Happy Friday everybody. Welcome back Lesson a week away for Labor Day. How's everybody doing good to see you all bones. Good to see you That's C2 John rich. Good to see you all Eric everybody mark. Good to see you can everyone. All right guys So before we get into some excitement the like the OPTT going on today The market is down about 125 points so far in pre-market. I rarely would ever say this But am I allowed to say that it kind of Ducks in the morning. I don't see anything going on a pre-market other than some ETFs. I really don't see that much going on I'd be honest with you. I'm looking around. There's a couple of stocks on the short side, you know Sometimes it happens. It does happen But we always know that something might come out of the gate at 930, but well check I got about like four or five stocks. I saw I found this morning I know some of you guys were looking at it but other than that pre-market I mean some of the ETFs go moving on pre-market. That's about it. I mean unless you guys see something differently I don't really see too much going on out there What's going on the market now?  I've never seen it rain so hard yesterday in front of my house yesterday in New York it's raining again here. So I always like not to give you a weather update not because I'm the weather guy it's just that Weather does have effect when especially going into a weekend because people think it well should I leave early? Should I go to the Hamptons out east today? I'll get ready for the you know get back to my summer home and stuff like that and As of right now, I think it's gonna be kind of quiet So that's good because then I mean people gonna stick around we might get some volatility out there But there are a couple of things out there. We're all gonna check out But but the OPTT was actually we'll talk about this one a little bit some of you remember back in April We trade this stock it gapped up from five. It went opened up at seven shot Right up to like 16 one about three four hundred percent movers of the day. I always love to see that coming back to it Just make sure you check your Check your journals and make sure that they if you did trade it You were with C2 back then definitely check it out and see how you did on it LB though I want to talk about what happened yesterday There were a couple of good stocks yesterday that we did trade It was a good pre-market short right there and that LB that did just phenomenal and then we just had a nice little bounce What do we always remember about? You got to remember regarding about Stocks that get destroyed we know about ETFs and we also know about Stocks that are I'm sorry stocks that are pharmaceutical stocks that don't come back and other ones that aren't do come back So we got a little bit of action on this one any NETE was pretty decent going into the close yesterday She gapped up pretty nice went from 350 to 550 nice little move there also and then she kind of like flatline But that was about it.  I'm telling you We talked about this during the Christmas holidays. We talked about this, you know During tax season. We talked about this during Thanksgiving. You know what it is what it is and Just be very fortunate that we did get some pretty nasty volatility going on and you know I'm not a fan ETFs, but that kind of more or less With with with what's happening in the in the in the Dow being so volatile That's really pretty much what we've been doing pretty well on other than a couple here and there And for some of you guys that are new just keep in mind. We do definitely You know this list gets about 10 to 15 deep when it when the market's really fun So whatever you miss you could always do it and that's why we're doing the classes right now Remember you're right now in phase two. It's almost done because it's Friday and next week's going to be phase three with me And uh, there's no better time to learn now than then in the busy time, which is September, October, November So what is moving this morning and what is look pretty good? Let's go start off with uh, hula packer HPQ the stock is just getting pretty decimated lately Took a nice little hit right here want to hold it overnight wake up when it was at 21 50 boom at 18 90 now It's down 17 60 looks like it's testing some support levels I think from that chart, but uh, who knows the stock's not looking too well could be a nice short You know going into the open footlocker I don't just have this company stays in business.  It did have a little bit of a push Recently, but looks like it's going right back to where it started So footlocker, I'm not going to hold anything against them. Actually, I think I bought my first pair of sneakers a footlocker for the first time about March I can't forget because that's actually when I started with my personal trainer So I haven't been there probably since I was 18 years old. So It's still there. It's still it's still chucking away, you know OPTT another one once again, that's the one that's on the watch list I want to keep a close eye on it. Um, it's testing some support levels from yesterday's previous resistance levels TV I X Is one of the ETFs that did pop up on the radar you could see here at eight o'clock one from 1640 to 1780 Be careful if you're a beginner trader if you're new to cyber train diversity If you're not one of our students at least you're about two three months into our training stay away from ETFs guys There are 25 000 stocks out there. You guys know students been here long enough.  That's the way to go DWT is also another one also Regarding about the ETFs there that one is also moving pretty nicely too But other than that, I don't really see anything that much out there I mean you got the footlocker down 12 with 700 000 shares HPQ quarter million shares down 9 percent What's this seal that just came up right here? Oh, this one just tanked someone just came from nowhere. All right. Well, we know this one ain't coming back It's how do we know that just read the name Let's just read that name all right, so Yeah, OPTT's up 40 percent. That's it. I mean look at the percentage gainer's really not a lot out there Not I'm really a lot. All right. Anything guys that you found that I did not find We need to made about five cents uh on the FLHL All right, give him a round of applause ankle bloke taking a profit wings better than a loss All right, listen, I got told you earlier when we started I really kind of stinks out there It's perfectly okay We all and one of the big things we teach in phase three. It's not about um The goal is having a good winning day a good losing day and two flat days Not every day is all rainbows and puppy dogs So um gotta take what the mark can give you especially on a friday So be very careful how we trade on fridays. All right guys. Good luck today. Happy trading Enjoy your classes today with josh And if I don't see you, uh, we'll see you back next week and don't um, we'll see you back next week All right for our last week of summer. Good luck everyone. Happy trading


The key tool to keep your TEFL class managed, body language. In the classroom the use of body language is incredibly important in effectively managing the class. There are several different ways a teacher can utilize body language to manage the class. One of the most obvious of these is the use of eye contact. Eye contact can be used to show students they're involved and encourage them to contribute to the class. This in turn helps hold their attention, as well as allowing the teacher to ensure that everyone is participating. Conversely it can also hurt the class if used inappropriately, such as during not teacher-centric activities. Like all classroom management techniques, it is important to strike a balance to manage the class effectively. The same can be said of the use of gestures in the classroom. Gestures can be very helpful as they help convey meaning visually, whilst reducing the need for verbal explanations. The addition of visual gestures is something that naturally helps keep students in the class attentive. Similarly to the use of eye contact though, unclear gestures can have a confusing and negative impact on the class, so to maintain a well-managed class, it's necessary to make sure they're used correctly. The final major tool a teacher has at their disposal in this area, is the use of their voice. A teacher with clear speech who sounds enthusiastic, is going to have a much easier time holding a class's attention, than a teacher who speaks in a dull monotone and isn't visibly enjoying being in the classroom. When used effectively, all these techniques can come together to provide major help in managing the classroom. Thanks so much for watching. We are ITTT the leading provider for TEFL and TESOL training courses. If you liked this video, please subscribe by clicking that button down here, and click on any of the videos here on the left, for more interesting teaching tips for getting certified to teach English abroad and online.


Okay, we're online. So hello everyone and welcome to our 49th webinar of this series of these Latin American webinars of physics. My name is Nicolas Bernal and I'm from the University of Antoinio in Bogotá, Colombia. And I will be your host today. So speaker today is Sebastian Ingenhüt from Technical University of Munich and where he's a PhD student working the group of Professor Alejandro Ibarra. So Sebastian will talk today about dark matter and the decaying dark matter to the gravity portal. And we're super glad to have him here today as our speaker. So first, let me remind you guys that you can be part of the discussion, writing your questions and comments via the YouTube live chat system. Okay. And now I can hand you over to Sebastian. So are you there? All right, thank you. Thank you very much for the kind introduction and for having me, for allowing me to present my work in this format. Yeah, so like you already said, the topic today is going to be gamma rays from latex matter decaying through gravity portal. So just for a bit of context, I guess, this is the third in a series of free papers that I've been working on together with Oscar Cata and Alejandro Ibarra here in Munich. So the last one, this one appeared July this year. And so in the context of these papers, we're talking about dark matter that the decay is through a nominal coupling to gravity. And so I will refer to the previous two papers that you can see in the opening slide throughout the talk, but of course I will try to make it self-contained. And for the purpose of this talk, the focus will lie on light dark matter and the MEV to GEV mass region. We will see how this sort of framework leads to gamma ray signals, which might even be observable depending on the coupling size, of course. Right, so this year is my outline for today. I will start out with a brief motivation. So it's going to be about global symmetries that stabilize dark matter against decay and the interplay between gravity and these global symmetries. Then I will explain the setup in a bit more detail. So dark matter that can then decay via this sort of operator we dubbed gravity portal interactions. And then we will look at the experimental signatures that we studied. So in this case, the gamma ray flux I would expect from this kind of coupling and limits we can get from the CMV. And then finally I will conclude and show how far we can already constrain this nominal coupling. So since I have 30 minutes, I will have a dark matter introductory slide. So since the 1930s, of course, we have had an increasing number of observations that show us that give us evidence that there is a dark component because multiple fluid that we have some dark matter component. And we have evidence on multiple distance scales at this point. So if you look at galaxies where the rotation curves that we measure require some the galaxy to be embedded in the dark matter halo for it to be consistent with Newtonian predictions. Or whether you look at the collision of galaxy clusters here, you look at the gravitational lensing and you see that the mass distribution is not centered on the distribution of visible matter. Or if you look at the CMV the temperature fluctuations and you compare that to a prediction in the lambda CDM framework, you can see of course this perfect agreement here if you include a dark matter component into the equation. So we have evidence at multiple scales now but all this evidence is of course based on the gravitational interactions of dark matter. So of course over the past decades we've tried to measure dark matter properties in other ways. We've got direct detection experiments, we have indirect detection and we try to see if dark matter has other interactions. But well the simplest dark matter candidate I would argue is that of a particle that is uncharged collision less than stable and might just inter gravitationally. So you might have to think about well, what if dark matter really only interacts gravitationally? Can we still hope to see it in experiments and to find out about its nature? But then of course we can relax any of these three assumptions here. So we can for example look at millicharge dark matter or dark matter that's charged under dark gauge group or something. We can look at dark matter with self interactions which might help with what people call a small scale problems with lambda CDM. We can also look at dark matter that's not absolutely stable but that can decay and potentially give us signals that way. And this is what I'm going to talk about in this talk here. So let's focus on the third part here that the stability of dark matter. So what we know from observations is that if dark matter is made up of particles they need to be extremely long lived. So the dark matter lifetime needs to exceed the age of the universe which is about 10 to the 17 seconds. And this is actually quite long. So if you think about the visible sector only very few particles have that kind of lifetime. And it's usually linked to a stabilizing symmetry. So the electron for example is stable because it's the lightest charged particle, the lightest neutrinos tail because it's the lightest fermion and so on. And likewise the stability of the dark matter particle could be due to some symmetry protecting it. So this might be a dark age symmetry or it could just be like a global Z2 symmetry. So for example in the scalar inner doublet model you just have a second Higgs doublet which is stabilized by a global symmetry that you introduce to the model. Alternatively of course, dark matter doesn't have to be absolutely stable. The axion for example can decay into photons but because of its tiny mass the decay rate is so low that it's still perfectly fine with observations. Right, so the next thing to maybe think about in this direction is then if we have a global symmetry that stabilizes the dark matter candidate then what happens if you add gravity to the equation? So there are arguments in the literature where gravity does not conserve global symmetries. So I'm not going to pretend I'm an expert on these kind of papers but for the purpose of this talk let's try to just be agnostic and just say, well what if the dark matter particle is stabilized by a global symmetry that is broken by gravity? So this is the kind of framework that I want to talk about. And this is the framework as I said that we first talked about in these previous two papers that you can already find on the archive. So the scenario is that of a dark matter candidate where it's non-gravitational interactions preserve global symmetry like global C2 so it's stable against decay but through non-minimal gravitational interactions the C2 is broken and the dark matter can decay through this gravity portal. And in this case the long lifetime of the dark matter particle is linked to the Planck suppression of gravitational interactions. So that's one nice feature. Right, so in order to break like a C2 symmetry stabilizing the C2 we need to non-minimally couple the dark matter kind of to gravity. And this can be seen quite easily. So if you start like with a general agrangian like this here and you couple it the dark matter field file in minimally to gravity of course afterwards it's still going to be stable. So we need a C2 breaking operator. So from an EFT standpoint we asked ourselves well what is the lowest dimensional non-minimal operator coupling dark matter candidate to gravity that conserves Lorentz and standard model symmetries but breaks the C2? And the answer is surprisingly simple. So in the three scenarios that we talked about and that I'm going to mention later in the talk it always has this form here where Xi is a dimensionless coupling R is the Ritchie scalar and then F1 of Phi is a function linear and Phi with mass dimension two. Of course you could couple you don't have to couple to the Ritchie scalar you could couple it to the Ritchie tensor and some covariant fashion but we found that in three scenarios that we started in detail the lowest dimensional operators always turn out to be proportional to the Ritchie scalar actually. Right so if you add this kind of operative theory what happens is that you mix the dark matter candidate and the graviton and then what that means is that because gravity acts universally on the visible sector in the sense of the equivalence principle this means that the dark matter candidate ends up with a universal coupling to the visible sector and it can decay into visible sector particles via intermediate gravitons. So this can be seen quite easily so this is a bit of a math heavy slide here but so if you take the metric tensor you expand it around Minkowski background and here are Lampte as the graviton field and Kappa as the inverse Ritchie's plant mass then expanding the Ritchie scalar around this background means you have terms with two derivatives here and then terms linear or quadratic with a higher order in the graviton field so then if you have a non-minimal coupling term like this where M here is a mass scale and phi is just the dark matter candidate then of course you multiply this by the Ritchie scalar you end up with these kinetic mixing terms here. So then what you wanna do is to bring the kinetic Lagrangian into canonical form you wanna diagonalize it and you do that by performing a vial transformation on the metric tensor so you take the metric tensor multiply it by this functional omega square which is essentially one plus this non-minimal coupling structure here and then afterwards in the Einstein frame you end up with canonical Einstein gravity for the gravitational part and a modified Matta Lagrangian here which is now expressed in terms of the Einstein frame metric and picks up a pre-factor omega to the minus four and so in the Einstein frame the gravitational sector is canonical you just have pure Einstein gravity but the Matta Lagrangian is modified and because this functional omega includes the dark matter field you end up with explicit couplings between the dark matter candidate and the visible sector so schematically what happens is in the original formulation of the Jordan frame you have kinetic mixing between phi and the graviton lambda which then couples to the visible sector whereas after diagonalizing kinetic terms the dark and the gravitational sectors are decoupled and the interactions with the visible sector are manifest in this form right so as I said in the previous two papers we already talked about heavier dark matter above the GV scale so in this case the visible sector is just given by the standard model degrees of freedom and then we looked at three scenarios so we looked at a scalar singlet a scalar doublet and a fermionic singlet and then in each case we looked, we tried to find out what is the lowest dimensional a non-minimal operator of the form that we want so for the scalar singlet it's really simple you just have the coupling here the Ritchie scalar, a mass scale and the dark matter field for a scalar doublet this mass scale M here is replaced by the Higgs doublet so H1 would be the standard model Higgs and H2 would include the dark matter candidate as its neutral component and then for the fermionic singlet you need to make the operator Lorentz and Gage invariant so the lowest dimensional operator here is actually a dimension six already Braille's SU2, lepton doublet and H1 against the standard model Higgs and CHI in this case is the dark matter candidate and so for these three scenarios what we did in these previous two papers was to compute all the partial decay rates the branching fractions so on the left-hand plot here you can see the branching ratios as a function of mass between a GeV and 10 to the 8 GeV so as you can see since the coupling to the visible sector is universal the branching ratios depend on the dark matter mass so for example at the GeV scale you mostly decay into Ws or Higgs bosons at lower masses at the fermion thresholds here these channels spike up because the coupling is universal you preferably decay into final states that have a similar mass to the dark matter candidate until you reach this high mass region here which is kind of cut off we decay into the states with the highest particle and multiplicity and then what we did was to compute the total lifetime of these dark matter candidates so this is the total lifetime in seconds as a function of the dark matter mass between a GeV and 10 to the 12 GeV and the orange dashed line here is the age of the universe 10 to the 17 seconds this 10 to the 24 seconds is the well this is the kind of typical limit you get from neutrino telescopes for the lifetime of dark matter decaying into final states with neutrinos and so as long as the dark matter lifetime which is plotted here in red, blue and green is above these and everything's fine but as you can see at very high dark matter masses here the lifetime drops below these values for order one couplings was I equal to one so then we would need a suppressed coupling suppressed non-minimal coupling for the scalar doublet and the fermion singlet for the scalar singlet in fact the total lifetime always lies below this the age of the universe for order one couplings so as a summary of the first two papers if you want so since the scalar SC2 doublet and the fermion are additionally protected against decay by GaH or Lorentz symmetry we can allow order one couplings up to masses of 10 to the 5, 10 to the 6 GeV for the scalar singlet because it doesn't have this protection experiments might be sensitive to order one couplings so I mean this is the coupling that always appears in the rates so Xi is the dimensionless number M is the mass scale and Kappa is the inverse plane mass so for order one couplings we might be sensitive even at sub GeV dark matter masses so this means maybe we have a signal and the gamma ray flux maybe we have an imprint on the CMB so for the purpose of this talk I will talk about scalar singlet dark matter now in the light mass regions so kind of below the GeV scale so it took the left of this point here so yeah explicitly below 700 MeV right so in this case the classical action takes this form here so we have the ancient Hilbert term in front Kappa again a C inverse reduced plane mass ours the Richie scalar then you have this non-minimal coupling structure here which is exactly the same as the one I showed you before and then we have an effective Lagrangian for the observable sector and the dark matter Lagrangian of course and now in the observable sector below the GeV scale this effective Lagrangian describes photons, neutrinos the light leptons and pions whereas the electric gauge bosons and heavy thermons are integrated out and then the dark matter Lagrangian we don't specify any closer what we do as soon as as I said before that in the absence of gravitational interactions Z2 is conserved so dark matter stable as far as it's non-gravitational interactions are conserved and the only are concerned and the only Z2 breaking term is the non-minimal coupling to gravity here and then as before we can decouple the gravitational and the dark sectors via the spiral transformation here and then we end up with a canonical gravitational action in the Einstein frame but we modify the metal Lagrangian at the same time so explicitly in the Einstein frame the observable sector effective Lagrangian takes this form here so Tf, pi and gamma are the kinetic terms for the fermions, pions and photons these the potential with all the mass terms and all these different terms pick up pre-factors with omega and the exponent depends on the lowering structure of each individual term so the potential doesn't have any contractions with the metric tensor so this is why it picks up an omega to the four the kinetic term of a scalar has one metric tensor in it so this is why it's an omega to the two and so on then for small field values and small couplings so if this combination here is smaller than one we can expand these pre-factors in powers of the non-minimal coupling and then of course the linear terms the terms linear and phi will explicitly give us the decay vertices so on this slide you can explicitly see three of the vertices that you can just read off in the Einstein frame formulation so all the vertices are proportional to the non-minimal coupling proportional to psi times m all the couplings are of course also Planck mass suppress they all have a couple squared in here and what you can also see is that there's basically two kinds of couplings so the two body decays usually are proportional so the vertices are proportional to the masses of the final state particles and then there's another kind of vertex which comes from the gauge interactions which proportional to the gauge couplings and then in the mass region that we're looking at below a GV the decay modes that we find are metafotons, neutrinos, light leptons and pions as I said one other subtlety that arises in this framework is that when transforming into the Einstein frame when transforming the Ritchie scalar there is an additional term in that range that appears it looks like this so it's the derivative of this omega factor here squared and what this does because omega includes the dark matter candidate what this does is it modifies the kinetic term of the dark matter candidate so you need to redefine the scalar field in the Einstein frame to bring the kinetic term into canonical form and this essentially introduces this pre-factor here square root of one plus six times non-minimal coupling and this has quite a subtle consequence actually so this means that all the vertices are also divided by this factor here so all the decay rates are proportional to this expression here on the bottom of the slide so this means that for small couplings so as I am kappa the rates go as the coupling squared whereas as soon as the coupling is larger than one the rates go increasingly insensitive so in the limits I am kappa to infinity this just goes to a constant so the rates go like I said we lose sensitivity to the coupling but I will comment on that later in the conclusions and how to make sense of that right so what we did next was to compute all the partial decay rates again so these are the branching fractions of a scalar singlet between like an MV and a GB roughly so below the electron mass we have photons and neutrinos to decay into but the decay into photons is the dominant one and then as I said, since the coupling is universal you always decay into final say particles with a similar mass so at the electron muon and pion thresholds these two body case they start dominating the rate very quickly whereas then here, somewhat later the three body case take over right, so let's take a quick step back and look at what we have so we saw how such a gravity portal coupling such a non-minimal coupling to gravity leads to universal coupling to the observable sector and we have specifically in the MV to GEV scale mass region we have to cave into gamma, sleptons and pions so this means we might have spectral features in the gamma ray flux so specifically, if you look at the channel phytogamma gamma for example this would be the perfect channel of course it would give you, this would give you a gamma ray line which would be easily visible above the background but in our framework this channel is loop suppressed the partial rate is very low so for order one couplings you wouldn't see it the next channel here that fly into two neutral pions is also very nice because when these pions decay into pairs of photons they give you a gamma ray box in the spectrum which is distinguishable above the background and this channel has a much larger partial rate so this could be visible for order one couplings and then finally there's an additional bump light feature from these three particle vertices so from these channels we expect spectral features which shouldn't principle be detectable over a smooth background so now we can confront these with the measured x-ray gamma ray flux so in order to do that we computed the gamma ray flux that we would expect from dark matter decay and the gamma ray flux here at Earth is made up of these two components here which turn out to be roughly comparable in size so we have the cosmological dark matter so this here in front is the dark matter number density the average number density and you integrate over a redshift you sum over all the final states and these are the photon spectra evaluated as redshifted energies and then you have a second component from our own Milky Way halo that we modeled with an NFW halo and in this case of course the gamma ray flux you expect depends on the direction you're looking at so you have to integrate over the line of sight and then what we did is to average over all the angles to get the average flux we would expect that we then can compare the isotropic flux that we've seen in experiments and the channels we included for these calculations were the ones that produce hard photons which are visible above a smooth background so in this plot you can see the gamma ray flux as a function of energy for dark matter candidates of different masses so this is for 550 and 500 MeV for a non-minimum coupling equal to 1 and this is the gamma ray flux from these two contributions I just mentioned and you can also see the data points are the x-ray flux measured by integral and the gamma ray flux measured by comptile-agrin-firmilat this is the isotropic diffuse gamma ray flux and as you can see already above 5 MeV the flux from dark matter alone that we would expect for order 1 couplings can be larger than the total measure flux by orders of magnitude so even without making any assumptions on the astrophysical backgrounds we can constrain the lifetime of the dark matter particle so this is what you end up with if you do that so this is the limit on the dark matter lifetime as a function of mass between a bit over an MeV to a GeV so the limits lie in the Bohr-Pucker 10 to the 24th, 10 to the 27th seconds as gamma ray limits usually do with current data so this dip to the right here is at the muon threshold because then you don't get many hard photons and this is when the pi-zero channel kicks in again and then another way we can find constraints on this scenario is looking at the CMB so for this we followed an approach suggested by Tracy Slatner and Chilean Bou in a paper that they uploaded to the archive late last year and I'm just going to briefly explain how it works if you're interested in details you can ask me after the talk or look at their paper directly so essentially the impact that a generic dark matter model has on the CMB mostly depends on the energy that you inject in the early universe into the intergalactic medium and the main impact of a generic dark matter model is due to the electrons and photons that you dump and that you use to ionize, heat or excite gas so then what you can do is to define a set of basis models so for example you fix the species for example electrons that you inject you fix the injection energy and then you can compute the effect of these basis models on the CMB and this is what these people did and they're providing interpolation tables online here for people to use and then what you can do is you can derive a constraint on a generic dark matter model by just decomposing that dark matter model into a linear combination of these basis models which essentially means you compute the electron and photon spectra and then you convolve them with detectability functions for electrons and photons and then an approximate limit on your generic dark matter model on the lifetime is given by a weighted sum over the limits on these basis models right and that's what we did and so on this plot here you can see the limit on the dark matter lifetime as a function of mass from the CMB so the plots for gamma gamma and E plus E minus were already published in the original paper these are the these ones we reproduced and then the other colored lines are the other partial rates that appear in our scenario so for example the limit on pi zero per zero is a bit stronger as you get four fours instead of two for example and then the black dashed line is a combination on these limits taking into account the branching ratios of our dark matter candidate into the individual channels and the channels we considered for these limits are the same ones as for the gamma ray limits plus cascade decays into pions where the pions decay into muons and then the muons decay into electrons and so forth so all channels that produce photons or electrons that way right and then finally you can convert all these limits on the lifetime on constraints on the non-minimal coupling parameter this is what you can see on this plot so this is the limit on this combination psi and kappa as a function of mass between an MEV and a GEV so the shaded regions are excluded so the green, blue and red regions that we exclude based on the gamma ray data so these are calculated by demanding that the gamma ray flux from dark matter decay does not exceed the total measured flux of these experiments by more than two sigma and any individual energy bin and then the black shaded region is the limit from the approximate limit from the CMB that I just described so the CMB limit is slightly weaker for most of the parameter space which means we can still improve the limits with the upcoming experiments such as Amigo or the AstroGum you can see the muon and pion threshold nicely here and what you can also see here to the left is that the limits turn upwards sharply at order one coupling so this is exactly what I talked about earlier so because the rates are proportional to this factor here as psi and kappa goes to one or grows larger than one the rates grow insensitive to this coupling so if we can't constrain the coupling to be smaller than one, we can't constrain it at all right, this already brings me to my conclusion so we saw that based on the evidence that we have we require dark matter particles to be extremely long lived so this might be a sign that the dark matter candidate is stabilized against decay by a global symmetry so then I try to motivate to you our idea of looking at what happens if gravity breaks such a global symmetry like a global Z2 and in this case the gravitation effects actually the dominant ones because the non-gravitational interactions of the dark matter candidate we assume to conserve the Z2 so we can hope to see these rotation interactions and then we saw how such a gravity portal scenario such a non-minimal coupling to the Ritchie curvature leads to a universal coupling to the visible sector so the preferred final states depend on the dark matter mass and then we saw how specifically a dark matter candidate in the MEV to GEV mass range produces photons, electrons muons and pions so for order one couplings we would expect a spectral feature and the gamma ray flux so we would expect an imprint on the CNB and since we don't see any of those already with present data we can constrain this non-minimal coupling to values smaller than 10 to the minus two for a scalar singlet above 15 MEV in line with the CNB limits. Now one thing that one of course needs to think about is well is that a small value like what is a natural value of this kind of non-minimal coupling and of course what this might look similar to models of Higgs inflation where you have a similar operator that couples the Ritchie scalar trillinally to the square of the scalar field and in order to be consistent with inflation your observables you need this coupling to be like 10 to the fourth, 10 to the fifth but of course this is a different operator than our operator so it looks similar but it's a different scenario so you shouldn't compare really these two numbers and yeah what's also interesting is this sensitivity cut off at large coupling that I talked about due to the field renormalization because the rates as I said are proportional to this factor here and one way to make sense of this is if you think about how we define the non-minimal coupling kind of somewhat redundant split up the coupling into a dimensionless number xi and the mass scale n whereas the coupling only really appears in this combination so what we could have done instead was to just introduce a mass dimension one coupling mu which would be xi times m and then this expression here approaching one would mean this coupling approaches the Planck scale so then couplings larger than one would correspond to mass scales larger than the Planck scale so this is why this might not be so transparent what happens there exactly but this is mostly an issue for the scale of signals for the scale of double for example you would also get a correction like this but here the mass scale is the electrical weak scale so this means you have like v over m Planck down here so unless there's no minimal coupling is of all like 10 to the 16 you wouldn't see this modification anyways I guess it's a good time to stop at this point thank you for your attention and I'll be happy to answer any questions you might have I am okay great okay thank you Sebastian for this super nice talk so before starting with the question let me remind you guys that you can ask questions to Sebastian via our chat in the YouTube website so are there questions from the audience, from the local audience here yes can I ask something sure go ahead Diego hi to answer the question how do you avoid the Hitsport I don't like, oh okay the other question they can make so we don't actually so I mean we avoid the Hitsport by demanding or assuming that the non-gravitational interactions of the stagmatic candidate high Z2 conserving so we assume that if you take gravitation interactions out of picture then the action is conserved to Z2 so you don't have any linear terms so if you're talking about the Hitsport with dimension one coupling this one is forbidden by the Z2 symmetry and now of course you can have dimension four Hitsport like five squared H squared and this term is very much allowed and that can be in the potential but the point is that that one doesn't induce dark meta decay because it's quadratic in the dark meta field it can of course give you a scattering or something but this kind of term five squared H squared can induce another signal that is true that is true you can have signals from annihilation from that that is very much true we just wanted to look at what the effects are of this non-minimal operator that give us decay but of course you would see additional features but this of course depends on the coupling parameter then to the Hitsport to the Hitsport my second question is if this dark matter candidate can also be used as the inflaton that's a good question we actually looked into that so there are papers in the literature already actually that try to do something like this so they introduce non-minimal coupling to gravity and then they try to to make the field both the inflaton and the dark matter candidate but so in these papers at least in all that I've seen they were looking at again at this Hitsport kind of interaction which is quadratic in the dark matter field so in our case it doesn't really so it doesn't work with the linear coupling itself because what you need for Hicks inflation to work is for this potential to go to a constant value and this is based on the fact that the potential has a quartic term and then you have this non-minimal coupling squared in the denominator which gives you an h to the 4 so in the large field limit it goes to a constant but our operator is only linear in the dark matter field so it would go as 5 squared so if we have quadratic terms in the quartic terms and the potential we didn't have a plateau at large field values so what we thought about was to look at the scalar doublet scenario so in this case of course you have two scalar fields and then you could think about regions in parameter space where you can find inflation there but then of course you in addition to this operator that I showed in my talk then of course you need to also consider the two non-minimal couplings to the Ritchie scalar that are quadratic in the individual fields you would have psi 1 are h1 squared plus psi 2 are h2 squared plus psi 3 and then the product of the two and then you would need to I mean then what you could do is just to use one of the operators for the decay the one that couples h1 to h2 and you could have inflation with one of the diagonal operators this is actually what people have looked at in literature but just from this operator that we introduced alone it's hard to do okay thanks are there more questions? yes I have another question sure go ahead Juan yes my question is regarding the the choice of the specific form of the non-minimal coupling term which is linear usually you see that this coupling term is quadratic I mean is c times the Ritchie scalar times the field to the power 2 over a mass term why do you use this linear an advantage of this quadratic is that there is a connection with this conformal conformal coupling for the scalar field which is kind of important and the other advantage is that you only have one parameter which is this psi which is dimensionless and instead of 2 you have this M parameter this mass mass parameter at this side so I was wondering why you use this linear coupling well that's true I mean we need the linear coupling such that that can decay if you look at these operators that are quadratic in the dark matter field of course you can induce annihilation into visible sector particles but we were interested in decay so the operator has to be linear in the dark matter field okay have you also considered kinetic couplings there are other possibilities to introduce non-linear coupling and a very famous one is to introduce kinetic coupling to gravity and in these cases I think that it is also possible to introduce decay I mean like I said the form of these operators so all the operators I was talking about were proportional to the Ricci scalar but like I said of course you don't have to do that you can couple it to the Ricci tensor something like r mu nu and then d mu phi d nu phi coupling with a derivative coupling but these are these are higher dimensional operators so we found that the lowest dimensional ones were always proportional to the Ricci scalar so this is why we focus on those but you're right that in principle you couldn't of course write way more of these operators which are then higher dimension right can I comment on that or maybe just continue with the question so your choice this operator was really a choice right so these are by mass scale and the field it's not that you're not really produced such a term no I mean we introduce this operator by hand I mean for example the quadratic operator that that we were talking about earlier I mean this one for example arises in curved space time just even if you set it to to to zero from the beginning just by by loop diagrams so this doesn't happen for this operator that we were looking at of course so you're right in the sense that we introduced this operator kind of ad hoc so the justification as I said is that we don't know what gravity ends up doing we just made the assumption that somehow it breaks this global Z2 symmetry but then from an EFT standpoint well what is the lowest dimensional operator that we can write down that has these properties and then these are the operators that we found right thanks are there more more questions? I have a question okay thank you it's a very short question it's about well I was like I don't know if you mentioned this well there is this new proposed telescopes to look for MEV gamma rays and you take a look to those prospects that you I don't know if you can improve those kind of new telescopes also I think there is this Chinese telescope that is already taking data that they claim that can go very low in the gamma ray signal yeah so the two I know of E-astrogram and Amigo which are both however still in the process of being suggested and approved or maybe not you know so of course our limits will get stronger with this additional data because the CMB limits are weaker than the gamma ray limits this means that the CMB doesn't preclude this kind of coupling so we could improve our couplings with additional data yeah I haven't looked at the specific prospects though so I can't tell you any numbers well the point is that if the community start to say that well we need that kind of telescopes making prospects of using those telescopes maybe they will approve right right so maybe we should we should look at how much it gains us yeah yeah then maybe this is some kind of support for the people doing that proposals yeah thank you okay so I have a question for Sebastian so it's regarding the question that was before the one of Hermann so with this minimal coupling with gravity in principle you are going to break not only the set two symmetry I mean you're constructed to break the two symmetry but in principle the same mechanism could apply for any global symmetry that is present even in the standard model for instance left of number could be broken in the same way right so and then the other question regarding with the same problem with the same idea is that at the end when you break when a global symmetry is broken in these type of models then as soon as broken the ready correction is going to start to mess up all your parameters of the model how do you kind of control this type of effect like change reaction that has the to break this the stability of the armature is going to start to affect other type of processes in some sense I'm not sure if I understand your question 100% so you're right in that if we assume that gravity breaks this global symmetry of course we should also expect it to break other global symmetries definitely we so we've only looked at we've only looked at what happens to dark meta stability though so we haven't looked at what happens to other global symmetries in this in this case yeah so so maybe that's the answer to the question we don't know we haven't checked no I just not that question but maybe it would be most interested to maybe to create the for neutrino masses or something like that no but I was more trying to understand the part of relative correction because this is usually a problem that happens with other models that as soon as you break the symmetry the global symmetry is protecting some observable the relative correction is going to start to move all your parameters to such value that it seems tend to be order one this type of parameter grows very fast and even though they are very small they grow fast so and in that case also is because what you were talking in the talk is remind me this conjecture that if quantum gravity is present and it has effect in particle physics observables no global symmetries should be permitted I mean gravity would be any global symmetries and one way to escape is that is to promote your global symmetries to gauge symmetries it's impossible to have the same approach with this type of non-minimal coupling to instead to have as a 2 to have a u1 gauge in the in your dark sector to try to non-minimal coupled to gravity in the same way without surpassing this type of conjecture yeah I mean the thing is if your dark meta candidate is stabilized not by a global but by a gauge symmetry for example well then you would expect it to be stable also as far as its gravitational interactions are conserved so I mean what we did see was that so for example the scalar doublet because it has a its charge under SU2 so it has some sort of additional protection against decay so the limits were much weaker than for the scalar singlet but yeah just on marigou and air grounds I mean this argument only holds for global symmetries so if the dark meta candidate is charged under a gauge symmetry then we would expect it to be to be stable yeah so that means that this type of non-minimal coupled are forbidden by the fault let's say yeah and another question I was also wondering because you applied this idea to scalar dark matter is it possible to realize it in the case of ferminar matter at a gravitational light in that sense even though it has to have could be a spin in one half only so this is we actually looked at fermionic dark matter in the previous paper so the one before we had a longer paper we looked at scalar singlet dark matter scalar doublet dark matter and then a fermion too and so the the general phenomenology is similar so you end up with a universal coupling with a visible sector and so on but the difference is that the lowest dimensional operator that you can write down for a fermion is a fire dimension then for the scalar singlet so maybe I can show my slides again with the non-minimal operators for the fermionic case let's see so the operator that we found for the fermion had this form here exactly so we need a left and doublet to make it hexablet to engage the operator dimension 6 now this mass scale here of course well you could either say well this arises some sort of quantum gravity effect so you could set this to the Planck scale but this kind of operator can also appear for example if you start with a with a scalar that couples non-minimally to gravity like this like if you have two scalar fields and then this scalar couples to the dark matter candidate Kai with the Yukawa kind of interaction then if you integrate out the heavy scalar you end up with an exactly an operator like this where M is the mass scale of the heavy scalar but of course it also works for other spins so the term is going to be similar to the one more or less at least the output signal the observable is going to be a neutrino with a heavy Higgs I mean with a Higgs or with a set boss and depending on the case so so the words are the questions thank you okay I have a question so at the very beginning you say that your lowest non-minimal operator is proportional to the Ritchie scalar but not to the Ritchie tensor is that obvious well if you take the Ritchie tensor for example if you want to couple it to a scalar then where do you get the lowest indexes from then you need derivatives of the scalar so yeah and then for the other so for the fermion it's slightly more so for the fermion we had a couple of candidates I think but they all ended up either being identical to zero or higher order in all three cases yeah it's not quite as obvious as for the scalar but for the scalar it's like that okay are there more questions from here okay I see that in your chat you have at least two questions one is from Marie-Anne from D'Arcia so she first is a great poet Sebastian and then she's asking do you think that other finite scalar objects I think she's thinking about the transparant something like this where gravitational redshift is where gravitational redshift is strong could lead to some signatures well I'm not sure how exactly the question is man so these I mean these gamma rays that we get from this kind of interactions are just like regular gamma rays from dark matter decay so maybe the question is related to since our operator is based on gravitational interactions if there was some sort of change close to a region so space time with high curvature like close to heavy objects and these questions I would answer with no question because in the Einstein frame the gravitational action is absolutely canonical you just have Einstein gravity so and you just have a dark matter candidate which has direct couplings to the visible sector with the universal coupling so this is a peculiar feature of this kind of operator so we don't expect any exotic effects just from this kind of operator yeah so I'm not sure if that answered the question I'm presumed so of course the gamma rays from dark matter decay via this interaction would undergo a rotational redshift as photons do okay and there's another question from Nicolas Fernandez so he first said he asked for the great talk and then he's wondering about the dark matter like abundance so he asked what's the production mechanism for this dark matter do you produce the correct dark matter like abundance that's a very good question actually so I mean for the purpose of this paper and also the previous papers we haven't actually looked at producing this kind of this kind of document so what of course doesn't work is a typical freeze out scenario because all the interactions that plant might suppress so the couplings are all very very low so you do get I mean if you take these prefactors omega and you expand them like we did you don't all only get you do not only get decay vertices you also get like scattering vertices so you could try to produce dark matter that way but it would have to be some sort of freeze in scenario with a very very low coupling this is actually something we want to look at in the future alternatively the production of this dark matter kind of does not have to be linked to this non-minimal coupling to gravity so for example for the scalar singlet we could just imagine we have a Higgs portal coupling in the potential like h squared phi squared we produce the dark matter via the coupling to the Higgs just a regular freeze out but then looking at the decay phenomenology that is governed by the non-minimal coupling to gravity so yeah this is the standpoint that we took in this paper in particular we didn't make any definitive statements about how we produce it but it's definitely something we want to look at if we can produce it with the same kind of operator yeah thank you for the question I get that the freezing will always work here yeah maybe should okay are there more questions I have one basic very basic question connected to the last question so if you don't know how much dark matter you have how strong does that make the bound due to the lifetime because of course the lifetime doesn't mean that the dark matter will decay at once right so how much space do you have left to play with the lifetime bound well I mean you know how much dark matter there is just from from sebaceans right from Planck we know the one that you start with I'm not sure I understand the question so you will start I think I got enough so I mean in all these I mean we demanded the lifetime of the dark matter to always be longer than the age of the universe so we assume that the abundance does not change significantly over the cosmic history yeah that is true um right yeah so is that the answer to your question so we assume the dark matter to have a lifetime much longer than the age of the universe such that the abundance remains essentially constant right but if you allow that to change then the bound on the lifetime wouldn't be such a hard bound right yeah but I mean as we saw the bounds you get from cosmic ray experiments from the gamma ray flux from neutrino telescopes are stronger than the requirement that the lifetime be longer than the age of the universe so this means we would see signals in these experiments long before the lifetime of the dark matter candidate drops below the age of the universe okay perfect that answer thank you very much okay great maybe last question yes for my part is this possible to have dark matter masses around the age of the universe okay 100 GeV so yes definitely so I mean this is this is actually part of um the analysis that we did in one of our previous papers so let me just bring up this plot here again so I mean it all depends on the on the coupling so for zy equal to 1 at say 100 GeV a scalar singlet would decay far too quickly so in this case you would need the non-minimal coupling to be suppressed by many orders of magnitude to push this limit up above the age of the universe and then above the detection limit of cosmic ray experiments for the scalar doublet or the fermion singlet here um as you can see the lifetime is way above these these two limits here for order one coupling so in this case it could the coupling could be order one yeah but it depends on the scenario and on the value of the coupling of course but wait a second at some point you say that you want to restrain yourself to dark matter light intensive 100 MeV or something like this yeah this was this was for the for the for the for the last paper that I was talking about primarily in this case because in this case you have these these gamma ray signals that I was talking about so for large dark matter masses you decay here into into W6 so you get different kinds of final state particles so this is why for this talk I was focusing on on lifetime matter okay okay that was a choice okay I think that so no no more questions so okay so let me thank you Sebastian once again so it was super nice to hear about this research and one more thing that reminded me that in two weeks we'll have I forgot okay we have a great talk it will be a surprise and so hope to see you in two weeks from now guys so thanks a lot Sebastian see you all soon thanks a lot