 Okay, we're live. Okay Hello, everybody. Welcome to the Latin American women Arab physics Camilo Garcia Selly from Desi in Hamburg and I'll be your host today this time We have a very interesting colloquium by Andreas Ringwald who will tell us about the quest for the axion He's one of the authors of the review of axions for the particle data group And it's one of the leaders of the artist's collaboration whose main goal is the search for axion like particles Andreas Ringwald obtained his PhD at the University of Heidelberg in Germany and After some research positions Desi and at CERN he became staff scientists here at Desi and Okay, so before we start the talk, I would like to encourage you to ask questions You can do that by typing them in the designated box in YouTube Which you can find on the right hand side of your screen at the end of the colloquium. I read the questions for everyone and Okay, so thanks Andreas Please go ahead with your presentations No, thank you very much for the invitation. So I'm doing this with pleasure So I'm talking about the quest for the axion and we start right away so So we all have appreciating the Success the overall access for the standard model which describes the interactions of all the known particles with a remarkable accuracy Which I have here for example Is here summarized by by the comparison of the standard model total production cross-section measurements of the atlas a collaboration at LHC Comparison of them their measurements with the theory with the theory in gray and you see I mean Where where where there are really very good data so that the data the data look are exactly on the on the on on the theoretical predictions and and so it's and and there are Many many other examples there are there are few places where the standard model might be might be Endangered, but but there are typically maybe two two or three sigma Things for example in B physics. There is at the moment. They're in flavor physics There are some some hints of things but Overall the standard model at the moment describes the interaction of all the known particles with remarkable accuracy But as soon as we as we go out and look into astrophysics or into in cosmology Then then the standard model Doesn't seem to fit. So there are observations in particle physics astrophysics and cosmology Which strongly suggest physics beyond the standard model. So there is one in the neutrino masses and mixing Which are not contained directly in the standard model There is the dark matter in the universe which makes for from the from the from the total amount of matter in your universe more than 84 or around 85% are not of the stuff From from the standard model there is the bio and asymmetry Of the universe which which cannot be explained from first principles within the standard model There is there is the question the question how we should describe inflation the very like Exponential expansion of the universe at the early stage before the so-called hot Big Bang started There is grand unification, which is only there's only a hint from the evolution of the couplings but but the hints so so so Within the within the standard model these couplings do not meet but maybe there's some physics beyond the standard model such that That that that these couplings meet and give grant unification and there are naturalness problems So like the hierarchy problem So the question why the Higgs the Higgs mass or the electry scale is so much Be smaller than the than the Planck scale or there's the strong strong CP problem Which are naturalist problems which are not not not an observation in particle physics Which strongly suggests physics beyond the standard model, but maybe with this one could understand these problems or puzzles better if one has Introduces physics beyond the standard model and I will of course we are doing axiom physics So I'm concentrating on axioms. So I I concentrate here now And at the beginning I concentrate on the on the strong CP problem And we will later see maybe one can also solve other problems with the solution of the strong CP problem So for the to go into the strong CP problem We have to understand the notion of the theta term in QCD now already very early after the Invention or the discovery of quantum gromo dynamics or the proposal of the formulation of quantum gromo dynamics It was it was found that that the most general gauge invariant Lagrangian of QCD on on the renormalizable level does not contain only the gauge kinetic terms and and and and and and and the gauge invariant Or gauge covariant terms for for the thought of the Kinetic terms of the quarks of the quarks, but there is also a third term Which in which looks very so from the gauge field content. It looks very much like like the the gauge Kinetic term There's only there's this little tilde which means that that it's a Gluonik field strengths but but Contracted with a four-dimensional epsilon tensor. This is the so-called dual dual field strengths and and now So it was due to these gentlemen here like below in Edel Gertrude, Kellan, Ross and and Chakeef and Revy due to these to these people they they they found that their that that this term On the non-perturbative level cannot be neglected in QCD So why so so why this term at the beginning wasn't wasn't considered It's just because you can write this term this G G dual term You can write as a total derivative of a of a current the so-called churn simons current and so so normally you would say so if the fields rapidly decay at infinity you cannot neglect such such such term because you because it will be a surface term in the in the in the in the in the action and And you so you don't need to consider it if you derive for example the Feynman rules and the rules for perturbative QCD however So so so it was noted by this by this gentleman that that this term cannot be neglected because because in a non-abillion-gauge theory You you cannot neglect so to say even if the fields rapidly decay at infinity You cannot neglect that because there will be a contribution to the to the space-time integral of this of of of this quantity that this the space-time integral of This quantity alpha s of 8p 8 pi of chi chi dual will give an integer number Which is the so-called differences in churn simons number or the ponderi again index so it's it's a top It's will give a topologically invariant so you cannot so in in general There are so so these these fields Cannot or such fields cannot be completely neglected and the strengths of this term then Is is is now is is now measured by a by a by a Another by a by a new Parameter the theta angle It's an angle because because as I said so so this so this gives rise to an integer So it's so this will be so the space-time integral so in fact So this so this this this quantity Will have this kind of period Introduce this kind of periodicity and therefore this theta can only range from minus pi to pi say so this means now that that the parameters of Qcd are not only the strong coupling alpha s the quark masses here in this in in this in this M But there is a third another parameter. This is so-called theta angle Now what what can be the observable features of this theta angle? Now There is the top a lot. So this term this topological theta term chi chi dual if you write it in field strengths It's something like like the the chromo electric field strengths dotted into the Chromomagnetic field strengths and now you can easily convince yourself that this E dot B violates the parity transformation parity transformation symmetry and the time reversal symmetry and thus it violates CP because of the of the CPT theorem and and the and the most and the most sent now now the most sensitive probe of P and T violation in flavor conserving interactions Because this this should be now a flavor conserving interaction unlike CP violation in in from from weak interactions So this is flavored. These are is is CP violation in flavor changing interactions So this will be the electric dipole moment of the neutral neutron because the electrolyte dipole moment of the neutron will violate P and T and thus CP now so in order to Estimate so it's so this now to calculate the prediction of QCD for the for the electric dipole moment of the neutron You need now of course something like you need some non-perturbative methods So this has been calculated in in chiral effective Theory and it has also been calculated by using QCD some rules. However, you can also Very easily so so so get a get a Rule of thumb or or some estimate how big this should be so it should be So it should be proportional, of course, it should be a dipole moment So it should be should have the the units of e times centimeter So they so it should be proportional to one over a hatronic scale Now first you would expect it goes like one over the the mass of the neutron to turn times theta times e however we know so Because of because of the because of the chiral anomaly in in the theory or chiral water identities We know that that that that that the effect should be zero if one of the quark masses have zero mass And therefore they have it's so that it's so it's so this process should go Proportional to the reduced quark mass so to say so if you have a if you are in now in in you assume now that You have just the two lightest flavors You and then it should be proportion to m u times md divided by a mu plus md So this is the reduced quark mass and now in order to do the dimensions, right? It should have a one or mn squared. So so so the naive Expectation would be 10 to the minus 15 theta e centimeter, but because of this factor you get One or two orders of magnitude suppression in addition So the expectation would be six times 10 to the minus 17 theta e centimeter for this dipole moment of the of the Neutral however the experiment gives A 2.9 times an upper bound of 2.9 times 10 to the minus 26 e centimeter So you you you infer from that that this the absolute value of theta should be less than 10 to the minus 9 and So this is the strong CP problem So you want to you would like to to to understand why this theta is Is has such a small value? now So already so it was it is an observation that that that on which so the Axionic solution of the strong CP problem is is based is it was was an observation by Petrion Quinn namely So they they they use the fact that That the vacuum energy in QCD if you just now consider QCD as it is So so after Lagrange of QCD and you calculate the vacuum energy of QCD as a function of this theta Then you find that this has a localized minimum at theta equal to 0 So and that it has a localized mean minimum at theta equal to 0 You can all of this has already been shown by by Waffa and Witten on very general arguments But but the explicit expression for for the vacuum energy of QCD as a function of theta can be inferred from the fact that That that the so to say that that the low that the low energy theory of QCD is the chiral effective theory And one can in principle one you can calculate So the vacuum energy of QCD then by you by calculating the vacuum energy of of of the chiral of the vacuum energy of the trial effective theory and And here I have given the expression which which which people like the back here and when it's yeah No found and there is a nice paper by Lord we're in Smilka where this is all derived So you see so then you have a you have a you have a potential which is You have a potential which which which is periodic which is periodic in in in theta and it has a has a localized minimum at at zero and and and so to say and and therefore and and Therefore if theta were a dynamical field Then it's vacuum expectation value would be zero just because of because of this fact So you have now you have some high to find a theory Which gives that low energy Dynamical field which looks exactly like giving rise to a to a to a dynamical theta term Here just as a final explanation here the sigma is nothing else than the quark condensate and Mu and md are the quark masses. So but this can you can infer you get can get directly as the as the people Divakia and Venetian Venetian I have shown you can get directly get from from the form of viral effective field theory now so So so what is now then the the simple idea of patching green was now taken now in in simple words If you read the paper, it's much more complicated But but because it does it in a special realization But they are now from a from now from from from from a modern perspective If you would say just you add to the standard model an angular field So a scalar field theta a of x Which which which looks like a of x like a dimension mass dimension one field a of x a normal scalar field divided by f a which f a is a dimension full constant has Units of dimension of of mass and if this field respects a Shift symmetry that if theta a of x goes to theta a of x plus constant broken only by by a coupling to the topological Density to this cheat sheet dual like a like a spacetime dependent theta term Then if you have such a such such a field then of course you can eliminate the theta the constant theta term of Qcd just by a shift and because you have said I mean it should have a shift symmetry then then then so So yeah, you have animated this term and then of course the effective potential of this field of this shifted field Will have will be exactly the Equal to the vacuum energy of of Qcd as a function of theta And this will predict then the vanishing best So P and T and CP are conserved in the back in in in the vacuum in the Qcd vacuum Now and of course you will have a particle excitation around the zero You can you can directly read off from that the mass just by the second derivative of the of this of this potential now with respect to to theta and And and so the mass will be given by by by this combination and and and you can relate the Vacuum the condensate the quark condensates you can relate to the pion mass and and and to the to the Pion decay constant like that And so you see you will get so if you insert numbers for the pion mass Pion decay constant and for the quark masses you will get something like 6 Millielectron volt if this constant f a which which is called the the axiom decay constant like the like f pi is the pion decay constant If this is of the order 10 to the 9 gv and the strengths of the interactions with the standard model of this particle will be controlled by this decay constant f a Now you can embed so so now we have just introduced this this this field this So we recall this angular field theta which which which which takes value between minus pi and plus pi Now we how we can get this from a uv completion It's very simple So these are so-called patch egg win extension of the standard model So you start from us from a singlet complex from a singlet complex scale of sigma Which features a global u1 patch egg win symmetry To the standard model and you assume that it has this kind of Mexican head potential such that this u1 patch egg win symmetry is broken by the web Of this of this sigma field Now of course if you now expand this sigma field Around this web Then you will get excitations in the direction So to say in the radial direction Which will have large masses proportional to the vacuum expectation value Of of the of this of this field And but you will also have so in in in the in the angular In the angular direction So the the excitation of the face So to say in in in this angular direction will have a zero mass So it will be a massless goldstone boson just from the from this breaking of this symmetry Now this is still not the axiom because the axiom should should behave like a theta term So it should have the coupling to the gg dual. So this This combination a of x or vpq should be Should should now have this in this interaction. How you you get that is if the standard model or extra colored fermions in the standard model Or extra colored fermions carry patch egg win charges So charges under this u1 such that this u1 patch egg win is broken Due to the gluonic triangle anomaly So if if you if you if you calculate the divergence of this u1 patch egg wins current Then it should not be should not be zero But it it should be violated due to this triangle anomaly Where where you have again this alpha s over 8 patch gg dual which is exactly the top The the topological charge density and there's an there's a number n which essentially counts the number of Counts the number of of of quarks or colored fermions in this loop so if you if if If this is the case if you have If if the fermion content of the theory is such And and the patch egg win charge assignment is such that that you have this anomalous violation of the of the Of the of this patch egg win Current then the low energy effective field theory at energies above lambda qcd But below below the below the electric Scale which is assumed now all always to be much much Smaller than the patch egg win symmetry scale breaking scale. So in this case the this This afx or vpq this c or or or or this There is a there is a there is a a theta So then and then the field theta afx divided by f a where where f a is now given not just by vpq but vpq divided by this by this num this n this factor from the gluonic triangle anomaly Then this theta Field will be so to say the the angular axiom field and Exactly as a as a spacetime dependent theta parameter and solve the strong cp problem And so so you you see this is the how you embed Embed the axiom solution to the strong cp problem into a uv completion, which is renormalizable Now just to to to to to end this So the the low energy the the low energy couplings the axiom couplings to the standard model at energies below the The qcd scale can finally be obtained again by using the chiral chiral effective theory So as I already said the axiom mass So if you if you now integrate so to say this this chi chi dual term you integrate out the gluons by using By matching the theory to a to to a chiral effective theory Then then you can read off the the axiom mass and also the higher the a to the fourth term And so on all these terms are directly given by the by the by the by this expression for the for the for the vacuum energy of of of qcd But but the mass term will be the most essential first of all And and and this mass in principle can also can can be also be calculated beyond the leading order chiral perturbation theory So this has been done by recently by by by really the cortona edal and velodoro and also by led by by led in next to leading order chiral perturbation theory or by borsani edal by by ledges By ledges with similar errors So so so the axiom mass if you know the the the axiom decay constant is now very Is is determined by by up to an error of of of a percent or 10 percent so which is really which is really Impressive, but of course this is the this is the unknown the unknown Parameter in the game this f a And all the couplings to the standard model partings for example to the photons Or to or to electrons or nuclei uh are are Are suppressed By by the by this axiom decay constant So if this is very If this is very large, then the axiom is invisible It's not really invisible because we will see that it will be it can be dark matter And it will always decay into two photons. It's not completely invisible, but it's uh, it has very weak interactions with the with the standard model and for example the photon coupling is then related to to to There's a there's one piece in the photon coupling which arises for mixing of the axiom with the pion Which is determined again by by by the chiral effective field theory And there's one piece e over n where e is the is the electric is the the electromagnetic anomaly Contribution and n was the was the color Anomaly contribution This is the model dependent factor and also in the nuclear nucleon couplings There are there is a model independent factor And there are factors which depend on the on essentially on the pentagon charges of the original of the of the of the uv completion And and the electron coupling is very model dependent So so if if this extra pheromones have have have no electric charge then then On the three level level with no electric coupling and so on So this is now this was now in a nutshell the axiom solution of the strong cp problem and and the And the and the predictions from QCD for the low energy properties of the axiom which are very much fixed So there's no uncertainty in the mass And and and in the others there are model dependent factors and model unindependent factors Now we we turn to axiom dark matter so Because the interesting thing about the axiom is it it does not only solve the strong cp problem But it also is a very well motivated dark matter candidate In fact, uh, it in for for in in certain scenarios they It is inevitably reduced and so you cannot you cannot So so so dark matter can can even give a very strong constraints on the on the existence of the axiom now, uh So now we are assuming that the axiom that is a decay constant or the vpq scale that is very large And therefore the axiom is very weakly interacting and so can be a Uh, uh, a very long lift particle So which which would mean It can be dark matter and now we we assume so, uh So now now we assume that in the early universe When the temperature falls below the below the paycheck win symmetry scale scale Which are below the critical temperature of the paycheck win Symmetry transition Where the paycheck wins symmetry goes from an unbroken Phase into a broken into a broken phase Uh Then there the axiom comes into the axiom starts to to to to come into the play And therefore and and shortly after this paycheck win phase transition the axiom will take Random initial values in causally connected domains in the universe So in each causally connected domain, it will it will it will have uh, it will have a random initial values Now, uh later Then when and and and it will be frozen at these random initial values because because if the Hubble expansion if if if the if the Hubble expansion is very rapid so in the early universe Uh, so the the Hubble drag term in the in the in the evolution equation of a scalar field Will fix the value of the scalar field at the initial value And so here is here we we show the generic evolution time evolution or one over temperature evolution Of of the of the axiom field or of of this theta field And and and you you see as long as the as the Hubble expansion rate Is is uh much larger than the than the mass of the axiom And this is illustrated here. So so the the Hubble the Hubble expansion rate drops If you go to to later energies, uh, and and and and the axiom mass as we will show the axiom mass turns on Because the axiom mass will be will will be will be proportional to the Will behave As as we as I will show A bit later will behave Will be proportional to the square root of the topological sustainability in qcd And and it will it will slowly turn out on around At at at low temperatures around the qcd phase transition and at some point The the Hubble expansion rate And and and the axiom mass will be of the same order and and then and then the So so then the the axiom field will start to feel the drag The the the drag towards the cp conserving minimum and will start to oscillate around this minimum So and then you have these these these oscillations around around zero field so uh And if if if you if you look if you look, uh, so to say the equation of state for that to calculate the the the Pressure of the axon field divided by the energy density of the axon field. This will behave Exactly like cold dark matter. So it will be pa or rho a will be will be, uh Very small and and this means that you that that this this oscillating Scale of this oscillating scalar field will behave, uh, like Like a coherent state of of many, uh, of of many, uh Axial of of many non relativistic axions and and and so Uh, so you will you will create, uh, and and inevitably Axiom dark matter via this via this mechanism So very recently so there has been there have been Computational progress in order to to for example to to predict Within the standard model the the Hubble expansion the the the the Hubble expansion rate As a function of temperature and also the axon mass as a function of temperature So and for for that, uh, one one needs input from the lattice or from non-perturbative calculations For example, the Hubble expansion rate is determined if you know the equation of state Uh, uh, if you know the equation of state, uh, and so in particular the the the number of relativistic degrees of freedom of of of of And of of the entropy degrees of freedom and of the heat capacity degrees of freedom And uh, so this has been determined to a very good accuracy now around the relevant temperatures around 100 Mev to to one gv or so which is the relevant scale for for for looking into the axon dark matter And the topological susceptibility Because the temperature dependent axon mass is given by the square root of the topological susceptibility Incusity divided f a so this is nothing else So to say that then the two-point function of the topological charge density. So so this chi chi dual Chi chi dual correlators And and this has also been determined to a very high accuracy recently on the lattice in this In this paper above And uh, before we had for this we had only a dilute instant on gas Estimates So, uh Now if you if you if you take all this together then you have to to decide Then you have then you have to to discriminate two very important scenarios For axon dark matter. There's one is the pre inflationary petric win symmetry breaking scenario If the petric win symmetry is broken before or during inflation and not restored afterwards Then of course the the the axon cold dark matter density depends on the single initial value In the in the domain which becomes later our observable universe and uh And f a so we have so so so the so the uh, so the uh prediction of the of the relative, uh Of the of the of the relative energy density in in uh axon dark matter coming from this vacuum realignment mechanism To to the to the critical density in the universe Is is uh is given by by this by this relation. It depends on f a Power like to 1.165. This is essentially given This this this index essentially comes from the from the slope of this temperature dependence And uh, and it's proportional to theta i i squared. So at least so this this is valid As long as f a is larger than 10 to the 11 gv or so And you see so you see so if for theta i Initial value of order 1 then you then then you need Axon decay constant of the order of 10 to the 12 gv in order to reproduce the food the dark matter Here is the here's the the the the general The the the the general result for the pre inflationary scenario Of course, so you can say you can say there is no not really a prediction. So there in this case So you you can always So if you are on this line, then 100 of the dark matter is made by axons so, uh So if you prefer now an axon decay constant out of the order of the gut scale Then you read off from this curve. You would need an initial Alignment angle of of the order of few times 10 to the minus 3 in order to explain the universe everything above here would be would be Overdense and everything below would be would be a subdominant So axons would be subdominant dark matter in this pre inflationary scenario Importantly in this pre inflationary scenario, which is less predictive or is not so predictive as you said importantly in this in this Uh case you will get an upper bound on the scale of inflation from iso curvature fluctuations Which are produced by the axon during inflation and not erased afterwards So but but there in in this case you're still you have an you have an andropic axon window Which is where where where where essentially you can always so where Where the axon can be 100 percent of dark matter without Without contradicting the iso curvature fluctuations and so on Now we come to the post inflation of petric win symmetry breaking scenario so in this case if if if if the if the petric win symmetry is restored after reheating after inflation then We have to average over the random initial axon field values because now the present universe consists of many of of many patches so to say where which have which have different initial conditions At petric win symmetry breaking so to say and so In so if you do this averaging you find this result From using using the latest results on on the Hubble Hubble on the equation of state and of the topological sustainability so you find This result for the contribution from from the vacuum realignment mechanism So there is of course now a first consequence of that is so If you now Would say so this should not be larger This contribution should not be larger than you observed Dark matter abundance which is point one two Then you find from that an an upper limit on f a or or correspondingly a lower limit on the mass of the axon which should be larger than 28 micro or say 30 micro electron volt So So this this is the first consequence of that so in in the post inflation scenario You have a lower limit on the axon mass or an upper limit on the on the decay constant However, in this case So when when we did this average of a random initial axon field values We were not taking into account that there are of course boundaries between these domains of of of initially fixed values of the die and in in in these boundaries or There can be topological defects And so and so notably there can be strings axion axion strings And there can be domain walls between between this between these domains and and here and and in order to and The collapse of of the network of topological defects consisting of strings and domain walls will also lead to to axion to to axions which also And therefore also contribute to the To the dark matter abundance of axions and in order to to to get Their contribution one needs to field theoretical simulations to determine their contribution to dark matter And so this is a very active field at the moment So So there is so here i'm i'm reporting now Of results based on the on the on the simulation of a japanese group If you take these their field theoretic letter simulations and and take the update to the latest Determinations of the topological sustainability and so on you find that the cold dark matter would be explained In this in the scenarios with this with n this n equal to one Which now i can can also call this n this was the the factor from the From the from the anomaly But but here it turns out this is also the so-called domain wall number This is the uh, and so for domain wall number one You you uh, you find that the cold dark matter is explained For for axons in the mass range between 60 and 150 microelectron volts This is still So and and and this is only This is this is not so so this arrow just takes so to say the The limits which they found from from which the japanese found in there from their lattice simulations, but But they could do the the the lattice simulation only at very at unrealistic values of the string tension and uh recently Uh Claire and gaimur from damstadt. They they they have found a Or developed a new simulation technique, which was designed to work directly at high string tension And they they they gave a very narrow result for the for the axon mass in this n equal to one post inflationary Patrick wins symmetry breaking scenario of 26.2 plus minus 3.4 microelectron volts They are still So so uh At the moment there's of course, there's there's some tension with this with this Between these results. However, uh, uh There are further simulations ongoing as we speak by other groups Which which try to clarify this issue and to to see how Rare it is. I mean if you take this at face value, then you would say Okay The strings and the domain walls. They don't do any Contribution to the dark matter and everything comes from the virtual realignment mechanism Whereas in this case you would say, I mean There's at least half of the dark matter arises from the from the collapse of this string wall networks. So there's So this this still has to be clarified For n larger than one. So so if this domain wall number is larger than one Then there is there is no there is a domain wall problem because then there are topological obstructions that that that these topological defects Can decay. However Nobody assumes. So I mean, uh, that the Patrick wins symmetry is is completely exact because everybody uh, so We expect that the Patrick wins symmetry will be explicitly broken at the end For example by blank suppressed operators and uh, and if you if you somehow find a way that that that the blank suppressed operators, uh, they start only at at at Dimension nine or 10 uh Then then Then so to say then there is enough symmetry breaking that the that the that the top top That the topological defects decay Recently still recently fast to produce to to not to be excluded or Not to be excluded cosmologically but and and and but still the effects are Not so uh, so the symmetry breaking effects They don't spoil the solution of the of the strong cp problem by by by spoiling the the the So by by moving the minimum of the of the potential away from zero so to say And if so if if you take this then you'll find something that that that that that that axiom That that that an axiom mass between 0.6 milli electron volt and or 100 milli electron volt can be can be Explain for the whole dark matter In order to you can realize this that that the lower dimension are forbidden Uh, if if you postulate it, uh, if you postulate a discrete symmetry And By the way, so an an DFS set axiom, which has domain wall number equal to six in this mass range Would explain excessive cell energy losses, which I will show in a Very soon now so here is uh here is so to say that the the So I wanted to to so that the dark matter axiom mass can span Really a very huge range So in the case that that the that the axiom in the pre inflationary scenario the axiom mass can be can can be between say 10 to the minus 12 electron volt up to up to a milli electron volt And in in in a huge range You need of course some tuning in theta i in order that that that it can be 100 percent of dark matter There is one region where it can be dominant or sub dominant dark matter And then you can again with with the tuning you can explain the the the the uh dark matter in the universe There is one region which is which is so to say in this case preferred Uh And there's the post inflationary scenario now if the domain wall number is equal to one you have a quite Small region which is which is allowed and where axiom can be 100 percent of dark matter And in the and if you have domain wall number larger than one for example here six for the DFS set axiom model You would be in even at at higher masses now very importantly In in recent in the recent years there has been have been a pro proposal of of of axiom dark matter experiment Uh, which which go over all the all all these uh mass ranges So for the for the for the lowest For the lowest masses for katsky laxions There is this kasper proposal Which want to use mr nuclear magnetic resonance techniques to to really to to measure directly the oscillating dipole moments Oscillating due to to to to the dark matter. Uh, so you have Essentially an oscillating theta term Which leads to oscillating dipole moments and and this experiment wants to to directly measure these dipole moments There is apra kadabra, which is which is superconducting current ring experiment Then at in in the region where where where you have the the least fine-tuning for the pre inflationary scenario There is the the admx experiment and the haystack experiments which use uh microwave cavities And these experiments they are They are they are active. They are working and producing data as we as we speak and sure searching for the axiom And there are other proposals like kaltask in korea in south korea We will want also to build new cavities in this range then in in in the range in in the range, which is which which is which is now Most motivated in a post inflationary scenario. There are new experiments Proposed like mad max and all fours and quarks mad max Is is is is a magnetic dish experiment based on the idea we developed First with with some others here in hamburg And and which was then then boosted by by by chavi redondo and others in then later in munich to to to a die die electric Resonator experiment you had the latin american seminar about that by chavi Self and and there is the the brass experiment Which which which Here in hamburg is it's been it's been built using just a huge or proposing then a huge dish experiment without this Without these cavities Interestingly enough also the mad so so the mad max collaboration has now has now decided to if so so to to take Daisy in hamburg as a site to build the experiment. So I'm really looking forward to to to to this now As I as I promise there are some astrophysical hints for axion and alps Maybe there are some excessive stellar energy losses which So first of all, I should start this by Emphasizing then that the evolution of stars for so starting from the from a main sequence over over the red giant branch To to the to the to the to a helium burnium star and then and then to to to the white dwarf Is very sensitive to non standard model energy losses. So energy losses beyond the the loss by by emission of neutrinos, for example and and So so this has always been used to to put limits on on on on on axions or on axon like particles just by just that that that this that The evolution of stars would be changed if there would be too much energy loss and But nowadays it's it seems that practically every stellar system Seems to be cooling faster than predicted by models. So this is for this is for for helium burning stars for red giants for white dwarfs And so on for neutrinos stars. So they are they are all all Cooling faster than predicted by models and it's a natural effect that these excessive energy losses of how the helium burning stars red giants and white dwarfs Uh, if you take them all together can be explained at one stroke by the production of an axon or axon like particles miscouplings to photons and electrons So for so here is the coupling of the photon. So we would say it's given by c a gamma alpha 2 by f a So by coupling of photons or the coupling to electrons so electron Bremstrahlung of axions can lead to the to to to uh to excessive Or extra stellar energy losses and if you take all the datas together which we which we saw here Then we can fit everything together by an axon like particle So the best fit would be an an axon or axon like particle with a mass less than Kilo electron volt or so the temperature in the inside of these stars And And so so so it should now should have an electron coupling of the order of of 10 to the minus 13 and and and the photon coupling of the order of of of 10 to the minus 11 gv to the minus one And and you see so at least in this direction So so this this is more than it's nearly three six So the best fit is nearly three sigma away from zero at least for the electron coupling So it's quite remarkable that that that this works and here I have also plotted in two two lines These are the the the sensitivity curves for the protected sensitivities In the photon coupling of alps two, which is a light shine through a wall experiment and of yakso, which is a helioscope Of course, we have to assume here in both cases So the mass should be much less than kev and for alps two Alps two is not sensitive at kev Not even it's only sensitive At at energies below 10 to the minus four electron volt. So we have to keep this in mind So what is alps two? Alps two is a light shine through a wall experiment as I said and it's as as as we speak it's it's being constructed or built in the In in here are north in one in one of the of the straight sections of the previous here are collider and And yakso is a helioscope. So it's it's a magnet pointed towards to to also the the the sun And and this is the successor of the cernaxi on solar telescope and also Similar to met max also yakso the yakso collaboration has has has decided that if it's built if it's constructed Then the then the the site will be at desi Now here I have just We just see so that this energy this excessive energy losses can be explained and once so By the production of an axiom And here it's the it's it's it's the example of a dfs z axiom the dfs z axiom is is is characterized by two by two quantities. So It's of course f a and the domain wall number six in this case as I said and it's time the tangents beta which is the the Because the the dfs z axiom model is based on a two Higgs doublet model it has two And this is the this is the ratio of the Higgs which gives masses to the uptype quarks divided by the Higgs by the backfiring expectation of the Higgs which gives rises to rise to the Down quark masses And here you see here is the best fit the best fit of for for for for the explanation of these of these things is of this stellar energy losses Is in the region which can be probed by yakso and And partly so so so this because this best fit the one sigma region extends here along all these lines Can also be partly probed by ariatne where ariatne is a fifth force experiment using again nuclear magnetic resonance techniques And and and would be sensitive from the lower mass side So finally I will turn I will switch gears and now so we have I have I told you that that the axiom can solve the strong cp problem It can be dark matter Now I want just to emphasize that the axiom even or the suction now that's what to say the the the the radial the the radial field The radial part of the patching wind field can be If mixed with the with the hicks can be the successful a viable inflat one candidate So you use now one field to solve them all the strong cp dark matter and inflation So this is based on so so So as we have shown Guillermo biesteros carlos tamarit cabi redondo and myself We have shown that the mixer of the of the suction so the so to say that the radial part of the of the patching wind field With the hicks modulus is a viable inflat one candidate if one takes into account It's possible non-minimal coupling to gravity. So so which which is this kind of terms size star sigma star six sigma star r And uh, which is which will be in any case, even if you set it to zero at some scale It will be generated By radiative corrections in any case So what you need if to get viable inflation To get this as a viable inflat one candidate You you need that this psi sigma Should be of the order of two times ten to the five Times square root of lambda sigma where lambda sigma so this psi sigma is this non-minimal Parameter and lambda sigma is the quartic coupling of the patching wind field And all this psi sigma should be larger than psi Hicks the non-minimal coupling of the hicks and moreover the the the uh The the hicks Portal coupling should be less than zero in this case You you you find in the in the in the einstein frame for the the the potential scalar potential in the einstein frame as a function of the of the hicks and of the Of of the of the of the row and and of the radial direction You find it looks looks like that at a very large field values at field values of the order of m plank You find you find if if if these conditions are met you find A rich so to say or a valley a valley along a direction very near to the to the succion direction And and and and and a rich along the hicks direction So so uh so very natural you can realize inflation along for the field for the for field For for slow roll along this One of these valley directions A good thing about this is a very predictive theory Because it has a very predictive reheating so now Uh for for f a of the petrific winds symmetry breaking scale Less than 10 to the 16 gv the petrific winds symmetry is restored after inflation already in the preheating stage So you you you calculate now these oscillations of the Of the of the of this of this background field after after uh after inflations And and then so to say the fluctuations in in the direction of the of the inflaton and also the permedicular to the inflatons They are very quickly Reaching the the the the same values and the petrific winds symmetry is restored So this means you are in a very predictive post inflationary scenario the dark metro axion mass Will be larger than 30 micro electron volt or so And uh so this is one of the predictions of this theory immediately And then moreover the Higgs component of the inflaton Will allow for the production of standard model gauge bosons and the results in a in a quite large reheating temperature of the order of 10 to the 10 gv Which means then also that the also the axioms so to say the the thermal axions produced in the early universe They will be thermalized and you will get you will get you will get you will get after after the coupling of this You will get an axion dark radiation prediction of the order of 0.0 0.03 Which can be detected by next generation of of cmb experiments Furthermore the expansion in the thermal history of the universe is very much predicted because i mean you can you so so we can We can predict so to say the so the the the the expansion the expansion theory And and and calculate so so this reheating takes place very to you get very rapidly from a from a from a from an inflationary phase Into a radiation dominated phase so to say And therefore the number of e-falls from the time a coping co-moving scale Leaves the horizon until the end of inflation is predicted And this is has a very important consequence namely that you get a very sharp prediction of the of the tensor to scalar ratio versus versus R versus the the the spectral Index and so so you get this tiny band is the prediction of of this succion hicks inflation And and this prediction here is is now here it's compared to the present bounds From from cmb tt and and other Other Cosmology cmb data And and now if you now consider and this The the the protected sensitivity of the upcoming cmb experiment for example here cmb stage four You see that this this sharp prediction can really be probed within that this the the the the upcoming decade of of uh cmb experiments which i find very exciting Now and so this brought us to the idea to to to unify now even more the To unify inflation dark matter and the seesaw. It's a pet shake wind field So to get one smash to rule them all so not only to introduce now the The the the axiom and for example here like in our k k s v set type Heavy quark to get the anomaly so but we introduce also right-handed neutrinos and Which get them their mariana masses also through the pet shake wind weff then you solve All the problems which i mentioned in the in the very beginning in the dark the actual nearly all the problems in one in one smash So then you solve the the the strong cp problem dark matter inflation neutrino masses and mixing and biogenesis via Laptogenesis so this is Very nice and this gives you a complete and consistent history of the universe from inflation to now And it's very much much testable in the next generation of axiom dark matter experiments and of cmb Experiments So this brings me now to my summary So i find pet shake winds extensions of the standard model very attractive because the axiom solves the strong cp problem The axiom is a dark matter candidate This requires then a lower bound on f a or an upper bound on m a The suction hicks is an inflaton candidate and and a pet shake winds Standard model pet shake wind extension of the standard model with suction hicks inflation It's very predictive and thus experimental testable in the near future by cmb observations and axiom dark matter experiments I think we should just stay tuned and let's see So At least this theory can be falsified within my hopefully My lifetime So thank you very much Okay Thank you very much for the very comprehensive and interesting talk I'm really excited to understand to learn about all these things. So I will open The possibility to ask questions. So is are there questions here? Okay, luka Please go ahead ask your question. You're good. Hi. So first of all, thanks It was really great Um, so just a quick question on the last thing you said about um inflation in smash um You you saw the the the parameter space ns versus r Yeah and your prediction the What runs on the curve is the the um And the number of E-fold That's the only parameter In principle. So we we predict so to say we predict the number of e-folds. Yeah, yeah, exactly because You see but you saw also. I mean you so so in principle So what what you saw this you saw this this equal lines of xi sigma equal to 1 10 to the minus 1 10 to the minus 2 and so on yeah and this So so you you see in in in a sense. So yeah I mean if if now if if they would now uh, so to say if if they would now measure this Exactly here this point. Yeah Okay, then then you could say, okay this size this size sigma must in our model So if your interpret is in our model size sigma should be of the between Between say here 9 times 10 to the minus 1 and 0.9 or something like that So and you from that you would learn something about square root of lambda sigma Also, or lambda sigma because of this correlation So there is always a correlation between uh Between lambda sigma and psi sigma okay So in principle you you you measure if this if this will be measured then Then you learn even more about this theory Yeah, thanks And and what is also, I mean there has been very long time ago so young p So young p's she has She was the first to say that the that the succion could be the inflat on yeah But the suck without taking into account the non-minimal coupling. So this is of course excluded nowadays. Yeah, I mean I mean here above the the highest line here this corresponds Essentially to psi equal to zero. Yeah So that's the would be the would be the quartic inflation about quartic inflation is ruled out by already by the By the data so to say. Yeah Okay, thanks. Yeah, fair. Okay. Uh, there is a question by carlos jaguna Okay, uh, uh, can you hear me? Hello So I'll read a question Okay, uh, what if a future experiment were to find a non-zero electric type of moment? What would that imply for the axiom? This would imply I mean or even in the standard model. There is a contribution. There is a We expect to there to be a A non-zero value of the it's only the qcd Part is set to zero by the axiom but in in in principle Uh One has to see how how how big this electric type whole moment is then at the end So, I mean, there's a very small value which will be induced by the cp violation in the standard model There will be a induced electric type whole moment Or okay Well, I guess the question is what would happen if it's bigger than the what you would expect from the standard model prediction If it's bigger than from a standard model I think yeah, I mean, uh, they could first I would I would not see how they how this would be This would be no problem for the axiom, but uh, yeah How should I how should we raise that? So maybe Maybe I don't understand the question so but nevertheless so so, uh Well The I try to I try to answer it If you are here, if you're listening to me, can you, uh, reformulate the question in the meantime I can, uh, I mean, uh, there are other questions here in the Yes, I have a question. Okay good So, uh, so the action has these shift symmetry, but if I understand correctly this action has, uh Does not follow this symmetry, right because it's like the longitudinal component I'm correct What do you mean by Because the action Has the shift symmetry, right? Axiom has a shift symmetry. Yeah, but not the suction suction The suction has not a shift symmetry. Yeah. Okay. Yeah Yeah, yeah Okay, and and I have another question if you go back. I think to your slide 29 Yeah, and you show this plot of the No, the next one I think Yeah, exactly. Just okay 30 just out of curiosity. What's this plot? What are you plotting there? What is plot? This is something like like the the spatial average of of the of the of the axiom Of of the of the uh of the scalar Field values. So one is so to say the As a function of time. Yeah, and so you use so, uh And and the time is in is in is in in certain dimensionless units So to say and is fi is in certain dimensionless units. What is illustrated here? It's in blue or in black The black and blue are essentially Essentially at the at the beginning is it's the same line. So these are the oscillation Of the because this goes on up to up to one. These are the the other oscillations Of the of the of the background inflat on field. So to say, yeah So they so so so as soon as so As soon as the field so to say you could you could see it like that as soon as the field, uh So the inflation ends so to say when the field It rolls down this valley and as soon as as the field As as has a value of the order of m plank. Yeah, then it it falls down into this Into the standard model In that into the direction of the standard model minimum, so to say, yeah Or and and but but at the at the beginning It doesn't feel everything which is which is down going down here But it starts to oscillate in around around the zero values. Yeah And and and so what what you see here Is the is the field evolution when it's when it oscillates around the Around the vacuum, so to say And then in these oscillations because you have also you have an also you have an expanding Field in this oscillating you can have parametric resonant production of the of the components of the fields which are parallel Of fluctuations of the field which are going parallel or perpendicular to the To this background field. So you are exciting. So to say modes You are you are exciting new Spatially not constant modes in in this background. Yeah And these are these these are these these are these Fields which are starting here and this is so to say you are now transferring So to say the energy from this homogeneous inflaton mode into into the Into into into into the into the directions of the field space Into the other directions of the field space and this you see already after a few oscillations of this field after a few oscillations this uh, so to say, uh You are starting to populate. Maybe you could could look at you are you are starting to to to uh To uh You are you are starting to to uh Restore the patchy green symmetry because because of course at the beginning The patchy green symmetry is completely broken You have you go into in a certain radial direction of the patchy green field And this has a very very large classical value So effectively you are not in a in a in a in the in the patchy green symmetry phase but uh symmetric phase but uh When when this when these other modes are excited then effectively Your your theory is in the in the in the symmetric phase. So the symmetry is restored Okay, see thanks Um, actually I have a question. Uh, well, I guess it's a very simple question on this slide Why do you need to have a mixing with the hicks? This was because we because we we we we considered in in this paper we considered both We we considered the case where lambda h sigma is larger than zero Then you have don't you don't have a mixing with the hicks Yeah, then you have only a valley along along the row direction And then there we but there we found in this case. We don't have We we we because we we cannot get this this nice effective production of standard model gauge bosons We we we get a very suppressed We get very low reheating temperature Actually reheating temperature will then be only of the order of 10 to the 7 gv or something like that And this is then a problem with the axiom dark radiation because in in this case the axioms Because I mean by by by in in this reheating phase I mean there are in in principle you get then at the end you get a lot of relativistic axioms. Yeah When this symmetry is broken, you have a lot of relativistic axioms and they should be also very quickly if they are not thermalized They they will they will sort of say, uh, we will we will get in in nowadays in in in in the in the So to say in in the late universe. We will have too much relativistic Particles too much dark dark radiation And so so what what we found is that for the typical values, which we for the typical parameters We would get in this in in pure section inflation We will get delta new and effective of the order of one Which is which is excluded by uh by cmb Okay, so I mean By fine tuning of parameters. We have seen maybe it's possible But we didn't investigate this Longer because it it seemed to us that the the other possibilities and and this Other possibility arises just by flipping the sign of lambda h sigma from From lower to larger than zero. We said okay, this is This is certainly viable and everything works, but in poor section inflation. It seems to be Uh, it seems to be problematic But in principle, I think one one it would be a good thing to check this in more Detail but already now so our our paper was 100 pages and therefore Okay Okay, this too much for us. We did somebody else can do it But nobody did it unfortunately Okay, there you go. So Are there more questions here? Yeah, I have a question for for Andrea. First of all, thank Andrea for this colloquium was very very very interesting Especially since I am not from the I mean, I'm not expert in actions But I was wondering some kind of naive question is Uh, it's possible with the action to fix this Problem more or less that has the standard model with the meta stability of the I mean here. So what we also did, I mean this I I didn't show here. We of course I mean, this is a Higgs portal model in a sense every Patrick win symmetry every Patrick win Stun extended standard model is a Higgs portal model and now via this Via so as is well known uh You can you can fix the meta stability problem by by by Threshold effects if you have if you have such such a theory With a with a threshold effect and we have we have we have explicitly shown also in this 100 pages long paper so in this in this paper we have shown that that that You need something like That you that this model and this we had to show. I mean, it's of course you have to show if you want to do this kind of Of of saxon Higgs inflation. You should you should be sure that this theory can be Can be used up to the planks scale. Yeah, or even even A bit higher. Yeah You have to to ensure that it's stable So to say in both in the in the Higgs direction as as well as in the in the Patrick win direct in the sigma direction Uh, and so we did this and we showed that through this through this To this mechanism you you get a a condition On the on the on the on the threshold parameter, which is essentially lambda h sigma squared divided by lambda h or so Yeah, and you and this should be of the order of Of 10 to the minus 2 so To to to get to get vacuum stability and everything right so so it it's it's true I mean you are solving in in principle you are solving also the vacuum stability problem Which which I didn't want to to to add to the to this list. So so you with this extension of standard model Because because I said because we said this is part of the inflation of the inflation by so so you should not have a Uh vacuum stability problem and therefore Vacuum stability is part of inflation in in a sense, but in in in the in our long paper. We discussed this in in quite detail Okay, thank you. Yeah, you're welcome Okay, uh, no, I see again. I don't know why this Do you also also this this infinity? Uh Uh Is it my fault? Uh, okay, so I see that there are no more questions Uh, so then, uh, I would like to thank uh, andrea stringwell again for this very nice, uh, colloquium and Yep, then, um Uh, see you next time. Okay. Bye. Bye. Bye. Ciao