 Okay. Hello everybody. My name is Joel Jones from the PUCP in Lima, Peru, and I'll be today's host of this webinar in the Latin American Webinars of Physics. Today we have a very interesting talk about neutron anti-neutron oscillations in supersymmetry. But before we begin, let me remind you that you can ask questions via the Q&A in Google+, these questions will be answered at the end of the talk. Or you can use a hashtag to ask us questions on Twitter. The hashtag is this one. So that's that. Remember also that if you miss any live transmissions, you can watch the transmission later in our YouTube channel. Let me tell you also that we have a WordPress page where we also centralize all the information. I think you can see it right there. Okay. It's not very difficult to remember, right? Law physics. WordPress. So okay, let's get to business. The speaker is Lorenzo Calibi, and he's currently a senior research associate in the Institute of Theoretical Physics at the Chinese Academy of Science in Beijing, China. So he's practically giving this webinar close to midnight. So I guess we should be very grateful for Lorenzo to give this talk, right? So Lorenzo received his PhD from the University of Padova and has carried out postdocs at CISA at the Max Plagg Institute and the Université Libre of Brussels, right? And the title of his talk is Neutron Anti-Neutron Oscillations as a Probe of Supersymmetry Beyond the LHC. So let me present Lorenzo. Let's see, present to everyone. Here we go. We're all yours, Lorenzo. Hi. Hi to everybody. Thanks, Joel, for the presentation, and yeah, thanks for inviting me to give this seminar. So I think now I should just share my screen somehow and show you my slides. Can you see it? Everything good, everything good. Okay, so here we go. I'm going to present a recent work that I've done in collaboration with these friends who are both theorists and experimentalists from the University of Gothenburg and Stockholm in Sweden. So as Joel anticipated, the topic is Neutron Anti-Neutron Oscillations. So why to study such such process? So of course, this is a process that violates the barion number by two units. And we know that barion number is just an accidental symmetry of the standard model of particle physics. Basically, the Lagrangian of the standard model is invariant under barion number just because you cannot write any barion number violating the operator respecting all the other symmetries. Nevertheless, it is actually violated. It's broken by number-turbative effects, but this gives very tiny possible visible effects. So in a sense, if we observe any process violating the barion number, it's a clean signal of new physics. So this is the first reason why we might be interested in looking like processes of Neutron to Anti-Neutron Oscillations. Furthermore, we know that barion number violation is one of the requirements for having a successful biogenesis to produce the barion asymmetry in the early universe than we observe today. So we expect that any extension of the standard model of particle physics will give substantial barion number violation for this reason. The first process that we can think of as barion number violating process is of course proton decay. As we know, this has been searched for since many years and present constraints are already very stringent on the lifetime of the proton and this process is of course requires the violation of barion number by one unit, but also violation of the lepton number simply because for conservation of spin basically a proton cannot decay to anything else than a lepton. So if instead we have a theory that gives substantial barion number violation, but no lepton number violation, the only new effects we can observe arise at a level of delta B equal to. So violation of the barion number by two units and processes of these kinds are precisely Neutron translation and as we will see later, possibly also dinucleon decay, so the decay of two nucleon particles inside nuclei. The main motivation for studying these processes or for reviving this process that has been studied quite extensively in the past, but not so much lately in recent years, is radar experiment. So that was our starting point. Why? So the present limit on neutron anti-neutron oscillation using three neutrons is this one, it's a limit on the oscillation time of the order of 10 to 8 seconds and it was established already more than 20 years ago by this experiment in Grenoble in France and this is a sketch of what was the experimental setup. More recently, Super Kamiokan in Japan established undirectly in it based on the observation of the fact that as you know they have a big tank with a lot of water, so this means a lot of oxygen, so they can constrain on the oscillation of neutron bounded within oxygen nucleus. Then relying on some nuclear physics, you can translate this bound, as you can see it's very very stringent in terms of a lifetime, but the processes as we will see in a minute are very different if the neutron is a free state or it's bounded in a nuclei. It can be translated to a bound on the oscillation time as a free neutron of the same order of magnitude of the Grenoble experiment, slightly more stringent. Of course this translation involves some nuclear physics uncertainties, but it should be pretty robust. So our motivation was that there is a new facility under construction in Lund in Sweden. It's a European project, it's called the European Spallation Source, but it's a new source that will be made in the process of intense neutron beams for new experiments on neutron-20 and neutron oscillations. So this is also why my collaborators in this project were old people working in Sweden by the way. And so this project has not been done in Lund, and it came up with the solution of the neutron oscillation by three orders of magnitude. So it's a quite remarkable improvement, which translated in a limit on the oscillation time will be a factor of 30 or so. So this is a sketch of the proposed experimental setup. Here you have the neutron source, then the neutrons are guided within a pipe, vacuum of course, and they are let fly for about 100 meters. There is a magnetics fielding, as we will see in a second, this is an important requirement for this experimental setup. And finally, we can detect this process. It's a very simple equation, so this kind of Hamiltonian matrix is very familiar to those who work in neutrino physics. Here we have the energy of the energy of the anti-neutron and some mixing terms. Of course this mixing is an interaction that violates the barrier number and it is required to induce our process. So from this we can calculate very similarly to again to the neutron oscillation the probability that's a neutron after a time of flight, t-oscillator, an anti-neutron. So as you can see, this probability gets suppressed by this delta E, which is the energy difference of the neutron and anti-neutron states. So this is the reason why this experimental setup requires a magnetic shielding because the energy difference given by the Earth's magnetic field would be enough to decrease, to suppress this transition probability to unobservable levels. And by the way, this is also the reason why in nuclei where of course a neutron and the anti-neutron feels very different potentials, the transition probability is so low that an experiment like supercamucanda can set, I mean even if it can set such a huge bound, then this just translates to 10 to the 8 seconds in terms of free neutron oscillations. So how can be induced a mixing between a neutron and anti-neutron? Of course we can just work in a low energy, effective theory, writing effective operators that can give rise to this kind of mixing. The simplest are of this kind, so you see these are six quarks, effective operators, possibly of different chiralities. So this means that these are at least dimension 9 operators. There is a full basis of operators. If you write it in an SU2 invariant way, you will see that there are possibly 14 combinations of six quarks operators up to mass dimension 14 because of course for SU2 invariance some of these operators require insertions of Higgs-Vab. What can be the underlying new physics, so the UV completion giving rise to operators of these kinds at low energy? In this work, in order to have a definite renormalizable setup and to compare basically the discovery potential of these new proposed experiments with other kind of experiments, for instance high-energy collisions, DLAC, we worked in a very well-established concept, namely supersymmetry with a apparent evaluation. Arparity evaluation of course is required because the supersymmetric Lagrangian will be by your number conserving if arparity were exactly conserved. So we did the simplest possible choice, so we extended the minimum supersymmetric standard model just with one set of operators, those precisely that violates arparity and the barion number. So you can see here we have three quark superfields that then translates in the Lagrangian in interactions between a scalar quark, a quark, with two ordinary quarks. If we write only this new term in the superpotential, we have no lepton number violation, at least at the perturbative level. So this means that as I was mentioning before, no proton decay can be induced. But this term violates barion number by one unit. So we already see from here that we will require this kind of interaction twice in order to induce two units of barion number violation. And given this tensor structure, these are SU3 indices. So this is an SU3 contraction in order to have an SU3 singlet. This is a totally anti-symmetric tensor. We can see that these terms do not vanish only if these two fields are different, namely if the flavor indices of these two quarks or quarks are not the same. In other words, these, the terms induced in barion number violation, we require flavor mixing, flavor violation too. So again, this is our model. As I was mentioning, flavor violation will be required in order to generate an embarrass violation. So first constraint that we will have to take into account comes from flavor physics. So ray of flavor and CP violating processes induced by supersymmetric particles in the loop. For instance, in meson oscillation, KK bar mixing, BB bar mixing. This will be first constraint. Second set of constraints will be given by other processes that violate barion number, namely dinuclein decays. So two protons or two neutrons in the nuclei decaying, for instance, two counts or two pines. These kind of processes have been searched, again, by supercamucanda, observing possible decays, of course, of oxygen nuclei. And they can be translated in lifetime of protons or neutrons, diprotons or dinutrons, again, of the other of 10 to the 32 years. So these processes can set relevant constraints on the parameter space. And then, of course, we are dealing with a supersymmetric setup. So we have these new supersymmetric particles, squirks, gluinos. So we will have to take into account constraints coming from direct searches for the production of these new particles at the LAC. But we are in our parity violating setup. So, as you know, the lightest supersymmetric particle is not stable anymore, which means that we are not going to deal with a more canonical Susie signature based on a large amount of missing energy at collider. So the collider phenomenology will be quite different, as we will see in this slide. So we have squirks, and gluinos. They can both now decay to ordinary quarks. So this means that at LAC, they just will give rise to jets. For instance, this scalar quark, this quark, can simply decay to two quarks, given our parity violating interaction lambda double prime. And this is very simple expression for the decay width. And in this figure, I'm showing the squirks lifetime, so the squirks decay length, as a function of this value number violating coupling. So here we have 10 to the minus 5, and I'm taking lower and lower values down to 10 to the minus 10. So, depending on the decay length, so how fast is the decay of this of this particle, we can have different regime, different phenomenology within an LAC detector. So if the interaction is strong enough, namely above 10 to the minus 6 or more for this new Yuccava coupling, the squirks will just decay promptly. So the two jets will appear as coming from the interaction point. While if we lower this coupling, the squirks gets more and more long lead and gives rise more likely to displaced vertices, namely it travels through the detector for a while from the tracker and then decays. So the two jets points to a displaced vertex, a vertex which is the finite distance from the primary interaction vertex. If you lower more and more the coupling, eventually these objects will result as stable on the detector time scale, which means that it would look like what people call our addrons. So it's a relatively long lead, strongly interacting particle which will adornize, we will form bound state with ordinary quarks. So it will look like a heavy colored object, heating the material of the detector at any place and eventually leaving the detector. So for the three of this kind of regime, there are of course dedicated searches at LAC experiments. So these are very different possible phenomenologies. The same we can say about the gluinos. If the gluinos are the lighter than the squirks, they can still decay to cork through this with the mediation of a off-shell scourk with a veal plus cork. So this is just an ordinary SU3 interaction and this is our apparently violating coupling. So this is a three-body decay and so it's farther suppressed by phase space. So this is the reason why on average gluinos tend to be, if lighter than squirks, tend to be more long-lived. Here if you can can see I start plotting from 10 to the minus 2. So the lifetime depends also on the ratio between the squirks and gluinomass, but as you can see below say 10 to the minus 4, the gluino tends always to be long-lived enough to give rise to displaced vertices. So only for very large, apparently violating coupling, we will have prompt decays. And in general, even if the gluinos are heavier than the squirks, they will still decay through this diagram. This time much more efficiently, this decay will be on-shell. So you can see that pair producing to gluinos will give rise to events with six jets. So we can expect a substantial, I mean, quite high jet activity in the signals for this kind of apparently violating setup. So to summarize what we expect at the LSE to constrain this kind of of models is absence of missingity and either events featuring many jets or long-lived hard runs or displaced vertices. So we have to look for the appropriate analysis performed by Atlas NCMS in order to set the constraints of the LSE on our parameter space. We had basically to recast the bounds given by the two experimental collaboration on our add-ons, so long-lived color, the super particles, displaced vertices. So this we employed a recasting done by these two gentlemen in 2015, where you can see for certain ranges of the, in this case gluino to three jet lifetime, a CMS analysis can set already constrained, which are quite strong at the order of 1.4 TV. And then in case our objects decay fast enough to give rise to prompt jets, we had to employ multi-jets searches from Atlas. And we also used the constraints by CMS on die jet production, namely to constrain the the squawk per production. In this case, this can give a bound on the squawk mass of the order of 300 GB or so. Okay, so let's come back to our NN bar oscillation process. As an example, I will just consider this diagram that was for the first time proposed by Skian Er, already long ago, as you can see. So this gives rise to our six quarks operator, as you can see in this case, all right-handed quarks. And third thing that we observe is here, we have our operative violating coupling. So this here, this is the two vertices that violate Mario number. And as I was mentioning, we, in order to discover, to be non-vanishing, we require flavor changing. So the squawk here must be either second or third generation. So a strange or bottom squawk. This means that since we have to go back to the first generation, because in our operator, of course, we require only first generation quarks, we also require flavor mixing. So a mixing between second or third generation squawk with the first generation squawk. So, and here we just exchange a gluino. So these are just SU3 gauge interactions. So in the end, we can integrate out the supersymmetric particles, which are, of course, much heavier than the energy scale of our process. We obtain this operator, and the coefficient of this operator can be written like this in terms of our high energy parameters. Again, we can see two times the value of number of violating coupling, two times this parameter that parametrizes the flavor, the squawk flavor violation, the suppression given by the supersymmetric masses, gluino and squawk masses, and SU3 interaction. And then we can simply use this coefficient to estimate the oscillation time, which just results, just given by this expression, so one over the value of this coefficient times an addronic for fact, which is our main source of uncertainty in this business. So we know that this number has to be of the order of the sum powers of the QCD scale, but there are no definite prediction for this, not even from lattice QCD. So let me plug in some numbers in order to get the value for the oscillation time of the order of the present bound. We need, as you can see, supersymmetric particle of the order of 1TB, 500GV from the squawks. Raiders more value number of violating couplings are sufficient. I'm taking this value for flavor violation, and as I was mentioning, I'm taking the addronic for factor of the order of, for dimensional reasons, six powers of the QCD scale. As I was mentioning before, we have other constraints to take into account, which comes precisely from this flavor violation and, again, the value number violation. So flavor changing neutral currents, so we can write diagrams like this, so box diagrams that gives rise to KK bar and BB bar mixing. Of course, if these flavor violating parameters are complex, this can give rise also to CP violation in KK bar mixing, and the dinotland decays. So if we have this lambda double prime UDS, we can write a diagram like this that allow decay of two neutrons for two protons, two kaons. In case we employ the coupling involving the third generation, the bottom, just for kinematical reason, the nucleons cannot decays to B mesons, but, of course, we know we have, for NN bar oscillation, we need flavor mixing, so we can employ the flavor mixing to write a diagram like this that gives rise to decay of the dinotland two pylons. So our approach was defining some simplified models, so rather than having a definite top down sucy breaking scenario, we just worked with a simplified model as low energy defined only by the supersymmetric particles and interactions we need in this diagram. So we could compare in pretty straightforward way the strengths of all these different experimental informations, the impact of all of them on our parameter space, and our goal was basically highlighting the complementarity of our neutron oscillation experiment and the direct LSE searches. So let me show you some colorful plots. Here I am employing, in this left panel, the coupling involving the second generation, here the third generation, I'm setting this value, this intermediate value, 10 to the minus 6, it's a eucada coupling. So in a sense, we can expect some eucada couplings to be small, if you think of the eucada coupling of the electron, for instance, which is more or less of this order of magnitude. And then here we just show the plane of the escorque and the gluinom axis. So first of all our NN bar present, NN bar constrain is given by this blue line and the expected increase of the sensitivity of the proposed NN bar experiments should test this region up to this dashed blue line. But of course we have other constraints, the strongest in this case is the, comes from binocline decays, which seems to be more or less of the same order of the proposed increase of the sensitivity in NN bar. But we have to take into account that, as I was mentioning, both processes are affected by strong adrenic uncertainties. So here I'm just plotting the central value, but you should really think of these curves like bends which overlap and can span a little bit of this parameter space if you vary this adrenic for factor by an order of magnitude also, since we don't know much about its actual numerical value. Then we have these colored regions which show the constraints, the direct constraints from the LSE on the parameter space. These green ones which are in this part of the plane where the escorques are lighter than the gluinos come from prompt decays. So basically you pair produced escorques or you pair produced gluinos and you obtain bounds from die jets and multi jet surges. Dark green is multi jet and this green one which does not depend on the gluino masses from direct escorque production and bounds on die jets. While on this part of the plane, well the gluinos are the lightest particles you can produce in strong interactions at the LSE. The particles tend to be longer lived, so the main bounds are given by searches for direct displaced jets, this yellow region here as you can see is pretty strong. It goes up to 1.4 Tv for the gluino mass. Then if you have a maximum CP violation in K kebar mixing, that all the region below this red line is excluded by epsilon K, so by CP violation in K kebar. Of course you can reduce this constraint if you assume that the phase is somehow suppressed. While on the other hand the flavor constraints is not so strong in the B sector, so in case of you have this interaction, the constraint from flavor comes from BB bar mixing, which constraints only this region. So you see that your parameter space is much less constrained, you have more room for improvement in a sense from N and bar alone. And also the dinucleon decay is less constrained because in this case the dinucleon cannot decay directly to chaos, but they decay to pion through flavor violation. So you have a a further suppression of the process. So you can see here you have of course for this setup, the parameters you have a quite promising situation, but already the N and bar constraint is pretty strong, tend to be stronger than the constraints set by ELAC, at least on the score mass, already at a level of 1 TV, and the future constraint can be up to go up to 2 TV or so, which is a value which is maybe even beyond the reach of the ELAC itself. On the other hand, if we take this operative violating coupling and we lower it, in this case by 2 order of magnitude, the situation is reversed. All our low energy processes are not sensitive anymore, so the constraints are not irrelevant, while ELAC gives the strongest constraint. In this case also the scores are always long, it tends to be cannot decay prompt, because the coupling is too small, the decay is too slow. So also in this case, in this case we have also a constraint from displaced vertices on score, which gives a bound about 1 TV, and one of the strongest constraints on supersymmetric particles so far, so a constraint on long lived gluinos, which is more than 1.5 TV on this part of the play. So as you can see, I mean here we have really an interplay between this kind of low energy test of this kind of models, and the high energy test of the ELAC. Depending on the regime of these parameters, we can better probe this parameter space with an embargo or directly with the ELAC. So as usual it's important to have both kind of experiments to set complementary constraints. Here we can see the same thing, here I'm simply plotting the coupling versus the squirt mass. So when the coupling is low, this ELAC constraint dominates while if you raise this value-number-violated coupling, of course, then value-number-violating observables give the dominant constraints, and as you can see they can really already exclude up to 2 TV or so our squirt masses. And if we go to an extreme case, if we take even order-1 couplings for the value-number violation and order-1 flavor violation, the situation becomes like this. This is now TV. So this shows basically the potential of this kind of experiments of testing three-level new physics that gives rise to an environmental violation with large couplings. So in principle you see we can already exclude scales which are of the order of hundreds of TV, and you can have a substantial improvement by the observed experiments up to 1,000 TV or so. So here I'm plotting the same thing this time just setting the value-number-violating coupling to 1 and plotting the oscillation lifetime as a function of the squirt mass. And here you see the present bounds and the projectile sensitivity. While these bands give you the feeling of this infamous hydraulic uncertainties I was mentioning before. But you can see anyway there is a lot of room for improvement for this new experiment. So in principle you can really go up to again 1,000 TV in testing this kind of models. Okay, I think I'm running out of time. So let me just mention here very quickly that this was just one possible way of giving rise to an environment oscillations. If you have a look at the paper we collected several more diagrams that do the job. This is an example of a loop-induced an-embar oscillation which requires electro-wick interactions instead of strongly interacting supersymmetric particles as before. So here you have further loop suppression but your flavor violation is automatically given by this vertices by the ordinary CKM matrix. So in this case you don't have to assume anything. You don't have to assume a source of flavor violation beyond the one that it's already present in the standard model. But the effect is much smaller. So in terms of but also the bounds are much weaker from DLC. So here I'm showing the present constraint from an-embar and the possible improvement by the proposed experiments. Anyway, also here we can test squark masses up to order 2 TV if the coupling is large. Okay, this brings me to my conclusions. So I just show you that this future neutron and neutron experiments proposed that the ESS has indeed the capability of probe number by a number of violations beyond the present constraints. So we worked in a specific setup where as you can see different information from different physical processes are required to assess the sensitivity of the experiments. We have on one side flavor constraints on the other side, LAC constraints, dinoclon decays. So but even if you consider all these bounds, still I show you that at least for certain setups of the parameter you can indeed test the models beyond the present bounds even if you discover something. And in our example, I mean what is remarkable is that squarks and gluinos in the multi-TV range in principle can detect them. So this is beyond what we can do at collider, at least at DLC. And if you are in a crazy situation like that, of course you can even test physics which is really beyond the reach of any collider we can dream of. Okay, I stop here. Thank you very much. Okay, thank you very much, Lorenzo. Get back, stop presenting. Okay, so it's time for questions, I guess. Let's see, let me remind everybody that you can, here we go. Give me a second that there's some funny screen sharing going on. Let's see, let me, here we go. Okay, I think it's working now. Okay, very good. So, okay, let me remind everybody that we can, you can ask questions via the Q&A on Google Plus and via Twitter. So we already have one question which is by Roberto Lineros, but I guess that he can make it directly through our audio system. So here we go, Lorenzo. Thank you, Jorge. And thank you, Lorenzo, because it was very interesting, the talk. And I have two doubts. One is because you mostly in your study, you constrain this lambda UDS or UDB bottom. Yeah. And my question is if it is possible to go to access to higher older generation like, I mean, with Charms or, I mean, lower mass, but with higher generation. It's a good question. Let me share the screen again. I should have a backup slide. You can see it. Okay, so for instance, oh, sorry. Here we have another possible electroweak contribution. So which involves a loop of third generation quirk and squirk. So tops, tops, bottom and bottom. So in this case, the coupling that you can probe if, I mean, with an NNBAR experiments and a setup like this is of this one. I don't know if you can see it, but it is basically three, one, three. So yeah, it involves the third generation. While typically diagrams with that for the second generation science here instead, you put the charm since you need some basically some kind of additive flip. So you need mass insertions. This would be very much suppressed by the charm mass, of course, compared to the top mass. So it's not going to give a visible effect. But in principle, yeah, even though most of these these are the basically the models we study, most of them are basically sensitive to the two couplings that I have shown. There is this further contribution which involves a different combination of coupling and a different entry of this lambda double prime tensor. Yeah. Thank you. And another doubt that, I mean, but this is more like transversal. Do you know, do you know if it's possible to, for instance, this experiment of double beta decay, the detector, can be sensitive to such low signatures? I mean, because this is a rare process. I mean, if you have neutron anti-neutronation. Yeah, but I mean, in the, well, in this experimental setup, basically you have a neutron beam. So you let the neutrons fly, and then you observe, you observe some of the neutrons actually convert into anti-neutrons. So in this case, you have no, no nuclei involved. A super camiocanda, I have no idea. But I mean, you know, there you have basically just oxygen. So I don't think you can do double beta decay with oxygen nuclei. No, no, I mean, I was referring that if this kind of rare process may play a role, or may be detected in double beta decay experiment. I mean, because either the double beta decay and either this effect, I mean, other the neutron anti-neutron oscillation are so rare. Well, yeah, yeah, sorry. But you know, I mean, if I don't think you can do better than a super camiocanda, which has a huge amount of material and observed for many years. So they had a lot of bound neutrons compared to the, of course, to the size of a double beta decay experiment. I mean, they set already constraints of the level of 10 to the 32 years on the on the oscillation in the in the in the in the oxygen neutrons. So yeah, I think it's. Yeah, I think because of the mass of the camiocanda, super camiocanda is almost impossible to or the experiment to complete. I mean, at the level of having something similar. I wonder about ice cube, but that might be there might be a problem of the energy thresholds. Uh, maybe they're not sensitive to. I mean, yeah, this process will be too low energy probably for them for for ice cube. But I mean, if not, you know, they have even more oxygen than the super camiocanda in principle. Yeah. They will have to install different the apparatus in on the ice to broke the threshold. Maybe. I guess. Maybe if there is someone from ice could listen, maybe can have an anyway. Thank you for having for my question. I guess that's all. Thanks to you. Let's see. Let's see if there are any other questions. Okay, there's none left on the Q and A, but I have I have a couple of questions myself. Please. So, so one of them is when you present your your initial slides, you present the initial Hamiltonian, right, or oscillations. You don't include an absorb, absorptive term. So, so why is this so the decay, you mean? I mean, yeah, yeah, the width. Yeah, exactly. Because basically on the time scale of these experiments, our neutrons are to large extent stable. If you think about it, the neutron, the free neutron lifetime is about 15 minutes. So I don't know how fast they are, but of course, they travel this 100 meter pipe in, yeah, much less time than 15 minutes for them. But it's, I mean, in principle, I should take into account, yeah, the imaginary parts here and have the width. Yeah. But of course, for this kind of process, I mean, and this experimental setup is irrelevant. Right. And in principle, you could also have CP violation, right, on the deltimes. No, I guess, yeah. Now, the other the other the other question was you've been using the right right insertions. So, right. Is this due to the to the operator that you're using? Or is it possible also to pose left right operators or left left operators or a mixture of left left and right, right? Yes. Yes. Good point. I mean, here, I mean, it's the simplest thing we could do with just with right hand, I mean, generating a fully right handed operator. Yeah. And of course, as you were mentioning, then you have to assume a source of flavor violation in the right handed Scork sector, which is beyond the minimum flavor violation, as we know. But in principle, you can do something different. So, you see, this is the full basis of this you to invariant operator. So, you can have also processes that involve left handed Cork doublet. And in our context, here, these two professors in 86 basically draw this diagram. Let me zoom for you. In this case, you have the flavor violation in the left between among left handed Spirnian left handed Scorks. And you need a left right carotid flip. So, it's a kind of different contribution also because I mean, different supersymmetric parameters are involved. And you see you end up with a different operator. So, involved into left handed down Corks. But if you look at the results, okay, they're kind of different from the LAC side, but mostly because my choice of the parameters here. But I mean, as you can see, I mean, qualitative, we can get to the same conclusions. Right. Yeah, that's more or less what I wanted. So, the orange region, what is the orange region? This one, you mean? And then the dark one. Ah, yeah, this one is from flavor changing neutral currents. In this case, the most stringent process turns out to be B2D gamma. So, from B2D gamma, you can give a pretty strong constraint here. Well, also because here I was taking a quite large value for this flavor violating parameter above the minimal flavor violating prediction, by the way. So, anyway, you need some substantial flavor violation for these processes to give rise to NN bar oscillation observable value. Okay. But anyway, the flavor constraints is strong, but it's not as much as the NN bar constraint. Cool. I don't know if anybody else on the audience has got a question? Yeah, I have one that is very naive, I guess. For instance, in this model, the one that I analyze, you didn't consider or you didn't add, because mostly relevant, I guess, the Gravitino setup. In the sense that usually models with a variety of violations, you can have that your Gravitino, the Gravitino can take the role of the dark matter. So, my question was, because it's the mass plan surprise that it came with, and it's a good point, actually, because, I mean, you know, I mean, we didn't consider the Gravitino mainly because our phylaws of your just defining simplified models with just the ingredients we need that for NN bar alone. But we have to say that, sure, the Gravitino cannot be lighter than 1gb in this setup. Because if not, then the proton decay to Gravitino. So, you have proton decay. Because in this case, you don't need to violate lepton number anymore. So, this kind of value number violating coupling that I was employing, if you want, if you have a fermion lighter than the proton, then it's enough to give you a fast proton decay. So, the model is completely excluded, or at least it's excluded. I mean, any possible large effect in NN bar oscillation is, of course, excluded. So, any fermion lighter than the proton cannot be there. So, also, axinos or other kind of exotic things. So, this means, for instance, that, yeah, either you are not engaged in mediation, or you have a very high mediation scale. So, you need a relatively heavy Gravitino, or like in Gravitino, mediation and Gravitino, with the mass of the same order of the other supersymmetric part. For sure not a light one. So, I don't think you can have, it can be long lived, I don't think you can have a Gravitino dark matter in this case. So, you should radar invoke a completely different sector, like an axion or something like that, for that matter. Yeah, that's, you know, one of the problems of this parity violation. It was lately got a bit of a revival of interest, because of course, you can sum up in certain setups, you can hide a little bit the supersymmetric particles from the LAC searches, because you don't have missing energy. But on the other hand, you have a lot of jets, or in case of leptonica parity violation, you have a lot of leptons, also the bounds are kind of strong. But you lose anyway, your dark matter can't do it. But we like axions. Yes, very nice. So, in principle, it's kind of set up with a Gravitino dark matter, it's not, it's unlikely in this kind of. I did start with it in detail, but I would say so. I don't think you can have a long lead Gravitino. Thank you. Okay, I think this is all. We don't have any further questions that I've noticed. Let me check Twitter. No, nothing else on Twitter. Okay, so I hope you all enjoyed this webinar. Before I finish, don't forget to subscribe to the YouTube channel of the webinar if you want to watch the seminar again. Well, I hope to see you all on the next Latin American webinar on physics. Thank you again, Lorenzo. I guess that you can now go to sleep. And we'll see you all next time. So, let me put it.