By Fady Bishara.
So please, Fady, you I you you share the screen so you can start now.
Okay, sounds sounds very good. So, um, so I'll talk about um
some theoretical aspect and aspects in dark matter direct um I will talk about direct
detection, but I will explain why um this is relevant for LHC searches. And um uh I have
15 minutes, so I'll do my best then. Try not to have too many details. So if there are
something, there's some things that you want to know um that I didn't cover, please
ask me. Okay, so, uh, well, since it's the beginning, I can I can do a motivation,
even though Oh, I think it is really needed. There's overwhelming observational
evidence for dark matter. We know it exists. But all of these observe all of
these probes are based on gravitational interactions. But we know that there's
particle physics beyond the Standard Model, this is something we know that we
know that it has to be something and we know that it has to be a particle, we can
discuss to which direction you know which which puzzle we need to solve that can,
has to be solved by a particle in which not. But um this can also include particle
dark matter. So, it's a it's a reasonable uh uh it's a reasonable hypothesis that dark
matter is a particle in nature. And this has motivated many many searches for dark
matter at the LHC direct detection in direct detection and all kinds of new
probes are being thought of in a theoretical and experimental communities.
And if dark matter is a particle, then there is a variety of searches that we can uh
have we have that we can look for it. So there are three main pillars sort of
direct, indirect, and Collider. And uh in order for for one for us to build uh uh uh uh coherent
sort of big picture model of the dark, oh oh big picture of the Dark Matter model that's
behind these these signatures hopefully we'll start seeing signatures. We haven't
seen any smoking guns for particle nature of dark matter yet. But hopefully we start uh
seeing them and in order to know disentangle the nature of the sector, or
this particle or the mediators that come with this particle, we need to connect all
these different experimental searches. So there are really a couple of questions uh that that that
we want to address. One, how can we compare the results in different search
strategies. So at the moment, everybody's sort of doing their thing. And uh for direct
detection, are all the relevant defects accounted for because this is actually
quite quite important and and it ties into sort of historical precedents of of looking
for certain for new interactions, and not having to write not having to correct
effects and and taking care of you might have seen something much earlier than you
expected or not see something things like this. And both of these questions are can
be answered in in the complex of dark matter effective field theories, which is what I'll
I'll just describe for you uh in in the coming slides. So first, uh let's look at the LHC
versus direct directions so the super, super simplified picture of of what's going
on there many many searches at the LHC and there many searches there are many direct detection
probes, but just for just a simple naive picture, let me show that uh so at at at the at
the LHC either you can produce uh dark matter particles directly. Which Can you
see my cursor?
Yes, yes, yes.
Good, I will not point all over the place. So here you can see the top at the LHC
panel on the right here you produce two dark matter particles by a mediator. For
example, if the mediator is not too heavy, Meaning if it's accessible within the LHC
energies, you will produce the mediator. And if it decays only, I mean clearly it
cannot only decay to dark matter because it couples to the standard model.
But there are many, a lot of theoretical model building goes in this direction.
But, uh so either you observe it directly for the decay back to standard model like dijets or
things like this, or it's missing E T signature and then the other side, there's
some other standard model particle that's produced, let's call it x. So there are
two different uh broadly speaking, uh signatures at the LHC. Of course, you'll hear more
about that in the in the coming uh uh specific searches at Atlas and CMS and, and and one such
signature with Higgs. Uh and for the direct detection, what you have is, again, your
coupling, still the Standard Model, to the Dark Sector with some mediator, it's
probably the same mediator, but now it's happening at a much different scale. And
I'll talk about scales in the next slide. And so this nucleus gets elastically
probed and it just uh gets excited and and radiates a photon, etc, etc. If you zoom in on
this interaction, you see that again, uh it's something similar to what we have here.
But I just took the proton and I just integrated out the mediator. And proton can
be proton or neutron. And if you zoom in even further on this interaction, you see that uh
Well, you have to couple the dark matter to the quarks and then the quarks have to
interact have to, well, the quarks, you know, make up the hadrons make up the
pions and the nucleons. But in order for uh for you to compute this rate, uh you need to uh
compute some uh non perturbative objects, and I'll talk about this a little bit next.
So the idea is that uh this what happened here at the LHC is what's happening here,
it's just happening at a very different scale and the physics is different. And
what we want is we want to say, Ah, you know, Atlas CMS, they saw this, uh you know,
this dijets signature that that looks like in this mass range and direct detection we saw
we saw, you know, dark matter in this range, etc etc. And you know, put these
two together we want to know we want to be able someday to say this dark sector has
this kind of mediator couples to dark matter couples to to quarks, it doesn't
couple to leptons. And in order to do this we need to we need some framework in order
to combine all these researches. And um uh before I I tell you about the effective
field theories that are involved here, uh let's let's talk about scales because that's a
very important aspect of what's going on here. So scales. What's happening at
the LHC. I'll start from the right and then go to the left. What's happening at
the LHC at collider searches uh is you produce standard model uh Standard Model
particles collide with the quarks, gluons, blah, blah, they collide, they make uh either
a mediator uh which which decays into standard dark matter or or just a mediator something
like this. Okay? This uh energy scale is set by the by the partonic center of mass energy at the
LHC, which is roughly of a quarter TeV. For indirect detection, what's happening is
that uh you turn this diagram. I mean, you've seen this pictures with people putting
arrows all over the place during one diagram. But here I draw the diagrams for
you. So uh uh from the left to the right, you have uh dark matter dark matter going into standard
model standard model, and since dark matter is nonrelativistic, uh in our Halo,
thinking broadly about some GeV to TeV particle and uh and of course, that that's just a subset
of models, but Okay, uh just to to to to think about something concrete, uh that's set by the the
twice the mass roughly of the dark matter, which is around 100 GeV or so. For direct
detection, the relevant scale is the momentum transferred to the nucleus and the
momentum transferred to the nucleus is roughly uh 200 MeV, at the moment maximal,
let's say 200 MeV max is this momentum of transfer, there's yet another scaling
problem. And that's the scale of the mediator. So here, I didn't draw the
mediator, but of course at the LHC, uh you're, you know, if if the mediator is not
too heavy, you're most likely to see to see that first at the LHC. So that's
another scale in this in this problem. So, there are many, many scales and when you
have many, many scales, the first thing that comes to mind or the go to solution,
when you have separate scales, like this is effective field theories. And, uh and I
see a tower of effective field theories, because really, these are very different
effective field theories that that that you
that that you have to construct. So starting with a very high scale. So let's say, at
or below the scale of the mediators. Uh You can have some effective field theory that
couples dark matter to. So below the scales of mediators, you can just
integrate it out. And you can just have the dark matter directly interacting with
a standard model, but also you can have a simplified model, which is something
that, you know is useful at the LHC, which combine some effective operators plus
a few extra light states if you want, light meaning of order the dark matter mass or
below some uh cutoff to integrate some stuff out of the Dark Sector, but not
everything. Uh If the dark matter is roughly of the electroweak scale, for the sake of
argument, let's say that below that you have to integrate out all the heavy
states. So the heavy states in this case is the Higgs, the top, the uh uh uh the W and the
Z and also the dark matter mass itself. If if it's heavy, you have to use a heavy
Dark matter effective field theory. So now we have heavy dark matter effective field
theory plus five flavor QCD. Now we're out of essentially out of the realm of, of
LHC, LHC was above now we are below, okay, but uh we need to keep going below because we
need to get from the LHC energies, okay, above M Z all the way down to the nuclear
scale. So now we're here Go down below the bottom threshold integrate at the bottom
for flavor QCD plus heavy dark matter, etc etc until you get to one GeV or two GeV. When you
get to this scale you can no longer talk about quarks uh interacting with dark matter
you have to talk about dark matter interacting with pions and nucleons with
hadrons. So, what you have to do is you have to match from above this three GeV one GeV
scale to below it. And when you do this, you have you go to uh non perturbative if if you
want this non perturbative matching in in a sense to uh uh uh effective field theory with with
nonrelativistic nucleon physics heavy baryons in effective field theory of external probes
that are the dark matter. one step further is now you have to match on to this
nonrelativistic effective field theory which the nuclear theorists use in order
to compute these response functions of uh uh the the response of the nucleus to the dark matter
external probe. And so there are some references below. Lots of work in this
direction for many years, there's a bunch of papers I was involved in, there's more
and more things. So just some references. I'm not going to talk in details about any
of these things, because I I only have three minutes left. Uh So uh uh it's such as the nature,
but what what you need to compute I mentioned earlier is these nonrelativistic sorry,
these non perturbative matrix elements, all you know is that you can organize
these matrix elements. So what you want What you want is is I have a
dark matter talking with a quark current, I want to know what the dark matter
interaction with the nucleus with the nucleons in the nucleus is and what I can
do is I can just write it by by uh Lorentz invariance, I can write whatever
everything that can appear by parity Lorentz etc. and uh stick in front of these
these these Lorentz structures, some form factor, which is non perturbative. You can
compute this systematically with uh with Using chiral expansion, I'm not going to
talk about this. Uh Once once you do this, then you can match up to this
nonrelativistic effective field theory. And uh in this nonrelativistic physics, effective
field theory is Galilean invariant At leading order in in in the momentum expansion there are
these sort of 14 operators. If you restrict it, if you impose certain
restrictions, if you don't, they're more and maybe I put your attention to a couple
of them, which you're familiar with O one n is the uh uh uh spin independent uh
interaction. And O four is the spin-dependent. If you see there's a spin dots spin
here, and here, there's the number operator on dark matter side, on the
nucleus side. So we want to match onto this. There's some form factors. uh I only
have two minutes so we'll just go to an example and then you can ask me
whatever you want back back on top of this. I have a few minutes. Three minutes for you. Sorry, you have three minutes. I I
Yeah, yeah. Oh, maybe your clock is that one minutes ahead of me but all I want to
All I want to show is one example uh which is uh uh
you know connecting. This is really maybe maybe more for the for the those who do
direct detection of of dark matter. But if those who are doing direct detection of
dark matter want to correlate their experimental searches with things that are
seeing at the LHC what's best to do is to put bounds on the operators
between dark matter and quarks and not on these nonrelativistic coefficient. This is
an example of just a simple uh uh electric dipole interaction uh uh with with the with
dark matter, uh uh tensor current, and you see there are many operators in the
nonrelativistic theory that enter. uh Some of them dominate in different regimes
different experiments, fluorine versus Xenon, etc, etc. So the the point of of this Here
this this this lowest uh uh black curve is what you would expect as a bound from the dark
detection experiment. Forget about the y axis, it doesn't really matter. And uh all
these other individual contributions of the different operators, these operators
interfere with each other. So for example, for fluorine, you see that the some curve
is actually higher than one of these lower curves because they interfere somewhat,
the interferences are negative. So, uh so, uh all this is summarized in a in a public code,
that's Mathematica. And Python, if uh uh you want to do either translate a direct
detection result up to uh LHC result or the other way around. Ideally, what I
would really just like to to get across from hopefully to get across from what I said
is that we want to correlate these these search the search strategies with each
other. We want to be able to build a coherent picture and uh For this, it's best
to try to put things on the same plane. And and this, this tool or tools like it allow
you to direct detection or LHC, put bounds on certain uh coefficients, either simplified
model parameters, etc, something like this and talk about the same quantities, not
different quantities. And that's what we want. We want to do this consistent. So I
will close with just a quick summary of what I said, there's overwhelming evidence
for the existence of dark matter, it's reasonable to posit that it is a particle
in nature. At least we don't have any evidence to the contrary of this at the
moment. Uh So we want to discover and if that's the case, we want them to discover
the model and disentangle the structure of the dark sector. And and and you've probably heard
this 1000 times. But let me also emphasize that there's most likely a Dark Sector not
a dark matter particle, it's probably not going to come by itself. I mean, we know
it's not going to come by itself, because we already know there has to be a
mediator, but it could be even more complicated than this. Uh uh to To this end, you
know, we need we need different we have different probes at different scales. And this is a
classic setup for effective field theories, we should be using something
like this in order to correlate these signatures. The public code exists. And I
should tell you that if you want a a much broader overview of dark matter, uh uh progress
and model building, etc, things like this. There's uh the dark matter at LHC next week,
and there's the indico link for for your convenience. Thank you.
Thank you very much, Fady. This was very interesting. um
So now it's time for questions or comments. So to remind you, you can raise
your hand with the button at the uh the bottom of your zoom window.
Any questions?
I don't see any Julien?
I wanted to ask you
On the practical side, so for for an experimentalist at the LHC. So, what what
can you be more specific how to use your code
for an experimental setup okay uh
yes I mean one okay.
I mean one one thing is so there there are for example, simplified models at at the LHC
which uh you guys are already using. uh
The question is the question is uh
is uh for you maybe you already putting bounds on on a simplified model with a few
parameters. The idea mainly is for the for the direct detection experiments to use
the same simplified model with the same parameters matching onto the effective
field theory and running down to their scale and then Compare the bounds, which
already has been done. Actually, it's not i'm not saying anything super new. I mean, um
some people are doing this, but it's certainly not adopted by the experiments
on a wide scale. I think. I think, I don't know if there are any direct detection
experimentalists in the audience. But that's really the where the push needs to
happen. I think there's been a slow trickle of direct detection experience
putting pounds on these nonrelativistic operators. And I think that's preventing
the ease of comparison with LHC results. So there's nothing you need to do per se,
even though you could if you want to take this, put in uh the bounds from a recent
search on some simplified model, match it onto the effective field theory, the
matching could be done at tree level, depending on the model. And just uh and if
you need Of course, if you need help doing that, we're also happy happy to do to do
this if it's a in some paper already, and then you can compare ATLAS Results
directly with LHC rather than I mean, I should Atlas or CMS, but rather than I
should mention uh uh the attempt of of plotting Atlas or CMS results, maybe I should have
said this first, sorry.
Plotting Atlas or CMS result as a single uh uh uh
cross section per per nucleon. At zero momentum transfer. I think that's maybe, uh
maybe that's the message. No, you don't need to do that. And I think there's been
already a push away from this in recent years. I don't think this is being done
actively anymore. But there were lots of Atlas and CMS trying to put bounds on on
dark matter in that same plane of direct detection, and that's simply not the right
thing to do. But
I see.
Not the best thing to do I should say, I understand. So yeah, this is this is good
yeah. Indara, you you raised your hand, but I don't see it anymore, raise it. I
hope it's fine. Don't we have another? Oh yeah.
Hi. Yeah, I guess I'm still a little confused. So do we as LHC
experimentalists benefit from this tool? Like will we get what would be if we are
already doing interpretations ah In simplify models, ah, what would we get
out of this tool?
That's not clear to me still, right?
Okay. If you're doing if you if you have a simplified model and the model is not
sick, for which there has been also work on on on on making sure that models are are are S U
Two gauge invariant, etc, etc, then you're doing the right thing you don't need to
worry okay. But if you want to compare, which as I mentioned was done before
compare on the same plot with direct detection, then you need to use this
because you need to put in your, your model you match your model to effective
field theory. And then from this extract the the direct detection cross section and
rather than converting results into uh cross section, cross cross section for single
nucleon at zero momentum transfer, which works for only some interactions, but
mostly, if you start going to spin dependent stuff, it becomes very awkward
to do, then that that's it. No, I mean, that's only for comparing between if
you're if you're using simplified models and you're putting bounds on a few
parameters, the mass, the mass of the mediator, the mass of dark matter or the
coupling, then everything is okay as long as the model is not sick because
simplified models can also be sick, sick, meaning they could have unitarity
violation problems, or they could have gauged invariance problems above the
electroweak scale. So this but this has been addressed also in the literature.
Does this answer your question? I'm sorry, if I'm not being very precise, I can reach
out to you offline. I guess I'm just curious about what the output of This
would be okay, please, I would be happy to to please send me an email and we can go by
email or chat if you wish. It would be very happy to do it.
Thank you. Yeah.
I see two questions in the chat. Uh uh One question uh is is the EFT is this EFT to include
gravity somehow?
Okay, we're we're working around the electroweak scale. So this is not EFT for
gravitational interactions. It's just for Yeah. Not sure if I'm answering the
question in the way it was meant to be asked But yeah no, this doesn't include
gravity. Let me say it this way.
Then there is there is another question. I don't know Yong Du, Do you want to raise
your hand rather than chatting in the window? So that we Yeah.
Uh huh. Can you hear me. Yes, yes. My question is so in the nuclear nuclear
Matrix element you include, for the form factors, you include contributions from the second
class currents and I want to know how large those contributions and and do
We really need to include those at this moment Can you can you explain
what you mean by second class currents. Uh
So basically
those are ah the ones that are suppressed by the by the mass of the nucleons the second term in your in your
the second term in your
higher terms in the in the heavy baryon expansion?
Yes.
I mean,
yeah, these effective field theories are very complicated because there are many
parameters. As you mentioned this already one, one thing, there's one over. I mean,
you're used to you, people are used to writing uh uh a Wilson coefficient over lambda
squared, for example, like you do in SMEFT, or something like this. But here,
lambda squared is actually many, many parameters. There's the dark matter
masses, there is the baryon masses, as you mentioned, there's the Q squared. Uh There's a q squared
expansion q squared over lambda chi expansion. Uh We're interested in the leading
effects because there are many uncertainties. So if there was a reason
that the leading order contribution is is is we think the leading order one so if the
leading order one is not that uh
one over m to the zero then you take the one over m.
Yeah, but higher order corrections are not included at the moment. I see Thank you,
but they and let me let me let me let me follow up on this question because it's a
very nice question. Why do you use EFT you use EFT is because first you can do the
leading order thing. And you know what it is, it's very well defined, you have power
counting everywhere. And if you want once we discovered dark matter and you want
more precision for some reason, there's some area where you need better precision,
you know how to improve you can go to the next order in one over m um um m nuclear,
nucleon and you can go higher order in q squared over Lambda Chi for example, and
we do all a lot of this, these things so you can you can improve easily and in this in a
controlled way.