 Going live. Okay, I think we are live. So hello everyone and welcome back to the Latin American webinars on physics. Even though you cannot see me, I am Gerald Jones from the TUCP Peru who is having a day with a bad connection but I will be your host today. So this is webinar 142 and we're having Kevin Hinsen as a speaker. Kevin is currently a third year PhD student working at the University of Basel under the supervision of Stefan Antusch. Today Kevin will give us news about SU5 grand unified theories as well as its connection to axion dark matter and we are very happy to have him as a speaker today. So before we begin, let me remind the viewers that you can ask questions and make comments via the YouTube live chat system. And this question will be passed on to Kevin at the end of his talk. So, okay, Kevin, please share your screen. Excellent, everything good. So thank you, Gerald for this kind introduction and thanks also for this great opportunity to present my work here at Log basics. So this talk is actually based on these four publications here that have been worked on in collaboration with my supervisor, Stefan Antusch and then Shakespeare and recently also with Ilya Dorschner. So unification is actually an idea which has been around for quite some time in physics. And here are some examples of unification already in the 17th century. Isaac Newton proposed a unification of celestial and terrestrial gravity. Then even more impressive in the 1860s, there was a unification of electricity and magnetism which resulted in Maxwell's equation and also allows to describe light as an electromagnetic wave. And more recently at the beginning of the 20th century with Einstein's theory of relativity, a unification of space and time was achieved and also a unification of mass and energy. This is maybe also, this maybe also led to the most famous equation of physics. Then in the 1960s with the invention of the Higgs mechanism, a unification of QED and the weak nuclear force was achieved. So naturally some physicists wonder whether this concept of unification can be brought into other aspects of physics. And one idea which goes in this direction is actually the idea of grand unified theories. In a grand unified theory, we would have a unification of the electro weak and the strong nuclear force at some very high energy. Now what are the motivations of such a grand unified theory? If we look at the standard model gauge couplings and we run them up to a very high energy, then they come very close, which is not something which one would expect. I mean they could also drift apart or just run parallel, but they come very close. And if we maybe have some additional threshold corrections, it could also be possible that with these new corrections that they unify in a single point. And if this is the case, then this could be a hint for a grand unified theory. Then apart from this, there are also other motivations to have a grand unified theory. First of all, the fermion content of the standard model is quite complicated. I mean, we have five different representations for each family of fermions. And yeah, they live in sort of strange representations within a gut can be simplified. So for example, in a C5 gut, one only needs two different representations per family or in other higher gauge groups such as SO10, single representation for the standard model fermions of one family. Then moreover, in the particles which we observed for some reason seem to have a quantized electromagnetic charge, which is not something which one would expect, right? I mean, the hyper charge is just some U1 factor. So what we could expect some very strange charges such as square root of pi or whatever, but for some reason the electromagnetic charge is quantized. And this can also be explained by a grand unified theory. On top of that, in the standard model gauge anomalies just randomly canceled and they just canceled for each family separately just because of the matter content that we have. And what's also interesting is in order for the gauge anomalies to cancel, one really needs quarks and leptons together. And yeah, all these things can be explained financially within grand unified theories. Okay, now to the outline of my talk, I will start with SU5 guards. So the minimal SU5 guard model which was proposed by Howard Sharjai and Sheldon Glashow. And I will also discuss the shortcomings of this model. Then I will present an approach to build realistic guard models which also predict fixed quark lepton new cover ratios at the gut scale. Then I will turn to the strong CP problem and discuss the veggie quinn solution to it. And last but not least, I will show you how this veggie quinn mechanism can be combined with SU5 guards. Okay, let's start with the Georgia Glashow model. So in the Georgia Glashow model, the standard model field content is embedded into two generations of representations under SU5. So in this five bar representation, we have the right-handed down type quarks as well as the left-handed lepton doublet. And then in the 10 dimensional representation, we have the right-handed up quarks, the left-handed quark doublet as well as the right-handed electrons. On top of these fermions, we introduced two scalar fields. One lives in the 24-dimensional representation, which is the adjoint of SU5. And this is needed to break the SU5 gauge group down to the standard model gauge group. Moreover, the electromere kicks doublet is embedded into a five-dimensional representation of SU5. And the rest of this fields then is responsible for the electromere symmetry breaking, which we also have in the standard model. Okay, let's look at the Yuccava sector of this model. So with the field content and the gauge symmetry, there are actually two Yuccava couplings which are allowed to write down. One is this coupling with five bar, 10 and the five fixed. And then there's another coupling with 10 and five fixed. Then from this first coupling, and once the gauge symmetry is broken, we obtain these two standard model Yuccavas. And then from the last coupling, we obtain the uptype Yuccava matrix. And then we obtain these two predictions. So here we can see the uptype Yuccava matrix is actually predicted to be symmetric. And for the downtype quarks and charged leptons, we have this relation that one is the transpose of the other. This in particular also implies that the singular values of these two matrices are unified. So this is actually a quite nice prediction at the qualitative level because it explains why the charged lepton masses in the downtype quark masses are so similar. However, on the quantitative level, it's just not true. We can see this by taking the observed values at low energy and running them up to high energy. So here the red curve represents the second family which that means the new Yuccava coupling is divided by the strange Yuccava coupling. And if we run this up to a high scale, this is roughly equal to 4.5. And then for the third family, here represented in blue. So the tally Yuccava coupling divided by the bottom Yuccava coupling, if we run this up to high energy, this is roughly equal to 1.5. And obviously both of them are far away from one. So one natural question, which one can ask is whether such ratios like 4.5 or 1.5 can be explained in the gods. This is something which I will turn back in a few minutes. Okay. Then neutrino masses, this is another problem of the Georgia-Gleiser model. The Georgia-Gleiser model predicts masses neutrinos. This is simply because we don't add any singlets or anything else, which could give neutrino masses. However, the problem in SC5 is even worse than in the standard model because in SC5, if we want to write down such a 1.5 operator, a dimension 5 operator, then this has to be suppressed by some scale which is larger than the gut scale. And with this, we predict neutrino masses which are too small. So that means we cannot solve the neutrino mass problem with higher dimensional operators and we should solve it differently. Okay. Then there's also a third problem of the Georgia-Gleiser model. But before I can come to that, I first want to discuss how the gauge bosons are embedded in SU5. So here we have 24. So the gauge bosons are embedded in a 24-dimensional representation. And this would be the blue ones. This would be the W bosons of SU2 left. And the hypercharge is embedded here on the diagonal of this 24-dimensional representation. But since the joint of SU5 is 24-dimensional and the standard model only has 12 gauge bosons, we have to introduce these 12 additional gauge bosons on top of the standard model field content. And these additional gauge bosons are actually both laptop blocks and die blocks. And because of this, they can lead to proton decay. And moreover, once the gut symmetry is broken, these additional gauge bosons obtain a mass, which they get by beating up some scalar field, some scalar freedom field. Okay. So how does proton decay work? As I said, these gauge bosons are both die blocks and laptop blocks. And then we can have processes like this where proton can decay into a anti-lacton and a meson. And with a dimensional estimation, we can find that the mass of these laptop blocks, of these gauge bosons has to be larger than 10 to the 15 GeB. And this also means that the gut scale has to be of this order. And this is something which cannot be realized within the charge eyeglass model. So this is actually a third problem of this model. Okay. An intermediate summary of all the shortcomings of the charge eyeglass model. So first of all, unification cannot, yeah, appears at a scale which is too low, which means that proton decay is actually predicted too rapidly. Then we predict massless neutrinos. And thirdly, we have a wrong prediction for the Yuccava matrices. Now, how can we solve all these shortcomings? So for the first two, one just needs to introduce additional fields. And if some of these fields have intermediate scale masses, which means between the electroweak scale and the gut scale, then these two problems can often be solved simultaneously. Okay. Let's look a bit deeper into the neutrino problem. So actually in this standard model, we have three solutions to generate neutrino masses at three level. And all of these solutions can also be embedded into SU5. So if we just introduce right handed neutrinos, we can have a type one CSER mechanism, same as in the standard model. Then for the type two CSER mechanism, one needs a SU2 triplet scalar field. And this lives in the 15 dimensional representation of SU5, which means if we introduce this 15 dimensional representation, we can have a type two CSER mechanism. And then the joint representation contains a standard model singlet as well as triplet under SU2 left. And therefore by introducing such an adjoint fermion field, we can have a hybrid of the type three and the type one CSER mechanism. Moreover, there are several solutions to produce neutrino masses at the loop level. One of these solutions I will discuss later in my talk. And for the bad mass relation, I will discuss on the next slide some solutions. Okay. One very straightforward solution is just to allow for any high dimensional operators. And with this sort of just destroy the prediction. This is maybe a solution which is not so nice, but it works if one wants to allow for all high dimensional operators. Then a second solution would be to introduce vector like fermions, which are, which then mix with the standard model fermions and thus interplay with the mass relation. I will discuss one such solution later in my talk. Okay. And then there's also the possibility to have a second X doublet, which is embedded in a 45 dimensional Higgs field. And another solution, which is called single operator dominance. I will discuss both of them basically now. Okay. So let's say we have the standard model, sorry, we have the charge high glass high model and we add an additional 45 dimensional Higgs field. Then we can write down an additional you cover coupling. Okay. We can also write down other things, but we are now interested in this additional cover coupling. And with this additional you cover coupling, we get then a different mass relation where we have this factor minus three. And that means what we could do is we could consider linear combinations of these two matrices. And with this, we would have enough freedom to fit everything. However, if we do this, then we sort of lose some predictivity in the you cover sector. So one idea, which was proposed by Georgia and Fjall's book was that if an additional family symmetry is introduced on top of the gauge symmetry, then it's actually possible that different generations of fermion fields coupled to different Higgs fields. And therefore we can have different mass relation, different relations for different entries of the mass matrices. So they actually proposed such a texture for the mass matrices. And in this case, only the two-two entry is generated by a coupling to the 45 dimensional Higgs field while the other couplings, the one-two, the two-one and the three-three are all produced by a coupling to a five dimensional Higgs field. And if the mass matrices are of this form, then we get other ratios, namely for the third family, we get the ratio of one. For the second family, we get the ratio of minus three. Both of them are directly coming from these operators. And then for the first family from the diagonalization of this matrix, we would get a factor of minus one-third. Now, this model is quite old, 1979. At this time, these ratios were working, but with the current data, this is a bit outdated as we have already seen before. I mean, for the third family, a ratio of 1.5 is working much better than one. And for the second family, a ratio of 4.5 is working much better than three. So the question arises, can we get such factors, let's say 1.5 and 4.5 out of some gut operators? And this question was actually answered by Stefan Antusch and Martin Spienrad if one allows for higher dimensional operators. So what they did, they were considering higher dimensional operators of this form. And two of these external fields have to be standard model fermions. So these have to be such fermion fields. And the other two have to be Higgs fields, one of which gets an electroweed scale wave and the other one gets a gut scale wave. Then here we have heavy messenger fields. They should have masses above the gut scale but below the plunge scale. And Lambda just shows how the messenger fields obtain the masses. So this could be a singlet mass term just writing down the bare mass term or this could also be a mass term which is effectively generated via a coupling to the joint Higgs field. And if we then look at the catch-order coefficients of such operators, then we actually obtain the power ratios. So here are a few examples of such operators and such an operator here where we have a 24 dimensional Higgs field, a five dimensional Higgs field and the messenger is also five dimensional and something like this could give us a ratio of three over two. And if we replace this five dimensional Higgs field with a 40 five dimensional Higgs field then we can get a ratio of nine over two. Then here in this example, it's important to note that this is actually also a dimension five operator, not dimension six, this 24 dimensional Higgs field here just indicates that the messenger fields get their masses via a coupling to the 24 dimensional Higgs field. And an operator, a diagram like this can give us a ratio of two and this last diagram here can give us a ratio of six. All of these ratios will be important in the following slides. Okay, but okay, it's not, of course nice to have these operators but if we have a given model, how can they predict, let's say you cover ratios? The first of all, the you cover matrices have to be hierarchical and secondly, the three three and two two entries need to be dominated by a single operator. So that means if we have the SU five gauge symmetry then we need to add an additional family symmetry on top of it, which ensures that these three three entry and two two entry only comes from a single gut operator. Similar as in the case of the Georgia-Jarles Koch model. Okay, what we have done is we have investigated a few gut scenarios where the neutrino masses are generated via different mechanisms and we have for each of them investigated the viability of such fixed gut ratios. So in the first scenario, we have added one-dimensional fermion fields as well as a 45-dimensional Higgs field on top of the Georgia-Glashow model. Then these one-dimensional fermion fields allow to write down neutrino masses via type one CSO mechanism. So this works exactly the same as in the standard model and then the 45-dimensional Higgs field allows for gauge coupling unification and it also allows to write down an operator giving this ratio nine over two. Okay, now if we look at the running of the standard model recovery matrices we actually see that this gets changed by the new dirac coupling for the neutrino. And what's particularly important is this term here which indicates that the running for the charged lepton-ucava matrix is slowed down if we have this dirac-ucava matrix. Well, you can see it in this plot. If the dirac-ucava matrix has entries which are much smaller than one, then we get the same running as in the standard model. But if these couplings are of order one, then this can slow down or even reverse the running. And with this, it's actually possible to obtain a ratio of 1.5 at the God scale. Okay, so let's say we have the ratio of 1.5 for the third family and the ratio of 4.5 for the second family. Then there are quite a few possibilities to build full models which have this property and one question which one can ask oneself is how to distinguish between all these possible models which all have the same property. So what we have done is we have just analyzed two toy models and we have shown that they have quite different predictions for the new key on decay. So in this first model, the down type and charged lepton-ucava matrix have a non-trivial one by two block and the up type-ucava matrix has zero entry in the one-three and three-one and it's also a symmetric matrix. In the second model, the up type-ucava matrix is a general symmetric matrix and the down type-ucava matrices and charged lepton-ucava matrix is a diagonal. Okay, and what we have then found is if we consider the predictions for new key on decay and we take two different decay channels and compute the ratios, then they have quite different predictions. So if we in the very far future are able to measure these ratios of different new plan decay channels, then we could distinguish between, at least between these two models. And if we could measure several such ratios, then we could maybe even distinguish between several models. Okay, for the second scenario, which we have considered, we have added a 45-dimensional Higgs field as well as a 15-dimensional Higgs field on top of the standard model on top of the Georgia-Glashow model field content. This 15-dimensional Higgs field allows for neutrino masses via a type-2 CSER mechanism, while the 45-dimensional Higgs field again allows for gauge coupling unification and also an operator giving the ratio nine over two as well as an operator giving the ratio two. Okay, how does neutrino mass generation work? So first of all, this is the standard model decomposition of the 15-dimensional Higgs field. So the first entry is the SU-3, then SU-2, and here U-1. And this data one here is actually the triplet which we need for a type-2 CSER mechanism. So with this new Higgs field, we can write down the U-cover coupling with the five-bar fermion field. And this decomposes under the standard model in these three U-cover matrices. The first one is the one we need for the type-2 CSER, but on top of that, we get these additional two U-cover couplings. And they are related by a gun-scale prediction, okay? Okay, then to have the type-2 CSER, we need an additional coupling between the five-dimensional Higgs field and the 15-dimensional Higgs field. And then we also need a mass term for the Higgs doublet. And under the standard model, this decomposes into these lines. So from the U-cover term, we get exactly the U-cover term that we need. And from this tri-linear Higgs coupling, we get the tri-linear Higgs coupling that we need. And from these terms here, we get a mass for the triplet. Okay, and with this, we can write down the typical type-2 mass. Okay, then another question is how does the running of the down-type U-cover matrix and the charged left-on U-cover matrix, how is this changed with these new U-cover matrices? We can see this here. So what's particularly important here is that this Y1 speeds up the running of the charged left-on U-cover matrix, and Y6 speeds up the running of the down-type U-cover matrix. So if we have a scenario, for example, where this delta one has a small mass and delta six has a large mass, which means that this would mean that if we run everything down from the gut scale, that delta one is much longer in the spectrum. And by this, we would speed up the running of the charged left-on U-cover matrix and not change the running of the down-type U-cover matrix. And on the other hand, if, for example, this delta six has a very low mass and delta one has a mass closer to gut scale, then we would not significantly change the running of the charged left-on U-cover matrix, but we would speed up the running of the down-type U-cover matrix. And with this new freedom, the running for the U-cover ratios for the third family and second family are a bit more arbitrary. So, yeah, so this upper line would sort of correspond to having a small mass for delta one and the lower line sort of corresponds to having a small mass of delta six. And what we can see is that now, on top of the ratio three over two, nine over two, we have the additional possibility to have a ratio of two and six, okay. Then let's say we impose this ratio, three over two and nine over two or two and six, and we fit everything to the observed data, then having these two ratios actually allows to have all of these four particles light. They are not predicted to be light necessarily, but they are allowed to be light. If they were observed, they could come from such a model, but they don't have to. The same thing here. We predict these three states, we predict these three states can be light, but they don't necessarily have to be light. Okay, then what's also interesting is that these two models have a different prediction for the gut scale, and this directly translates into different predictions for the nucleon decay rates. So model one or the full one sigma HBD interval of model one will be tested by hypercomioconda, but for model two, we will only be able to look at a very small part of the predicted parameters of the prediction, okay. Then our last scenario, which we have considered is a hybrid type three plus type one season mechanism, and this can be achieved by introducing this 24-dimensional fermion field, and we again introduce a 45-dimensional Higgs field to allow for gauge coupling unification and also to allow to write down some of these operators. Now it actually turns out that three such combinations of you cover ratios are viable. Then how does neutrino mass generation work? So the 24-dimensional fermion field, it composes like this under the standard model gauge group. Here is the SU2 triplet, and here the complete singlet under the standard model, and this is needed for the type three season, and this here gives the type one season. Okay, we can write down these terms here. So one coupling between the five bar fermion and the 24 fermion and the five Higgs, and then the same coupling, but with the 45-dimensional Higgs. And from these two Yukavas, we actually get 19 new Yukavas under the standard model, which are related by some clutch factors. And these four here are used for the type three season mechanism, plus type one season mechanism. And this is then how the neutrino mass matrix looks like. It looks quite complicated, but actually just all of these matrices are just rank one matrix, and they are connected by attached coefficients. Because, and as a result of this, this is just a rank two mass matrix, which means that only two neutrinos are predicted to be massive. Okay, now this scenario also allows to have some right light relics in model one. Actually the triplet, which gives neutrino mass could be light. Then in model two, this laptop bar here could be light, and in model three, also this laptop bar could be light. But now we really predict that this has to be smaller than 100 TED, and in models three, it even has to be smaller than 10 TED. So this will be now a strict prediction, otherwise these two scenarios cannot work. Okay, then the gut scale is also, we also get very different predictions. This is actually a logarithmic scale. So in model one, the gut scale has to be smaller than 10 to 16. However, in model two and three, the gut scale gets very close to the plunge scale. And because of this, the proton decay predictions for model two and three are very small. So we will not, we should not observe proton decay if model two or three are realized. If we observe it, then this would contradict these two models. On the other hand, model one is predicts quite rapid proton decay. And again, hypercomic Honda will measure the full one sigma interval of this proton decay channel and almost the full one sigma HPD interval of this neutron decay channel. Okay, a small summary on these recover ratios. So actually if we have higher dimensional operators, they can lead to fixed gut scale recover ratios. And we have investigated such fixed gut scale recover ratios in different scenarios. So if neutrino masses are generated by a type one CSO mechanism, we have found that only one, such combination of ratios works. However, if we have a type two CSO, then there are two possibilities which work. And if we allow for a type three plus one CSO mechanism, then there are three combinations of these ratios that could work. Okay, now sort of changing the topic because so far we have not really talked about dark matter, but there's also a possibility to have dark matter in SU5 guts. And one nice example would be an oxygen dark matter. So to discuss this, and let's have a look at the strong CP problem. So in the Lagrangian density of the standard model, we can write down such a GG dual term. And this theta bar is then a combination of some term in the Lagrangian density plus some in the Lagrangian density, term from the mass matrices. Now, since we are allowed to write this term down and by the symmetry, we should also do that. But if we write this down, this allows for some phenomenology. For example, it gives a non-zero neutron electric dipole moment. But if we look at the current measurement, this translates into a prediction of this parameter, which is very small. So one question which one can ask oneself naturally is why does this parameter, why is this parameter so small? Is there maybe some nice solution to it? And there are a few solutions. One of them is the Patrick Quinn mechanism for which an additional Zula scalar is introduced and an approximate shift symmetry is also imposed. And if we have these two assumptions, then this is the Lagrangian, which one can write down. And here we have an explicit breaking term for this shift symmetry. Now, if we have these terms and we minimize the axiom potential, then it actually turns out that this term exactly cancels with this one in the minimum. And thus the strong CP problem is dynamically solved. Also by using Karel techniques, one can compute the mass of the axiom and one actually finds that it is inversely proportional to this decay width. Okay. So since the shift symmetry is broken by a dimension five operator, one requires a UV completion to it and one possibility of such a UV completion is the KSVC equation. About the KSVC axiom, we take the standard model and we add vector lag blocks on top of it plus an additional scalar singlet. Now, we also introduce a global V1 symmetry and we let these vector lag blocks transform differently under this global symmetry. Then this global symmetry can be broken by the scalar field. And after it is broken, this is sort of the expansion of the scalar field where the A describes the Vef, row A is the regular part and A is the angular part. This then turns out to be the axiom. Okay. Then with these charges which we have imposed, we can also write down a U-cover term between the vector lag blocks and the scalar singlet field. And after the scalar singlet field has obtained its Vef, this then translates into a mass term with this additional phase which depends on the regular part of the scalar field. Now, what one can do to remove this phase is a chiral field transformation which looks like this but under this chiral field transformation, the fermion measure transforms non-trivially and this introduces exactly this coupling which we had before. Okay, so what we have done so far is we have considered the case Vc case with a simple quark but in general this could be a reducible representation under the standard model gauge group where just one of these SU3 representations needs to be non-trivial. And in such a general case, we not only introduce a coupling of the actual field with the blue ones, but also a coupling with the fermions. This just comes from the fact that the Q is non-trivially charged under SU2 cross C1. Okay, how can we compute this coupling to the fermions? But this we introduce the QCD and QED anomaly coefficients and they are just given by group theoretical constants as well as the charge of the axiom under, sorry, by the charge under the patchy-quin symmetry. Okay, then another UV completion of the patchy-quin mechanism is given by considering a two-higgs doublet standard model plus again a scalar singlet. Now the two-higgs doublets transform like this under the patchy-quin symmetry and the singlet again just carries a charge of one. Now if we write down the scalar potential we can write down all these modular terms and on top of that a coupling between the fixed doublets and the scalar singlet. Now after both the patchy-quin and the electroweak symmetry breaking, we can expand all these fields around the VEF and the term which we are in particularly interested in is just the VEF multiplied with this phase. Then it turns out that the axiom is a linear combination of all of these phases and also the VEF is a linear combination of all of these VEFs but in most models one expects that the VEF VEFI is much larger than the other two VEFs and in such a case the axiom is dominantly sitting in the radial component of this scalar singlet. Now looking at the Yuccava terms for this DFSC axiom, and one actually has two possibilities. How one couples the standard model fermions to the Higgs fields and the difference is just given by this last term here. One can decide whether one couples it to the down type Higgs or the up type Higgs. Now after the patchy-quin and electroweak symmetries are all broken these Yuccava terms translate into mass terms with an additional phase and we can again do some carrier field transformations to remove these phases here but by doing this we again introduce coupling to the GG dual and also to the photons. And here this E over N which we had in the case we see is given by eight over three. And if we instead look at the DFSC two we would have exactly the same but the factor two over three instead of eight over three. Okay, now the question is, how can we embed something like this into SU five? And this was first done by Weiss, Georgi and Glashow. They took the Georgi Glashow model and added an additional E1 patchy-quin on top of it. Then they considered a model with two text doublets and they embedded this scalar singlet into the 24 dimensional Higgs field. Now in the Georgi Glashow model this 24 dimensional was a real field because it's in a joint so it can be chosen to be real but if you want to charge it under the patchy-quin but this has to be a complex field. Then they chose this chart the E1 patchy-quin charges for the field and by this choice one can write down these terms in the Lagrangian and this exactly resembles the DFSC one model. So that means we have successfully embedded the DFSC into SU five. However, same as the Georgi Glashow model Weiss Georgi Glashow model suffers of all these shortcomings but what's nice in this model is that since the 24 breaks simultaneously SU five and patchy-quin that means that the Axion mask is actually directly related to the God scale which means if we have such a such a scenario in a God and we can predict the God scale then we immediately know the Axion mask. Okay. Now let's look at a realistic SU five cross E1 patchy-quin for this we took the Weiss Georgi Glashow model and we added back to like quarks on top of it as well as this 35-dimensional Higgs field. Okay, with these vector like quarks and the 35-dimensional Higgs fields we can have neutrino masses at the loop level. On top of it, these 15-dimensional Higgs fields contain also a three, two, one over six representation which mixes with the quark doublet of the standard model and this corrects the fermion masses. Then we also have an Axion which is then given by a combination of the DFSC and the KSBC mechanism because we both have vector like quarks and two Higgs doublets. Okay, how does the fermion mass correction work? So this is the composition of the 15-dimensional fermion field under the standard model gauge group and this sigma three is exactly the same representation as the quark doublet of the standard model and because of this we have some mixing. So that means that the down type to cover matrix is now four by four and only this three by three upper block is shared with the charge vector to cover matrix. And if we then do a block diagonalization of this four by four block then the three by three part obviously gets changed and this exactly corrects this mass reduction. Then for the neutrino mass, they are given by such a loop diagram and if this is computed then this is how the result looks like and this YA and YB are both rank one matrices which means that the full neutrino mass matrix is rank two and we have two massive neutrinos on top of it because the neutrino mass, for the neutrino mass generation, we need this YA and this YA also is also needed for the down type mass correction and the combination of these two effects only allow for a normal ordering. But that means this model directly predicts that neutrino masses have to have normal ordering. Okay, let's look at the nuclear decay predictions. So these are the two sigma HPT intervals and the blue lines are the current bounds while the red lines are the future bounds of hypercomic under. So what we can see is that hypercomic under will probe part of the parameter space in this particular channel and it will also probe part of this particular channel. And then what's actually nice is that the ratio of these two channels is predicted to be very sharply which means if we could observe both these channels then we could look at the ratio and we could also compare it with this prediction here. Okay, then the more interesting and more predictive part is actually the oxygen phenomenology. So we get a QED anomalous parameter of 52 over three and then for QCT we get 13 over two and we get this relation between the oxygen decay and the gut scale. And because of this, we have a direct relation between the oxygen mass and the gut scale and the gauge coupling at the gut scale. So this is predicted which means that just from gauge coupling unification we immediately know the oxygen mass. And moreover, the couplings of the axiom are also depend on the decay width which is directly linked to the gut scale. This means that also these couplings are predicted. Same for the neutron electric dipole moment also related to the gut scale. So interestingly, there are a few experiments which are planned to be built which look for such axioms. So here in this upper figure, we plot the axiom mass against the axiom coupling to the photons and the blue line is out of friction. And then this ABD, this means ABRA-CADABRA, this is a experiment which is planned and this will actually probe some part of our parameter space in its final state. Moreover, another experiment which is going to be built is dark metal radio gut and this will probe an even more significant part of our parameter space. This black line here, you can ignore because this is just some experiment which is theoretically proposed but it's not planned to be built yet. Then for the neutron electric dipole moment, and there's also an experiment called Casper Electric which will be looking for this and this will probe almost the entire parameter space of our model. That this means if we combine both of these two predictions with each other, then the entire parameter space will be probed by future experiments. This is also nicely shown in this figure here. So the points which we have generated here, we have generated them with a Markov chain Monte Carlo analysis, which means that all these points have a very low chi-square that they can be almost perfectly fitted to the low energy data. And as we can see, for example, the experiment which looks at the neutron electric dipole moment will probe everything here on the left. And then the two experiments which look for the axiom to photon coupling will probe everything on the right. And already the combination of these two kinds of experiments will probe the entire parameter space but on top of it, proton decay experiment will also probe a significant part of our model. And if we are lucky and are somewhere here in this region, it would even be possible to probe our model with three different kinds of experiments simultaneously. Okay, so the conclusion. And if we combine the Petri-Quinn symmetry with the SC-5 symmetry, this leads to a prediction of a very narrow axiom mass range and this mass window is actually determined by an interplay of gauge coupling unification constraints partial proton decay lifetime limits and also the needs to reproduce the experimentally observed fermion mass spectrum. The model which we presented here predicts two massive neutrinos which are Majorana nature and the entire parameter space of the presented model will be probed by a combination of three different kinds of future experiments looking both for axiom dark matter as well as for proton decay. So that would have been my talk. Thanks a lot for your attention and I'm very happy to answer questions. Excellent, thank you very much for the talk. It was very, very detailed, very, very nice. So we are open for questions. So there is usually a lag between the talk and the time that this reaches YouTube. So let's start with questions from the Zoom audience. I have a couple already, so let me start. So I was wondering, so you use effective operators to devise these labor ratios but at the same time you also impose particular structures on your Yukawa. So the question is what family symmetries are you using for this? So we have just analyzed these scenarios. We have not constructed a full model at the current point in time. Oh, I see. One could use some Q1 factors but yeah, we have not constructed it at this point. I see, I see. So what motivated this particular structure, the placement of zeros in specific positions? So let's look at model one. Yeah, that's the one that I would, because for instance you have in the lower Yukawas, you have all of the entries and then the upper one, you have the zeros and the one three and the three one. So initially that all of these must be a consequence of whatever flavor symmetry they're using. But if you're putting a zero, then that means that there's something that might go wrong if you put a number there. They were wondering what's going on there. Yeah, so actually if you have zero mixing here, then just, this is something which we also have worked on in another project, then you can get some very nice predictions for the PMNS parameters. Okay, for this one also needs to have the neutrino mass matrix, but let's say one has this ratio and one predicts out of these ratios, the one two mixing in the charge lepton sector. And if one has a particular form of the neutrino sector and for example, try by maximal mixing or something like that, then one can get predictions for the two, three PMNS parameter. Then one something which is also interesting is let's say the up type of color matrix could be completely real. And in the down type of color matrix, one could just have I here, just one imaginary entry. In such a case, one out of this immediately reproduces the correct CP phase for the CPM matrix. And one also gets predictions for the direct CP phase of the PMNS matrix. But so this is just motivated by other work, but we have not, yeah, we've not done such predictions in this particular case. Right, so in principle, tentatively you do more than just to reproduce the ratios, you also get to reproduce the flavor structures. Yeah, I mean, this is something which has been done in other works and we have just analyzed these models which are motivated by such, by giving such predictions. Okay, okay, great. And these effective operators, do you, are they, you see, I mean, are they straightforward to get from like an ultraviolet completion, like can you connect it to, okay, SO 10 breaks to SU 5 and then you would expect these operators to come about it. Did you look at these things? Yeah, this is actually not, if you have SO 10, and this is not so easy to get because then you also have some correlation with the uptype Yukawa matrix. And this is then like too much, you have sort of too many constraints to fit everything. So in SO 10, it's not really working in SU 5, it's working very well because the downtype and charged left-hand masses are very similar. The uptype masses are a bit more distinct. But yeah, these operators come out of such, so you have to introduce such fields which have masses above the God scale. Fine. Okay, great. I don't know if anybody else has got any questions from the audience. I have a question for Kevin. Kevin, in your slide, 41, you were giving mass to the neutrino via kind of loop. Yeah. Diarrheum that is very similar to the scotogenic model, but with multiplets and so on. My question was regarding, is it possible to have any kind of accidental symmetry in this model in such a way that you can have in the loop a neutral and stable particle to take the role of dark matter beside the action because you were talking also to have action or in some aspect action could be the dark matter. But in this case, if you have a massive particle that's also gonna be stable and neutral, you can have also dark matter in the wind sense, let's say. I don't know if you have considered also this piece. We have not considered it. So I don't really know. No, because this is the same diagram that you have in this scotogenic models in which you have in the loop. The loop is protected via Z2 symmetry, let's say the simplest that the people used to have. So in that sense, if one of the particles is neutral and is the lowest with that extra symmetry, it may become dark matter. For the reason I was asking about this, especially this diagram that you have here in this slide. We have not looked into it. So yeah, I cannot really answer it at this point. Yeah, I was wondering if you check that up, maybe later you can see if it is possible in your model. Okay, thanks. Thanks. Okay, I have a couple more questions regarding your light relics. So I was, of course, wondering if these relics can affect like electro-wig fades, you know, the SDU parameters, or maybe contribute to flavor in a way as you know, this RD anomaly flavor universality or anything, like it can affect flavor in any way. I don't know if you have checked. Maybe you can have a lift of your violation, things like. Yeah, I mean, for example, this particular laptop clock has been extensively used to explain the RK-RK star anomaly. However, yeah, this is since it's not done. We're not talking about that one anymore. That's maybe not the best one anymore. But RD-RD star cannot be explained by this particular laptop clock and which requires some different one. But still the upper bounds on the masses are not that terrible, right? So in principle, if these things are heavy enough, then you can make them not contribute to anything giving you problems, I guess. Yeah, yeah, this we have... Yeah, I mean, we also sort of assume... Sorry, aha. Okay, sorry. We sort of also assume diagonal texture for the recovery matrix, and then you wouldn't have any violation. Yeah, then it's okay. Yeah. Okay, great. So we did not get any questions from the YouTube audience. So unless, I don't know, Roberto has got any other question? No, I don't have any. Okay, great. So then that would be it. Thank you very much, Kevin, for this very detailed talk. And to all of the audience, we'll be seeing you in two weeks with Miguel Romero giving a talk on machine learning, right? So see you soon. Thank you very much for being here. Thanks a lot for the opportunity.