 Thank you very much. It's always a tough task giving the last lecture in a two-week summer school then all of you thinking just want to get out of here go and get some alcohol on the streets of Trieste and stuff like that. So I'll try not to delay all that happy stuff for too long. So but today we're going to talk about something fun. Okay, we were talking about the future of at least axion physics. Interesting things that are happening in the field right now. Things that are actually I think very exciting in terms of both experimental ways to push forward in the field as well as so I think some interesting theoretical developments. So just to give you a very quick overview we think axions are good and cool because they're very general. You mumble a few things about some global symmetry that no one knows about. Somewhere in the ultraviolet it's broken. It's like magic. You mumble that and out pops a goldstone boson and you can go detect it at really low energies without having to spend a gigantic amount of money to build a huge collider and if you succeed if you actually detect that then you learn something about very high scales. We said that the one particular goldstone boson the QCD axion was particularly well motivated because it solves a strong CP problem but in the same philosophy there could be other such particles and one should go search for them. Okay and one interesting thing we learned was that very easily these particles can be all of the dark matter of the universe simply because if these fields exist then in the early universe in general they will have some initial value and that initial value of the field will correspond to some energy density and that energy density can easily be dark matter. That's what we learned yesterday. And here is a review of all of the constraints etc of this phenomenology. Most of it is directly applicable to the QCD axion but similar things are also true for axion like particles okay. I mean there are a few things here and there but in general this is sort of the ball game. Roughly if the coupling constant F A okay that is the scale at which the symmetry is broken if that is in a sense you know too small so in particular smaller than about 10 out of 9 GeV it's just ruled out right. It's too strongly coupled to standard model it will be produced in stars, white dwarfs, a lot of other things making you know it's just too observable. Anything below that essentially ruled out above that is sort of essentially open territory and for the QCD axion if this parameter F A is above 10 to the 12 GeV and larger it can be all of the dark matter and around 10 to the 12 GeV there are these experiments that we talked about things like 80 and max which we will sort of review again later today where there is a good way to search for this if it happens to be the dark matter of the universe but you know the parameter space is huge right. So this just raises an interesting theoretical question right if F A happened to be big right how do we find it how do we search for these things the challenge of course is that for large F A one has to beat a small coupling right because all of the couplings of the axion are suppressed by this big scale. So how do you overcome this big scale in your ability to search these things and some people do theoretically also think that large values of F A are in a sense theoretically more reasonable because you know we're breaking some global symmetry here to get these axions and you might think that these global symmetry should be broken you know the gut scale or the plonk scale you know things were fundamental for supposed to arise from. So your naive expectation from theory for where these scales might be is also actually pretty high. Of course that's just theoretical prejudice but still you know it's a it's a good thing to keep in mind when you want to think about why you want to search for these high F axions. Okay but experimentally you can just ask what can we do you know to beat this small coupling how do we go after these things. So I want to talk about two ideas these sort of experimental ideas if you will both of them very recent and you know sort of two strategies one is if you have a new particle one thing you can try to do is to produce it somehow and then detect it okay that's one way to do it. The other would be to say that maybe the Almighty has been kind to you and he's provided the entire universe with axion dark matter okay it's a reasonable assumption. So if you you know are in that kind of world where the axions are dark matter you could then try to think about ways to detect that okay so those are the two you know ways in which you try to detect a new particle you produce it and then detect it or it's already there and try to detect it. So this game of producing and detecting this thing remember we're talking about a particle that is super weakly coupled so we're going to talk about a new phenomenon okay something that most particle physicists are not familiar with but it's a well understood phenomenon that is called super radiance we'll describe what that is and we'll discuss how super radiance and sort of realistic astrophysical systems can actually could potentially constrain this kind of particle and if the axion happened to be dark matter then we will talk about a new class of experiments that essentially leverage nuclear magnetic resonance or NMR as a way to search for these particles so that's going to be the first part of the lecture today. Alright so let's talk about super radiance and extremal astrophysical systems we'll define each of these words shortly. Here is a basic plot okay there is some phenomenon called super radiance I'm sure most of you don't know what it is so don't worry we'll sort of define what it is pretty soon and but here's what it really does okay so it turns out to be an instability of rotating systems or really any rotating system okay so if you have some rotating system because of super radiance it will slow down okay so in a sense in particular if there are light massive bosons such as axions there are coupled to some rotating system this rotating system will slow down by emitting these axions okay so that's that's what this phenomenon ultimately does for you and the basic idea is that we have seen such rotating systems out in the universe so you can go and measure and say oh there are some star for example that is spinning at some certain rate and then what you will do is you will calculate and say oh if this axion existed then the star cannot possibly be spinning at that rate and given that we have seen stars spinning at that rate we can therefore place constraints on such particles okay that's a basic idea if you observe a system rotating at a certain speed that can put constraints on these kinds of particles okay so that's just the game of putting constraints if you're a more optimistic person then you might say well let us say we go and observe a huge number of such rotating systems and maybe you will find that there is you know some range of frequencies where there are no rotating systems at all right you find some statistically significant gap in the rotation rate of various stars for example and that statistically significant gap may imply that there are such light bosons in the theory because they're actually causing these objects to spin down okay that's the basic idea there's been some work done on this the previous work has been largely limited to black holes and in fact this is a much more general instability and can also be used to you know one can also use things like millisecond pulsars to actually search for this and that is something that I've been working on for some time okay so that's the basic idea right you look for a star that is spinning you see a star that's spinning that puts a constraint and if you don't see the star the particle makes this there yes there is a non-trivial dependence on the rotation rate well we'll see that shortly all right so what is super radiance right before we get into super radiance specifically let's understand you know something very boring okay this is radiation from just some rotating object so for example let's say we take a pulsar okay or just some magnet or whatever and that's a pulsar that pulsar has some rotation rate and it's got a magnetic field right pulsars have big magnetic fields and the reason why pulsars are pulsars is because the magnetic field and the rotation rate are not aligned with each other right there in general at some angle so the star is spinning and as the star spins there's going to be a time-varying magnetic dipole right because it's a magnetic dipole moment it's spinning and as there's a time-varying magnetic dipole there will be dipole radiation at the frequency of rotation right that's not you know that's just standard stuff that you calculate from Jackson nothing deep about this let me ask you a question what if the magnetic dipole is aligned with the rotation axis does this system emit radiation electromagnetic radiation what's the answer come on you know it yes or no 50-50 right huh no yeah why why is the answer no right so if you think about it the you know in in the first case when the when the magnetic moment was not aligned with the rotation rate of the star one reason why the star was able to emit radiation and slow down was because well you know it can actually produce a photon and by doing so it can conserve energy and angular momentum right that's just some kinematics you can produce a photon the photon carries away some energy from the system decreases the angle of the star that's an allowed process it's kinematically allowed so when the magnetic field is aligned with the with the rotation rate of the star that kinematics is still true right you can still limit a photon and you can still slow down right that is still kinematically allowed so when something is kinematically allowed and it doesn't occur what is the only possibility the coupling must vanish right that's what must happen right in quantum mechanics in general if you've got a phase space for a process and a non-zero coupling then the process will occur right so in this case the phase space is always non-zero right because you know you can just easily calculate that so the only reason why when the magnetic field when the magnetic field is aligned with the rotation rate of the stop with the spin axis of the star if there is no radiation it's because the coupling must somehow vanish okay and why does the coupling vanish it's actually pretty easy to see right because in reality think about your star right this is your star and you know it's supposed to be completely axi-symmetric that is what we've assumed over here right when there's exactly aligned and you're trying to emit some photon which has some angular momentum right is some e to the i m phi times some y lm or something right or maybe the y lm actually contains that whatever there's some azimuthal angular momentum that's in the system now the key problem is that if you try to couple that state right to the star you've got to perform some integral around the star right and if the star is completely symmetric okay then there's a natural vanishes right because you're integrating e to the i m phi around some symmetric thing and the word zero okay so the coupling vanishes and the moment that coupling becomes non-zero because let's say you put a little dent over here there'll be radiation right like nothing surprising about that okay so you've got to break that axis symmetry in order for you to have this kind of dipole radiation okay so the kinematics is still a lot right so actually this is just a slide that in a sense reinforces that point the radiated photon must carry angular momentum which means it has to have some e to the i m phi right and it is unable to couple to an axi-symmetric system precisely because of the symmetry the symmetry essentially cancels the coupling even though kinematically the star can lose energy and angular momentum by emitting light degrees of freedom right that still kinematically allowed the coupling is zero that's why it doesn't occur okay but come on this is crazy right because we do have light degrees of freedom that are coupled to the stellar medium they exist photons or whatever they they are coupled to the to the stellar medium so at some level there must be radiation right because come on it's quantum mechanics right you can't really have something where there's a light degree of freedom existing you can emit it and you can slow down but still you don't do it right so the reason why you didn't do it here was because of something stupid it's because the fact that somehow you lost your coupling due to some symmetry right that's why there was no radiation let's think about a closely rated problem the problem of absorption okay suppose I take a star right that's sort of axi-symmetric right nice axi-symmetric star or a pulsar where the magnetic field and everything is aligned in the direction so that guy is not emitting standard electromagnetic radiation we know that doesn't happen but let's take a photon and throw it at the star right what happens to that photon will it get absorbed or will it just bounce around what would it do well I'm title is absorption so clearly the photon gets absorbed right so if you take a star and I throw a photon at it it's gonna get absorbed what happens is that the the photon comes in there's a star sitting there and the photon will excite some angular momentum mode right some you know some stellar excitation it will be some eddy currents or phonons or whatever in the stellar medium and the star will continue rotating right so what you realize here is a central point which is that the angular momentum of the photon will couple to moments of the stellar excitation right so it is true that the photon a photon with angular momentum is unable to couple to a rigid star right if the star has no degrees of freedom at all then the photon can't do anything but the moment the star has excitations phonon modes you know eddy currents or whatever your photon can couple to it right that's exactly what happens the moment there's absorption your photon which has an angular momentum is able to couple to the star even if the star is symmetric right because these excitations if you will break the symmetry so that means you've now found a coupling between a axis symmetric star and a photon that has that has angular momentum so now turn the problem around right so if you have a star that is let's say completely axis symmetric it is possible that it can emit a photon creates some stellar excitation like some eddy current or whatever and then still continue rotating right the fact that absorption exists means that this matrix element is non-zero it is the same process all I've done is flip the direction of the arrows is that clear right you know one of those things where you just rotate which thing is happening where so this process has a non-zero matrix element simply because absorption is true that is the previous slide we had the photon come in hit the star and get absorbed by creating some stellar excitation which means that if I read the arrow this way the star can come in emit some photon create some stellar excitation and then slow down right that process that angular moment that coupling exists the matrix element exists and this will obviously happen as long as it's kinematically allowed that's quantum mechanics right once you've got a coupling and you've got phase space should happen right I don't know if I can swear here you know anyway so that's right so once the kinematics is allowed this happens so let's just calculate the kinematics right when does this process actually occur so what is the kinematical calculation the kinematical calculation says that it better be the case that I'm able to emit this photon this photon must have positive energy and angular momentum I mean the angular momentum can be plus or minus of course but the energy of the photon must be positive and the star you know has some initial angular momentum and it's going to some final angular momentum right and this must be bigger than that obviously and it's create some positive energy excitation for the star so you can go through the rigmarole of calculating this right sort of conserve energy and angular momentum in this process and you will find that as long as the emitted angular momentum of the photon satisfies this condition that is m omega is bigger than the energy of the photon as long as this condition is satisfied one can actually have I mean the kinematics is satisfied that is this excitation can have positive energy right so what this is telling you is that if I emit a photon of the right angular momentum right if this m has been sufficiently big such that the this quantity m omega minus the energy of the photon is positive as long as that condition is satisfied I can create a positive energy cell at excitation and there is phase space for this process to occur right so one can indeed therefore ask the question which is that if I have the star that is spinning down right this star can emit a photon of sufficiently high angular momentum and create some excitation that is you know will therefore we have positive energy and the rotation rate of the star will thus decay okay so this raises an obvious question which is that all I have said is m has to be big enough for this process to occur right so why do I not produce m's that are arbitrarily big you know m of infinity or whatever right in which case it would seem like a star that is spinning at some relatively low frequency is able to produce particles of arbitrarily high energy right something was break down and indeed something does break down which is that if you if you were trying to produce modes of very very large angular momentum okay condense yourself that if you have a motor very large angular momentum that mode will be far from the star right if you because you're a motor large angular momentum you're pretty far that's how that's where your localization exists your mode is very far from the star which means that you are very suppressed coupling with the star itself because your star is some finite size object okay and if you have a mode of high angular momentum the mode is far away so there is no overlap between you and the mode so even though you can kinematically produce it the rate for that is very slow doesn't doesn't occur okay so but it does tell you that as you decrease the angular momentum right eventually you will have enough of an overlap that you can efficiently produce this object so this is the comparison between multiple radiation the things that you know and love from Jackson maybe love is too strong a word things that you know from Jackson and the super in the phenomenon multiple radiation exists any time you have a non-axis symmetric system right there is some star that is you know the magnetic field and the rotation rate are not aligned the moment you have that this process occurs because there is a non-zero coupling and there is a non-zero kinematic condition allowed and this guy will just emit this photon and radiate importantly the radiation will always occur at multiples of that frequency right that's what multiple radiation is that's a fundamental frequency which is radiating at super radiance is an instability of any absorptive rotating system this is important right when they when your star is axis symmetric this vertex gets killed so the moment your system is absorptive that basically means that you know there are these soft excitations in the star itself then your star is able to emit some photon create some excitation and then decay down okay but this is a three-body process right I'm producing three different excitations this is basically continuum emission in multiple radiation is to body right I always go produce one thing and slow down okay so that's why it occurs at fixed frequencies here it's basically continuum I can sort of emitting an arbitrarily soft or arbitrarily high energy photon the coupling of these things of course will depend upon what the frequency is but I can you know do that for any of these energy okay so that's how they're pretty different between these two things so usually okay when you think about pulsars and stuff like that you'd be a crazy person to go and say oh the pulsar is emitting super radiant photons it of course because the pulsar emission is dominated by absorption by the standard multiple radiation because most pulsars you see are you know the multiple radiation when it exists it's just a single vertex like that it's sort of it's dominant right it just happens very nicely absorption is a higher-order process it's got to create all this you know funny modes in the star and stuff like that so it's more irritating it's a weaker process so that's why typically when you have electromagnetic radiation what you study from Jackson is correct that it is indeed multiple emission that dominates there's an important difference between things like photons okay that that you normally calculate where multiple radiation can easily dominate and in fact does dominate versus things like axion so why am I for example standing here and saying oh you know we've indeed observed these sort of sort of rotating pulsars right and they're indeed slowing down because of electromagnetic radiation electromagnetism is like way strong more strongly coupled than axions obviously right so why is there even a hope in hell that I can actually constrain something about axions but by observing this rotation rate of a pulsar when electromagnetism is so much more strongly coupled right how's that ever why would this process that is so weak to begin with ever useful there's a very important difference between a massless particle like a photon and a massive particle like an axion that's a mass right so what does that mean for you so if you take a star and and you know think about an axi-symmetric star right a couple it could be a pulsar a black hole or whatever I mean the axis of it is not even that important just that it's a big gravitationally bounces you know from big star like a lot of gravity around it now if you take your axion particle which has a mass then quantum mechanically there are gravitational bound states of that field of that particle around the star right so if you have a star and there's some gravity around it you take your axion field and then you calculate its modes you will find there are you know bound states around the star right just like a hydrogenic atom right exactly the same way there are these bound states of these axions or whatever that are around the star and the Bohr radius if you go if you trouble yourself and calculate what the Bohr radius is the Bohr radius is like 1 over gm mu squared okay because gm mu is like the alpha of the thing whatever calculate you'll just find that okay obviously as the mass of the particle goes down these gravitational bound states are far and far away because obviously if your particle is massless there are no bound states right there's like you can't but bind it all so you already see that once you have a mass interesting things happen because you have these gravitational bound states of your axion or whatever around the star they just exist automatically okay now here's where the cool thing happens right which is that if you take your super radian phenomenon the super radians is going to produce a lot of photons that's what will be dominated by but once in a while it'll produce axions as well okay like a very weak way and but it can emit into these gravitational bound states of the axion around the star okay it'll populate that very weakly but this bound state is stuck that is not going anywhere it's stuck right there which means you have the possibility of a Bose enhancement okay you will slowly populate that mode and eventually that mode will become auto on and then exponential amplification occurs okay so once you are in a situation where this Bose enhancement become significant this process that is happening into you know the slow way of populating this mode with axions suddenly becomes way faster than your electromagnetic emission right because you're exponentially amplified okay that is how even though these axions are much more weakly coupled than electromagnetism precisely because they have these bound states around the star which photons don't have the super radian emission can be very very effective okay and slowing this down that's the key idea okay and the central point then is that this process will be efficient in certain cases we will shortly see what those certain cases are they could be very efficient if there are new light particles that are sufficiently strongly coupled to the stellar medium we will define that and the basic idea therefore as a following is that you can use the observations of say rotating black holes or pulsars these happen to be the systems where this emission is particularly useful where it's enhanced and we will again see why that is a case so the idea is that if you see such rotating systems you can then say oh this process did not occur so axions of that particular mass for example did not okay that's the idea all right so that was like the broad picture of you know the global physics idea for how that actually occurs let's see some mathematics right how does it happen here is the set of equations that tell you how the system happens so all we're going to do is take a particle psi okay like an axion or whatever some field psi it's got a mass okay and let's say it's interacting with the medium and the medium itself is moving with some velocity okay so this is the equation of motion for this is a Klein Gordon equation box psi plus mu square psi right plus the effective potential that the size sitting in so for example if this is a saw like an axion field sitting in for in gravity this v effective is just the gravitational potential that is sitting under what is this term okay this term which is C v alpha grad alpha psi that is an absorption term okay it's telling you there's absorption in the system and absorption exists because I have coupled the system with the medium and I'm allowing for absorption to exist let's analyze this system let's look at what it does in the rest frame I go to rest frame of the system the full velocity is just 1 0 0 0 and that equation of motion is just simply this okay it's the box 5 mu squared except this v alpha grad alpha thing is just C times psi dot okay nothing brilliant and the brilliant thing is that you will solve for what that you know what those modes do and you find that the mode grows as either the grows or decays as either the minus ct over 2 okay so just you know plug in some answers and solve for positive momentum or whatever and you will find that the amplitude of the mode depends on as either the minus ct over 2 the crucial thing is that and C is positive this mode is damped that is called absorption right that's typically what happens but of course if the C happens to change sign the mode will grow right mathematically that's what that's how you see it okay and let's see how that happens so let's take a system the same system as before the C is still positive so you would naively expect this thing to be you know the mode should be absorbed but now we're considering a medium that's just not moving but it's actually rotating it's spinning okay it's rotating at something so the rotational velocity of course is this thing right 1 0 0 omega r sine theta okay the spherical and it picks vertical coordinates that are aligned along the rotation axis and actually this phenomenon in this particular language was discovered by zeldovich back in the 1960s so you really know this is true I'm not just making this shit up it's actually true okay what are you gonna do we're gonna take this equation of motion there is this coupling and we're gonna look at the angular momentum modes of this field psi okay that is the size for example the axiom field right that is bound to the star so let's look at the angular momentum modes that's what they look like okay you know as a mutually quantized and plug in okay some grunge grunge grunge the key point about this grunge is that when you plug that in over here you're gonna find that the coefficient for C contains this term mu minus m omega okay that's what happens when you plug that in there okay and what you see is that when m is sufficiently big this term flips sine right so this is exactly the same condition that we that we arrived at for previously just from energy considerations talking about absorption and asking when the absorption can become an emission we said for sufficiently large angular momentum the kinematics that was allowed and you would have thought in like in that language oh I now have a phase space I should be able to do it in this rigorous mathematical language you see that when m is big enough this term flip sine which means that instead of this term being absorption it becomes emission right the amplitude of the mode will start growing okay so the same kinematic condition that we saw before and absorption then becomes emission okay and that was what Zelda which claimed it's true back in the 60s so now that we have I've convinced you with Soviet mathematics let's figure out how efficient the system actually is okay where does it grow how big does it actually happen okay the key point to note is that this absorption is all happening only inside the star right I mean if I'm out in free space there's no absorption happening so who cares so all of this growth is only happening like within your star which has a radius of size r and obviously the rate the rate at which you can enhance the rate of which you can emit will depend upon the overlap of the mode that you have but with the stellar medium because the stellar medium is this small and your mode is gigantically far away there's no overlap and like nothing happens okay so unsurprisingly the rate of growth will be proportional to the probability of finding your particle your axion or whatever in the star right because there's some mode sitting somewhere if most of the time your particle is sitting far away it's not gonna have a big chance to get absorbed alright so how do we calculate that so once again this is a picture we've got a star that is spinning there are gravitational bound states of this axion or whatever around it they automatically exist once they exist once the particle exists and these wave functions are essentially hydrogenic levels right this is some one over all potential the potential is gravitational not some electromagnetic thing but there's some gravitational potential so there is some you know Bohr radius and hydrogenic atom with a short in your problem which is localized at a position 1 over GM mu square that's what it is okay so you can open up your favorite book of quantum mechanics and you can figure out how these wave functions behave at short distances right so you'll find out that at short distances because you know most of the time you care about the overlap with the star where the star is at no center of the system and has some six size are what you find is that at short distances these wave functions look like are over the Bohr radius roughly to the power L where L is the angular momentum of the Bohr of the of the mode right so you know that if you have an S wave the S wave always has support at the origin but the higher angular momentum modes don't right they vanish at the origin and the rate at which they vanish is given by this okay and for super radians we always have a purpose have positive angular momentum right we're always emitting angular momentum modes so L is always at least bigger than or equal to 1 right that's what happens so now we can plug that in so we see that this is r to the L times whatever GM mu square to the L okay strongly dependent on what else okay so that we already know so that's the size of the overlap right now you can kind of estimate what the rate should be the rate should go as some size squared right the probability distribution that's what it should be okay so and then you do some volume integral okay I don't want the exact details of how you do this but it's not too surprising right so the probability of finding the star inside this it's the probability of finding this particle inside the star should go as size star psi right and size star psi would mean you get r to the 2l over here the 2l there and then you would do some integral over d cube r which gives you an extra power of 3 okay that's the basic idea and you can kind of rigorously show this as well but you know this is the intuition and then you see that this basically grows as GM the mass of the star mu square where mu is a mass of the particle and r is the size of the star and the whole thing raised the power 2l plus 3 okay so pretty rapid dependence on power if you look at that all right so let's look at what kind of systems are most efficient all right so for you to be super radiant you've got to satisfy the condition that mu minus m omega is less than zero okay and you know that that's when you're super radiant that's the condition and if you have sensible modes sensible angular momentum modes you always require that the the orbital angular momentum is bigger than the azimuthal angular momentum m okay so that is if you want large m you also have to have large l that's what it is okay so there are sort of two ways in which this process can be suppressed so if you have a particle whose mass is really small right like a like a photon for example was masses zero or a super light axion when it's very very light then even the lowest angular momentum modes even the l equal to one mode is super radiant except the ball radiance for that guy is super far away if you're a light particle you're super far away so your overlap is killed and your overlap is killed as mu squared to the raise the power 2l plus 1 so rapidly rapidly kill right so if you're a light particle super radiance is super inefficient so you want to essentially go for the you want to keep tweaking up your mass you want to the mass has to be very big so that the particle is bound close to the star but if you have too big a mass right the mass is let's say a hundred g e v or something gigantic then obviously it is true that there are certain angular momentum modes that will be super radiant but those will be modes with super large angular momentum so once again they will also be far away right so there's kind of a natural sense in which the most efficient particle the most efficient particle production occurs when the mass of the star mass of the particle is comparable to the rotation rate of the star right because that way you minimize yourself on this side and you minimize losses on this side right it's sort of like roughly it's not a resonance but it's sort of a that's a broad region where this is most efficient okay and so okay so let's pick mu to be order omega the rotation rate of the star and then what you then want to do is maximize everything else right you want to make everything else as big as possible right so you want to basically say I want to take the largest possible mass here and the largest possible radius because the biggest those two things are the larger my effects right that that rate is directly proportional to those numbers raised to some high power the bigger they are the bigger my own but I can't make something if some object is rotating I can't really make a size arbitrarily big right because at some point omega r will become order one and then the special order really kills you okay so what you need is that given a particular sort of rotation rate you want to pick the largest possible object that is spinning maximally at that frequency okay so in particular given a rotation rate if you let's say you want to constrain a particle of mass mu you want to find an object which is rotating at that rate omega where mu is order of order omega and then you want to find an object that is spinning as fast as possible at that frequency okay that's an extremal object that's it's called so the examples of these kinds of things are extremal cur black holes right those are supposed to exist we don't observational evidence a little bit sketchy but theoretically you can have a sort of a cur black hole which is spinning as fast as possible okay so if you see such spinning black holes that are as fast as possible there would be a good environment for you to go and search for these things the second object possibilities are these things called millisecond pulsars so for example millisecond pulsars are not quite as extremal as extremal back holes in the sense like your extremal back hole is only bounded by general relativity it can really be super extremal millisecond pulsars are sort of more bounded by reality the sense that you know we've you know QC doesn't let you spin arbitrarily fast but they can go pretty damn fast so for example the fastest objects we've observed in the universe are of these millisecond pulsars spinning like 714 hertz that's a pretty rapid frequency to think about right a star spinning like 700 times a second okay and that's the maximum thing we've actually observed so you know there's a lot of stuff to say over here but let me just give you the overall view on where we are in this case okay so if you have extremal back holes okay if those exist then they are naturally absorptive right so remember for super radians we said we need absorption okay the moment you have absorption you always have super radians and in an extremal back hole there's gravity gravity can absorb stuff and in fact in a black hole you go in there you can absorb by gravity okay and so that's a very clean way in which the object actually your your your axion for example can get absorbed with the black hole and the moment you have that absorption you always have this emission once you satisfy the kinematic condition for millisecond pulsars absorption can happen to non-gravitational interactions gravity of a millisecond pulsar is not big enough to make things absorb right because if you just throw a particle at a millisecond pulsar and gravitation will just go through and bounce out right when I throw it at a black hole it gets absorbed so gravity is not strong enough but particles like axions typically have non-gravitational interactions so you can try to use the non-gravitational interactions to create the absorption necessary to do this sort of emission so for the case of gravity things are pretty clean for absorption and from from for millisecond pulsars a little bit more different the difficulty though is that it's very hard to actually measure the rotational rate of a black hole right a black hole is black so you can't really look at it with your eyes and be like oh that black hole is spinning at some rate so there is a lot of unknown systematics sorry there are a lot of systematics in this in this case okay which is that you have to ultimately model some astrophysical system pretty well in order to be able to extract the spin from it and that's an evolving field I think definitely progress is possible in that field but there are definitely systematics involved with astrophysical modeling and the unfortunate thing of course is that these these bounds as we said they depend upon very sharp powers of the rotation rate right they go as some power 2 to the L plus 3 and stuff like that so even if you screw up a bit on your rotation rate you actually have large uncertainties on what how rapid the rate actually is so the case of black holes that's kind of a problem in that it's hard to measure the spin directly for millisecond pulsars that the good thing is that the spin and the orbital issues are well measured right you can go look at it with your eyes at some pulsar and you know what rate it's spinning right you can't really argue about that so the spin etc are very clean and it's possible to make clean measurements okay but the difficulty of course is that you don't know the interior of the neutron star that well of the pulsar that well right so the black hole the interior is very simple you know what the black hole is very clean well for things like neutron stars you actually have to calculate the absorption and the calculation of the absorption is messier because a neutron star is a messier object than the black hole right so it's kind of a funny situation where theoretically the black hole is clean but the measurements are hard while for millisecond pulsars the measurements are straightforward okay but the calculations are ugly because it involves the interior of the star itself okay anyway this is an evolving field and I expect actually good progress to be made here so but that is very clean simply because of the fact that that's a situation where all you need to do is to postulate that the particle exists if it exists somewhere in the spectrum then super ratings will produce it populated and you can go and actually make a measurement and things are good so we're going to move on from that story to talking about how one can detect axions if they were the dark matter of the universe and in particular I'm going to be talking about this experiment that is likely to happen very likely to happen called the cosmic axion procession experiment or Casper so let's review what axion dark matter is okay so going back we were talking about you know if you want to think about a boson like a photon one very sensible way of thinking about that is this as individual particles moon around another way is to say that the photon is nothing but some electromagnetic field some classical electromagnetic field that is has an amplitude and is oscillating at some frequency omega right and one way in which you want to detect things like photons is by measuring the time varying electromagnetic field associated with it so if you have a photon some radio wave for example you can have an antenna sitting there and the time varying electromagnetic field off the photon will come in and drive currents in the antenna and that's something you can go see okay so that's one way to measure this as I said yesterday the particles like axions you can think of them as individual particles but just as legitimate way of thinking about them is just to think about them as a classical field exactly like how you think about photons from a laser as a classical field you can also think about these kinds of particles these super light bosonic particles as some kind of oscillating classical field right the key difference of course is that these guys have a mass so they have no they have a mass and they're very cold their velocity is very small compared to their mass so essentially all that matters here is a time variation but for a photon because it is a mass less particle the momentum and the frequency are always coupled right for for things like the axion the velocity part is not as important although we will actually use it but still it's not that important okay and of course in the early universe we said these fields are just completely constant throughout the universe you know dead constant field they're just coherently oscillating as a not cosine mt okay but we don't have the luxury of living in the early universe we live today and today we said that the axion is actually a you know random field right it's sort of fallen the galaxy bad things have happened to it they're all these bumps and wiggles everywhere but even though it's a random field I can still think about it as a random as a random classical field I can still define a correlation length I can say the field has one value here how far do I have to go before the field becomes order one different I'm just reviewing what we said yesterday and thinking about that in previous space tells you that the correlation length is about 1 over mv where m is the mass of the particle and v is the velocity okay now usually for an experiment we're not just interested in a correlation length we're also interested in the coherence time which is like how much time do I really have to sit somewhere and and like observe some effect right like if you have an antenna for example you and there's a radio wave coming in you want to ask for how long can I sit and have the radio wave drive the antenna right that's how you build up the current of the antenna to see it but similarly when you're trying to do something with these axions and these axions are oscillating and there's some detector out there you want to know for how long can you sit there and have you and have the axion drive something to see it and so the coherence time is then basically given by the fact that the earth is moving through the axion field right and the axion is be going to have a constant velocity is going to feel is going to be more or less constant over a distance 1 over mv and the earth is moving through that field at a speed v as well right because that is a relative velocity between the earth and the dark matter is also the same v that is sitting in here which means that the coherence time is 1 over mv square okay and it is very interesting coherence time basically because let us say that the mass of the axion has a megahertz okay some a typical number that you get in these in these fields and you find that when v is about 10 to the minus 3 which is it which it is in the galaxy the coherence time is about a second okay and that's again a crazy number because the second is nothing compared to the Hubble scale right that is a natural time scale of the galaxy right so if you look at galactic time scales of 10 billion years a coherent style of the second is useless it's nothing but a second is very interesting for human beings because that's the scale at which we operate so we can actually go and build experiments that are able to you know do stuff at like second time scales for us to go see it so the central idea behind pretty much all axion experiments and how they detect it is that somehow they're going to leverage the fact that this there's an oscillating classical field that is moving around and much like how you detect photons by the fact that you can have a radio like some antenna and electromagnetic field goes back and forth and drives it similarly you're going to come up with some way to make use of the axion fields oscillations the axion field be oscillating it'll be driving something and you want to and you want to detect that and in these systems there is a natural possibility of a resonance okay basically because the field is coherent for about 10 to the 6 oscillations right so if I have the coherence time is 1 over mv squared and v is about 10 to the minus 3 the field will then be coherent for about 10 to the 6 oscillations so there's a natural resonance possible so you can enhance your signal in this game that's kind of the broad plot of pretty much how every axion detection experiment works in this frequency range so how does the ADMX work ADMX are these microwave cavities we very briefly discussed them yesterday for we run out of time so ADMX is trying to detect axions if you know this parameter FA is about 10 to the 12 GeV okay microwave cavity experiments how do they work they're making use of the fact that axions coupled to electromagnetism a or f of dual e.b or whatever and then you basically have some microwave cavity and you put some large magnetic field the axion comes in it's some classical field coming in there's a there's a there's a classical magnetic field out there and because of this coupling e.b you put that in your I mean you just take that into your classical Lagrangian and you will find that because there's a coupling e.b your your classical axion field in the presence of a classical magnetic field will drive a classical electric field okay not not all that brilliant and so that's what they do so they build a resonant cavity they build a resonant cavity because you know they would I mean there's a resonance possible so essentially the way you want to think about it is that like you know when you normally take a cavity right if there's some electromagnetic cavity you drive it by pumping electromagnetic fields into it here you have a cavity there's a magnetic field the axion is driving it because the axion comes in creates a tiny electric field which drives the cavity right that's basically how you see it and 80mx is a great experiment and they can search for axions if f is about 10 to the 12 g e.b however it is basically impossible for them to go to search for axions at much lighter masses or much larger fa right it's just impossible for them to do this and this is really due to like two fundamental reasons okay but there's a very way of detection the first is that ultimately they're searching for a conversion of the axion to a photon that's what they're looking for right and that is basically a so if you convert you know if you calculate the rate for this all of the interactions of the axion are suppressed by 1 over f so when you go from the matrix element to the cross-section for conversion you're gonna pay a 1 over f squared okay matrix element squared that is true they're also suppressed by another big factor which is that for them to convert you know this axion resonantly okay they have to match the size of their cavity to the wavelength of the axion right because when you have a resonant conversion it better be the case that your resonator has the same size or somehow resonantly locked to the frequency that you're converting okay so if f is about 10 to the 12 GeV for the QCD axion this gives a wavelength you know if you look at the wavelength of the particle to be about a few centimeters so they can easily build a few centimeter size cavity and have this resonant conversion of axions to photons and that's something they can see but when f becomes bigger remember that the mass of the QCD axion goes down it's lambda squared over f right so when f becomes bigger the wavelength of the axion gets enormous okay so they would have to build a gigantic cavity in order to sort of resonantly convert this very low frequency axion into a photon that can sit in there so for example when f is let's say about 10 of us like around 10 of the 16 GeV like the gut scale the cavity size has to be a kilometer right so you're not going to build a kilometer size cavity and be able to control it that well and if f is at a plong scale that's a thousand kilometers the size almost the size of the earth no you know there's no way we're going to build that right so if you don't do that if you don't if your cavity size doesn't increase to match the size of the axion wavelength you know your signal efficiency is rapidly killed okay in fact it dies is one over f cube so you put those things together that's one over f to the fifth okay and you know pardon my French here but like that f is not the right f you want there okay so this therefore raises a theoretical question right it's super reasonable that axions exist over here but you need a different operator a different way of detecting this because this operator just wouldn't do it's not going to work okay how do you how do you do that okay so let's see what happens going back to one of the earlier slides here think about the problem very globally right all we have is some goldstone bows on how can light go so goes on coupled with a standard model they can couple to electromagnetism I mean this is just f of dual I was written that in a fancy way I was trying to please someone wealthy once and I stole the slide from there but anyway this is f of dual so that the that's what all current searches are looking for right and but the two of the couplings that the axion can have it can couple to glue on fact that is the defining coupling of the axion to QCD right the gg dual or g by g the same thing or it can also couple to firm me on to this very general operator d mu a psi bar gamma mu gamma phi and the Casper experiment it's a proposal to go and search for these two couplings of the axion okay so here's the idea behind Casper okay the strong CP problem remember that's a reason why we even introduced axions in the first place was that if you had an operator theta gg dual that will create a nuclear on EDM that is order 3 10 to the minus 16 times theta okay that was a strong CP problem now let's say that the axion is a dark matter of the universe the axion is a dark matter of the universe there is a background value for the axion field a is non-zero right that's all this energy density so there's an a or f sitting in there okay and but exactly the same physics this will create a nuclear on electric dipole moment that is ordered 3 10 to the minus 16 times a or okay same physics let's estimate how big that is okay so what do you do you say a of t is a naught cosine mt you know the mass of the axion the QCD axion was lambda QCD squared over f a which is about this number and then what we say I have to figure out how big this amplitude really is so I'm gonna take the local dark matter density and equate that to m squared a squared and m squared a squared is number point three sorry this local dark matter density is a famous number point three g e v per centimeter square so with that I can calculate this ratio a or f okay and what you find is something very interesting which is that this number a or f is three times in the minus 19 independent of f a so no matter what scale the axion comes from this ratio a or f is independent of f okay why is that well basically because I have made the assumption that this this quantity ma is a constant that m squared a squared I've assumed that no matter what f a I'm sitting at this is all the dark matter of the universe and then it is just the case that for high f axions the mass is so light that the ratio that this quantity ma is a constant okay so sorry that's quantity a or f is a constant right so this is cool if you had some way of detecting this very tiny field value right so this tiny field value will give rise to a nuclear on EDM as they said earlier okay because a or f exactly gives rise to EDM so if you had some way of detecting this tiny EDM you are suddenly able to detect a wide range of ax of f a right doesn't matter what the value of f a is it's all going to give you the same EDM value and that becomes a very powerful way to search for this unlike ADM x but as you went to high f your signal was dropping less like as f to the fifth now this is a super small EDM this is about nine orders of magnitude smaller than the current bound on the static EDM of you know there's a search for but very importantly the electric dipole moment introduced by this axion is not static it'll be oscillating okay the frequency set by the mass of the axion which kilohertz to gigahertz how does that happen because the axion field is some a not cosine empty and this m is some mass of the of the particle right so it is true that we have searched for the for like a time independent EDM like a theta QCD that doesn't change at all and that is constrained at some level but this EDM induced by the axion is varying in time okay and the fact that something is varying in time is experimentally super useful as we will shortly see okay so that is one operator so when you when your axion couples to gluons it's able to give rise to a time-dependent electric dipole moment the other thing is that axion also couples to fermions we talked about that and this is true not just for the QCD axion is also true for axion like particles the general way to look for them d mu phi over f psi bar gamma mu gamma phi psi go to the non-revistic limit of this operator and you will find that if you take the nucleon operator then this field couples to the nucleon operator like to the Hamiltonian of nucleons as grad phi dotted at the spin of the nucleus okay that's what that looks like in the non-revistic limit now if you have axion dark matter okay since there's a great spatial gradient I'm gonna expand it out in space as well so it's axion dark matter it's on phi of px that's a local field it's some phi not cosine mt as it you always used to be but then I also have a small piece that depends upon the velocity of the dark map right that's what it is like nothing brilliant this is just e to the i you know omega t plus kx so the presence of axion dark matter your nucleon Hamiltonian okay all I'm going to do is take this operator plug it in there is going to be and then calculate what it is right so this phi is phi not cosine mt plus m phi dot x take the gradient you'll find the nucleon operator is basically m phi times phi not times the velocity of the axion dotted the spin of the nucleus that's just coming in from plugging that okay so if you look at this coupling this looks exactly like how a magnetic field would couple to a spin like b dot s right so here we find that if you if you're in the galaxy these axions are moving with with a certain velocity and there is therefore a velocity dot spin coupling which looks exactly like how a magnetic field couples to a spin okay so if you have a if you have a spin and there's a magnetic field this that'll cause us that is say perpendicular to the spin the spin will start processing right and now here you've got an axion velocity okay the velocity of the dark matter if you will if you place a spin perpendicular to it the spin will start processing in exactly the same way okay you can estimate how big that procession thing is so this quantity m phi times phi not turns out to be about 10 to the minus 5 tesla it's pretty big okay there's a lot a lot of local dark matter density so this estimating how big m phi times phi not is just taking the square root of dark matter density that's about 10 to the minus 5 tesla it's pretty big magnetic field okay so once you put in the bound that this guy is very weakly coupled a 10 to the 9 gv or so that's the most strongly it could be coupled that is something like a femto tesla oscillating magnetic field you know that's so of course a small magnetic field but i would argue it is within the capabilities of precision instruments but that's what we're looking at right we're looking at if the axions exist and the dark matter and a couple of that thing you're with that strength you're looking at a femto tesla oscillating magnetic field okay in your system all right so let's put it all together in a nice picture here's what happens okay for axion like particles i also call them general axions whatever bad name for axion like particles suppose you have a neutron okay the neutron sitting there it's got a it's got a spin you expose it to the velocity of the axion this is the dark matter velocity of the axion because of this operator okay this spin will start processing about the direction of that velocity just like how a magnetic field will cause the spin to process this velocity will also cause the spin of the of the neutron to process like so okay and uh if you calculate what it is it's something like a femto tesla magnetic field okay oscillating at some frequency given by the mass of the axion uh we can ignore that comment take the qcd axion okay that is the axion that couples to glue on specifically and now if you have a neutron okay again sitting in there then uh all you do is you expose the neutron to the uh i mean like to the axion dark matter because of qcd because of all of the reasons why we introduced the axion in the first place uh this neutron will acquire a tiny electric dipole moment okay this dipole moment will be along along the direction of the nuclear spin that's the only vector in town and uh uh if you put in the numbers it gives rise to an to an electric dipole moment that's over 10 to the minus 34 centimeters oscillating at a frequency equal to the mass of the axion what do you do you can apply some electric field and that electric field will then cause the nuclear spin to process so if you take a magnetic dipole and you apply a magnetic field the spin will process similarly if you have an electric dipole and you apply a an an an an electric field the spin will again process okay so the fundamental idea is that what we have seen is that under appropriate conditions axions can cause nuclear spins to process either it is because of the velocity of the axion that causes the spin to process or it's the qcd axion it acquires an edm and you apply an electric field and the spin processes so if you had some clever way of measuring the rotation of the spin you can detect the axion okay that's the basic idea of casper and hence the name cosmic axion spin procession experiment how do you do that thankfully well before any of us in this collaboration uh was born there's a technique called nuclear magnetic resonance that's been around for 60 years or something right it's fantastic here's what you do you take a block of material and you align all the nuclear spins in one direction okay and uh you know this can be done okay now let's say you apply some electric field okay what that's going to do is that if the axion is the dark matter of the universe then all of those spins will start processing that that's what we argue right if you take a if you take a spin and you apply an electric field then the spin starts processing each spin of course has its own magnetic moment has its own magnetic field right and as the spins process there the magnetic field of the spin will start rotating as well right so if you have a bunch of spins are all in one direction and the spins turn slightly the magnetic field will also turn slightly okay and that slight change in the magnetic field can be picked up by what's called a squid the squid is a very fancy uh uh device that measures magnetic field okay it's a very sensitive way of measuring magnetic fields so so that's what you're trying to pick up that the presence of the axion the presence of the axion the nuclear spins will slightly process okay and that's something you can that you that you can detect with a precise magnetometer okay and there's a natural possibility of a resonance in the story because of the following point I can apply some external magnetic field to the system okay so it's just like NMR so when you apply an external magnetic field there's a lot more procession frequency in the system this is just a standard story if you have a spin in a magnetic field you apply a B field there's a natural resonant frequency for the system set with a lot more frequency okay now the axion effect is also time-bearing remember that was very crucial to the whole story right the axion is either causing nuclear electric dipole moments that oscillated a frequency given by the axion mass or with velocity the same thing happens they they keep oscillating back and forth it's a femto tesla magnetic field that's oscillating back and forth so if the lot more procession frequency of the system is equal to the axion mass there's a resonant enhancement right when the two of them match you have a big spin procession and that is something one can use okay of course in practice we don't actually know what the mass of the axion is nobody's told us what that is so what one would actually do is that you would pick some external magnetic field and you will slowly keep changing it and you will find one point where there's a big resonant enhancement and that's the place where you detect the axion if you see it so I'm not going to go into details of what these plots are and whatever but this is basically the projected sensitivity of these experiments okay so this is the coefficient of the axion coupling to the EDM here and this is the mass and electron volts I guess it's kind of a little messed up in the in the slide here when it shows up and in in EV at the bottom and frequency in hertz at the top okay the crucial point to notice this this purple line is where the QCD axion exists if that is a dark matter of the universe okay and this blue region here is where ADMX is searching for it right now a rather narrow set of frequency and anywhere where this solid red line intersects and goes below this purple line that is where this experiment will be sensitive to the QCD axion so as you know with some reasonable technological improvements this experiment has the ability to search for QCD axions above a scale of 10 to the 16 GeV okay so if FA is above 10 to the 16 GeV if this experiment really works as we think it should it can search for the QCD axion so you really have an ability to search for really higher axions above the gut scale if they're the dark matter of the universe similarly if you are looking for the velocity of the axion the axion wind it's in a sense a simpler experiment because all you do is just take a bunch of nuclear spins like you don't even have to apply like some electric field all you're doing is just putting the the the spins up there and that the velocity of the axion will cause the all of these spins to process and as the spins process the magnetization of the sample will change and that is something you can pick up with your magnetometer okay and the same is the same idea this is also a time-varying field so by tuning the law more procession frequency you can pick up a a a big resonance okay so again so this experiment has an ability to probe pretty deep into the parameter space of axion like particles it doesn't quite have the sensitivity to get the QCD axion but you know there could be this axion like particles out there and one can really you know go a lot in the parameter space as opposed to ADMX which only scans of rather narrow range of frequencies here we can go many many orders of magnitude into the parameter space of these particles so here is sort of the discovery potential for where we think this can really work right going back put everything together this is the you know parameter space available for axion everything below this is ruled out everything about this is open and this is where the microwave cavities exist these NMR style experiments they're sort of laboratory experiments right they're not some you know massive experiment they're things it's like it's it's a fancy NMR device okay and it really has the abilities to search for axions in this range of frequencies kilohertz to about 10 megahertz corresponding to f of a bow you know from our 10 to 15 GeV onwards to the Planck scale okay high f axions they're definitely you know technological challenges ahead we are pushing forward with this right now and if you do detect this this would be a discovery of dark matter that'd be pretty awesome you'll also discover the axion and really we'll be telling you physics at some very high scale okay so a lot of interesting things happening in this field right now as we ramp up let me summarize sort of the experimental part of this story which is that you know a lot of interesting things have happened in axions recently you know it's really pretty amazing there's not a lot happening for a long time but now in the last few years I think a lot of interesting developments happening both in terms of theory and experiment in terms of theory there's possibly the super radiance could be a way in which you can really probe these systems using extremal astrophysical systems subject of course to uncertainties but still it's a very interesting way to go forward and experiments like Casper which are a way of searching for these things in the laboratory okay so as I promised you know I couldn't help myself but want to talk about the my own paper so I'm going to talk about very briefly since some of you also asked about how there's also another use of axions that's basically I think why I think it sort of ties in a lot of interesting theoretical things happening recently but how one can actually have cosmological relaxation of the electro big scale as you all all know there is you know a hierarchy problem to be solved we've proposed ideas like supersymmetry composite higgs you know a lot of extra dimensions many interesting ideas out there they all typically tend to produce a lot of particles of the LIC right and we've not seen them and that is the big question of the hierarchy problem are we sort of is there a natural solution to this or do we live in some anthropic multi worse sort of scenario depending upon which university you come from in the world one of those things is more popular than the other you know but here it's kind of my claim right if you want to solve the hierarchy problem and and you know and it's not due to like some new brand new facets of the LIC I think this is a possibility which is that the Higgs mass was not always big it was was not always small that in the very early universe the Higgs mass would have been super super large and something about the evolution of cosmology puts you in a situation where the Higgs mass becomes naturally small and the bold claim is the following if the QCD axion existed it's not that it's not a vanilla QCD axion it's a little bit different but if the QCD axion existed and let's say you had a long period of inflation our claim is that that is sufficient to solve the hierarchy problem cosmologically okay that's the claim how does it happen well here's the Lagrangian that does it okay so this is a Lagrangian of the Higgs for example this is the Higgs standard model Higgs it's got a gigantic mass this m is at the cutoff it's not it's not at the weak scale it's some huge mass which you think it should have from loops and all of that stuff right and this phi is just your axion okay so this phi is a standard axion it's got a cosine potential as we argued this is the QCD scale to the fourth that kind of stuff okay but that by itself of course doesn't do anything for you so we're going to couple the axion slightly differently in the story in particular we will give a coupling of the axion to the Higgs field right so we will say that the axion also couples with the Higgs through this operator this specific operator breaks the shift symmetry of the axion as we talked about earlier these particles like axions have you know their goats on boson so they're supposed to have some derivative coupling that has a shift symmetry but we break that explicitly by giving this particular coupling okay and this and this G will be tiny will be a small coupling but what this does for you is that once you have this coupling this tells you that the value of the axion field also controls the mass of the Higgs obviously right given a particular value for the axion field there's a particular mass of the Higgs okay so that's you know guts of the idea and the moment you turn on this coupling you've obviously broken the shift symmetry of the axion it's no longer shift symmetry invariant so you'll end up generating all these other terms that break the shift symmetry all of them of course proportional to G itself so there'll be a g m squared phi if you will that comes about because I closed the Higgs loop here was the G squared phi squared and so on and so forth okay so the way to think about this from the point of view of quantum field theory is that this field phi is some you know non-compact field that's that technical term for it some it's some scalar field okay it's got a shift symmetry the shift symmetry is preserved by this operator okay but it's broken explicitly by this coupling and all of the breaking is parameterized by that coupling G that's the right way to think about it the scale m is the scale where we cut off all standard model loops it's not the weak scale it's something very hard and here is what can happen so in the early universe okay we will assume the story is such that in the very early universe this field has some order one value okay some big value and the Higgs mass is something big and positive some huge value is big and positive it's not of the weak scale okay so the big so when the Higgs has a positive mass squared the Higgs has no bev okay that's crucial okay so when the Higgs has no bev the axion also has no mass right as we said earlier uh it was important for the axion to have for the axion mass is controlled by the Higgs mass by the Higgs web sorry because when there's a massless quark in the theory the axion formally has no mass okay so in the early universe when the Higgs has a positive mass squared there is no uh uh uh mass of the axion okay there's no sorry this this this term doesn't exist for the axion this term is zero it just has these terms that are sort of hard breaking term they exist this term is zero okay so we just have uh these terms that's it now what we assume is that during inflation the axion is not the inflaton it's just some field sitting there during inflation we assume that the field five will slowly roll much like how other fields roll during inflation so the field rolls it will scan a variety of Higgs masses right different values of Higgs mass will be there there will be some point where the mass of the physical mass of the Higgs will go from being positive to being negative but that will just occur as you scan okay that's an interesting point right because when the Higgs mass goes from being positive to being negative the Higgs will acquire a web that's what happens right and that web can then be used to turn on a back reaction on the motion of the field five and prevent it from growing right the key point is that if this five field rolls such that at a particular point in the Higgs mass is tiny you know when it goes from being positive to being negative if there are barriers that pop up that prevent it from growing then you can make the field five get stuck at a particular point for a long period of time thereby making this mass squared very small dynamically okay through cosmological evolution and the central claim is that the QCD axion does this for you automatically why is that well as we said earlier the mass of the QCD axion secretly depends upon the Higgs web right and the Higgs has no web the the quark masses don't exist formally there's some tiny you cover coupling okay there's some contribution from that but that's a small number and the Higgs has no web this barrier term doesn't exist this term is zero okay so the field just keeps rolling however as the Higgs web turns on this barrier starts popping up preventing things from rolling okay so you know you can just estimate how big the weak scale really is it's sort of given by a fight between two terms there's like some linear slope this g m squared five that's actually causing the field to roll and then there is this barrier that's popping up and when these two things become comparable that's when the field stops rolling and you have a formula for the weak scale right the weak scale is given by a combination of parameters like this okay so naturally so by picking parameters correctly so you you do have to pick small numbers these g's that we pick will be very small okay but they're technically natural right so by picking the appropriate numbers there you can get the weak scale to be correct like in a technically natural way okay so there is a long you know story about how big can we push the cutoff etc etc you know discussing that will take too much time i don't quite have the time for that i'm happy to talk about it privately if you want but in sense you know you know in a reasonable class of models we were able to push the cutoff all the way up to a thousand tev so like this would be a scale like this would be a story where there's no new physics at the lhc right nothing is seen yet the Higgs scale is not some tuned parameter picked by anthropics but rather it's a parameter that's tuned by cosmological evolution so that's the story thank you