner

okay so let's go ahead and and start I know it's early but but we've got a lot of stuff that I want to cover so so we ended the last lecture talking about thermal relics and the thing that we concluded with was this idea that if you have a perturbative coupling the cross-section that you need or something like alpha squared over 200 GeV squared and this is sort of the basic starting point for for whip model now I'm not going to spend too too much time talking about wind models because there are plenty of opportunities to discuss them elsewhere but it's still good jumping-off point so if you ever have seen any talks about wimps at all then you have seen this plot here which is that you say that you have a thermal relic a thermal relic in the early universe has a situation where dark matter comes in and annihilates into standard model stuff and one of the most important aspects of dark matter and thinking about its formation is it gives you some clues of how to look for it and one of the reasons why the WIMP has been such a popular models because there are a lot of opportunities to look for it and so the the thing that you will hear is the following that you draw this diagram where dark matter comes in and turns into standard model stuff and then you say well I can draw that diagram I can now consider this diagram in all sorts of different possible directions and think about the different signals so I can consider the signal that we started off with the direction this way where time goes that way where dark matter comes in and produce a standard model and that would be like cosmic ray signals indirect detection signals so in the halo of the galaxy or throughout the universe or in the early universe dark matter annihilates produces stuff and then I see that stuff I can consider time running this way where dark matter comes in and hits a standard model particle and goes out and and that would be naturally interpreted as possibly a nuclear recoil or some deposition of energy of the dark matter into standard model particles direct detection Dark Matter comes in smack something and transfer some of its energy to us or I can run time this way where standard model particles come in and I make dark matter and that's what you would do with a Collider and this is sort of the make break or shake directions of looking for wimps and this is a very nice plot and it's very good for a colloquium it's it's somewhere between PR and reality it's not it's not totally reliable because you never know what these final state particles are so the idea that I can really do this rotation is not obvious right if you're at the LHC then these particles better be gluons or quarks if you're going to make them right if you're doing a direct detection experiment then likewise this particle here better somehow be inside your nucleus or whatever your scattering off of and if I'm doing indirect detection then these particles better be something that I can observe right and so and different models are work better in different directions so the idea that you can really just say well I've got these three different rection to look for them is true is sort of a jumping off point but in particular it's not it's not a anything like a robust you know rotation of a diagram where you're really where you're really considering in two different directions but the caveat to that is that there are specific models where in fact you really are rotating the diagram and when you really are rotating the diagram it becomes very very powerful when you can in those specific models directly relate the annihilation cross section to say a direct detection cross section so how do we think about these signals well as I said before your indirect detection signals you have some thermal average which is some expansion in velocity and if this is a non-trivial piece then you have a signal you can look for but only then because the universe is cooled down so much that this is significantly turned off direct detection signals and I'm being very very sketchy about this in part because when ruben comes he will be talking about all sorts of different direct section possibilities okay but when you look at a direct section possibility what you're looking at is a possibility that dark matter comes in as some mediator that for the moment I will just leave it as a question mark and then you have some nucleus that is scattered by the dark matter and the energy is deposited into it now dark matter if it's a wimp as a mass of around 100 GeV and the characteristic velocity is in the Milky Way is around 10 to the minus 3 so the characteristic energy that you're talking about depositing is up to about 100 ke V that's sort of the rough energy scale that you're talking about for these sorts of direct section experiments so there are two basic categories of direct detection you have what's called spin independent and spin dependent spin dependent is a perfectly reasonable name the idea is that this interaction here is somehow couples dark-matter to the spin of your target so only targets that have spin can have any sort of scattering that's a perfectly reasonable name spin independent is a terrible terrible terrible name because it implies that is simply something that it is not and it's actually much more than that and typically in the spin independent case which is sort of the prototypical example of spin independent would have been Dark Matter scattering by a Z boson you end up with a cross-section which is proportional to the atomic number of the nucleus square so that is that you couple to some net charge of the nucleus and you scatter off of that and so it's enhanced because you're scattering off the nucleus coherently and so spin independent which you could think of as coherent scattering off of the whole nucleus tends have a much much larger cross-section because of this a squared factor and so almost all the plots that you see not all but almost all those the plots you see are are this type of scattering so what does the direct section plot look like a rack section plot typically has a shape that looks like this I'm just going to explain what it is on the x-axis you have the Dark Matter mass and on the y-axis you have the cross section per nucleon so it's a way that you try and compare different experiments because of course you might have one at target that has germanium another target that has xenon and another target that has sodium and you need to be able to compare these things and so what you do is you calculate the scattering of Dark Matter off of a single nucleon off of a single neutron or proton and then you imagine what the total cross-section you compare that to the experiment by scaling it up by the pria kinematical factors and a squared factors so you calculate the scattering off of a single nucleus you relate it to the scattering off of the nucleus in question and that allows you to put all the different experiments on the same plot to do that then you also have to make assumptions about what's the distribution of velocities in the galaxy R and what the local Dark Matter density is and these sorts of things these can matter in details and for specific cases they tend not to matter sort of in the Middle's of these plots so all plots have this basic shape and there's a reason for this we can understand the high mass region here which is just to say that the number density of dark matter goes like the density of dark matter divided by the mass so as you go to heavier and heavier masses they're just fewer and fewer dark matter particles around the relevant kinematical factor at high masses is the reduced mass of the dark matter nucleus system so when you go to infinite Dark Matter mass the kinematics of it are just dominated by the nucleus so it's irrelevant what's the dark matter masses for very very very heavy dark matter if you want right it doesn't matter if a nucleus is bouncing off of a bowling ball or if it's bouncing off of a you know a freighter it's bouncing off of something which is infinitely heavier than it so at that point nothing matters except for how many dark matter particles there are so as you increase the mass they're just fewer and fewer particles so the limit gets weaker and weaker and weaker and I should have said this is the excluded region at low mass what happens is that you have an actual physical detector there's some energy threshold you can't see signals that are below to ke V or 3 ke V or 10 KB or whatever your experimental threshold is and so as the Dark Matter particle becomes lighter eventually the characteristic energy that your dark matter is carrying is so low that it just doesn't actually get a signal into the detector now it's not an abrupt cutoff as you move to lighter and lighter particles you start sampling the higher and higher velocity tail of the Maxwell Boltzmann distribution but it's rapidly starts turning off and there's some cutoff which is set by the escape loss so the Milky Way has some escape velocity and we don't expect to have particles that have velocities higher than that around us so once you get efficiently low there simply should be no dark matter particles that are capable of depositing energy in your experiment and you lose sensitivity so at low energies your sensitivity goes to zero it's a high mass is your sensitivity goes to zero and somewhere in between you have some some best points which usually tends to be in sort of like the 30 to 50 GeV range these days the best limits are coming from xenon experiments xenon 109 on one ton and Lux and spandex and the mat best limits are in the few times 10 to the minus 46 centimeters squared range of cross section for nucleons by comparison the cross section mediated by a Z boson is up here at about 10 to the minus 30 9 centimeters squared so dark matter that scatters coherently off of a nuclei by a Z prime which would have been your sort of most canonical conventional length you could imagine has been ruled out and was indeed ruled out when I started graduate school so I'm not going to go into collider Mans because you'll have individual lectures on that we know go to okay so this is the WIMP now from that jumping-off point I'd like to start discussing various other possibilities those other possibilities are going to be other production mechanisms and other thermal variants that moving into the lighter mass regime I'll go do the lighter mass regime last and I'll do the other possibilities first so the first possibility that I want to discuss in slightly more detail and again this is going to be more better sketches than in the glossary but not complete models so let's consider a non thermal model but a very important one or scenario I should say it's not a specific model which is asymmetric dark matter there's a very nice review by Katherine Zurich where you can find a lot of this so asymmetric dark matter remember is the idea that dark matter carries a fundamental asymmetry there's more Dark Matter than anti dark matter or vice-versa and the most exciting models of this are the models where that asymmetry of dark matter is somehow connected to the fact that we have a baryon asymmetry in the universe and so there's two basic approaches there's something called a shared asymmetry which is a fiscally for our purposes and unspecified origin and then some process shares be the dark matter number and then there's a separate idea which is Co Genesis which is where you have some process that generates dark matter and baryon number simultaneously so the shared asymmetry would be you just have some mysterious source that creates some dark matter number and then you have some higher dimension operators that chair that number to the standard model maybe through into into left ons and then use Feiler on to transmit the left on number into the baryon number co genesis a sort of very simple example of Co Genesis is one that uses the neutrinos so you imagine you have a bunch of right-handed neutrinos so this model looks a lot like left Oh Genesis and they have interactions with the Standard Model Higgs and the standard model leptons and then there is some additional interaction between that and some dark matter and some dark Higgs then you can calculate some asymmetry factor which is the decay of n into Chi by minus K of n into y bar y bar divided by the total and you can calculate the similar number for decays into lepton all right so this looks very much just like an ordinary left Oh Genesis model you create some particle it has a Meyer automat so it doesn't have a well-defined you violate your quantum number via its mass you have some CP violation in these couplings that allows you to distinguish matter from antimatter and then you have some out of equilibrium process which is the decay of this particle and the difference between this and a standard left Oh Genesis model is just that instead of only generating an asymmetry and leptons the simultaneously decays and generates an asymmetry in the dark matter so that would be an example of Co Genesis and you can calculate these things as you would in any left to Genesis mode now there's another possibility which has both physics and PR lessons within it which there's a class of models we go by a bunch of name one is Darko Genesis but at the basically the same time you have people come up with names which were high-low genesis and EXO genesis and the only points out of make is these are all basically the same model and i don't know if you've ever heard of any of them but if I tell you Darko Genesis you probably from the get-go or like well before I even tell you what I'm going to say you kind of know what I'm talking about right whereas if I tell you these things you don't so if anything sticks around is kind of this name so just be aware of how clever you're trying to be when you name things the idea there is that you have a dark sector and you have your three conditions in the dark sector right so the conditions that you need to satisfy to generate an asymmetry CP violation C violation quantum number violation and out of equilibrium you put that all into the dark sector and then you have some operators generally higher dimension operators they transmit that number into the standard model so for instance you could write down an operator where X is your dark matter you write down for instance X u DD in supersymmetry some sort of super potential operator like this and that would then connect your dark matter number to baryon number and so you generate the asymmetry over here then some processes then transmit that number into the into the scatter model and in any given model you can calculate with this on a dis rative these are very very interesting models for a variety of reasons one because as we said before asymmetric models don't have the same annihilation signatures that symmetric models do and also this finding that gives you a nice explanation for the origin of the baryon asymmetry however as i was all the saying yesterday there is this distinction between what is science and what is stuff that i tell my kids and and these are beautiful models but on the other hand they're very very hard to test because you have moved all the sort of interesting CP violation and quantum number violation into the dark sector so you've got to do all the hard work over in the dark sector and then you transmit the results to the standard model doesn't mean it's wrong just means it's hard to test sorry well this this this is not very own number violating because this operator just tells you that X carries very own number right so at that point it's totally fine and you're not going to have any processes you act and then go into the dark sector find out about the X number violation here before you get anything and at that point you're starting to talk about much higher dimension operators and loops and things like this and it becomes and you can make it safe you can make it safe so that's all I want to say about asymmetric dark matter so now I want to talk about thermal ish models so we described freeze out so that was dark matter which was in thermal equilibrium now we can talk about categories of models that are in equilibrium but in sort of non-trivial ways or not quite in equilibrium there's something that I don't think has a name that I know of so I just refer to it as incomplete thermalization and the idea there is that you have some process some rates that's going to allow your dark sector to be for your dark matter to be produced from interaction from the thermal bath and it goes like some power safety to the fifth over lambda the fourth just like in a conventional wimp scenario and as we know that if you have something that goes like T to the fifth over lambda to the fourth that this has a scaling that drops off more rapidly than the Hubble which goes like e squared over N Planck and so we did in the context of wimps was we said well if you go to an early enough time this process dominates is this how larger than that and that's the part will comes into thermal equilibrium you wait eventually goes out of thermal equilibrium and then that's what you're left with and that was the idea freeze out but that assumed that we ever reached a point in the history of the universe where this actually was larger than that when this was sort of a weak scale type cross-section then that was great but when this is something which is lower it's not necessarily going to be or when this cross section is more suppressed and this is not necessarily ever going to reach equilibrium so in that case you have a process where you have the thermal baths to the standard model producing this dark sector but it never actually reaches equilibrium so examples for this are the AXI know and the gravity know at least in certain regions of parameter space gravity know and the critical point about this is then that the number density of dark matter in this case is directly related to the reading temperature of the universe because pretty much your dominant production process is at the highest temperature that you start off with right after that the annihilation rate the production rate drops precipitously as the universe cools off so however much of this stuff you make you make at the very very beginning and after that your production rate becomes less efficient so these models to have this sort of non thermal production through this non thermal but incomplete thermalization process are hard to pin down because they're really dictated by this Reedy temperature so for summary d-10 per atures you have the right amount of dark matter for some unique temperatures you have too much dark matter and some icky temperatures you have too little dark matter but this is one possibility of production next next is the possibility of something called freeze in so I don't know the first time that anybody talked about this the first time that somebody coined this term that I know of was haul dude am sick March rustle and West you can't read any of that that's why I said it out loud in 2009 this is called freeze in and the idea for freeze in well again in mind that for the freeze out situation was something where you had a annihilation rate that was proportional to some high power of temperature so it dropped faster than the Hubble rate but if you have dimensionless coupling that was for instance for instance like wimps where your cross section was dominated by you know heavy mass scale particles but you can actually have situations where the annihilation is not suppressed by some dimension full scale but is in fact proportional to some dimension less scale in that case your rate is proportional to those dimensionless quantities times T so rather than having a process that becomes less and less important compared to the Hubble race this becomes more and more important compared to the Hubble rate as the universe drops because even though this rate is dropping since the Hubble rate is dropping like T squared over m plank this is dropping more slowly so its production process is actually dominated by whatever the last thing that happens for it is and so some examples of this are well a good example for this is for instance a right-handed neutrino or right-handed neutrino with the Dirac mass because the you cowell coupling gives you the dimensionless coupling that allows you to produce this but its dominant production comes late in the universe the next thing that I will discuss and I think this is maybe some of you gets a lot of interest these days is three to two processes so we assumed that dark matter was a to tissue process but you can have three to two processes for dark matter so you can have something where three particles come in two particles come out obviously you can't have five fermions but I'm just drawing these lines to be illustrative in cases where this you can add processes where this is dark matter and this is dark matter where dark matter of three goes to dark matter of two and that's called cannibal dark matter which is a separate situation from what I'm talking about here I'm considering here three to two processes where three dark matter particles go into two standard model or other types of particles so if you do this you can go through basically the same exercise that went through before so you imagine you have some thermally average cross-section which goes like some power say alpha cubed over mass scale to the fifth then you do exactly we did before you say that N squared Sigma B is equal to the Hubble constant that then tells you what the number density is at that time where once again you assume that freeze that happens sometime near when this particle goes nonrelativistic you so for this to be stable you can have some sort of like z3 type symmetry or something like this that allows you to have three to two to type in I elation so it's true that because I have an odd number of particles this doesn't allow me to have just a straight-up parity here but you can have something that will keep it adequately stable that's a good question not dumb question with that ah so so so if I'm talking about the direct detection signals then you'd be absolutely right because the rate would be proportional to the amount of stuff that I have but when you're calculating the equilibrium process what the way you should think about it is I imagine that I'm a Dark Matter particle I'm just going to be one of those things and I want to know the probability for me to annihilate in the history of the universe so what I'm really looking forward in the to-to-to case is proportional to n because I'm just asking what's the density of particles that I might run into and here it's n square cuz I'm asking what's the probability of me running into two particles at the same time so so I'm just going to repeat that exercise that I did for the case of wimps so N squared Sigma V is T squared over n planks you imagine that the temperature freeze out is approximately the mass of the particle in question which I'm assuming here is the same as the mass scale that's setting the cross section which needn't be the case but for simplicity that's what we're assuming and then I asked the question about Rho so Rho which is M times n which then goes like m to the nine halves over alpha to the three-halves and Planck the one-half and then I do what I did before which is I redshift it from then until now so I take three matter radiation equality over m cubed times this number and I set that equal to the energy density and photons that matter radiation quality remember the energy density in photons was just T to the fourth it matter radiation quality this is what the dark matter energy density is going to be this is what the photon energy density is going to be I set them equal I do some algebra when you do some algebra you get the M is sorry two-thirds and Planck one-third so before for the WIPP miracle we found that the characteristic mass scale was the geometric mean of matter radiation equality and M plank for a 3d to process you get that the mass is the T to the 2/3 and Planck's the 1/3 so if you set alpha equal to 1 imagine it's a strongly interacting particle then you get M is just equal to this which is around 100 MeV and so people like to call this the symptom miracle or strongly interacting massive particle miracle this 100 MeV is of course very similar to the scale of strong interactions in the standard model but that doesn't necessarily mean that you're literally talking about this thing having a bottle strong interactions and indeed such models are very hard to build but it does tell you that a particle that has characteristic mass scale like this that annihilates through three to two processes like that very naturally can give you the right relic abundance oh it's a relevant temperature in the sense that it allows me to if someday at some point in this calculation you want to say that I calculate the amount of dark matter in the early universe and I want to match that to the amount of dark matter that I see in the current universe one way to do that would be to redshift it from when it formed to now and then just compare it to now but another way to do it is to say well at matter radiation equality I know how much dark matter there was then it was the same amount as there was in photons so instead of so all I'm doing is instead of saying I'm going to compare the amount of dark matter that's produced the amount of dark matter now I'm saying to find the amount of dark matter this produce and compare it to the amount matter radiation quality same basic concept is just normalizing it to a number that I know in our existing universe and I know that the at the matter radiation equality the dark matter energy density is the same as the photon energy density and the photon energy density is just C to the fourth so this is just a simple way of trying to match the calculation on to the observed universe in a way that doesn't have to meet because we're kind of at an ad hoc time right now so you have to put in all sorts of random factors this makes it very nice and clean also t matter radiation equality is an Eevee so it makes my math very simple yeah was it three dark matters to our matter you have to be a little careful with that particular model though because because it's cannibal thank you so this is remember an interesting scale because this particular scale is one where you have naturally scattering processes that can be relevant for if you have an annihilation cross section which is like this you also can expect to have scattering cross sections which are characterized by the same scale and if so we know that this scale remember is roughly equal to one centimeter squared per gram which is the relevant scale that you need to do things like change your galaxy cores and address the too-big-to-fail problem and things like that so this is a very interesting scale because of that other people would say that the beryllium excess pointing to something around 17 MeV also is sort of pointing to the same energy scale so possibly there's something something to that next how do what well this is the Dark Matter annihilation process so it's not necessarily alpha of its coupling to us so I can imagine this is for instance breathing out into say an unstable particle in its own sector will discuss more models like this in a second so next you have forbidden dark matter which was discussed in the context of beliefs 2d type models back in 91 and more recently by dan jello and Ruderman who kind of understood it in sort of a modern and proper context and so the idea is there that we always assumed that dark matter was annihilating into standard model particles so let me call this dark matter and dark matter let me call this X and X which is some nadir model particle or it could be a non standard model particle that then itself is in thermal equilibrium with the standard model particle but something this X is what's going to be maintaining the equilibrium and usually we assume that dark matter is annihilating into something lighter than it so for instance dark matter is annihilating 2ww dark matter is at t VW is 81 GeV whatever or they'd it's dilating the Higgs bosons or something like that the idea here is that the mass of this final state could actually be larger than the mass of the initial state and in that case the cross-section estimate that you do which is alpha dark square divided by and dark matter squared comes with an additional suppression to Delta M over T which is just to say that I need to find two dark matter particles that have enough kinetic energy in them to overcome the fact that they kinematically cannot actually annihilate right so I go out on the tail of my Boltzmann distribution if I go out on the tail my Boltzmann distribution I find these particles that have enough energy to annihilate and then i mediate my annihilation process from that tail if you do that you can now consider much much larger coupling constants because you're sort of compensating for it by this exponential suppression and you can right an overall plot where you have some coupling constant here and you have a mass down here this is ke V and this is a PE V and so so up here you pick the unitarity bound along here you have a nice thermal Dark Matter particle so if your cross section goes like alpha squared over M PI squared then you can dial down your Dark Matter mass and your coupling constant at the same time up here you have wimps here you have ultra weakly coupled Dark Matter then up here you have forbidden dark matter and sort of around here you have symptomatic strongly interacting massive particle dark match so that sort of fills out the at least in some dimensions the sort of coupling constant mass range of the types of dark matter you have there's a thermal band this is all thermal you have a region here where it's just standard to-to-to annihilation coupling constants or perturbative math skills are weak scale you can go above that or below that by going to stronger couplings or weaker couplings and later masses at some point you have to stronger couplings and you get the unitarity bound and then in this region you can still get dark matter but the only way you can get dark matter is if you kinematically suppress its annihilation or you do something like three the two processes yes that's 4 PI alpha is a characteristic interaction strength yeah yeah from depopulating Dark Matter oh you mean like just the reverse process well the idea would be that X has to be somehow unstable and it decays dominantly into other things that would be the easiest way to do this so let's see it's now I start at 915 and I'm allowed to go until 10:45 okay so I'm going to come back to thermal models in a second when I come to portal model I want to talk about one slightly different production mechanism which is relevant for the acción but what I'm going to write down right now is not literally the axiom so I'm gonna put it in quotes but it'll be relevant for perceptive Michael talking about and it's relevant not just for the acción it's relevant for any type of coherently oscillating scalar fields for dark matter so if you write the klein-gordon equation for a scalar field in an expanding universe then it's the ordinary klein-gordon equation with this additional drag term and so you can do a very simple exercise and imagine that you're living actually in de sitter space just to simplify calculations so imagine that this hubble constant is just constant and then you can try solving this by putting in an oscillating scalar field when you put in this I'm using a real phase right here or it's very real yeah real phase real frequency then you can solve for the frequency and when you do that you all know how to do the quadratic formula and yet I will write it nonetheless so here's what you find so the frequency is this so you can take two limiting cases you can take first that n is much much less than Hubble now remember we said if M is much much less than Hubble then that means that effectively the particle is massless and then the two solutions you get are are these so if you take a couple to be constant then you can imagine considering the mode you can commit it consider this mode first so imagine what kind of energy density that has well the energy density reapportion L to say M squared Phi squared which is like M Squared Phi naught squared but since W is minus 3h then that tells me that this feel then is going to sorry scale like e to the minus sorry since a is proportional to e to the HT in de sitter space and this is now going to go like e to the 3 HT Phi square goes like e to the minus 6 HT which tells me that this energy density goes like N squared Phi naught square ne to the minus 6 so if I consider this mode the energy density in that mode damn Soph extremely rapidly on the other hand I can put in this mode here what do I get I get N squared Phi naught squared e to the minus 4 M squared over 3 HT which is like M Squared Phi naught squared times e to the minus 4 M Squared sorry M over 3 H squared n squared over H G if I plug in T which is comparable to the Hubble time then this is a to the minus 4 M Squared over 3 H squared but by definition we are taking the case where was much much less than Hubble since M is much much less than Hubble in one Hubble time this thing this coefficient here is very very small which tells me that the energy density in this scalar field is barely changing this regime is probably well known to many of you this is the slow roll regime of the scalar field which is just to say that if I have a scalar field whose mass is much much less than the Hubble constant then it effectively is massless and even though in the early universe you would expect it to drive down toward zero it doesn't it more or less sits there and drags very very very very slowly if you consider the off opposite limit where M is larger than the Hubble constant then you have frequencies that go like that so you have both a real and an imaginary part to it in that case Phi will evolve with some decay term and some oscillating term and of course this oscillating term is the usual piece for klein-gordon field which is just something oscillating in its space and if you look at how the energy density of this field goes well as we said before so if Phi is going like e to the minus 3 HT over 2 but this is the sitter space so the Hubble constant is just going like e to or SAR as the scale factor is mine like e to the HT then this is telling me that Phi is going like a to the minus three-halves so the energy density in this field which is approximately M Squared Phi squared is going like a to the minus crease and this is the important result if I have a scalar field whose mass is larger than the Hubble scale and I allow it to oscillate freely in the universe the energy density in that scalar field will decay off like a to the minus 3 but remember that a particle has a decay which is related to its a for ageing of state parameter and if you fall off like a to the minus three that means that you have a pressureless matter so this type of matter here is effectively diluting like cold dark matter so this is a way of generating non-thermal dark matter you start with dark matter which for whatever reason in this case is slow roll but it doesn't have to be slow roll you start with dark matter some initial condition energy that's up on its potential for whatever reason possibly because of a thermal phase transition possibly because of just this effect it starts oscillating once it starts oscillating it gradually will decay away and this energy density will die off like a to the minus three and this will act like dark matter now the acción is not literally that because it doesn't go from this slow roll to non flow roll you have a QCD phase transition but much of the dynamics can be understood from just a oscillating scalar field questions about that sorry well properly the energy density is M squared Phi squared plus v dot squared over 2 or Phi dot squared right oh but this is not this is that's the point this is not even though even though M is very very small this is not a this is a non thermal process so this particle doesn't have kinetic energy that's set by T that's the interesting thing about this is a very very light particle but it's sitting there doing nothing starts coherently oscillating and when it starts go Herrin oscillating you can calculate what kind of dilution it has and it actually dilutes like dark matter not like radiation even though it's very light but it doesn't have a thermal it doesn't have a thermal distribution it's obtained by a combination in any model be different it'll be obtained by a combination of initial conditions when the oscillation starts which is going to be dependent on the parameters in the model so it could be the initial value of the field combined with when it starts oscillating what do you mean that's right I'm assuming that there is no decay of this particle in Jordan I'm assuming that it's evolution is straightforward like this that's right so all the processes should be much longer than Hubble so there are a lot of really interesting ones so - so so I don't know how much Michael's going to talk about this but I know Peter Graham next week is going to be talking a lot about the signals of oscillating scalar fields and their experimental consequences because there's been a huge experimental effort by a number of people including Peter especially so you will hear a lot about that okay good so let me now consider more or less more exotic models so up to this point thinking about the thermal models we're really thinking about models where we are either totally unspecified what the process was by which dark matter annihilates into the standard model or you're talking about a wimp with a capital W where you mean literally that this thing interacts with W bosons and be bosons and things like that now I'd like to change gears and start talking about other ways that dark matter can interact with a standard model and thus have both signals and direct indirect Collider or produce it thermally in the early universe so let me start by talking about effective V Prime models these are by and large just with models but with some additional knobs so if you imagine that in your universe you have some additional you have some additional you one gauge boson which is fixed at a scale G sub X and you can imagine that you have Dark Matter couples to the to visit eprint then you can ask the question how is that particle going to interact with the standard model well if that scale VX is above the weak scale then you actually have a lot of freedom because that is a Higgs V prime which means that it can more or less from the effective theory point of view have whatever interactions you want it to have with standard model formula let me give you an example of how this works so you imagine in the standard model you have your Tyrell farm yawns - you dle and then you imagine that you have some dark sector not necessary dark sector but but partner for me on I'm going to write with capital and their vector conjugates so Q is a three under su 3 and a 2 under su 2 with hyper-charged of 6q conjugate is a three bar with hyper charge - a six but then I also assume that under this u1 X these guys have plus one and these guys have minus one now in any real model you don't need all these things you just need one pair of these things and the reason why you do it like this is so that anomalies cancel tribulus so imagine that you have some Higgs boson that acquires the Bev D sub X then you can write down the following terms you write down lambda phi for instance you knew conjugates okay so when P sub X gets of EV this is going to give a Dirac mass between the standard model up quark and this right-handed upwork but you also write down some math which is a bit larger than V sub X between you and you conscience well if you do this what happens is that you tries to marry you conjugate and capital u tries to marry you conjugate but you have to if you want to say left-handed field and only one right-handed field which means that this you conjugate can only marry one linear combination of little you and big you so one linear combination is massive and one linear combination is massless so you end up with some light U which is some mixing angle of you and some mixing angle of you and this light up quark is the thing that we then call the up quark because it's the massless degree of freedom that picks up its mass at the end of the day via you call couplings with the Higgs boson right but this up quark is secretly containing a portion of some fields that carry the additional gauge interaction and thus this residual up quark then carries that effective interaction and so this is what you refer to as an effective Z prime because it's an effective interaction there's no point in the theory where the degrees of freedom that we are have gauge couplings they're just effective operators the low-energy but as a consequence you can now have situations where Dark Matter then annihilate to these things so Dark Matter can go through this new Prime into standard model Fermi on at a low energy scale where this coupling constant here is just gee that's great and since you know that these sorts of things have the expected coupling constant that you need to get the right relic abundance is something like a coupling constant of a thirtieth and a mass-scale of a TeV even with a mixing angle which is relatively small you can still achieve this sort of of a mop yeah well since they carries and use u 1x charges that forbids these interactions because the standard model is neutral under UN X these things carry the UN X charges so they can only get mass terms with each other so the only kind of mass term you can get with the standard model is once that UN X is broken and the reason I point this out this kind of model out is just emphasize it once you go below the scale of the Z Prime you know people talk about B - el models people talk about you know hyper-charged like models kinetic mixing models but as long as you're below the scale to Z prime you can really have any coupling as you want that F can be leptons can be up quarks can be bottom quarks you have to worry about flavor-changing neutral currents and all these things but a priori from a theoretical point of view you can do whatever you want now this is very much just a conventional wimp though with just some fancy couplings because experimentally we know that those quarks and leptons have to be very heavy otherwise we would have seen them at colliders next so a lot of attention these days has gone into discussions of what are called portal models so these have gotten a lot of attention in part because as we've done a lot of wimp searches and as we've done Collider searches and not found anything people have started stepping back and saying okay more generally how are we going to have dark matter that talks to us and so the idea is that you have your dark sector and you have your standard model and then there's some sort of operator that connects these two sectors and any operator you write down that has standard model on one side and dark sector on the other side would be a portal but for a variety of reasons people are course interested in the lowest dimension operators that can do this and so that leads us to three-and-a-half portals so I will write down those portals those portals are the Higgs portal the neutrino portal and the gauge or kinetic mixing portal so there's a neutrino portal this is the gauge or kinetic mixing portal and this is the fix portal there are obviously two operators here that I've written down and I've categorized them as the Higgs portal there's the renormalizable Higgs portal which is dimension 4 so 5 here would be your dark sector particle 5 AG Rifai the Higgs would be the Higgs by the HDH but you can also if that by is a singlet you can write down a superb renormalizable operator a by h h dagger that also gives you a connection between a dark sector particle in the Higgs in that case course pi is not the dark matter but it can be part of the dark sector and you can actually usually achieve this operator trivially by taking this operator and giving a bit of 2 pi obviously so there's two different scenarios that people typically talk about for thermal models via portals you have hidden sector annihilation [Applause] and you have direct annihilation so hidden sector annihilation would be something like Dark Matter annihilating into five particles where those five particles are part of the dark sector and then five maintains equilibrium through some other process or it's unstable direct annihilation is something where you have some process by which say the standard model or a dark matter and I lead directly into the standard model and these are qualitatively very different in their signatures and types of things that you get so let me start with the Higgs portal now there are all sorts of you know twists and turns and variants that you can do on these sorts of models the most important thing to keep in mind is that at least for the Higgs portal that the Higgs boson itself has very very small coupling to fermions so if you want to get into sort of a light Dark Matter model the Higgs portal oftentimes is not the one that you use because it's coupling to light particles are so suppressed there's a classic paper on the Higgs for ttle by Burgess Paschal love and care Feld we so you can look at that and references there too and the idea of the Higgs portal and how you can do Dark Matter with it is you can just imagine that this five particle is your dark matter and you have a process where you can have annihilations like this or you can have anihilation once the hit you get the Babs through an s channel into gauge bosons or fermions and obviously depending on the mass of the five the coupling constant that you need here lambda varies but lambda is typically of the order of ten to the minus two a nice perturbative coupling for a weak scale particle five for lighter Phi's as Phi gets down to sort of like twenty ten GeV because the annihilation goes through the Higgs the coupling constants that you need rise rapidly and as a consequence there is a direct connection signal where Phi can exchange a Higgs boson and scatter off of the nucleus for in this sort of 60 DB range with this sort of a coupling constant this coupling this direct section cross section is around 10 to the minus 45 centimeters squared so over a lot of the parameter space this model as it's written is excluded by the direct detection there's specific region right around 60 gve where you go through resonance where the coupling constant here can be very small and there the direct detection cross-sections can be smaller and this can be safe but over a lot of the parameter space this model currently is excluded by recent direct action experiments or you can go to higher masters would you call us here so the interaction of the Higgs boson to protons and neutrons is a deep and important subject because there's contributions to the coupling constant of the Higgs through its interactions with up works down quarks strange quarks because even though there's very little strange work content in terms of number it's got a bigger coupling to the Higgs and also through its coupling to the gluon field strength because it has you wiggle the big mass and you're changing the mass on top quark unless you're changing alpha strong and all these things are contributing overall the coupling constant of the Higgs to nucleons is about drove a few down from em proton over V so it's about ten to the minus three defective one sorry you haven't measured these but but that's actually not the dot that's not the dominant uncertainty not on uncertainty for this I believe it's David or was the strange board content I don't think that yeah it's it's if you change the up for Q call coupling by a factor of two you're not going to change this by that much so the Higgs portal is is a very very nice portal but at least as you write it down like this this is still something that looks very much like an ordinary whim the mass scale that's relevant is still sort of in the hundred GeV range its annihilation is into either Higgs bosons or into standard model fermions or gauge bosons so it still looks very very wimp like even though it's a portal model there is a variant where you go through a hidden sector annihilation where Dark Matter annihilation to Phi and then Phi decays and just data model things that looks different but I'll discuss that better in the context of the kinetic mixing models so the next portal that I want to discuss is the kinetic mixing portal this is the one that's gotten by far the most attention of late and it's very well studied at this point and there are a lot of interesting experimental efforts that are underway and Rubin will talk about them usually the normalization of this the term of you write down your Lagrangian is epsilon over 2 cosine theta week the reason for that is that people are usually so GME news of course hyper-charged from anthony knew here is you one for the dark sector so there's some dark sector you one you imagine that it's Higgs by some dark Higgs at some scale most often people are interested in these scenarios where that Higgs in scale is sort of in the many GeV 2 GeV 2 MeV or lighter regime at least that's sort of what people are interested in right now and as a consequence you're at a scale below electroweak symmetry breaking so you're most interested in actually mixing F dark with Fe NM so that's what this cosine theta cancels off so in your place this beam you knew by F mu nu enm it looks just like epsilon over 2 and so this normalization means that at the end of the day you have some kinetic mixing matrix between your dark u1 and at the end of the day um and when you diagonalize that you end up where the standard model fermions couple to the dark photon with something which is proportional to the electric charge coupling constant their electric charge whatever it is one two-thirds one-third and epsilon this small parameter here which is typically something like 10 to the minus 3 or smaller there's an important besides that I want to make about this particular model that can often be confusion which is that we always end up picking a basis for discussing these types of models where we say there's a dark photon and then there's the ordinary photon and we say that the standard model talks to the dark photon with dis coupling and we never say that the dark matter talks to the ordinary photon with a small coupling and there's a reason for that and that is that you have a dark Tigs fie and you have your Dark Matter Chi and the assumption is that they start off charged under the same u 1 when u diagonalize your kinetic mixing matrix they are still talking to the same u 1 so when Phi gets of EV it gives events to one linear combination of the use vector bosons that massive linear combination is precisely the same linear combination that Dark Matter talks to therefore the thing that this gives a mass to is the same thing as this thing talks to which means that dark matter only talks to the massive dedos okay if you wanted to have dark matter V Miller charged you would need to have had its u 1 charges initially misaligned with that which is to say that you effectively would have had to have given dark matter a tiny tiny mil charge to begin with if you wanted to have a tiny tiny mill a charge to end up with if it starts off with the same charge or at least if charges are aligned with the Phi then when Phi gives the mass 2 linear combination and that's the one that this talks to and it only talks to the massive component in contrast standard model fermions which talk to V mu nu or f mu nu electromagnetism what we defined by the photon is we mean the massless degree of freedom right that's what we defined be the photon not the linear combination that talks to Schneider model particles so the linear combination is off the standard model particles is some combination of the mass flow state and the massive se and thus all ordinary particles have their usual charges and interactions with the massless gauge boson but they have an epsilon interaction with the dark photon that's a long way of going through this story except to say that basically most of the time we're talking about a situation where you have standard model you have a dark photon and you have a dark Higgs and you have dark matter and the effect is that that dark photon talks to Santa model particles proportional to their charge so these models have two scenarios they have the hidden sector annihilation and the direct annihilation so the hidden sector annihilation looks like this equilibrium in these models is usually maintained through a process that looks like Compton scattering so an electron comes in couples to a dark photon with a suppression epsilon then emits an ordinary photon or vice-versa so this is usually the equilibrium process for the two thermal baths so what keeps our bath in the dark bath in thermal equilibrium and Dark Matter annihilates directly into gamma dark in this case the cross section for annihilation just goes like alpha dark squared over m dark matter squared which it looks just like an ordinary wimp raw section so the to the extent that this doesn't look like a wimp it's because you make health the dark very very small which you can do you can just dial down Apple dark and dial down the mass and you can make this thing as light as you want but there's nothing fundamentally about such a model that wants it to be light dark matter if anything a model like this wants to be sort of more in the weeks to in contrast direct annihilation is more situated for being light dark matter so I think the first people to really look at these types of models were moment by a and so they're if dark matter is charged under this new one and you're directly annihilating into standard model fermions then parametrically this cross-section now goes like alpha dark from the Dark Matter interaction alpha standard model from this interaction so alpha electromagnetic generally epsilon squared it goes because the coupling constant of standard model for amounts is proportional to epsilon and then since we're assuming that that process doesn't happen these dark matter particles have to be lighter than the dark photon so this whole thing then goes like m dark photon sorry M dark matter / M dark photon to the fourth now typically you assume that these things have roughly the same mass scale so this whole cross-section then is going like coupling constants small number / dark sector scope that's sort of the rough scaling of this thing now we know that if alpha is sort of typically perturbative that we would like the denominator if you forget about that we like the denominator to be roughly TV but this interaction comes with additional epsilon which we know from all sorts of experiments has to be something like 10 to the minus 3 or so that tells you then that this mass must also be smaller by 10 to the 3 or so so it's very natural to imagine that you're in situations where this dark matter would be very like 10 GB 1gb 100 MeV and so on and so that's a lot of the discussion that's kind of what makes this interesting ordinarily if you have a perturbative annihilation cross section that just goes like alpha squared over 10 GV or 1 GeV that is way too big of a cross-section and that dark matter will deplete itself down and won't be the dark matter such dark matter though as we discussed has problems with the CMB in that it naturally annihilates into electrons muons things that give interactions and deposit energy into the CMB it also has problems with direct detection if it's kinematically accessible so you can calculate the cross-section for a nucleon and you can pick some characteristic numbers so if you have an interaction where dark matter scatters through this dark photon off of ordinary matter remember that this couples to charge so it will couple to a proton with coupling constant one times epsilon and so the cross-section per nucleon you can plug in your favorite nucleon this is set up for germanium with a coupling with a mixing of 10 to the minus 3 and alpha dark which is comparable to the electromagnetic flying structure constant a dark photon which is a GeV you get a direct section cross section which is 10 to the minus 37 centimeters squared the Z member gives you 10 to the minus 30 9 centimeters squared so this is a huge cross-section current limits are down to 10 to the minus 45 and better centimeter squared so this dark matter if you have a dark matter particle interacting via a dark photon like this you need to do one of two things you either need to turn off this direct section cross section or you need to move this thing down into the light mass regime okay one way to turn off the direct section cross section is to do the splitting effect that takes care of the CMB so if you imagine that your dark matter is split into Chi 2 and Ty 1 then your vector interaction is now off diagonal and so if it's kinematically impossible for dark matter to scatter into the excited state you can turn this off and when you do that you also turn off the CMB annihilation so it's not impossible to save these models but naively they have very very big CMD signals and they have very very big direct detection signals unless they get light enough these models feature a couple of interesting signatures if you're talking about light dark matter or not if the mediator is lighter than the dark matter then you can have a phenomenon which is known as the Sommerfeld enhancement which is pretty commonly understood now the idea of the Sommerfeld enhancement which is known to all nuclear physicists and recently particle physicists is that if you have a long range interaction between dark matter ordinarily we calculate the perturbative cross-section of pikaia going into whatever but if there's a long-range interaction as these particles come near each other that attractive interaction can essentially pull the dark matter particles together and boost their annihilation cross-section the analogy is if you take the earth and you throw a rock at it the cross-section is PI R squared but if you throw the cross the rock very slowly there will be a gravitational focusing effect that will lead to an enhancement something like that and this is the analogy for Dark Matter you pull you throw the dark matter particles at each other they tracked each other and you get an enhancement of the cross-section that can be very relevant for directions if you happen the other interesting signature which is sort of new for these types of models is the fact that you now have this dark photon and if it's sort of in the GeV mass range you can look for it at a variety of experiments Ruben's going to talk about all sorts of new experiments that are going on so I'll just mention one thing which is that if you have some process at a Collider that produces the dark photon so you have some process key P goes to something that then spits out of dark photon that's our photon will be very boosted it'll typically have energies which are comparable to the energies of the system so when it decays it decays two pairs of leptons that are highly collimated most LHC analyses most high-energy collider analyses look for isolated leptons not collimated leptons like this so this object has been termed a lepton jet not just to left on sometimes you have more leptons than just two but the idea is that if you have a highly boosted object that decays into leptons it looks like a jet because the total and very mass of the system is just like a GeV but it's got a high leptin content and so that's a signature of these types of models and Rubin will talk about all sorts of of decays now that's under the assumption that Dark Matter carries the you one charge and annihilate thermally there's an alternative possibility which is that the dark photon itself could be dark matter if the dark photon is heavier than electrons then it will decay very promptly into electrons but if it's lighter than electrons then all it can decay into is three photons and that process is very very suppressed so it can very easily live the age of universe once it gets down below the mass of the electron so the question is and how you make such dark matter most processes that people thought about originally were not sufficient but it was pointed out by I don't have it on this piece of paper if you have it on this piece of paper I think it was gram rajendran and Martyn rid of that write that point don't have the number of written down but the expression you get is something like Omega dark matter can be something like the Omega of the dark photon can be something like what you want times I'll make sure I get the scaling right am over ten to the minus five Evie I think times H over ten to the fourteen GeV I think I'm getting a power counting right the idea that was pointed out by Martin rajendran and Graham was that inflationary perturbations naturally generate any approximately massless modes in the early universe so during inflation you should produce these things and you can ask how much of that stuff should be around to get the right dark matter and if you take a public constant which is 10 to 14 GB you can have a ten to the minus five mass Dark Matter dark photon and as you lower the hubble constant you can raise the mass of the dark photon this model is interesting in part because it has a very special feature which is different from a lot of dark matter models which is that you can look for this through absorptive processes this dark matter is stable not because of some symmetry or something like that but just because it's too long-lived but it can actually come into your experiment and be absorbed and produce some energy just by the fact that it has rest mass so it's a very interesting particle to look for how heavy or what oh are you going to go you can start it around here and you can go up to bat AEV we just need to lower your Hubble scale during inflation sorry I should have said this is the Hubble constant during inflation so if you have very high scale inflation then you make a different amounts than if you have low scale inflation because your fluctuations are just smaller you have lower scale inflation this is not a thermal model this is a non thermal production process you're matching that your coupling constant epsilon especially small desisting stays out of thermal equilibrium you produce it through these primordial fluctuations and then it right it is not yet this is not a this is this is cold dark matter all the way then the last portal I don't have to talk too much about because Andre will talk about everything right Andre thank you the neutrino portal is just a new cobble coupling between the standard model left handed leptons and some sterile neutrino and as I said before this end does not have to be the gut right-handed neutrino it's just any sterile neutrino any sterile neutrino is quite happy to marry off against against this if all I write down is this then I get a Dirac mass if I add Amaya Rana mass then I have a seesaw which is nice of course because it can give me a neutrino masses but you can also imagine that this n talks to some bigger dark sector so if you integrate it out you can write down LH times o dark sector divided by the mass of the sterile neutrino to some power and actually two new sorts of models I'm actually at the moment that's the kind of thing that one of the things that I'm interested in but I'm not going to talk too much about any of that because Andres here you talk about everything about neutrinos and also I'm out of time so I'm going to stop before I stop I'm going to say one thing is dissolve in physics and now I'm going to say something which is not physics because being learned listings - and is that I'm not super old yet but I'm old enough that I've seen some changes in the field and so I don't know how many of you are going to work on dark matter or not I'm just talking about dark matter many of you might but the thing that I'll say is that when I started working on dark matter and I started writing that model everybody's like that is a crazy model that is a weird model that's a kludgy model people said all sorts of not very nice things about a lot of models that work on but then over time people got used to them and now people don't say those things anymore you know it used to be that people would invite me to give a lecture on exotic dark-matter models and now I get invited to give lectures about ordinary dark matter models and it's not because I've changed it's because our perceptions about models have changed and so I really want to emphasize that because you know there's a lot of built-in institutional opinions about what makes a normal or nice or good model of dark matter and I really want emphasize is where we started I'm going to end here nobody knows what they're talking about if you have a model that looks interesting to you you should work on it don't listen to anybody like me saying like mmmmmm that'll like it because that's just based on what I've used to and what I spent my time doing you should totally ignore people like me when we give you bad attitudes and you should work on it because there's a lot it's a huge space of models and signals and so I think there's a lot of fun to be having it so I will stop there [Applause]

Channel: Institute for Advanced Study

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Length: 91min 9sec (5469 seconds)

Published: Wed Jul 19 2017