No, we have.
Okay. Okay.
So it's our pleasure to have Melissa Diamond.
Coming from McGill, to give a talk.
So, today we have a downward fluctuation of grad students, but an upper fluctuation of faculty, so…
Like, the universe compensate. So, yeah. So, a little takeaway.
Hi. Hi, everyone, if you haven't met yet, as Nico just said, I'm Melissa Diamond. I'm a postdoc at McGill University, and I'll be talking to you about a combination of
work that I've already finished, along with ongoing follow-up work that I've done with all of these great people, some of whom were working late last night to produce plots that I could share with you today. So you're getting these hot-off-the-press,
Though they are still preliminary. So we know who's the boss now.
So, uh, what I'll be talking to you about is, uh…
Actually, we'll start here. But I'll be talking to you about is this basic idea that when I write down a model of dark matter, where I assume it interacts with one particle in the standard model, which is
Often away, we think about it when we're designing dark matter experiments, um…
That's not really the whole story, so out of automatically I going to pick up additional interactions. And sometimes these extra interactions that I get, these loop-level and effective interactions that I'll be showing you as we go through the presentation,
are the more important piece of the puzzle. Sometimes those are the more constraining thing that we should be paying attention to.
So, let's get into it. Now, I've been talking about dark matter, um…
But let's just remind ourselves what dark matter is and why we love it.
So, something like 80% of the gravitating matter in the universe does not interact with light. We've got evidence of this
at all different levels of astronomical observation, from looking at
The rotation girt curves of galaxies, where we see…
sort of the velocity of stars that we would expect if the galaxy were made only out of ordinary matter,
very… it looks very different from what we actually observe.
This tells us that most of the mass in the galaxy is something else, something that is not the stars and the gas that we can see.
The filler word we've been using for this dark, gravitating thing is
Dark matter. We see it at a variety of other scales as well. We can look at the collision between two different galaxies, such as the bullet cluster, where
This is two galaxies, or galaxy clusters that collided some time ago.
In the purple region, that's where most of the mass is. We can see that via gravitational lensing.
Uh, in the pink region,
That's where we see X-ray radiation.
They're not in the same spot. Why? Because in this collision, the stuff that had strong enough interactions got caught in the middle and heated up.
And the XA radiation. The mass, though, seemed to have passed right through this collision as if there was nothing there.
Within the standard model, we don't really have a lot of particles that do that, that don't interact with each other particularly strongly, where they'd be able to pass through just like this.
And so again, we're seeing evidence of something that doesn't really interact with us, doesn't really interact with itself,
But it is very gravitationally important.
And of course, the final nail in the coffin, uh, what came from the Cosmic microwave background.
We can look at the distribution of hot and cold patches left over from
Uh, when the early universe first became translucent to light,
And what we see is that the growth of these patches basically requires us to have
some kind of material that does not interact strongly with light, otherwise they would not have the same distribution that we see today.
So, most of the universe is made of something that's dark and heavy,
We're calling it Dark Matter. We don't know what it is.
But there's an exerted a large effort to figure that out.
And I'll tell you about a piece of it today.
So, as I was saying at the beginning,
A lot of the time, we look for dark matter that has some kind of interaction with the Standard Model, because simply
those models are easier to look for.
Um, usually we'll think about dark matter interacting with one particle,
But the standard model is a complicated beast. Once you introduce interactions with one thing, it's hard to avoid interactions with the rest.
your standard model Lagrangian written out, and all of its beautiful glory. It's complicated enough, there are many particles, many interactions between them.
When I introduce a dark matter interaction term with one of these particles, it's somewhat easy to see how that can start to grow and bring in other additional effective interactions.
Now, this can actually work in two directions for us. On the one hand, what this means is that I can take existing dark matter constraints and pretty much for free, uh, well, for the low, low cost of
me doing the calculations and slowly losing my mind. Um, we can figure out
Uh, how to apply these constraints to multiple different dark matter models that they weren't necessarily designed for.
It also means that you can take existing dark matter detectors and find new types of dark matter models that they can have reach for. Again, that maybe they weren't set up to do.
The downside is that sometimes these detectors may be looking in parameter space that is already ruled out for
the above reason.
But let me get a little bit more concrete with what I'm talking about.
So, the area… part of parameter space where this turns out to be most useful is in the sub-GEV mass range. The reason being that if I'm looking for dark matter that interacts with atomic nuclei, which is sort of a common target for a lot of experiments,
As I go down to lower masses, usually these experiments rely on the dark matter entering the experiment and hitting something.
And causing whatever it hit, usually a heavy nucleus, to respond in some way.
As the dark matter gets lighter and lighter, it has less and less momentum to hit these nuclei with, and it becomes increasingly difficult to actually observe these events. So you can see these experiments pretty much all lose sensitivity,
As you go to lower masses. Now, we are developing, uh,
New experiments that can probe this parameter space, but…
That requires developing new experiments, and maybe we can look in there for free.
One thing that we could do, potentially, is think about, instead of scattering with nuclei, which are quite heavy,
Can we relate these interactions to scattering with electrons? We already have, uh…
Dark matter electron recoil Experiments, electrons are much lighter than nuclei, and so you can sort of more easily probe lower-mass particles that way.
In addition, we could think about dark matter scattering and interacting with photons. There are a lot of…
fairly strong limits on dark matter photon interactions. It's in the name, it's supposed to be dark. Um, and so there's a lot of cosmological constraints that you can start to pull on when we think about dark matter picking up effective couplings to photons.
And then finally, a thing I'll be talking about is meson decays.
I'll explain in a couple of slides.
But once you have dark matter that talks to nuclei, you're also going to start picking up interactions with mesons, and you can start messing with meson decays. And those are things that we measure pretty well.
Sorry, these are three examples of dark matter interactions through these things that would happen at the loop level? Yes. Okay, so it's like, your idea is that it… the model is that it only interacts with…
nuclei to a tree level? Yes. And then it could pick up interactive… it would pick up interactions with these other things at the level? Yeah. And to some degree, it's…
potentially better than loop level, but I'll… I'll show that further down.
Like, tree level, yeah.
Or if you… if you count, like, pion decays to photons as tree level, then tree level.
When you say that you're… you're gonna show me. Oh, no, no, you can go ahead. No, no, uh, when you say it's nuclear recall, so you're assuming coupling…
Yeah, yeah.
Um, so the question is, of course, how are we going about doing this? How are we relating these different types of interactions? What you pretty much got at, uh, we're going from tree level to loop level.
But this itself isn't exactly a new idea. Um…
So, this has been around, uh, people have done similar things, at least in 2014, but they did the reverse version of what we're doing. So, as an example, if I've got dark matter, which interacts, say, at tree level with electrons via a vector mediator, something heavy,
then I could imagine just…
embedding that whole, uh, diagram into a larger diagram. My external electrons now become part of a loop.
And when I close my loop, I can get the whole thing to talk, uh, to nuclei via the…
photons. So this has worked out in these papers in 2014.
And they got some useful limits for, sort of, I think, a heavier dark matter.
Um, I'll also point out that
Effective interactions really aren't a new thing for dark matter searches. Most Axion searches are ultimately relying on an effective or a loop-level interaction. So, it shows up a lot, and it can be
pretty useful. So the original paper where we explored this idea was called Limiting Light Dark Matter with Luminous Hadronic Loops.
In that case, the first pass at this…
We looked at relating the dark matter proton cross-section to just a dark matter-electron cross-section,
In that case, we assumed we were working with a vector mediator. The relevant mass range where you got interesting results was about 1 to 100 MeV,
And these were the sort of cross-sections that we were probing. You need heavy mediators, right?
It doesn't have to be heavy. Okay.
Yeah.
Uh, I mean, the…
I guess I'll show you when we have the dots. Sorry, the mascot here is the dark matter. Yes, it's the dark matter mass.
Um, and so with this, you… we basically are able to show you can use electron recoil experiments to probe parameter space you can't reach easily with nuclear recoil experiments.
Now, the reason that the earlier papers that had been done on the topic were in 2014, and it took a while for anyone to do this version,
is that we need to call upon QCD to be able to think about this.
Basically, if I'm talking about dark matter interacting with nuclei, what's really happening under the hood is that the dark matter has a coupling to quarks.
And if my dark matter has a coupling to forks, I need to be thinking about QCD, which is…
not the most enjoyable thing to do.
Uh, fortunately… Says who?
fortunately, uh, most scattering experiments, and honestly, most interactions that are relevant to dark matter limits are happening at low energies.
And low energies, uh, the quarks are not the important players anymore. We use chiral effective field theory, and it's the light mesons, mostly the pion.
Um, who come in and save the day.
So, these guys are going to be the ones that are important for most of the interactions that we're dealing with.
The way we'd go about doing these estimates is I would say, I'm going to write down a coupling between my mediator and quarks,
So, in this case, in the first pass we took at it, we had, uh…
a vector mediator, it's got a mass.
Um, and it's…
We're gonna couple it to the quarks, and then from that, we'll get
An effective coupling to nuclei, so that we can compare it against the nuclear cross-section.
Uh, protons and quarks, they're all fermions, so you end up getting a coupling that has the same form, and at least in the vector case, very conveniently,
The effective coupling to protons comes out to just the sum of the coupleings to the quarks that
more or less compose the protons. So for a proton, it's 2 up quarks and a down quark,
The coupling looks like 2 times the up coupling plus the down coupling. They don't all work out like that, but in this case, it's pretty tidy.
And then, you'll want to find the equivalent interaction with the mesons, because they'll become important.
So, uh, for pions, if I use chiral effective field theory just to figure out what the interaction looks like,
This is what we get. Uh, so we get this scalar derivative coupling to the charged pions, we get the same to the charged kaons, they're heavier, so…
We include them in the calculation, but I'm not going to show it to you here.
And then the effective coupling looks like this. It's up minus down, which, again, actually lines up with what the pions are made of, which is an up and an anti-down, so…
still sort of following that story of what these things are composed of.
That doesn't work out for the other mediators, but it's cute for the, uh, vector mediators.
So then, now that we've got, uh, all the pieces of the puzzle, we can go about calculating our cross-sections.
For proton scattering, it would look something like this. We're starting with this underlying theory, and we get this contribution from, uh, the strength of that vector term.
We also automatically get these interactions as well. I don't get to have this guy without this… without these, at least not without some…
sort of model-building trickery.
These terms are going to, uh, have a factor of E times A up minus A down,
That comes from connecting our maisons to a photon, and from connecting our dark mediator to the mesons. We'll also get a loop suppression, or just a loop term that comes from calculating this piece.
No. Putting it all together, what I get is the ability to write down the dark matter electron cross-section in terms of a dark matter-proton cross-section, and then some model-specific terms.
So, here is the tree-level cross-section, this is the loop-level cross-section,
This is the piece that helps me get between the two of them.
This piece comes from the loop contribution.
This specifically is what we're getting out of the pion loop, and then this is just switching between scattering with electrons versus scattering with protons. So we get the extra E squared, because you've got an extra
Coupling to electrons, and then you've got, uh…
those reduced mass terms again, because I'm switching from…
protons to electrons.
Putting it together, this looks pretty bad.
Putting it together, I electron cross-section is about 10 to the minus 14 times the proton cross-section times some model-dependent terms.
But I've got these reduced mass pieces here, and so these can give me an extra factor of, like,
2,000 squared, depending on the mass of my dark matter. So, this helps us out a bit.
The other pieces you might be wondering about, like, what's this alpha? The alpha is the cutoff of the theory. It's when chiral effective field theory breaks down.
Depending on where you want to put that, we can call it maybe about the proton mass, you can call it maybe a few hundred MeV.
Um, it's not going to make a huge difference in our calculations, though, but it is something to be aware of.
When we're deciding where it's appropriate to apply these calculations.
So, putting this together,
We get this as our end result.
So, if I have dark matter that interacts with nuclei,
I'll automatically get some electron cross-sections, and I can just recast existing limits on dark matter electron coupling to get limits on dark matter nucleon coupling.
And that's what we did here. So, for these choices of, uh, quark,
Uh, couplings.
For a light mediator, and for a heavy mediator, these are the sorts of limits that we get.
The gray are the ones that already exist, and the red is what we get out of this work. So, not a ton of new territory,
But we do start to cover some new ground.
In both the light mediator and heavy mediator cases. Maybe more excitingly is that, uh, electron recoil experiments
dig very deeply into this parameter space, and…
based on their projected sensitivity, should be quite sensitive to dark matter nucleon interactions,
better than at least the existing experiments at the time were.
Can I ask this, like, what is the status of Oscar? Like, have you turned log in? Like, that's gonna happen, or no?
I know that you have, like, technical challenges, but… Oh, no, I… I'm not sure. Okay.
Yeah, uh…
Because it, yeah, I think, uh, we learned about it when we were talking about this elsewhere, and so we added it in, but I hadn't.
heard about it since then, I don't think.
Wait, so…
Sensei…
is… so these…
These are real. Sunset is real, but is that…?
that's measuring nuclear cross-section.
So, the gray is nuclear cross-section, and the red is dark matter electron cross-section recasted.
But you're parting the nuclear…
the equivalent nuclear cross-section of the vertical.
Yes.
So, the actual Sensei limits for their electron cross-section would come down.
A bit for… we'll come down further.
Dominic and Oscar are the limits on scattering these electrons that you're then recasting to…
they… that's the reach of the experiments.
So they're not limits, it's, like, what… No, no, but, like, the projected… Yes. The projected limits, but it's just…
I don't… I don't know anything about that experiment. Scattering against electron? Yes. And then you're just turning them on.
Yes. Yeah.
That was the nice thing about these calculations, is that you ended up just with a ratio between the electron cross-section and the proton cross-section, and so you could sort of easily recast them.
As I'll explain with the other mediators, it's not quite as simple.
But it's at least somewhat simple in this case.
Um, I'm trying to understand…
To what extent this is a…
a sharp calculation as opposed to something that has some…
quote, order one factor, saying that
you don't really know better than Joe Kit later.
So, I'm not used to seeing…
proton things related to pion things without any.
But too, so…
incurable perturbations theory. You know, you usually…
predict things about pione complex.
wrapped up in something definite about protons. Sure, so I guess…
For the proton case, we're pulling from the dark matter and the…
like, experimental literature on how to relate.
quart couplings to nucleon couplings.
So, we didn't use chiral effective field theory to calculate the proton couplings. I sort of trusted…
I trusted, basically, the scattering community on how to handle… yeah, I trusted the detection community on how to handle this. Also, to go from the park-level uplinks,
to the pione couplings,
There were 41 factors, right? You don't?
You don't know how to do that transition without doing…
Like the skage theory, so…
Do order one factors matter when there's, uh, 12 orders of magnitude on the y-axis?
No, no. Yeah, yeah, yeah, yeah. Yeah, and I think that's the answer, because, to be fair, I would say…
Order one, squishiness in the calculations, I think, is reasonable to…
to say this there. Okay. Yeah.
I have a different question, though, about the… so, I guess, so you're trying to…
Study a toy model where there's a Z prime that only talks to quarks,
But then, the fact that loops can generate couplings to D plus E minus…
seems to imply to me that
nothing forbid that Z prime from talking to E plus C minus in the first place.
So what… are these models, like, uh, I don't know, well-motivated? Yeah. Or are they kind of…
like, why wouldn't a Z prime talk to everything with some…
order one… I don't know. Yeah, yeah, that's fair. I think it's…
Because these are called leptophobic wells, where are these leptophobic models come from?
Uh, other than being, like,
technically possible.
I think it's just…
I mean, if you're ending up with, like, a mix… like, you're mixing Z prime and the photon.
loops, like, which…
As, like, a whole literature for dark matter and dark protons. Yeah, I think it's more like this is, like…
the minimum coupling you can get. So you… you can have naturally…
Well, no, you could cancel this off of a tree-level coupling and make it zero.
You wanted to? Sure, but that's sort of particular, isn't it? But I'm asking if this is particular, too.
Well, would you be able to cancel it off a tree coupling? Because, like, presumably needs to be some integer
charge for the tree.
You're talking about canceling it against electrons.
Mm-hmm.
Well, a 2C prime, it's not a…
This can't renormalize.
Right, but it has to be some… presumably some, like, integer related to the chart coupling to.
to U and D.
Right? Otherwise, we may have run into…
Anomalies.
It can't be some, like, arbitrary…
ratio of the…
the tree level above the dead.
If you tell me you can, that's a hurdle.
Fine, I hope.
I would have thought, if I want to build, like, an anomaly pre-model, I'm not allowed to pick the tree-level coupling to electrons. I can pick it to be zero, but I can't pick it to be… The ratio between up and down.
up and down in E.
Right? Depends what you want, right? With the Z prime…
Like, if you have a unique complete theory, right?
What's the charge there? Like, to be some…
You can allocation right there on the number? Yeah… Yeah, sure. If you do it in a way that… Yeah.
Yeah, it's very heavy. So you don't have to be…
So you mentioned here?
Uh… It depends out.
No, so it doesn't matter for this code? No, for the heavy median? For the ratio…
For the ratio with the proton coupling, the Z prime mass divides out.
And so you… the reason we have the different plots is more an issue of, like,
the existing constraint apply a bit differently.
Or behave a bit differently, depending on if you have a light mediator or a heavy mediator. Um, but…
In the other cases, we have to specify the mass of the mediator. Uh, in this one, um,
Oh, I see, lightning heater. Yeah. What does light and heavy mean, though? I mean, what's the… relative to what…
Uh, relative to the momentum exchanged.
So, probably, like, the dark matter mass times.
velocity. It's very light. Mm-hmm.
Alright, so these are all lights under the sound will come from.
Uh… I mean, all the dark matter's less than a GEV.
It's not like a… It could be heavy. It could be 30TV? Yeah.
Well, I was just wondering if it's really that heavy, why wouldn't integrate that out, too?
So you should have an effective theory that…
doesn't have the mediator or the… I mean, you already integrated out Proton, right? So… Like, integrating it out should give us…
Effectively the same result, shouldn't it?
That's a heavy mediator. Yeah.
So this is a little bit more general, because it lets us…
play with either of the cases.
You don't have in mind any, like…
you know, your completion for this, right? No. Because…
If you're doing a simplified model of your enemies a bunch of things, right, that can go into the loops.
Sure. I mean, these were sort of the biggest things.
That would come in the loop if we just assumed the, uh, the port coupling. But yeah, if you let it…
couple directly to other things that…
They'll get other extra interactions. The point is more that if…
Even if you're just thinking about that one couple and you can't escape these other additional effects.
Can I continue? Other questions?
Okay.
Um, so the other effect that we get to play with
is that in this case,
Uh, you'll pick up an effective millage charge, at least as long as the mediator is light.
Um, and by light, I mean that the master, the mediator, is light compared to the momentum exchanged relative to these experiments, or these different, uh…
limits, uh, so there are pretty strict limits on dark matter millicharge.
Uh, so basically, if you're above these white lines, and you have a very light mediator,
That dark matter would be problematic, because it would mess with, uh,
the distribution of galaxy clusters.
Or potentially introduce too much scattering in the Milky Way disk.
Wait, so the galaxy cluster is like the bulb cluster bound.
Where the… where does the… I think it's… I think it's, like, dwarf clusters around the… dwarf…
This is the dark matter standard model.
induced interaction, what's causing the problem here. Yes.
It's too much scattering with electrons, or it's… it's…
too much millitcharge dark matter.
Oh, through, like, magnetic field, like, as it passes through the magnetic fields, the long-range magnetic fields of the galaxy?
No, I'm sorry, I'm trying to remember. I think so.
I'm just, um…
Yeah, we can talk about it. I just… the spin-down one is not one I'm familiar with. Yeah.
Curious. But I haven't thought about Millacharge dark matter. Yeah, yeah, no, I can pull up the citations after.
Um, so that was the original project, and now, of course, the question is, can we expand beyond this? And that's the goal of our ongoing work.
Which is, we didn't want to just limit ourselves to the vector mediator case, we wanted to see what can we do with, sort of,
The remaining reasonable mediators. So we've got scalars. When I'm talking about axial vectors and pseudoscalers, what I'm really talking about is sort of…
Whether there's a gamma 5 on the coupling with quarks or not.
And then, with these new interactions, we do get new observables that were difficult to get in the vector case. So, now we can get dark matter-photon interactions,
Those were suppressed or difficult to get with the vector mediator.
What this leads to is dark matter overproduction via freezing.
Also, we were this time focused more on…
Maison decays, and there was a lot of interesting stuff in there. So…
Put simply, we'll get neutral maisons that can decay directly to dark matter, as long as the dark matter is light enough.
And we'll also get rare Kaon decays, where you get decayed dark matter plus pions.
So those are sort of the new, fun things that we get as we think about these mediators. I think these will also apply to the vector mediators, but we didn't know that when we did the original paper.
Um, yeah. Are you a throughout, or you're not assuming that these mediators give you the dark matter relic abundance?
Where you are? No. Okay. Uh…
Well, you do… you do worry if they overproduce. We worry if they overproduce.
Um, and…
Is that a line you can draw on your boss, though? Yes. Oh, like, if…
Getting the right relic abundance? Uh, yeah, it probably is.
Um, because I think it'll…
Yeah, no, it probably is. We haven't, but…
We definitely can.
So, um…
I'll also add that there's a group in Australia that's doing similar work. Um, they've only focused on
They've only focused on, sort of, the heavy mediator cases, the ones that you can integrate out, but if you're curious, I can also…
I'll show you some of that stuff afterward.
So, the first case that we can look at, again, the simplest of the remaining three, is the scalar mediator case.
Um, in this case, what you end up with
is, uh, the scalar coupling to the charged pions, like so, and so we get
These loops give us access to interactions with photons, and then we get this new decay channel for the k-on.
Now, there are, I believe, probably several other fun, weird, new decay channels that you can get.
This one is the relevant one, because this K-on decay to pion plus invisibles is rare and reasonably well measured.
So, of the decays involving other mesons, this one is sort of the rarest, and while still being well-measured.
You don't have, like, mix with the heat?
Uh…
How is coming to my mind from some reason, when I teach…
But I don't know what I mean…
Um…
So, for a mediator of this variety,
You've got a coupling that looks like this, and a coupling that looks like this.
Uh, for these choices of quart couplings, we just set them all equal to each other.
this, uh, I believe is one of the weaker combinations of quark couplings we could have picked.
Uh, these are the sorts of limits that you get. So, for the light mediator, uh, the existing Planck constraints still dominate, uh, for a lot of the parameter space.
This is the limit that we get from overproducing dark matter. This is what we get from archaeon decaying to pi plus just mediator, um,
It's the same as the diagram I showed you on the last slide, just pretend the Kai-Kai bar isn't there.
Uh, and so we get a little bit of new ground in that corner over here. There's clonk here is…
You don't have to do the loops or anything? No, no, no, that's the existing cross-section we're competing with.
Or those are the existing limits we're competing against?
So this is dark matter scattering against…
Protons? Yes.
Again, it's nuclei. It's nuclei.
Via a light spiller mediator, so it's, uh…
what team does?
I… okay, I'm updating.
I mean, I'm aware that there clearly is a limit, I just, um…
Oh, light mediator. Yes. Have I did the mediator there? Uh… Ballpark. I think he picked an Eevee.
Oh, okay, yeah, then I believe it. Yeah.
Yeah, so generally, uh, he didn't put the light mediator mass in there, but I believe it's generally an EV for the light mediator cases, and then we specify for the heavy mediator. So this one is for a 1GEV mediator,
For these bounds, the mass of the heavy mediator does start to make a difference.
So, for a heavy mediator, this is the overproduction limit, this is the limit from producing
canned debt decayed upon Kai Kai Bar. And then we've marked off this region here,
Uh, as parameter space for not messing with.
And that's just because…
in order to get cross-sections this large for a mediator mass that we've chosen.
the coupling to both
Both of these couplings up here.
would have to be 1, and so it becomes non-perturbative, and we don't really trust the calculations anymore above that, so…
some other kind of behavior up there. Sorry, just to go back to your 1EV mediator, in this case, are you basically thermally ordering the… for a lot of that?
scattering cross-section? Are you ending up in equilibrium?
Like, do I have to worry about the…
the dark radiation of your mediator. Is that part of your calculation? That's one of the next things we want to check. Okay, yeah.
Yeah, is like, uh, so I've done the calculation for production of light mediator, um,
Well, we haven't checked yet if that's going to cause problems. So, but this limit is really just your coupling, your baryons?
to your dark matter too effectively, and so, like, when you do the…
the CMB, you end up with, like, coupling your two fluids? Is that where the one is coming from?
Oh, oh, oh, oh. Um…
I guess so. Yeah, it's just, there's a lot of things that I could worry about with a light mediator in neural universe, and some of them are, like, extra…
bells and whistles that you don't necessarily want, and this…
think about which one is sort of the one I can't get away with.
Oh, sorry, you had a question.
I mean, any model like this, those…
extremely fine-tuned from the get-go to give you a bit of flavor treaty.
Neutral interactions, right?
But Chris, you know, we could have had…
slavery couplings between Fry and the Clarks.
That would have been ruled out.
from the beginning, we… Okay. And there's nothing that prevents us from being there.
So, once you introduce that skill, or you…
You've got a ton of problems in the…
In the model completely from the beginning.
So the minimal, like, the easiest way to get around that is to make it some extended eggs.
Right. It was like, you make that some sort of extended haigs that has Yukawa kind of interactions.
Generically… No, no, I agree, yeah. Supersymmetry.
Gives you extra flavor-changing foods.
You can always have a higher commitment.
a hierarchy with columns. Mechanic field.
Well, yeah. Yeah, you could have to force it, though. You'd have to do all kinds of work to…
MFP is just an assumption.
To explain why, yeah.
Okay. Yeah, I mean, so a coupling like this…
Yeah, yeah. So, a coupling that looks like this would correspond…
to your, uh, spin-independent, sort of, 01, uh,
coupling for…
at least the heavy mediator case, and this is sort of…
one of the more popular ones that they look for at detection.
So…
I would be… certainly believe that the more complex model is needed to handle the situation properly.
Um, but models that look something like this are definitely a thing I'm looking forward detectors.
So, this is created by… the letters come from caterpind.
Yeah.
Is there someone… isn't there, like, huh?
Yes, yeah, I think it's either…
Yeah, so we have CANs to invisibles, we have pions to invisibles as well.
Um, and…
those are weaker, generally, than these limits, and so we hadn't put them in yet. These are sort of the strongest ones that we…
We're finding.
Of the mediator? Yeah, Peyton, you…
I don't remember correctly, but…
Oh, no, I think… I'm not sure I understand what the question is. No, that you put only one…
say, like, one limit from fluorophysics, right?
Oh, yeah, yeah. …maybe tens of…
related decays to this, right? Oh, yeah.
for instance, this would be, I think,
I remember that D2… sorry, D2…
I left on this.
But that's, uh… that's a different… that's not chiral effective field theory anymore, that's a different…
No, it's just to limit the expense limit.
You have a brochure, like…
lifetimes. We looked… I looked at the lifetime, or I looked at…
various, like, masonic decay modes.
Um, at least of the Maisons that I could sort of easily do the calculations for, which is the Kons, the pions, the etas.
Um, so for those, this was sort of the one that was…
the best combination of being rare and, like, well-measured.
But…
If there's more that I haven't thought of, like, that… that's fine, we can… I'm happy to add more limits in here. Well, the one you mentioned, I mean, are you assuming it doesn't talk to Churn Quarks at all?
Uh, yeah, we're… we're neglecting interactions with the heavy forks, because we're…
So, so you say you did check, I guess, all the strange flavored meson, or not all, as many as you could think of, but strange-flavored, meson, rare case.
I basically have pulled up the particle data group.
page of all the different decays and looked through.
Okay. I guess it's fair, if you're thinking about, like, you wanted to have the
you wanted to compare to the scattering cross-section on… That's the thing.
require a light-quark interaction, more or less.
Or yeah, I want to compare to interactions with nuclei. If you scatter against charm and top and bottom, like…
the vertical axis disappears because you don't… you have a really minimal coupling to the…
to your museum on an experiment or whatever, right? Yeah, and we did actually see in…
one of the Australian papers we were looking at. They got pretty strong limits from
coupling their media… or coupling to the top.
But… that doesn't really tell you much about how it couples to the proton or to the nuclei, so that felt a little bit like cheating to us to get a stronger limit.
I guess I don't understand… maybe I missed it, but why are you cover this range? Why not just up and down?
Um, what's that?
Because…
You could just say, okay, this encompass the first generation, and of course, and this prevail.
the other generations.
It'll be easier if…
Well, I end up having to include in some of the other cases, like,
the ADA and the ADA prime, um, because sometimes the coupling to the pions, like for some combinations, actually,
For several mediators, this specific combination, uh, coupling to the pions, goes to zero.
So then I wouldn't get anything. Uh, but including the strange cork.
includes, uh…
I guess the Kaons, as well as the Adas and the Ada Primes, and those end up being important in some of the other interactions. But things like over…
production and funk and stuff like that, those are gonna be relatively insensitive to whether you go to…
the strange, I'm guessing.
Yeah, like, it's not… it's not a huge contributor to the, uh…
I mean, unless you live in some weird thing where they exactly cancels, or… Oh, I mean, I…
for… for this, like, even for, like, a simple choice like this, uh, this… it'll cancel off.
For some of the mediators.
Yeah. But you've obviously not turned to all of them off here, otherwise something…
Yeah, and you can't. You, you can't actually find a combination that'll get rid of, like,
every possible interaction with all of the mediators. When I include…
all the different mesons that could be participating.
Um, they'll always be kind of one of them showing up and mediating the interaction. You can make it weaker.
But you can't totally get rid of it.
By fiddling with the coupling to the quarks.
And I guess Todori's point, you could just look up how
the K on one depends on this exact coupling. Just rescale it if you put it your own.
return on anything in particular.
It is, um…
Okay, this case is sort of specific. This case isn't terribly sensitive to it.
Maybe I'll be able to say more in the other two cases, because I think they're more sensitive to our choices of relative couplings.
Alright, so the other, uh,
Scalar adjacent case, this one, uh, is where we've got a gamma 5 on the chi-bar coupling.
I separate… I include this one with the last one, because usually what's important for…
most of the phenomenology is more how our mediator couples to the quarks that's going to make
Most of a difference. Uh…
But for this case, this sort of interaction corresponds to a low-energy effective theory, uh, 05, if you've got a heavy mediator.
Um, the constraints are a lot weaker for these types of models, because they're just not models that people have thought about as much.
But we wanted to cover our bases.
So, for a light mediator,
this is how it looks.
And then for a heavy mediator, uh, we've got sort of a similar situation as previously.
what I'm calling the pseudoscalar mediator case is just saying that my coupling to quarks looks something like this.
So if I've got a field that couples to quarks like that, then chiral effective field theory will give me a coupling
to mesons that looks something like this.
So, I've got these funky terms here.
that are mixing my mediator with the Maisons.
These are weird, um, but they have the exciting effect that
My mediator picks up any of the couplings that the Maison had. My mesons pick up any of the couplings that the mediators had.
The result is that if I've got an interaction like this, where there's a gamma 5 hanging out secretly down here with the porks, I get
these interactions now, where the pine knot or the eta, and really the eta prime, if I want to include it,
And our…
Dark Mediator can all help.
Dark matter talk to photons.
The pine and the Ada cannot decay to kayakai bar.
And all 3 of these particles can be involved in helping Kions decay into pions, plus invisibles.
So, together, what this gives us are constraints that look like this. Uh, for this example,
We're actually just showing coupling to the up and not coupling to the others, and that's just because the, uh…
all equal coupling case is…
a little bit suppressed, it behaves a little bit differently than the others, and we're still working on getting those plots together.
Um, but…
This over here is the light mediator case. We get…
rather strong limits from just overproducing.
For the heavy mediator case,
It's a little bit trickier.
Uh, basically for a heavy mediator that has a coupling that looks like this,
the interaction with nuclei is very suppressed. It's…
Uh, goes as velocity to the fourth, and so it's pretty difficult to actually see this thing at, uh, direct detection experiment.
Um, so in this case, we've actually multiplied the cross-section by Q being the momentum exchange to the fourth.
Go to the minus 4. If I didn't do that, these limits would go down to, like, 10 to the minus 80, and they would be a little bit deceptive.
all that's happening here is that…
the… basically, photon annihilation that produce these, and that decay rate,
none of these have that V to the fourth suppression that you see in the nuclei scattering, and so actually,
These effects end up being, like, cross-sections that are often larger and more relevant than the nucleon scattering one is.
Oh, and this… if we're…
thinking about, if we're talking to the experimentalists, this corresponds to O6.
And then, finally, we've got the axial vector mediator case, which…
has sort of proved to be the messiest, but you're not going to have to see that. Uh, in this case, what we've got, if I have a coupling that looks like this…
Where I've got something vectoring, which has this…
sort of coupling to the quarks, then what comes out is a derivative coupling between the…
uh, mesons and my mediator.
Uh, now, what this means is that, again, all of the mix, they mix a little bit differently than they did in the pseudoscaler case.
So, the Maison's pick up any of the couplings that the mediator has, the mediator does not pick up the couplings that the mesons have, so now the mesons are sort of suddenly doing the heavy lifting of talking to dark matter.
Uh, oh, okay. Um…
So, the limits that we get as a result of that, we're focusing on sort of the same limiting behavior. We expect that there'll be a bit more, uh, as time goes on, but these are the ones we have.
We can show you now.
For, uh, this sort of behavior, we get…
these limits from overproduction.
We are covering a bit of new space, a bit of new space from Kayon Decay, and for a heavy mediator.
We again sort of cover
these cross-sections down here.
Uh, so…
I'll also note that if I were to
take the gamma5 out of this end here, then the entire interaction goes away.
it just goes to zero, so you don't… so if you wanted to get around the limits,
Um, that would be one place that you could potentially hide, um, because we don't get any effective interactions at all, uh, when there's…
sort of a mixed, no gamma 5 here, gamma 5 here, type coupling.
to the quarks.
So, thank you all for listening. Uh, one I'm hoping that you take away from this is that…
Loop-level and effective interactions are important when we're thinking about dark matter models, when we're thinking about what parts of dark matter parameter space are worth looking for, or are worth building new experiments to dig into.
Um, because…
If you're assuming a simple model,
your model might not be that simple. I guess, as you guys have all pointed out, there's a lot of places that we can introduce
new interactions, but even a very naive model will automatically get additional interactions, um, via these loop terms, which are sometimes very strong and not very loopy.
Uh, so what we're doing right now is we've used existing constraints, existing detectors, as a way to probe
Uh, additional dark matter interactions that these constraints and detectors hadn't normally originally originally been intended to do.
Um, we get effective interactions with the mesons, and the light mesons are doing a lot of heavy lifting. They've allowed us to show that experiments like DOMIC-M can be very sensitive to dark matter-nucleon interactions,
And they let us put limits on, uh, dark matter nucleon intercouplings,
Due to how they connect dark matter to photons, and basically how these interactions mess with meson decays.
So, thank you all for listening.
Right? A couple of minutes for questions, if we have more questions. I think I have a…
A workday game.
Yeah, can I look this also in Mooth?
With gamma… no gamma rays, but you know, like, something like MED, like, rates, or, like, where are you, like, uh… there's not, like, way that I can see, like, the decay of this, uh…
Yeah, yeah, no, that'd be fine. So if you wanted to look at… But this not competitive enough, I guess, yeah. Yeah, yeah, so actually, uh… For some of them, it probably is. Yeah, exactly. For some of them, yeah. I don't know, but maybe that's better. Depending on the spin side. I mean, the… Uh…
I think these might come from Dark Matter Annihilation.
But for CMB, yes, but yeah, but I'm thinking about, like, yeah, like, I'm not, like, the center of the galaxy, or, like… Well, I mean, the mass scale and all… Yeah, exactly, like, you want to look through fairly Fermi go?
And he goes down to…
20 MEV is, like…
Gamma ray E, right? Yes, it sounds absurd, so… so…
Yeah, so I think we…
at least thought about that idea, or thought about looking for lines. I don't know that we found anything that was, like, a dominant limit anywhere, though.
And also, like, during this limit, I…
Yeah, but you do totally get dark matter annihilating into photons, like, that's…
a thing that happened.
So you talk about that a little bit for me, yeah.
Um, but I don't know, I was surprised.
Uh, because we didn't know about these… it didn't occur to us to use these options right away, and they ended up being some of the strongest ones. So I'm definitely…
interested, if people have ideas about other ways to get limits on these. So, why on these am I not seeing the direct detection?
That's right.
Um…
I think they're…
Is it just off the scale?
I believe so.
I mean, I guess it's one GEV is the right-hand side. Yeah.
Okay.
I'll also scale in the weak direction? No, there are OMS.
They're too light, and they're sort of weirder, uh… these are, like, weirder couplings that I think a lot of the experiments are less sensitive to. Well, yeah, they want.
I believe, even though there's no Dominic.
Oh, well, this is… we didn't… we didn't calculate the electron coupling for these cases.
We just did the photon coupling and the mason decays.
Um, yeah, I think we'd have to go to, like, a second loop to get electron coupling.
But for Sinon and all these things.
Well, I can imagine, but they're not.
Museen doesn't want to get the answer to you.
Well, I guess moving goals. There might be something creeping in on the right. Yeah, exactly, maybe just a line or something.
Oh, so if I wanted to do, uh, get coupling to electrons…
Um, I think I'd have to go to a second loop.
You don't worry. Uh…
So, yeah, I guess the effective interactions that I get for at least pseudoscaler and the axial vector cases, um,
Or at least the dominant ones would be, like, uh…
So, I feel, yeah.
I was trying to figure this out yesterday, which is why I've got it on the brain.
Let's say I've got something like this.
Um, so basically I'm just relying on, like,
how well can I…
Okay, yeah, sorry, I see your point. Um…
Yeah, I could use the pion decay to E plus E minus. It's just suppressed by, I think, a factor of 10 to the 8 compared to the photon.
coupling. So it's there, it's just the first one that I could think of was weaker, and then I think other ones I'd have to…
After we've been together.
You're saying the loop with Kai-Kai, then quarks in a loop?
Wait, what's the diagram? They give you electron coupling before?
Okay, so the one that gave me electron coupling before was Chi, Kai…
I… aye.
And I can either put a photon here,
Yeah, this was the one.
This is the one that got it from me before. Um, if I make this…
a scalar in this loop is 0. I could replace this
I couldn't finish here.
Um, so that would be, I think…
When you're down by the electron mitts.
Yeah. Or you could put in some more weights off of the pione, maybe?
That was not… Is that true, Lou? Yeah. Sweet.
So it's there. I mean, it's definitely there. I think it's just smaller. Very small, yeah.
It's…
Okay. Just one question. So, kanos relations, that's…
Because, you know, a box with the size inside.
I don't know, Jake? No, this wasn't like Drake gave our mixed in.
So, not if it slavor day, I can…
Yeah, it's Labor Day, I can…
You would need a SD bar, hopefully, or something. Yeah.
Yeah, the Z prime… the Z prime is 5th, 70 or worse.
It doesn't even have to be flavor and universal, does it? Just flavored diaga?
Yeah, again, is the press belt?
So, the question here. So, like, also you can, like, recit all these, like, Axion chaos and all these things, too.
whatever it will break for, no, for days who's worst case.
Probably. Yeah, because I know for the accent, there's, like, a bunch of these that I ordered already. Like, it acts like the pseudoscaler. Yeah, exactly, yeah, yeah, yeah, because they also have, like, inoculation, and also, like, a case, and these things from…
Yeah. Yeah.
It's… so what I was saying before, so…
K0 that came along with the lifetime, yes.
That's been a little miserable.
This affects everything.
Uh… I think that certainly the other set of scheduling.
It doesn't…
Right?
It doesn't… it doesn't mix with the KLAM.
Um, like, I don't have… I don't have a term of, like…
I don't have a term like this.
That's what you're asking about?
No, I'm just asking the screen for the unions, these interactions that happen.
Yes.
It's time.
You have that. I mean, I've got Kay… Kay's with my site, so I actually have Kayla.
Now, I've been with so…
It just… it didn't… I guess I'm… I guess I'll say it didn't fall out when I expanded the Lagrangian, I didn't get couplings that…
would give that to me.
K02 to side, so…
Yeah, okay?
plus 2.
5 plus side, side.
should have played long.
Tukai Kai.
you just take a legit and…
Oh, okay.
With that…
Do you think that's, like, a… So, the lifetime of Knong was really well measured. Okay. I remember doing this in the lab, so… I don't know if it's better than this, but…
Yeah. And there are these other things that…
I do remember there was, at least for the DMesos, this came up,
Not in the neutral curse, but in the charge curves. This happens if we do also know that.
People realize that, for instance, that specific decade.
due to renew? Mm-hmm.
was actually really good in. Okay.
So I should… I should look into K-Long decay.
Like, into invisibles? Because, like, you see what it decays into.
Yeah, okay, but this… this is going to change their life? Yeah.
you measure a problem with your lifetime.
But I would… I could imagine that it's decay rate to invisibles is…
measured, or is out there. Yeah.
Because, yeah, this one, it's really the decay into nutrition moves, but…
I mean, I don't know how you'd be measuring those neutrinos.
If you're really confused how you're able to turn it into a pion if you don't have any flavor off the item or calculus.
You'll have that diagram back.
Yeah, I mean, I don't know that the diagram is the most insightful.
to your question.
It's, uh…
It's a weak interaction.
That phi coupling doesn't exist.
This coupling?
Yep. I mean, you assume it's diagonally?
So… So, it comes from, like, this…
weak, strange, changing…
interaction.
So it's not… it's not… Also known as the W?
That first protects us.
Yeah, so it is… it's…
It's a weak interaction. It's suppressed by GF.
GF squared.
So the W… Yeah, so this vertex…
Is it a youth?
The new physics here is that
The new physics here is down here. This exists. So, but how do you turn the…
First of all, W would be charged current. This looks like it's mutual permit.
So, like, the… the…
This decay, or these are neutrinos,
That exists. Oh, it's a Utah car.
Maybe you've made a part of my miscellaneous.
No, that would be a charge tube transition.
So, I'm sure by zero on the 8th.
Yeah, a K-plus can turn into .0 plus a W. Then how does that mix with the phi? Phi is…
You can't turn it into a fight.
the neutral.
plus the 5's flavor diagas.
We'll say for diagonals.
So with the neutrino case…
not be problematic for a different reason.
Oh, so the… the decay is that it's pi-plus to neutrino, neutrino.
Or that's, like, the decay that exists in the world that's been…
at least searches for.
K+. K plus to pi plus, plus two neutrinos. Yeah, yeah, yeah.
That's a neutral… that's a flavor-changing neutral current. Yes. It's forbidden in the standard model.
But it's a decay. Well, it is with super, super suppressed.
Yeah. In the same room.
That's what NA62 is looking for. It may be found, what, Three Sigma evidence of what they mean?
No, 3 plus the pipe, but they don't care, wouldn't they?
Yeah. So that…
The vertex for that is the vertex.
Here.
Do you have to expand out whatever the standard model…
the K… the K plus, pi plus, pi naught.
interaction there. That's the one I think we're all having trouble with. The K plus the 5 plus new new in the standard model is a… is a one-loop…
I think the one-loop diagram with, um…
What, 30 CKM suppression or something?
Yeah, that's why it's so small.
instead of the triangle. Right.
So…
So I don't see where you stick the 5, I guess is what I'm saying. Oh, the 5 picks up whatever the pi and the eta have.
You have to mix the phi into the pi zero. Yeah, so the phi is mixed into the Pi Zero and the eta, so if the Pi Zero and the eta have that couple inches high. I guess I'm not aware of this…
effective description in the chiral-Lagrangian for describing
big plus to pi plus, new, new.
Is there a pi zero to mu nu?
Hopefully, I'm not familiar with the Carlo Rengan.
Yeah. I'd love to see the, uh, expanded out diagram, not in the Carl LeGranium. How you stick the five… where you stick the five?
So, in the standard model, I think it's, like, you have the S coming in,
And then there's a W, which can turn the S into, uh, up.
And the up can, um, has to come back down.
And… actually, it's not just HUP, it's UCT.
that it comes back to Mary, the, um…
Great.
So the dam's just kind of there for the ride.
the spectator… in the K+, yeah, the down is the spectator… well, no, it's K+, so there's a pump, right?
Yeah. You have a chain plus, yeah, so you have UCT, and then it meets the W again, it becomes a D.
So it's suppressed by… there's, like, a unitarity thing suppressed by…
the CKM suppression.
Yeah, and then from the W…
blue. You can radiate off it.
Or the cork running in the loop, you can radiate off the Z.
Which maybe wants to make clearance.
So I think that's the diagram in the…
standard model. Okay.
So, where does… where do you specify that? I guess?
Uh, to the 5 couple… okay, the 5 couple set up.
up so you could stick it by there.
I see. Okay.
the and the Z, essentially, okay?
this.
If the phi and the Zika mixes, there are electrical… That seems pretty predictive to all of a sudden, well…
Yeah, have you checked the lecture week precision? Yes.
Um,
Not beyond, like, these sorts of…
decays. Well, like, the Peskin Akiuchi S&T parameters. No, no, it's been suggested, so I'd be interested.
Um, and seeing if there's, like, more limits I can pull out of those.
I don't know what stronger those… Yeah.
decision-let tests, or these European to check? Yeah, it's more, I don't know as much about.
Is Peskin and Taguchi? Yeah, there's the… the one that changed the…
Maso dei.
Oh, yeah, Suki.
That's different than EDM?
Yeah, well, even…
recent one?
Darius in his past life as a…
laborious. Oh, yeah. Yeah.
This is good. It's giving me ideas.
More ways to limit the dark. If you go back 5 years ago?
Priya.
a huge amount of literature of movie release type, and of course, they're much heavier. But it relies on recoupling to bees.
Yeah, true.
So?
The normal discussion, or we can, like, discuss offline, yeah. Christina, thank you very much, and let's thank goodness again for the…
Yay!
We're