 Okay, so hello everyone and welcome to our already 37th web seminar of the series of these Latin American webinars on physics My name is Nicolás Bernal and I'm from the University of Antio Nariño in Bogota, Colombia And it would be your host today So our speaker today is Enrico Nardi, so we're super happy to have you Enrico from the ENFN Frascati in Italy And Enrico will talk about action physics. I please the window for preferred action action models Right, and so I remind that you guys can be part of discussion writing questions and comments using the YouTube live chat system via Twitter So now I can hand you over to Enrico Okay, so Nicolás, thanks Thanks for inviting me to give this seminar. It's nice nice experience. Hope everything will We work properly So just confirm to me that you see the mouse and you see the slide Yes, perfect So that's a brief outline of my talk. I will give a short review of what is called a strong CP problem Just I will browse through the various experimental searches They're going and the searches that are planned for the next of next years. I will describe main main types of action models There are Generally, they noted as a KS2Z or QCD or a dronic action models. This refers to some single type and a dyno fishlers red Nicky's it means ski the FSZ actions, I Will describe What type of dark matter can we get out from action? through the misalignment mechanism and Then I will move to the original part of the talk Which is a description of the window where experiments should look for for actions so the phenomenologically preferred action models and For the dronic action and also I will add something for the DFS as the action models Where should we look for for the FSZ action models? So the strong CP problem QCD is defined in terms of two dimension as parameter not one, but two. They are not predicted by the theory So measurements yield a number which is pretty reasonable for the strength of the strong interaction The measurement depends that the energy where it is performed But is a number of order one unit unity roughly for the second parameter Which instead gives the amount of CP violation in strong interaction We have only an upper limit, but the upper limit is so tight 10 to the minus 10 For a parameter, which you would also expect is order one That the situation is really uncomfortable and we would much prefer if for some reason this parameter Is in fact zero vanish So I say that this parameter theta bar described by the amount of CP violation In fact, we can write the two sources of CP violation in the QCD Lagrangian one Is given by complex masses for the quarks for simplicity. I take just one copy of left and right handed quarks and one Is a a topological term theta multiplied by This combination ggt that was on the proper coupling which under integration in the 4x Is is a number is a topological In variant of the gauge field configuration So in the action you should read the second term as n time theta now These are not two independent sources because You can perform a chiral rotation on the mass term put the mass to be real And since the transformation is anomalous and the anomaly has Precisely the the structure modular factor of two Then you will have a shift of this theta in theta plus two alpha If you kill with a alpha transformation this this phase The other option is that you make disappear this term by putting everything inside a complex mass the relevant Point is that just the difference between theta and theta q is the physical quantity So there is just one one physical parameter that violates cp formally You can obtain this term in a beautiful construction due to fujikawa in 79 Where you can study If the measure of the path integral is or is not invariant under The chiral transformation you find that it is not invariant and when you properly regularize with the gauge invariant procedure You get that the transformation induce precisely this term that is written there Just a side remark now Theta different from from zero implies among other things and not zero neutron electron dipole moment How how big should be this quantity it's basically The size of the neutron so something of the order One fermi times a loop factor And times the value of theta So it's very simple At least on the basis of dimensional analysis you you expect this value multiplied by theta bar. You have This limit so ten orders of money to lower than what you Would expect which forces you to set these limits or there should be a an absolute value, of course Noted that this problem. This is a small number problem Is qualitatively different from other problems that we have in the standard model For example, theta bar receives the first finite log correction at order alpha square. This means that if you put by hand theta To 10 to the minus 10 it remains stable. You don't have a natural problem. You don't have a technical problem with natural This is unlike a m square h Which is quadratically sensitive to a cutoff scale And it is a very small number if you consider it on the scale of the plank of the plank scale Unlike the yukawa couplings of the first generation, which are also small even not as small as theta, but Not certainly not a border one Theta bar it evades explanation based on environmental selection So you cannot appeal to the idea that Why why so small otherwise the universe would look so different from what we know And I mentioned this paper from lorenzo valdi where This argument was was explored in some depth So you see, uh, it makes sense to study the The issue about strong cp violation independently of other small number problems Solution basically they are classified in three types of solution One is a massless quark. This is the simplest solution If you have a one massless quark, then you have an exact chiral symmetry So a theory with any value of theta can be made equivalent to a theory with a theta equals zero The only candidate For massless quark was until maybe 10 years ago So they have quark, but nowadays we know that Emma is different from zero by more than 20 sigma. So this is no more possible solution Another class of solution they impose theta equals zero by imposing cp conservation Of course cp is violated in weak interaction So then you need to do something to generate the phase of the ckm matrix and also to generate other phases that Might be responsible for the baryon asymmetry of the universe We know that we need cp violation for the matter anti matter asymmetry So this type of solution typically have a high degree of high tuning and very elaborated construction because If you allow for violation of cp in one sector of the theory In some way this with we leak in all sector within all sector via Loop corrections and we have still to fight with this number 10 to the minus 10 Moreover These type of models don't have a single unambiguous experimental signature This is not a theoretical issue is an issue that makes more appealing a model where you can tell what you should see To prove that the model is correct The last class of solution rely on the so-called pichet queen mechanism where you assume a global U1 symmetry It must be Spontaneously broken It must be qcd anomalous If you satisfy these two requirements, this is a good symmetry to solve the c in the strong cp problem spontaneously broken u1 implies An unbuggle stomboson, but since anomalies In an instant on the ground break explicitly the symmetry This is not really a mass less bone stomboson, but is what is called the pseudo bone stomboson It requires a tiny mass This object is known as the axiom. The axiom The u1 symmetry is reflected On the axiom transformation properties as a shift symmetry is written here Eventually the axiom will couple to everything only derivatively as a good and non-bou custom boson, but non derivatively to the Anomalous term because this is the explicit breaking now When you do things properly and you work out the potential for this type of of Scalar scalar boson You find that is a equipped with a periodic potential which brings The axiom writes to the place where in the background So its vacuum expectation value must cancel exactly a theta bar In few words, so this is a generally say that described as the theta becomes a dynamic parameter with space time dependence and is a driver dynamically to zero. It's the minimum of the potential Axiom models So the first attempt was straightforward. Well, identify The axiom with the phase of the higgs in a two-higgs doublet model Two-higgs doublet model because that's the only way you can enforce a petrified symmetry with one one-higgs. You cannot However, in this case the vacuum expectation value is the electro weak Value is written here and this implies that The axiom interacts too strongly with Matter the standard model particle. So the solution was ruled out quickly after being proposed You need to require that the vacuum expectation value of the axiom field of the scalar Is much larger than the electro weak web. So much larger than the 100 gv scale something around 10 to the 9 10 to the 12 That's the the right scale Those models are all together they notice invisible axiom models because the axiom interacts so weakly so weakly That is very difficult to detect it And here we have two types two classes of models. One is as I mentioned at the beginning DSFZ axiom Where the standard model works and the higgs are charged under the petrified symmetry You need two higgs doublet and one scalar singlet This scalar singlet can get a large level as large as you like without affecting the phenomenology Of the w mass and z mass The standard model leptos can also be charged in some model in other models. They are not Another option is instead to leave all the standard model particle Chargeless under the petrified queen and introduce new Firmium Charged under qcd transforming under the the su3 color and Again a scalar with the petrified queen charger. So in this case the complete sector of the Petrified queen type of solution is Is made of new particles Regardless of the fact that these classes seem to be quite different And there are some crucial model independent features One is that the axiom mass Is always inversely proportional to the To the petrified queen breaking scale Keep in mind if you wanted these simple relation approximate relation Where m axiom is equal to the pion mass Multiplied by the ratio between f pi. So this is 93 m e v and f a which is Around 10 to the time g v and you can recast in this way. So the typical Mass expected for the accent is very small Is around a million electron world and even less All axiom couplings also go inversely proportional to the f parameter So it's very useful in experimental exclusion plot to betray f For the axiom mass. So you can get plots where you have axiom couplings And uh As a function of the axiom mass which are the relevant parameters for long-term energy field knowledge Here is a short description of the axiom landscape. So possibilities in the first upper line You you have the axiom mass And below you have f a this is a capital f, but it's the same F a normal f there So we have exclusions from axiom production in the sun from the supernova From cooling of our giants Here from from uh, uh, the serna action search telescope and basically below 10 to the 9 Or 10 to the 80 if you want to be conservative uh as a value for f or above 5 in 10 to the minus 2 electron volt for the axiom mass The action is excluded on the small side we have searches from A dmx a dmx is uh, um, I will describe later, but he's searching for a dark matter in the form of axioms And uh, uh, it ranges the limit range around these values 10 to the 11 or so Uh, a strong argument is that axioms contribute to the dark matter and you cannot over close the universe so for natural values of the Parameters this region above 10 to the 12 is excluded. There is a still some controversy because of these it depends on on how how the topological susceptibility of qcd Goes with temperature. It's a very delicate and complicated argument typically what you get is between 10 And 5 in 10 to the 11 and few in 10 to the 12 depending on on what is what is The detail of your simulation typically on the lattice So I mentioned that axiom can give dark matter In fact, they can can give dark matter in three different ways one is through Thermalization so axiom can be also produced the interaction Interaction some amount of axiom is always produced the interaction the heavier the axiom And the the the heavier the axiom the Larger it's coupling the more easily you produce a thermal component Uh, another way is uh from a decay of topological defects Axiom physics is plowed by uh topological strings and topological domain walls Which eventually have to decay and can contribute to some axiom population But the most beautiful mechanism is what is called misalignment Which I will describe so as long as The temperature is below the breaking of the pechecum symmetry and above qcd We have a spontaneously broken theory with some massless constant bosons and a flat direction which is The minimum of this potential is represented here The axiom equation of motion Is described here as I said it has a periodic term Without a mass you see that a is constant and the solution of this equation is for A dot equal zero and a equal constant As soon as you go down with the temperature and you approach a lambda qcd then the potential becomes sensitive To the explicit breaking explicit breaking gives an explicit mass and these terms start becoming important Once this term dominates this one Eventually you end up in in an undamped harmonic oscillator so Keep in mind that uh at the scale of lambda qcd the Hubble parameter is 10 to the minus nine electron So it's already very very small So as soon as the mass starts going up No, because of the qcd effect you immediately fulfill this equality And a second not a second or an instant after This mass dominates And because this goes down as a temperature to the second power while the mass goes up As temperature to the eight at least is in a in a diluted gas instant on gas computation The potential tilts in this way The flat direction is lifted and and the axiom start Oscillating assuming that it was not accidentally sitting really here in zero Any other place even the axiom was sitting it will start rolling down and up down and undamped You can show that the energy stored in this oscillation Scales with the scale factor of the universe as a to the third power So it behaves as called that matter. That's the crucial point. It doesn't Also, the axiom is so uh, so light It doesn't scale as a temperature to the fourth as radiation, but as temperature to cube Uh, I will skip this And go to search strategies and current limits So astrophysical bounds are typically very strong and they can constrain coupling of the axiom to The photon to the electrons in case your model Allows the axiom to coupling to leptons to couple to leptons and to the nuclear we always have this copy and you see that this is The master of the model and the The limit on the coupling from the supernova implies this scale. So typically people assumes between five in 10 to the eight And uh, and below the 12 as I mentioned before So laboratory search techniques, they are virtually all sensitive at least until today to the axiom photon coupling They are of three pipes Light shining to the world Helioscopes we see a bit in detail So axiom typically coupled to photon and you can imagine that you have a magnetic field and axiom coming It converts and a photon coming it converts into an axiom It goes to a wall Again, it converts into a photon. So you pay a axiom photon coupling here axiom photon coupling there The square to get the rate. So a factor of g to the four To the fourth power. So that's an epictorial image of you see You shine a laser in the magnetic field Something is going through and some of these axiom that are passing through are reconverted Helioscopes they are looking for the axiom in the form of a dark matter. So if we have axioms oscillating around With a magnetic field We can hope to convert the axiom into the photon. So not the photon into the axiom, but the axiom into the photon the typical power in a cavity Absorbed by this conversion goes as the volume as the square of the magnetic field as a number of in the local patch of the galaxy and Multiplied by a coefficient, which is a quality factor You need to tune the cavity to meet the resonance condition. So just to tune you search for a specific mass of the axiom at each round of your experiment and then you tune you change the volume So you you change and modify a bit the resonance condition or you put gas you modify the apparatus Helioscopes The axiom that met our experiment at the university of washington is presently the most sensitive type of experiment of this This technique Helioscopes axiom are produced in the sun if they couple to photon and are emitted So the the sun is a potential source of a copious axiom flux You just need a magnetic field hoping that you can reconvert The axiom into a photon since the typical temperature in the sun are around Few kiwi what you get are photons in the x-ray band helioscope, there is The ongoing third generation experiment is cast ongoing and serma. It gave very good result and new results are expected for the summer and a project which hopefully will be founded but is still Going into an advanced state of rmd is is the axiom cast is using a superconducting magnet that was a prototype for lhc while For yakso that will be probably located in daisy Steel has to be decided the the magnet is is brand new And this is somewhere 20 meters object That has to follow the sun Now I go quick here just to show you some of the new proposals. So this is a princeton mit This is university of western australia This is in korea cool task in korea they even Founded an institute which is called for axiom and precision physics Mad Max Mad Max is mainly a german proposal Casper is in the united states. So this is very nice experiment, but I have no time to describe it This is an university of florida quax is is one of the i nfm proposals in lenaro in italy So you see with so many So many Proposal you have to tell possibly to the experimentalist where You should search for axiom where you expect to see the axiom Usually there was a window which is depicted here. Uh, that was in some way a bit arbitrary because It was centered on a reasonable value and The the width of the window was just taken from the literature from various models in the literature plotted here so The window from axiom models was plugged in some in some sense, but some arbitrariness in it's It's proper definition So now is our contribution in the last few minutes to To to few possibly So when we decide is okay take the draw the axiom model and they have a new quarks And they can see to these new quarks In representation of s u2 and u1 And see if they give problems. So what type of problems they can give I go quick here Basically if they would give a problem if they are stable we would have strong interacting Relics and strong interacting the relics are an issue in cosmology a serious issue Second if they sit in too large representation of s u2 Or or s u3 they can induce land out land out poles In in the running of the gauge couplings, which is a real unpleasant feature So we classified all the possible Cues that are allowed to decay into standard model particle fast enough That there is a limited number when you impose also The condition that there will be no land out poles in the gauge couplings below the plank scale You are left with 15 possibility So here also you have to go fast because I think I have half an hour Which is almost gone But uh The result is Okay, here are described a bit more cosmological constraint. You see what happens If the axiom if the q the exotic q decay before 10 to the minus two seconds No problem After 10 to the minus two seconds, they will start affecting big big bag of nuclear synthesis Longer After big bag of nuclear synthesis, they start leaving uh non-termal radiation that affects Recombination and leaves an imprint in cnb radiation After a combination if they decay they Contributed to the diffuse gamma ray backgrounds that has been constrained by Fermi If Eventually you say they have a lifetime longer than the lifetime of the universe So they do not affect all this type of phenomenological Events in the history of the universe Well, in generally they Contribute too much To the energy density of the universe. Uh, as we say they over close the universe So the limit is here 10 to the minus two seconds. They Are Forbidden not really rigourously forbidden, but let's say it would be unpleasant to have around particles that live longer than that Strongly interactive part here. There is a detail of the contribution To the dark matter. So this is a longer 10 omega H square omega of this heavy quark h square This is the limit which is the dark matter as measured cosmologically You see that If the annihilation of the quark is a free annihilation Basically, they cannot be heavier than maybe for tv Otherwise you enter in the over closure region This little corner might be well Excluded soon by lhc sooner or later. Maybe in the high There are other mechanisms to annihilate the qs bound states. I will not go into it And they give a lower limit. So the truth is in the middle But we have reason to think Motivated reason to think that the answer the real answer is much closer to the free Annihilation lines than to the bounded annihilation line. Yeah, there was a scheme of how Annihilation the bound state could could could proceed so That's the first election criteria. It forces us to assume that they decay through uh operator of dimension five or at the three level dimension six was already given to long lifetime and then the second criterion is that the The beta function should not reach the The explore should not drive the coupling to explode below a scale. We take it 10 to 18 gv just to avoid comments or maybe objection because it's known that the quantum gravity contributions tend to delay The occurrence of land outposts the sign of the contribution is known But at 10 to 18 gv you can expect that those contributions are still negligible So That's a list of the model where here you have Of the possibilities not more than the possibilities. So here you have The representation triplet of colors sextet of colors eight of colors 15 of colors This is su2. So we have doublet triplets Doublet's uh, and then this is a hyper charge Um, so these models are phenomenologically free of the two types of problem. I have described For this type of models you can compute the Axiom photon photon coupling, which is parameterizing in terms of this Or these numbers these numbers are related to the anomalies electromagnetic and color anomalies of these uh heavy quarks So you see the possibilities are restricted When you plot, uh, uh the possibilities you have The one with the weaker coupling and the one with the stronger coupling to the photon And you plot these on um on your mass Axiom photon coupling diagram And you see that you have a window which is now phenomenological motivated, which as a good overlapping with What was assumed before And if you want luckily it it drifted bit towards larger couplings Of course, you are also allowed to take more than one representation together Here we take only one if you take more representations You have more freedom, but you cannot take as many as you want because more representation You hit the land out pole condition at some point So we have computed the maximum allowed value of the axiom photon coupling Allowing as many representation you like subject to the condition that you have no land out pole We get a larger number which is here this described. I say the axiom photon coupling And uh, uh the window is here With two representation You can even also have uh if you want unfortunately Complete axiom photon decoupling at least within experimental errors so now you have to think that all this bench should be considered as a A phenomenologically allowed bend if you system only one type of quartz You are fixed in this stripe If you allow for two or three type of quartz then all this corner from here to there Is where your axiom model can sit I go quick to the conclusion Of course one say well, what about this the dfs at the axioms? Well for generic models which are natural which are reasonable You can show that you fall Always within the same band So this band eventually describes All natural axiom models that you can think of Um There are possibilities to get a larger axiom photon couplings and for this type of of models through a mechanism which Is a recent invention, which is called the clockwork mechanism but Which means that you besides the The scalax that coupled to uh to fermions you will introduce a Is a large amount of other singlets that do not couple to Directly to fermions just to boost up the the peche queen charges Okay, I will not go in detail because honestly, I don't like very much but You can add a scalar doubles up to 50 without violating The the condition of lambda poles So with 50 scalar doubles and each step each scalax connects to another to another to another to another you can announce Exponentially the charges and get to factor of these Ration that describes the axiom to photon coupling as large as 2 to the n So this is what is called a geometry It's called the exponential, but in fact is a geometrical enhancing of the coupling. So I reached the conclusions now The axiom hypothesis provides a well motivated scenario beyond the standard mode is by far The preferred type of solution of the problem, which is a real is a real problem a real serious problem Axiom models. So this is this transit the problem They provide an excellent that are met a candidate or thought they have not been invented for that This was a consequence that was discovered later And the nice feature is that There is an ambiguous test, which is just detect the axiom the tech the axiom measure his coupling today to the photon and then once you do that you you are confident That the strong cp problem is solved via a pchq symmetry maker and pchq mechanism theoretical developments are still ongoing. So There are some uncertainty that will be hopefully reduced as far as practice on the lattice theoretical uncertainty is due to model building also should be reduced And the final point is where does the pchq symmetry come from it is a global symmetry But it's not even a symmetry because it is anomalous So there is no reason why it should be respected by gravity not only gravity My other physics beyond beyond the physics of the standard modeling of axiom I have to mention that we are concluding a paper writing. So Lorentz or lucca diluzio Where I think we have an interesting proposal on how to generate Occidentally a pchq symmetry and how to protect the symmetry to basically any desired So that's would be would be I guess a relevant contribution to To fix to fix a disemplaison point in In axiom physics the origin of the pchq symmetry There is an healthy and lively experimental program Experiments are entering now the preferred axiom window for the qcd and for the the fsz axioms so still These windows have been only scratched a bit in the next years the intense experimental program will explore Large portion of this window New new ideas I put put forth for example casper. I mentioned before it's interesting Experiment because it wants to measure the axiom coupling to nucleons Not to photon. So even in our regional parameter space where the axon decouples from photon casper Would be able to get a signal coaxa coaxa is measuring the axiom coupling to electrons so again We have an experiment that is sensitive to axiom couplings Even if the axiom is decoupled from photon So until until today all the experiments are only sensitive to the axiom photon couplings is very welcome That we have proposals that tended to to to go beyond this So I conclude here Resuming what is the regional contribution of this seminar and what we have done is uh Defining An axiom for a window for preferred axiom models on the basis of precise phenomenological requirements And I thank you for your attention Okay, thank you Can you hear me guys? Yeah, I can so thank you Enrico for this super interesting seminar and now we should pass to the question round So, please, uh, let me remember you guys that you can ask questions to Enrico via the google's qna system At the webinar web page and also via twitter using the hashtag la wop So So I don't know if you guys have some questions From the audience Yes, I have a question for for Enrico So Enrico first of all very nice your talk and I wanted to ask you In this peche queen mechanism. Is it possible also to couple two leptons? Exclusively this action, right? Yes, it's mainly You can't I mean in the sense it's only possible because there is this qcd anomaly that perturbate The the potential I mean No, the the western Can be this mechanism be applied in the lepton sector is crucially No, no, no, you need the qcd anomaly That's the point you need a qcd anomaly because You have to cancel a topological term which has the same structure Then than the anomaly that's that's the thing, you know the thing is to have a qcd anomaly And the axiom couples to the qcd anomaly to the gg dual not to the dual dual term But in dine free share red niki and zit nisky models The the hicks carry a peche queen charge now You have the option to decide that the hicks Doubles that couples two leptons is not the same Than the x doublets that couple to the up and down quarks in that case It is not needed to be but The cheque in charges to the leptons and the leptons are a separate sector But if you want to to follow a more economical Type of models where for example, they are down type hicks Doublet couples gives masses also to the leptons Then since the down type hicks Doublet carries peche queen charges also the leptons have to check carry peche queen charges In that case it is unavoidable that the axiom which is composed by the Orbital models of all the scholars will eventually couple to To two to leptons. So in that type of models having couples to the leptons is I would say a natural expectation Not a not a mandatory expectation, but a natural one. You cannot build up a model that Is axiom coupling only to the leptons because In that case, you don't solve You don't solve the stronger qcd problem, but you can write models of that type in that case You you call axiom like particle So it's not an axiom The mass of the pseudo number was composed on doesn't come from the qcd anomaly. It's typically Put by hand as a As an additional term and you get a coupling only to the leptons. These are axiom like particles that are My opinion are less motivated than Than the qcd axiom Mm-hmm. So I'm a little bit continue with this question also with the what you mentioned in the in the conclusion about this experiment looking the The interaction with leptons and quarks What is more or less the the scape of these couplings with these fermions? in the sense because for the Gamma gamma axiom is more is a value doesn't more or less motivated by if you want to couple tag matters or like this, but The natural escape for these other couplings should be more or less the same order of these Couplings the photons all the couplings are given in In units of gv minus one This is because they are No, normalizable couplings and The scale is fixed by the inverse Of the symmetry breaking way so one over f as I tried to to explain F should be rather larger Larger than five in ten to the eight gv and not too larger Because if it is too large, uh, you would produce too much dark matter in the form of axioms from the misalignment mechanism So it's believed that it should be below ten to the twelve gv. So that's the window between let's say ten to the nine ten to the twelve gv and all the coupling go inversely with f measured so you see in these, uh If I can as we turn again the presentations You see the range here is Typically from ten to the minus fifteen ten to the minus eleven gv minus one Is uh depending on the axiom mass so, uh That's why it has been called the visible axiom because Larger the scale the more easily you can hide Here you go towards large scale in this corner and That's that's part of the difficulty To explore the parameter space at small masses And which means also small couplings here at large masses and large coupling. We are already doing a good job here cast And uh, and the yakso In the future we will just cut some slides Here is working, uh, admx with the resonant cavity type of experiments okay, these are is also A bit model dependent because it assumes that all the local amount of the meta is made up of of axioms So under this assumption they get these limits, but if axiom are only a partial contribution the limits would change Yeah, of course Yeah, thank you. So Thank the other question I guess Thank you Thank you riko. Yes. So are there more questions? I think I saw a question Okay, please go ahead learning some No, no, I said that I saw one appearing. I also would have a question, but there was already one by paola. I think Is that the one? Yes, yes, so paola Arias is asking you riko In this new axiom bands hole should be the dark matter window be understood And hope that we find a new course in the near future. So Uh, it's not Uh, it's not depicted here. You see now you see the diagram Can you see the diagram and yes? Yes. Yes So the region of uh, uh, where axiom could be A good cold dark matter candidate is around here Let's say I could tell you between a few in 10 to the minus six up maybe To five eight and 10 to the minus four That's that's a a good window if you go To larger mass and that is also to larger cap and you see this line Here you eat A limit where the axiom interact sufficiently strong That they get thermalized. So in that case axiom could be hot dark matter But uh, uh, in some way these Will be Sooner or later this part here would be will be excluded. I think In any case that that's nothing to do with the misaligned mechanism. So the the the window is around the axiom masses of 10 to the minus Five 10 to the minus four few in 10 to the minus six of few 10 to the minus four around here if you go to lower masses then Under some condition which I can mention and maybe if you want I can explain Um The axiom would be too abundant And they will over close the universe The reason is the following If you the axiom starts oscillating with an amplitude which is Typically a border f So the energy stored as is proportional to some power of f If f is too big, of course, you get too much contribution. So f big is in this corner Now there are possibilities to evade that One possibility is No, there is basically one possibility Which is imagine that accidentally the axiom Starts oscillating very close to its minimum. So you fine tune the initial condition You say the the the the axiom field was not distant something of border f from the minimum But in fact, it was very very close To the to the minimum by some some accident now This works only if the Pecèque symmetry is broken before inflation Because if it is broken before inflation, then a small patch which a single value of f gets inflated and All all the universe of the visible universe will have Basically one single value of the f of the axiom. So that's a new parameter in that case. This is really a parameter you have You have to measure You cannot play this fine tuning on the initial condition game in in post inflationary scenarios where the axiom Well, the the Pecèque symmetry is broken after inflation And and is not restored during reheating because in that case different patches of our visible universe and they have the size of Few few parses because the relevant scale is the the scale of 100 mev the qcd scale where the axiom start Oscillating around its value So in that case to get the amount of their matter is is correct to make an average over an angular variable and the average gives a value which is Square root of pi divided by three so the typical value of the amplitude of axiom oscillation is f square root of pi divided by three Which is a number of order one Or pi no pi divided by the square root of three, which is still a number of orders So in that case and no in post inflationary scenarios the limit 10 to the 12 gv is strict if you go to larger scales the axioms Axiom that matter from the misalignment mechanism of wood over close the universe so that can be safely ruled out Is a basically model independent way of ruling out those values under those conditions Okay, okay. Yes So polar you have a second question So she's wondering Suppose you have a discovery of an axiom like particle in an experiment that exploits Exploit the copy into photons and Supposed to have Okay, suppose you have a discovery of an axiom like particle in any experiment that exploit the copy to photons Yes, and hits into the region of these new action bands. So what information could you get from the new heavy quarks? well, and You see the the new heavy quarks are Heavy, but they don't have a bare masses The requirement for everything to work is that the new quarks get their masses from the wave of the axiom field So what you get? when you measure Presumably an axiom coupling and an axiom mass if you discover the axiom you will have a measurement of those two quantities then this would give you a value Of the vacuum expectation value of of the wave that breaks the pachet queen symmetry. So a value for f for f The masses of these heavy quarks are proportional to f modulo and yukawa coupling, which is unknown So under the reasonable assumption reasonable, I say also we see that Masses of the electron up and down are no way of the order of the electron we could have but With the theoretical preconcept that the dimensionless coupling should be of order one you would get an information on the On the mass scale of the heavy q. So this is what What you can get as an information? In another way you will measure also the value of f from the mass and directly the coupling The proportional the term of proportionality between the axiom photon coupling And one over f is given by the ratio of the electromagnetic and Qcd anomalies Which in turn depend on specific specific representations? So I would say that another information you can get from that measurement is What type of representation for the heavy q are ruled out and what types are are allowed If you have a very very precise measurement You would even be able to To pin down in which representation of the standard model group This heavy vector like q quark are sitting and this will be would be of course A great a great success just get into that point Okay So are there more questions? Lorenzo, maybe I didn't find how to end with the microphone. Yeah, I saw other questions. So that's why I was waiting Yes, a quick question So if I look at the plot that you're showing right now and rico on the It's interesting actually this is at least the second time that I kind of hear this story I mean not in your specific model But in general that it is easy to you know to build models that go in the you know lower right corner of your plot But it's incredibly hard to go the other direction Which would be the most interesting because it's where the experiments, you know could go Do you have an intuitive reason why also in your model like when you take this number of representations larger than one Can you explain intuitively why it's so easy to move all the way to cover the whole lower right corner of the plot? Yes, so uh, first of all It's not one model. It's the classification of All possible models that satisfy some phenomenological requirements So, uh, look, uh, just let me This precision look at this a combo shaped lines here Right one of these lines and there are more here that we did the knock plot Each one of these lines is a model So this gives you an idea of the model density in this density of models within within the band this band now if you go in this direction what There is a simple. Let me call it a theorem a simple theorem that tells you that If all the representation have a petri queen charge of the same sign then The maximum value Is the one the strongest coupling is the one you obtain with only a single representation So that's a simple theorem you say If all the petri queen Charges of the epic works are of the same sign. This is the upper bound You cannot as many more as you want. You cannot go But you have the option to put some with one sign positive and some with another sign, which is negative So why this option works? Well, it works because You see if I have here a different sign I can make this denominator very very small This is some type of effective coupling. So very small. It means this becomes big While you cannot go as much as you like to large couplings Well, because uh, this is a discrete set of numbers and you cannot get a sufficiently good cancellation And you cannot add More than free representation We have proved that with more than free representation of the one that we have classified You typically hit a land out pole. So you violate one of the conditions, no, you cannot add a 25 representation of strong interacting Quarks because you hit immediately land out poles in the hypercharging as you do in the color So that that's the reason why With these are within this approach, you cannot you cannot go More than that in that direction if you don't care about land out poles if you say that's Not something that I am scared about then You cannot many representation and you can you can go in that direction but we think that We are not saying Because if I All the models which are viable. We are more modest. We say the preferable Phenomenologically preferable access models. So models that are are viable without making Assumptions, no assumption like the access that the land out pole will take care about themselves about The coupling so the other region that's simply an accident. No, we We get that this combination or representation So you have a triplet of color a triplet of s u2 a cypher charge minus one third And also you have a sextet of color singlet of s u3 of s u2 with hypercharge minus one third If you compute e over n for this combination you get 23 divided 12 If you compute 23 divided 12 you get 1.92 Now you see that g a gamma gamma is e divided nc minus 1.92 with an error, which is four So we think this error These two representation give a complete and exact cancellation And this coupling is is consistent with zero We have found the three different Combination of a presentation that we think these errors are compatible with completely One gives a 1.1 1.92 1.94 another one and 1.95 another one note that There is no fine tuning. So once you choose the representation E over n is fixed. It's not that you are canceling by a fine tuning You can question if It is a kind of immoral To decide that you choose Precisely these two type of quarks and I would say yes, it's immoral But not fine tune. That's that's the relevant point. It's not an adjustment These are given by anomalies which are fixed by the representation. Yeah, very interesting And you get these already came with two quarks in two representation if you have a three and so on You get more cases, of course, right and these also You can have the similar situation also in the f s z models There are also the examples where you can get without fine tuning just with the choice of representation You can get Within experimental error. No, it's not experimental. This is a theoretical next to leading order chiral perturbation theory computation So it's not precisely It's not exactly an experimental error But within this error, let's say you get complete axiom photo decoupling And this remark is just to support the efforts of experiments that try to measure Axiom nuclear coupling or axiom electron coupling Because if by accident we sit on top of one of those Unlucky models, we will never detect the axiom photo Conversion Okay, thanks a lot. Are there more questions for the audience? Okay, there's one from Diego Restrepo Oh, they're concerning this Yes Say hi about the smash Hi, Diego from Enrico Uh, I'm concerning the smash model. So his question is Um Okay, concerning the question about the lepton sector in the smash models the scale of pechequeen pechequeen is defined with the scale Is identified with the scale of the siso A coupling between the peachy queen scalar and trinus is allowed You don't think you can comment on that? Which is a Mesh melon So repeat the quest, please So he's a concerning the question about the lepton sector in the smash model Oops, wait At the the smash model of ringvalde Exactly. Exactly. Yes The scale of the pechequeen is identified with the scale of the siso Such that the coupling between the pechequeen scalar and trinus is allowed So Could you please comment on that this question? And I No, I've not Not much to say. I'm not expert of that construction, but I wouldn't think there is a Nothing strange, you know, you couple The scale seems to be a good scale because 10 to the 10 is good for the siso and is good for for the art thing And uh, the The pechequeen breaking Scalar that can well couple to to the leptons like the trinus So, yeah, I believe that the construction is is fine It's fine. Of course, I'm trying to do one thing Two things with only one ingredient It's always I would say a good strategy because you can You can test or constrain the model from different approaches But uh, we didn't we didn't go in any Detail of that specific model. So my my answer is only a partial one just common sense Thanks Enrico. So are there more questions for the audience? So I guess that's okay. There's more questions. So Let me thank Enrico and all our viewers for this super interesting seminar Guys that in next week. So it will be april the fifth will have Marola Becky And well, I think yes, sorry talking about AMS the AMS experiment So we hope you have you guys next week As well. So thank you very much Enrico And thanks to all of you for for your attention and for following the seminar Okay, thanks a lot. Bye. Have a nice day. Ciao.