 Ευχαριστώ για όλοι. Είναι όλος καλύτερο να δούμε το ICTP. Είμαι πολύ καλύτερη να είμαι εδώ. Με στιγμή και στιγμή, δεν είναι στιγμή και στιγμή της QCD-αξιονής, δηλαδή στιγμή δηλαδή από τη QCD-αξιονή παράμετρα. Για να εξηγήσω πιο πιο, πρέπει να κάνω την εξαιρετική παράμετρα για το τι είναι η αξιονή της QCD-αξιονής. Πρώτας, για τη σύγχρονη ανάπτυξη, μπορούμε να δούμε ένα τρόπο σε λαγραγία. Η μυξία, εννοώ την εξαιρετική, και η μυαλτάτική παράμετρα από τις σύγχρονες ανάπτυξες, καταλλείφει παράμετρα την θέαση της CP-βιωλαίτης. Αυτή λάγεται ένα τρόπο δυοτηματοκοσυκλέτης, για την ντρονότητα, που θα πρέπει να είμαστε μεταφέρες, και δεν είμαστε. Φαντάly, δηλαδή δούμε την εξαιρετική Αυτό το μήνυμα που βρίσκουμε στο Λαγραγίδιο είναι 10 όρθους από τη μαγνήτωση πίσω πίσω όπου θέλουμε. Αυτό έχει been a problem for a long time, and in the late 70s, initially Pecha and Queen and then Weinberg and Wiltschek realized that if they turn theta QCD into this parameter, what's called theta QCD into a dynamical field the problem is solved. That field gets its mass from, they call it the axion, sometimes they call it the PQ axion. That field gets its mass from non-perturbative QCD effects, and its mass is very, very low. In fact it's much smaller than all, usually it's much smaller than all the scales in the standard model that we are aware of. It's determined uniquely by the coupling constant of the axion, what is called the decay constant, and for example at the decay constant close to the god scale of 10 to the 17 gv it's the axion Compton wavelength is several kilometers big. So this is a very, very light particle. And from the previous relation you can also see there is a one-to-one relation between the coupling and the mass of the axion and this is the full parameter space. The top axis is the axion decay constant. As you move to the right the axion coupling goes down, the axion coupling to the standard model fields goes down so it gets much harder to look for and at the same time the Compton wavelength goes up. For a large part of its parameter space it is a great dark matter candidate and we've been looking for it for many, many years. The strongest constraint so far comes from astrophysics and in a combination with laboratory searches basically the parameter space below an axion decay constant of 10 to the 9 gv is already excluded. The great news is that there is an experiment currently running in Seattle at the University of Washington that promises to be the first laboratory experiment to probe parameter space that is not currently excluded by astrophysics. This is the ADMX experiment and in the future, in the next decade or so, it will probably cover the blue region that you see up there. So this sets the stage for the axion right now. In this talk I will focus on two different parts as a set of the axion parameter space. The high FA of the axion which corresponds to axion decay constant at the gut scale or above and I will talk about how black holes can be our tool to probe that part of the axion parameter space and the low FA parameter space where the Compton wavelength of the axion is very small between 30 μμ and a few cm and there it can create inter-new types of interactions with forces between matter that can be looked for in the lab using nuclear magnetic resonance. So black holes super radians, the idea of probing the axion with black holes I worked with Sergey Dubovsky several years ago where we understood the dynamics of the effect and more recently with a couple of students, Marcia Bariakhtar and Singlu Huang Singlu gave a talk in this conference actually about the work that we did with the two students we fleshed out the signatures of how this can be looked for in the gravitational wave detectors in fact. The point is that of how black holes can probe the axion is that black holes has been intrinsic size and for astrophysical black holes whose mass can range between a solar mass and 10 to the 10 solar masses this corresponds to sizes between 1 km and 10 to the 10 km. Now if a particle's Compton wavelength is roughly in that region the black holes can probe that part of the parameter space similar to the ADMX experiment. In the ADMX experiment they use electromagnetic cavities whose size is matched to the Compton wavelength of the axion and then the cosmic axion will convert to photons inside those cavities. So we usually divide the black holes into stellar mass black holes the black holes that are products of collapse of stars and supermassive black holes that are believed to be in the center of galaxies and whose mass is very very high it ranges between 10 to the 5 and 10 to the 10 solar masses and they grow by accretion. So for the remainder of the talk I will focus on stellar mass black holes because they are more relevant for the currently developing and soon running gravitational wave detectors but whatever I talk about will also apply to supermassive black holes. The process that probes the QCD axion is called superadians and it's also known by another name also known as the penrose process and it's been known to people that work in general activity since the 60s. So in that process what happens is the following so if you have a rotating black hole there is a region around it called the Ergo region where even light has to rotate. So now because of this process if you take an electromagnetic wave pulse that you see the little orange you have to see this little orange blip here this wave packet if you take it and throw it towards the Ergo region towards the black hole going through the Ergo region but not through the horizon of the black hole there are trajectories for which the electromagnetic wave pulse can come out with higher amplitude than what it came in. So this is a process that extracts energy from the angular momentum from the black hole. Two people wrote this, President Tukolsky wrote this amusing nature paper in 1972 and said ok, let's repeat the same process by surrounding the black hole with a perfect spherical mirror. In that case the electromagnetic wave packet that we... ah, sorry, pressed the wrong button here the electromagnetic wave packet that we prefer we throw it back in every time it goes through the Ergo region its amplitude gets enhanced eventually grown exponentially and at some point the radiation pressure becomes so large that it makes the mirror explode. Of course we cannot create this type of mirror realistically but luckily nature has done this for us in the case of massive bosons. So if you have a massive boson in the theory then this particle, this massive boson can create a bound state with a black hole. In that case its mass, its own mass acts like a mirror confining the particle in the vicinity of the black hole. So its wave function slowly leaks into the Ergo region extracting energy and angular momentum from the black hole. What happens, turns out this processing is more effective when the particle cotton wavelength is comparable to the black hole size and what happens, what you will see happening is if you have such a particle for an astrophysical black hole what you will see happening is the black hole slowly spinning down and at the same time a very dense cloud of particles created around the black hole in a bound orbit. So this cloud is actually very similar to a hydrogen atom because unless you sit very close to the black hole the only potential you see is a 1 over r potential is a Newtonian potential. So you can have in order to describe the dynamics of this cloud and describe its properties, all you have to think about is hydrogen wave functions. So you can define a fine structure constant that is said by the product of G Newton the black hole mass and the axial mass and it's the product, so I would call it alpha and I would be calling alpha in the slides to come you can describe all these bound states by the three quantum numbers that are used to hearing when you talk about hydrogen wave and atomic wave functions the principal quantum number that determines the energy the orbital quantum number that determines angular momentum and the magnetic quantum number that determines the projection of the angular momentum in the z-axis and the formula for the binding energy is quite similar as you would expect compared to that of the hydrogen atom the main difference and what makes the dynamics of the system very rich is the fact that the occupation number of the levels of this atom, this gravitational atom instead of 2 that you have in the case of the hydrogen it can't be 10 to the 75 because instead of fermions we have boson occupying these levels Why am I going back? Sorry. So the, of course not all of these levels can cause superadiance in fact there is a condition for which of the levels can grow, have this exponential growth can grow around the black hole and this is the condition tells you that the total energy of the action bound to that state which is the mass plus the binding energy has to be less than the magnetic quantum number of that state times the quantity omega plus which is basically the angular velocity of the black hole This is a kinematic condition and the best way to understand it Singlu also mentioned this during her talk is that is through another analog of superadiance what is initially was called the inertial motion superadiance or Cherenkov radiation So if you have a particle moving faster than the speed of light on a medium then you have spontaneous and simulated emission of photon radiation Here you still have superuminar motion but now the motion is in the angular direction So the black hole or for example Zeldovich worked this out for a conducting cylinder So the black hole is spinning faster than the angular phase velocity of the wave that gets to be enhanced by superadiance So in fact not even gravity is special to this You can imagine that superadiance happens for any for all types of interactions electromagnetic or other What makes black hole special is that the rate for this effect to occur can be very fast In fact the fastest it can be is when the Compton wavelength is the same order of the black hole size It's 10 to the 7 times the time scale for this to grow 10 to the same time scale for a black hole For a stellar mass black hole this can be as fast as 100 seconds As you move away from the optimal condition as the action becomes too heavy or it's Compton wavelength too short then this time scale grows exponentially or it becomes too light and its Compton wavelength becomes too large it goes like a parallel But the point is though that in principle even though you would think that this time scale is very slow for black holes compared to the infall time the true dynamical evolution time scale for astrophysical black holes is the accretion time rate and the accretion time rate So if you compare 100 seconds to 10 to the 8 years you know you have a lot of time for this effect to happen undisturbed undisturbed and affect the dynamics of the black hole So in order to see how super radiant falls you need several ingredients at least a list of the ingredients So you need to know how fast it happens the rate, you need to know as I said the dynamical evolution time scale for astrophysical black holes is 10 to the 8 years You also need to know what are the interactions of the field that will be doing super radiant Turns out if the interactions are too strong they can actually shut down the effect but for actions which are intrinsically very weakly interacting it can also give rise to very amazing phenomena like the bosonova Basically when the self-interaction energy in the cloud becomes comparable to the gravitational binding energy the gut collapses with an explosion of axioms and gravitational waves but turns out for the parameters astrophysical parameters this may not be relevant for the QCD axion The signals, the main signals observational signatures come from gravitational wave emission and because we are talking about atoms the first thing you would expect to see is lines So you have transitions of axions between two different levels of this atom and the other signature comes from something that's special to axions So axions are their own antiparticle So two axions in the cloud surrounding the black hole can annihilate to a single graviton while the black hole itself while we are in the bound state are more than a momentum and energy are preserved The superactors also So before I go to discuss gravitational waves I would like to discuss bounds that already been placed in the action parameter space by black hole spin observations So this is a plot that shows the spin of the black hole normalised to 1 0 is Schwarz's black holes 1 is an extremal black hole and this is the black hole mass in solar masses Whatever you see in blue would be affected by an axion of this mass roughly of 10 to the minus 11 eV and in fact if such an action were there you shouldn't find any black holes in the blue region The data points that you see are in fact measurements of masses and black hole spins that have been happening for the past 10 years in a more intensified level with much more with much more robustness in the results and as you see already there is one right there in red that shouldn't be there if the action was there So we can use these measurements given the properties of the systems that they were observed at to constrain the action parameter space and this is what we have done So this is the first ever limit of this action again from astrophysical observations at the high FAA region at the K constants above the gut scale So whatever you see here in blue appears to be constrained by black hole spin measurements This is the two sigma exclusion derived from stellar mass black holes as a function of the this axis is the inverse size of the action decay constant and this is the action mass We've tried to do a similar thing for supermassive black holes but there the measurements are not as robust they are not as precise and the other thing we don't know much about the history of supermassive black holes The objects are too few and we cannot exclude the possibility that in the recent past there was a compact object like a black hole or a neutron star that fell in one of them and disrupted the cloud the process of supermassive black holes But bounds are not as exciting as signatures So as I said you should expect gravitational waves emitted from this cloud turns out that levels that have the same angular momentum quantum numbers but different principal quantum numbers just by one unit can be super radiating at similar rates that can be populated at the same time So you should expect there is enhanced rate of action transition between the two levels The radiation that is produced is very monochromatic it's like gravitational wave laser and the frequency for a 10 to the minus 11 eb action is at around 15 hertz which falls in the optimal sensitivity band for advanced LIGO which starts its science run this September So the signal strength is this is a size or the typical size of the strain of gravitational wave that you should expect to see on earth from a black hole that is close to the center of the galaxy and the signal duration for this type of signal lasts between 1 and 100 years it's very sensitive to the parameters of the system But the point is but because actually this duration is very short lived in the lifetime of the black hole So in fact many of the black holes that we observe in our galaxy may have gone through the process of transitions and may not be going through that process of transitions today So there are expected event rates if we try to calculate event rates how many events should you expect to see in advanced LIGO we find something that's not horrible but you have to be lucky to see it and the main reason is the signal strength is smaller but you're only sensitive to black holes that are inside our galaxy So there are always astrophysical uncertainties Here the assumptions we made usually pessimistic, optimistic and realistic assumptions in our error bars but still again as always due to astrophysical ascensors we're cognizing about the factor of 10 or 100 uncertainty in the factor of 100 uncertainty in the range of the expected events The most promising signature of the two is actually annihilations As I said annihilations happen because actions are there on antiparticles Now the energy of the gravitational radiation that's emitted during the process measures in fact the axial mass is actually twice the axial mass with small corrections that have to do with a binding energy of the axial and it appears at higher frequency than transitions The signal duration because this process is more slow is slower than transitions can last for thousands of years So a black hole that has finished the process of the growth of super-adiens can still be emitting the signal because the cloud will be sitting outside of it for a very very long time So it's highly likely that as we see that if you look at again plug-in distributions what is known for the mass distribution the spin distribution of black holes and their distribution is a function of the distance from our galaxy You can estimate now that you may see as many as 10 to the 5 events when advance light goes on which is very exciting Again there are huge uncertainties here and they become even bigger than transitions and the reason is that this part of the action parameter space as you see here is for action this is the expected event as a function of the axial mass The range where advance light goes more sensitive is for very light actions 10 to the minus 12 VV or lighter and in that range the optimal black hole masses are around 30 solar masses and these are black holes that we don't know many things about So to summarize the upcoming advance light go has a great potential to extend what we already know from measurements of spins of black holes due to black hole super-adiens and there are two things that they mentioned first of all the super-adiens effect does not depend on the action abundance it doesn't care if the actions don't matter or not as long as the particle is in the theory this process will happen under the right conditions and also the other thing it doesn't care the only thing it cares about is that the particle is a boson so that you can have the huge occupation numbers of 10 to the 70 10 to the 75 that give rise to these spectacular signatures So these two can be used for the QCT action but also can be used for any type of action for any type of photon for any type of scalar that is in the right mass range and interacts with us, of course, gravitationally which everything does So now I will switch gears and go to much smaller Compton wavelengths Tiny Compton wavelengths compared to kilometer-sized and talk about how actions can mediate interactions in matter Due to the couplings of the axion because the couple to standard model fields if you have a mass it will generate around it an axion field and depending on the type of coupling of the axion it can look like a monopole field or a dipole field So the axion if you have a tiny amount of CP violation of the theory the axion will have a scalar coupling to quarks So that means if you take a rock you can see that it will create one of the R potential around it The yukava this is a yukava form the yukava potential because the range of the axion is finite The coupling of the axion is a very, very small number it can be anywhere this coupling constant between the quarks the yukava is 10 to the minus 21 between 10 to the minus 21 and 10 to the minus 27 just to give you a measure the yukava coupling of the electron to the Higgs is 10 to the minus 6 So this is a tiny, tiny number The other type of interaction the axion can have is a pseudo scalar interaction which is natural to its nature and that coupling generates a dipole potential which now drops like 1 over R squared but for this potential the coupling constant is much larger 10 to the minus 9 for nuclear spins So how do you look for this? Now So the strategy is the following It comes from the observation that if I take a spin a nuclear spin and place it next to a mass of n-n spins all portalized in the same direction there is an interaction energy this spin will feel an interaction energy that's proportional to the gradient of the axion field times the spin and of course it depends on the strength of the reaction to the spin So if you look at it closely actually by dividing and multiplying with the magnetic moment of the axion you can rewrite it as a coupling between the magnetic moment of the fermion and an anomalous magnetic field a magnetic field generated by the axion This magnetic field is quite special, it's nothing like electromagnetic fields first of all it's very different between nuclei nucleons and electrons as you see here it's inversely proportional to the mass So when you divide and multiply it's inversely proportional to the magnetic moment as you see here So the effective magnetic field that you measure is in fact a thousand times bigger for nucleons than it is for electrons and because this is an anomalous magnetic field as I said it doesn't couple to the motion of charges it only couples to spin So for that reason it cannot be screened you cannot use the moment you try to screen ordinary magnetic fields is usually screened by currents on magnetic shielding but here this field will not be screened So we can actually use even these tiny fields we can use some magnetometry to detect it and by precision magnetometry in this case I mean nuclear magnetic resonance So the way NMR works is that if you take a big magnetic field and you have a spin in it the upstate and the downstate orientation of the spin will be split in energy that's proportional to the magnet of the B field So if I apply perturbation to the system that's resonant to the energy splitting between these two levels I can cause I can cause resonant transitions of the spins from pointing up to down and vice versa In the classical picture the way it looks is the following So this is a picture that I stole from Wikipedia So you have a B field and in the classical picture there's a huge magnetic moment and it rotates processes around the B field Now if I apply a small perturbation the perpendicular direction you see that the magnetic moments and its own resonance the magnetic moments want to process around this new perturbation This is the classic analog of the transition between spins up and spins up and down So now the way it works I have a bunch of spins I have a B field setting this external field sets a resonant frequency and I take a mass that oscillates to the resonant frequency of the system and what will happen is is this as the mass oscillates on resonance the spins in the sample will start processing away from the plane and I can pick the signal up the size of the signal that the switch picks up is proportional to the density of spins their magnetic moment and grows to the coherence time of the procession of the spins which is known as the spin relaxation time or T2 Based on this idea we designed an experiment and there is currently an experimental collaboration that's building this experiment but where it's going to be based we don't know yet because the collaborations between Stanford the University of Nevada Indiana and Korea and this is how it looks like this is the instead of vibrating mass we have a rotating mass with teeth the NMR sample is Helium-3 because they have great very long relaxation times and this is the squid pickup loop the effective axion magnetic field that creates this perpendicular oriented in this direction and the sensitivity of the sample for reasonable parameters is 10 to the minus 19 Tesla just to give you a measure the best squids right now are sensitive at the level of 10 to the minus 16 Tesla so in the process of trying to detect the axion we also created a very sensitive magnetometer this is the parameters this is an actual two size drawing of the experiment and these are the parameters who cares the first version of the experiment will be the source mass will be made out of tungsten which is very dense, very heavy unpolarized matter but the next version will also use polarized source masses the bottom line is this though that even the first version of the experiment will have great reach in the axion parameter space so this is the product of the monopole coupling the coupling that couples the axion to our source mass times the coupling of the axion to the spins, the helium free spins as a function of the range of the axion here you see in this grey-blue band this is the action parameter space up here there is this is the parameter space that is actually by combination of astrophysical and experimental bounds and even the first version of the experiment will improve on these bounds compared to what we've done now in the laboratory it can be up to 8 orders of magnitude and eventually by increasing the by increasing the spin density of the sample and the and using a larger NMR sample we'll be able to probe deep in the QCD axion parameter space these are similar plots for nuclear-nuclear interactions if the source mass has a polarization in spin and you see here the first version will be roughly the same it doesn't show here very well but it will be roughly the same comparable to astrophysical bounds but eventually we'll be able to probe the spin-spin interaction of the axion up to the K constant up to a few times 10 to the 10 GV I don't have time to talk about the systematics so they seem to be okay I didn't talk about this but this is also a technique that can be used to look for dark photons but we never sat down to work out what the reach is for that experiment the mathematics are also slightly different and the bottom line is this that it looks like even though right now the parameter space of the QCD axion seems sparse but in the next decade or so there are several experiments both from astrophysics and in the lab that promise to cover almost all of the parameter space other than a little blip right here which actually there are no good ideas for so thank you I stop So in the first part that you were talking about black holes as far as I know in this Penrose process the point of the process is where you get an extremal black hole so you cannot So the Penrose process stops when you get an extremal black hole No, it stops when you have extracted enough spin that you no longer satisfy the super radians condition it's not an extremal black hole for this process I don't know what you mean Are you thinking the process where you actually throw a particle in and then what is the maximum energy you can extract What you mean is irrespective of the details of the dynamics What you say is not true when you have an extremal black hole you can still extract energy you can extract as much spin it happens if you are in the right parameters you will no longer extract spin when you have dropped the angular momentum enough that's it this is where it stops We can discuss it later but Do you need to consider the back reaction of the energy that you have extracted on the dynamics of the black hole Yes, we think it's very small The bottom line is that you can see from the fact that the annihilation process which is in fact in the non-linear process what you talk about is non-linearities in fact we think for most of the parameter space is not an issue that's the bottom line in fact if you want to look at all the energy levels and do them properly when you do numerical all full numerical simulations of the thing you have to take them into account but we don't think there's going to be a problem in stopping the effect So we have time for one quick question here Another question for the super radians on black holes for the gravitational wave signals in that regime Do you know are there any significant astrophysical backgrounds So actually I don't think there are in fact there's a signature though one mimic this this is mountains and neutron stars so because neutron stars are are rotating with a very constant speed so the signal they produce the anisotropies of a neutron star would produce is very monochromatic but there are several things that can I mean first for turns out so neutron stars usually spin down this would look like spinning up because as the cloud empties out you are less bound so as you are less bound the energy of the emitted radiation because it's twice the axiomus minus the binding energy so you see it spinning up the other thing is that the amplitude modulates its time but that's hard to see given though the number of so the event rates that we estimate for this signal is much higher than the event rates that they know for neutron stars so the other thing the characteristic of the signal is because it's roughly the energy depending on the binding energy is roughly there is only modulation of 10% at most around the mass of the axiom so what you would see is a concentration of lines around the mass of the axiom I mean for neutron stars there is no reason why the lines all appear at the same frequency