Randall: I'm gonna spare you okay?
Georgi: Well, no. That's all right. I'll give a very short introduction.
It is interesting to
have students who make you feel stupid.
And Lisa is one of those.
Randall: Well that was a
very generous introduction because I can
assure you one of the things we all felt
as students was stupid, which actually
was kind of good because it inspired us
to try harder. So it actually worked out.
But that was very generous.
So I
guess I will welcome you to the last
installment apparently of colloquia at home which Subir asked me to do.
So I will tell you about some work that I
actually worked on a little while ago.
I'm sort of doing other things too now. But with a lot of great people here
including current and past postdocs who
are listed there and current and past
students as well. I guess Linda is the
only student who's here now who's listed.
and I guess Prateek and Matt are here and
everyone else is somewhere else.
But the general topic is going to be
obviously a new type of dark matter but
it's gonna be more general than that
I'll try to fill you in on where we are
with dark amount of research today. And
it is really weird giving a talk when I
can't see anybody's reaction so please
do feel free to ask questions because I
have to know you're there somehow.
Okay so let's just start. You've probably
seen this many times before. It might
even be slightly out of date but it's
basically what is the makeup of the
universe what is the matter content or
the energy content I should say of the
universe. This is sometimes called the
cosmic pie. The thing that is
labeled "atoms" is that mere five
percent is all the matter we actually
know and understand - the stuff we study
at particle colliders - like our particle
physics colleagues - experimental
colleagues - look at. I mean that's the
stuff we understand. I mean we say atoms
it includes of course other particles
that don't have a lot of energy because
they don't have a lot of mass like my
...[inaudible]  but most of the masses is
consistent is
the form of baryons like protons and
neutrons. In addition to that with
five times the amount of energy is
something called dark matter which from
a gravitational perspective is just
matter. It's stuff that clumps. It literally is defined as stuff that
interacts with gravity like matter. But
the difference is that it doesn't have
the same particle interactions that we know about. And in particular it doesn't
have the same electromagnetic charge or
the same interaction with the weak or
strong forces. And finally there is also
something called dark energy which is
not matter and it really is different
than matter in the sense that it doesn't
clump. It's something that's just
constant over the universe and as far as
we know has been the same over all time
as well.
And we discovered it because it's
what drives the acceleration of the
expansion of the universe. So the thing
that's really notable about this pie is
you might think at least we
understand the component that's atoms.
But actually in some sense we don't
understand any of the components fully.
Clearly the ones that are called dark are
ones we don't understand. Actually "dark"
more refers to the fact that we don't
understand them because if it was
actually "dark" it would interact with
light. It would absorb light. Whereas this
stuff is really transparent to light as
far as we know. It just doesn't interact
with it. But even matter - their is still
a mystery. It's one of the things that
I've been talking about in my class recently.
Which is why there IS matter - something
rather than nothing - in a sense - like why
there IS matter. Because if we just had a
thermal distribution of matter, basically
the matter and antimatter would have
annihilated and we'd have very little.
So somewhere in the university there
was actually an asymmetry created. So
this is just to say that every one of
these components has a really deep and
important mystery associated with it.
Why do I focus on dark matter here?
Well, several reasons but I think one of
the most important is that it although
there's no guarantee it's probably the
one we had the most chance of actually
learning something from experiments -
from observations and experiments. 
If there IS something called
baryogenesis it very likely happened at
a high scale. I mean those of you who are
reading the news which is usually hard
to do but there was actually a very NICE
news story about the fact that there is
a possibility that there was CP
violation detected in the neutrino
sector, which would be essential for
something called leptogenesis which
would help explain baryogenesis.
So there are little pieces of it that can
have testable consequences. But if there
is leptogenesis it really happened at a
very high scale and it's gonna be very
very hard to know about. Dark energy
 - the very fact that it has so little
structure and properties makes it hard
to study. There's some hope of learning
more about is it really dark energy is
it changing with time? But dark
matter - as I'll try to explain - really -
it's matter. It's stuff. And it could have
interactions. And that means we have a
better chance of finding it - we hope. Okay.
Finding out what it is - as I'll try
to explain during this talk and
finding out what it is - because it is so
weakly interacting - is a really
interesting combination of theory and
experiment. In fact it's kind of the perfect
thing in some ways for a theorist to work
on, because we know it's there as I'll
explain. But we don't know what it is.
So it's a mystery. But it's a mystery
that we have a chance of attacking,
as I'll try to convince you. So this is
basically what I said - that we have this
outstanding cosmological model. It works
really well, but the nature of most of
those components, or all of those
components is not fully understood and
some big questions remain. Now, people
get really upset about dark matter and
dark energy. They're like - you know - "Are
you sure you didn't get the laws of
gravity wrong?" and things like this.
But it's really not too surprising that we
don't know what it is if by definition
it doesn't have a lot of interaction
with us. It's very hard to know a lot of
properties of something that is not
interacting with you. We have only
limited measuring tools, so it interacts
gravitationally, and that's why we know
about it. But we literally can't see it
So why are we so convinced it's there?
Well the reason we're convinced it's
there - at least I'm convinced it's there -
is because it's been seen and it's been
seen in many different ways.
And they all agree with each other. And
this is something that sometimes lost
when people present alternative theories
of gravity etcetera. They might be able
to explain ONE of these on this list but
there's basically no new theory that is
going to explain all of them. So what are
these things? Well the first is really
how dark matter kind of got
established. The work of Reuben and Ford
showing - and other people in
France as well -
studying the rotation curves of stars in
our galaxy. It was shown that those
stars were rotating. As you went out they
were clearly rotating faster than could
be explained by the matter that was
visible.
Actually at the time I started my
physics career I think it wasn't
necessary called "dark matter." It was
sometimes called "missing matter."
It wasn't clear whether it was just matter
that had been missed - we just hadn't seen
it - it was just dark for some other
reason. But since then we know a lot more
and we're pretty convinced that there is
another form of matter that's there that
just does not emit light the same way
ordinary matter does - ordinary being the
matter that were made of and that we can
actually see. Similar to galaxy
rotation curves in some respects are
galaxy clusters in fact Franz Vicki had
first proposed Dark Matter. He proposed
it in German which has a kind of cooler
sounding name, but because he saw in
galaxies clusters that variation of
velocities were bigger than could be
accounted for by the matter that was
there. I mean he was off by orders of magnitude - 
well at least an order of magnitude in
terms of how much of it he thought there
was. But it still was quite interesting
that he actually appreciated the fact
that it looked like there was not enough
matter around to explain the velocities
that we're seen in a cluster. But
some other really interesting ways we
know about dark matter are given after
that. One is gravitational lensing which
has to do with the fact that we know
that light gets lensed as it goes around
- it gets bent - as it goes around
something energetic but it gets bent in
different directions depending on which
orientation it comes at you from. But
when you project that back you think
it's in a straight line. So it looks like
either multiple images or actually a
fuzzed out image. And this is
really important. It's because you
can sort of with this in principle you
can actually trace more about the
distribution of dark matter if you could
really do detailed measurements. That's
one of the things that people will be
trying to do - well they're trying to do
today - and they'll be trying to do more
in the future with these massive surveys.
Related to gravitational lensing, or at
least using gravitational lensing is
something called the bullet cluster,
which is probably one of the best ways
that we know about dark matter. And in a
sense that I don't have a picture here
but if you're at home you could go look
it up. But it's basically the bullet
cluster is really the merger of other
clusters. And the distinctive property of
the bullet cluster is that you can see
that - so clusters of galaxies have
gas, stars, and dark matter. And what you
can see is that the gas actually gets
stuck in the middle. Whereas the 
the dark matter just passes through,
which is what you would expect if it is
actually matter. And one of the reasons I
really like this is because it really is
what you would expect from dark matter.
You'd be hard-pressed to come up with
alternate theories of gravity that do
something like that. I mean this really
looks like exactly what you expect if
there was matter that wasn't interaction
or at least wasn't interacting a lot.
Another way is a supernova - type One-A.
You know we all know that supernovae
were used to establish the
existence of dark energy, but you really
could only establish the existence of
dark energy in conjunction with knowing
something about dark matter. They really
are determined together. And again you
get a consistent value of the amount of
dark matter in the universe.
But the way we really know those
percentages that I gave in that cosmic
pie in the beginning is from the Cosmic
Microwave Background structure. Because
matter and energy act differently.
Matter will help, and in particular dark
matter and ordinary matter also
interact differently because what
happens is you get these acoustic
oscillations and you have matter that
drives stuff in when you have
perturbations, but radiation drives stuff
out. So only the dark matter -  so the
dark matter sees one of those but not
the other one. So if you
look at the ratio of the acoustic peaks
and troughs they depend on the amount
of dark matter relative to ordinary
matter. And since we know the total
amount of matter, we can establish that its
critical density - for the total amount of
energy - we can establish all those
percentages, which is really quite
beautiful. But even more fundamental than
that - I mean that's quite detailed 
in the sense that we really can pin it
down and know the percentages. But a
couple of really interesting things are
that we know the lifetime of the
universe - pretty much. If you read Quanta
Today you know that there's some
uncertainty in that. But but we pretty
much know how long that universe has
been around. And if we had had only
ordinary matter and we know the scale of
density perturbations, those density
perturbations have to grow enough to
form the galaxies we see today. But if
because we if we had had only ordinary
matter radiation would have dominated
too long and we wouldn't have had enough
time for that to happen. So even before
we directly discovered - once we knew
the scale of perturbations we knew there
has to be dark matter because we just
couldn't have had perturbations of order 1
by today otherwise. And also this this
radiation also would have driven out all
the perturbations that are small enough
to form our Milky Way. So for two reasons -
just the existence of our galaxy tells
us that there has to be dark matter.
Any question so far?
Okay. So there's a lot of
evidence and it's all consistent which
is really one of the really important
things. And so - you know - again lots of
people get upset - like you didn't see
dark matter - bla bla bla - this is how new
phenomena and things are established. You find lots of evidence. Some of its more
intact than others. But it's all
consistent and that's how you establish
the existence of this thing. So we pretty
much know dark matter is there I would
argue.
And many other people would as well. But
what is it? And what do we even mean by
that question? What do we mean by the
question "what is dark matter?" We know
that it's some form of matter but is it a
particle?
What's its mass if it's a particle? What
are its interactions or its charges? Is
it even just one type of particle or,
like standard model matter, is it many
different types of particles? We know
only of the gravitational interactions.
We haven't seen any of the other ones.
But that doesn't mean they don't exist -
maybe we just haven't seen them yet. So I
say the existence of dark matter is not
necessarily so mysterious. After all
why should the matter that we're made up
of be everything? There's no reason for
that. And generally when there's no
reason for it, it's not true. But we - I
mean - if anything - the surprising thing is
that we are as big a fraction as we are.
I mean five percent is pretty
significant, but the question is "what is it?"
And that's the question we're trying
to answer.  So I'm not gonna promise we're
gonna have the answer because we can't -
you know - all we can do is come up
with ideas of what might be out there
and how to test it but we don't know for
sure what's there. And it could be that
dark matter ultimately will be
completely elusive to experiments. 
We just don't know.
But as theorists, one of the things we
could do is try to find every possible
way to look in the hopes that we will
find it. So I'm not going to argue that
any single idea I'm presenting has to be
correct. Although some people really get
their favorite model and they just work
on it a lot and because they worked on it a
lot, they think it's the right model. That's
not actually true. You have to actually
discover it. So we'll introduce some
possibilities and consider the
implications. Okay. So what are the
lampposts of dark matter? As I said, I
don't find the existence that mysterious.
Why should everything be like our matter? I
mean, and as I also said, it's what's
mysterious is maybe that dark matter and
ordinary matter have such similar energy.
So how are you gonna go about finding
what it is? Well we're basically gonna do
what we can, which is look under the
lamppost. So we're going to try to find
theoretical and experimental foods. And
we're going to try to consider different
possibilities and for every model we
propose we're going to ask "Does it have
particular
types of interactions?" Or does it
differently? But the question is of
course is "What are the right lampposts?" 
So, one nice thing is that it's almost
literally true that the right thing to
do is to look under the lamppost, in the
sense that if we look at regions of the
sky that are a light, they probably
have dark matter too because actually
the way structure formed, the answer to
the question of why the Milky Way formed
is that dark matter collapsed and
brought ordinary matter along with it.
When I said that we couldn't form
structure it was just ordinary matter
because it would have been blown away,
basically there was a big gravitational  potential produced because dark
matter could collapse. And along with it
ordinary matter can collapse. And that's
just generally true. Ao if you look at
galaxy clusters, which we can see, you
also there's also dark matter there. Now
of course the ratio of dark matter and
ordinary matter can vary and we're not
even guaranteed  - maybe something got
blown away - maybe ordinary matter got
blown away - maybe dark matter got blown
away. But it's not such a
bad lamppost, because it's likely that
where things are light is also where
there's dark matter. Okay. So that's the
basic introduction. Now I'm going to tell
you about a few models that are out
there. So until recently the most popular
candidate was something called WIMP -
weakly interacting massive particle. And
the fact that it was popular was
literally the fact that many people
worked on it and many people even
thought it had to be right. That's
actually not how it's determined - what's
right in the universe. That determines
how many references you get in HEP.
But it's not actually how things
are determined.  And so it wasn't at all
clear - ever - that this was actually right.
But there were a couple of reasons
people really liked it. One which I
didn't stay here is that if you have
some particle that interacts on the same
scale as the weak scale, that is to say
about the mass of the Higgs boson,
interactions of that sort, it looked like
if you did just even a
back-of-the-envelope calculation
because it goes out of thermal
equilibrium and you just ask how much is
left at the end of the day, you find that
the amount of energy carried by
Dark Matter with this property is just
about right to be that slice of the pie.
So that was such a nice coincidence
that many people thought that it just has to
be right. But whether or not you believed
it,
a couple of things that are nice about
it from a theoretical point of view is
that it gives you that right energy.
Another is that of course it would occur
in extensions of the standard model. It's
a particle that has some weak scale. We
don't believe that the standard model is
the whole story. We believe there's
something there that explains the mass
the Higgs, so it seemed reasonable to
think that that might have something to
do with dark matter. But the
best thing is because it's an extension
of the same model, it's testable, or is at
least in principle testable. Because it's guaranteed to have other interactions.
It's there in an extension of
the standard model which is basically
saying that it's connected to the
standard model in some way other than
gravity, which makes it very nice in the
sensor you look for it. The problem is
that people have looked for it, and it
hasn't been seen. And not only has it not
been seen, but nothing beyond the
standard model has been seen yet.
So, I'm gonna tell you a little bit more
about WIMPs just to remind those of you
who don't know about it,
what people look for. And there are lots
of experiments looking for it. And
it's not ruled out.
So although the parameter space is much
more strongly constrained than it was a
few years ago, but it is overhyped and
so we want to also think about other
possibilities too. So the the most basic
way to look for this type of matter is
what's known as direct detection - to
hope that dark matter is out there. It
interacts with a nucleus and leads to a
small recoil. These experiments are
generally underground to protect them from cosmic rays.
So they were built in tunnels or mines.
Having just detection is usually not
enough. Because the problem is
that not just detecting it but rejecting
background and that's really the art of
a lot of these experiments. So these
noble gas detectors like xenon - and
this is and old one - xenon-100 it's
since been upgraded to xenon-one-ton,
working on 5-ton, are nice, because it has
a smaller fiducial volume, so basically
you can use the xenon on the outside to
protect you from conflict against cosmic
rays. And the idea is the events on the
inside should be just from dark matter.
Another potential experimental lamppost
you've probably heard about is LHC. So
you can look for evidence of a stable
particle with weak scale mass or
interactions that would be generated by
the same processes that lead to the Dark
Matter abundance. But not only have we
not found WIMPs we haven't found
anything beyond the standard model. And a
lot of the time when people talked about
WIMPs, weakly interacting massive
particles, they thought about it in the
context of supersymmetry.  But I do want
to emphasize that it could be part of
any model that's beyond the standard
model that has weak scale stuff going on
as long as there's a neutral stable
particle. But none of them have been seen,
so we just don't know. And the final
thing people look for when they look for
WIMPs - 
and again you shouldn't be confused
because a lot of the time people say
we've been looking for a dark matter for
years. We've been looking for WIMPs for
years. We have NOT been looking
generically for dark matter for any time.
Mostly because the others are much
harder to find. But the other things
people look for are annihilations
of dark matter with dark matter to
produce something visible. So you just
turn around the same diagram that led to
the abundance today in the universe and
you can have it annihilate into quarks or
leptons. Now of course there's lots of
quarks and leptons in the universe, so
how do you find it?
Well, you look for something that you
don't see a lot of anyway so you want to
look for say anti-particles or a
distinctive distribution of photons - that
would be something you didn't expect.
And in fact these experiments have
happened and they generally do discover
things people didn't expect and it turns
out usually it was just the fact that
astrophysics predictions weren't what
they just integrate. So we just don't
know quite enough. So it's really hard to do.
Before I leave this topic of WIMPs, I
want to mention - well first of all, I'll
show you this nice picture because my
artist for my book did this really
beautiful picture of putting together
all three of these
things so I had to show it - having
to do with the fact that you could have
annihilations, you can have the LHC or you could have underground stuff.
This is just to say that I just out of
curiosity looked at wikipedia
because I really had just
mentioned one experiment just to see and
this is basically there are a lot of
experiments out there looking for dark
matter or looking for WIMPs. Some
recent work I did student Linda Xu,
who is online here, has to do is indirect
searches. But the problem is that you
might think antiprotons would be the
most likely thing to get produced but
there's a lot of anti protons in the
universe so there was this very clever
idea to look for antideuterons. Now you
would sensibly say well there's a lot
fewer antideuterons than antiprotons
even if they are produced. So it's a very
small production rate but the great
thing is that there is a really low
energy background because you basically
you can workout for small kinetic energy
you essentially have no background at
all. And so there's a really clever
experiment AMS looks for this, but really
there's going to be a launch of
something called GAPS, which is really
nice it basically an antideuteron comes in
makes exotic atom then it decays gives
rise to an x-ray and it's a really
beautiful way to look for these anti-
deuterons. And like I said, if they find
them it is very likely not due to a
background if they find it with small
kinetic energy. So I actually got
interested in this a decade ago.
Rene Ang who told me about this exciting
experiment he was working on at the time,
and actually with postdocs here Anna
Qui and John Mason, we actually worked
out what kind of parameter space they
can look for. Now, unfortunately
because of funding considerations, the
launch of this satellite was delayed. And
during the time it was delayed, they did
a lot of measurements of looking for
WIMPs. And so the parameter space - even the parameter space back then -
was constrained. But the parameter space we identified was mostly ruled
out already. So - you know - the question I
had that I
considered with Linda, was "Is there any
point to doing this now?" or "Are there any
models that you could even hope to see
annihilation that wouldn't have already
been ruled out?" And what's really nice
is - if you have models where you decay
through a photon and dark
photon mixing so the Feynman diagrams
look like this.
So if you see in the
bottom, rather than go directly to
standard model stuff, it goes to say a
dark photon which is labeled A-prime
there. And the nice thing about that is
in terms of what we see A-prime has a
lot of time, literally all the time in
the world, to turn into matter we can see.
But in terms of actually direct
detection, it would be very small. Because
that would be suppressed by the mixing.
So the decay - the annihilation - happens
independently of the mixing parameter.
Our detection of it depends on mixing,
but it has a lot of time to do it.
Whereas if you had just a direct
detection, it would be suppressed by this
small parameter epsilon having to do
with mixing the photons and dark photons.
So this is a class of models that you
really have a chance to look for. And
actually what's really nice is that there's
this interesting range of math that's
been suggested by various things. But in
this range of tens of GeV, that
really nothing else is really going to
find. So with these models with dark
photons, a lot of them look for very
light stuff, but really nothing's looking
for this. So there really is this
interesting range where gaps and maybe
AMS although with our weakened magnet
that's very unlikely can really have a
chance to find it. And here's a model
with a 50 GeV Dark Matter particle
and a 30 GeV dark photon. And it varies
with lots of things and there's lots of
uncertainties. But there's clearly a
chance that you could see something.
So we were excited because the
experiment is worthwhile and does
something that other experiments
really are not doing. So it's
really nice. But - like I said - we haven't
seen one. It's just one possibility. So I
think you know I think it's always been
the time but especially now that we
haven't seen things we want to reassess
the nature of dark matter.
Because I said the searches were not
searches for dark matter their searches
for WIMPs. And they're based on
optimistic assumptions that Dark Matter
does interact without matter at some
level. But so far we just have not seen
any sign it's right. So there's sort of
you know you can have many different
categories but I'm just going to say two
possibilities. You can have
two different kinds of things. You could
have no interaction aside from gravity
between ordinary matter and dark matter. Or you can have some other model that is
an extension of the standard model that
might give rise to some other types of
visible signals. So we talked about WIMPs
and I'm just mentioning Axions because
they're very well studied now, although
I'm not going to say very much about
them. But I just want 
to give them their due. A lot of
people like it and also Asymmetric dark
matter.
So Axions - there's a lot
of work on that these days I'm not
gonna go into any details about it. But
it was something that was sort of
theoretically motivated a while ago to
solve something called the strong CP
problem, having to do with charge parity
violation. The key point from an
observational point of view is that it
couples to FF dual so it
could also couple to electrons.
It's a parity odd scalar. It's
actually the CP odd scaler - the parity odd scaler. So that tells you the nature
of its couplings. And what people have
realized is that it's something that's
actually quite generic. I mean that was
designed to solve the strong CP problem.
But you might have it in string
models. There might be lots of different
parameter ranges etc. So people have
thought a lot about different ways to
look for this coupling. There was the old
idea of Tsu Kivi that's going on now the
ADMX experiment where you have some
background - you have some magnetic
field, and you hope detect some photon
going through or some Axion going through,
rather - that converts to a measurable
photon. But there are other possibilities
that people have been thinking about of
how you might check this. And so people
have had some very clever ideas.
Again, it doesn't mean that's right, but it
is worth looking for. And you might say
"How can this really light particle
be the dark matter?" And there's a
really nice analysis that was
originally done by Will Preskill, showing
that because it's so light it actually
acts like a sort of a coherent field.
Because when the mass first
turns on it doesn't know where it's
supposed to be so it's really large
amplitude. So there's  this is big
background of Axions that leads to structure formation. Okay. Another really
interesting class of models that most
recently I guess Katherine Zurich worked
on but a lot of other people worked on in
the past and since is called
asymmetric dark matter. So 
again i kind of emphasize that there was
a reasonably similar amount of energy
in dark matter and ordinary matter. You
might say "Well you know dark matter has so much more energy." It has five times the
amount of energy. But in principle it
could have had a thousand or ten
trillion times the amount of energy. The
fact that they're so similar is quite
suggestive. So maybe - maybe - maybe  there was an asymmetry that
produced matter. And it was somehow
related to an asymmetry that produced
dark matter as well. And based on that
people thought well maybe, you know,
ordinary matter is like protons and it's
a GeV mass. Maybe dark matter has 5 GeV
mass. That was the idea. But I'll
just mention some work I did with
Matthew Buckley where we just showed
that having having this - you know
because of the way thermal distributions
work, you can actually have much higher
masses. You know - it's still sort of in the
week scale range but it doesn't have to
be as light as 5 GV. And you can still
have asymmetric dark matter that works
quite nicely. So that's what
I'm going to say about models that are
connected to the standard model. Now
we're going to consider a different
possibility. Suppose it is really
unconnected to the standard model.
It really is different. There's no other
interaction with just the standard model.
Can we see it? Obviously, trying to do any
of those other detection methods is not
going to work. So is there any hope to
learn more? What I want to just try
to argue is that  - yes - if there are
interactions in the Dark Sector.
Until relatively recently it was not
that explored-
the idea of self interacting dark matter.
You know - we have a lot of hubris. We
think our structure is so complicated. We
have all these interactions - all these
particles, but we thought dark matter was
just one single basically non-
interacting particle. So what I'm gonna
explain is that not only could Dark
Matter have interactions, it could even
have interactions we might've thought
would be badly ruled out.  Like the fact
that they could exchange a massless
particle like a photon-like object, and
be charged under its own force, what I'm
calling darkly charged dark matter. So
what I mean by that is dark matter - just
the same way dark matter seems to be
neutral under electromagnetism we know
about, maybe dark matter has its own
charge that our matter is neutral under,
So it still seems kind of dangerous
because it would be quite a strong force
in the sense that you have this massive
particle - there's nothing cutting it off.
But I'll argue that actually that is
quite acceptable. So how are we going to
find that out? Well as I'm gonna argue, I
think you know the best tests are going
to be really from our astronomer friends.
Because it really is detailed tests of
structure/ If you have these interactions
it really changes the structure in the
universe in ways that we might actually
help to detect.
So what's nice about it is that the one
thing we do know is that dark matter can
be seen through its gravitational
effects. So if we do detailed studies of
its gravitational effects, we can hope to
find some properties that disagree with
what you would have predicted
generically for a dark matter particle
they had no interactions. So what we're
going to do is - we're going to suppose
the dark matter interacts, but only with
itself. So that the conventional search
constraints don't apply. But of course
it isn't entirely unconstrained. Okay.
Because I've been talking nonstop, I'll
just pause again and ask if there are
any questions. And I'll mention also this
is work I do with Pritik Agrawal,
Frances Cyr-Racine and Jacob Shultz.
Moderator: I don't see any hands raised, but people might want to jump in.
Randall: I'll wait one minute. Any questions? Anybody there?
Okay. All right. I'll keep
going. Hope you're still there.
Why is it thought unlikely that you
can have Dark Matter interacting with
a dark photon? Well, it was thought that
they would be quite dangerous and there
were several classes of things that were
thought that was dangerous it would do.
One has to do with the ellipticity of
halos. And one thing I didn't mention is
that Dark Matter
is thought to surround all the galaxies
It's sort of a
spherical halo  - a roughly spherical halo.
Ordinary matter collapses into the Milky
Way disc - as we'll talk about more
because it dissipates - it radiates. So it
collapses - it can cool down. While dark
matter has no such mechanism, as far as
we know. If it did, it would
change things. Now the odd thing is that
what they were looking for was actually
the fact that some of them do have some
triaxiality or ellipticity.
They're not perfectly spherical, and the
thought was if you have these
interactions it would just wash it out.
If you had ellipticity in a galaxy it
would be washed out.
There are also constraints from the
bullet cluster. Remember, earlier on I
said that the bullet cluster seems to show
that dark matter doesn't really interact
.whereas ordinary matter does.
If you now introduce an interaction - and
a fairly significant one, you might think
it would be ruled out. And the third one
which is actually pretty interesting, is
the survival of something called dwarf
galaxies in halos. Dwarf galaxies are
small galaxies, and even our Milky Way
galaxy can have not just starts rotating
in it, but you can actually have dwarf
galaxies that are bound to it. And those
dwarf galaxies have their own Dark
Matter - our halo has dark matter. And the
thought was that as the dwarf galaxy
goes through our galaxy - in the halo of our
galaxy - if there were interactions, those
interactions would cause it to evaporate -
would cause  the dwarf galaxy to evaporate. And at the time we started working on this,
we were curious about whether this was
true. It seemed to significantly impinge
on the parameter space. But I'm not gonna
have time to go through it all. But I
will tell you a little bit more.
I will tell you that the upshot was that
these calculations were all really hard
to do.
And they're hard to do
analytically which is really all that
had been done before. So without detailed
simulations of not just one object - with
sort of the whole distribution of
objects - it's really hard to firmly put
constraints. But even within the context
of the calculations that were done, there were
various error that we identified that
really opened up the parameter space.
So one of the things - so it turned out
that the most significant of those
constraints was supposed to be the
ellipticity of galaxy halos. That seemed
to be the one that was the most
constraining. And the way they did the
calculations, was - they said - well if you
have interactions it would tend to make
the velocity distribution in all
directions the same, which would tend to
make it spherical. So that's actually not
necessarily true. It depends on whether
the asymmetry is coming from velocities
or just from the potential. It could have
been some late merger or things like
that. So that's not even obvious.
Even within the context of that
calculation it's not quite clear how
to work it out. And we noticed a few
things that made it unreliable. So
one fix that was pretty funny
was that - you know they sort
of said - ellipticity, but it turned
out it was ellipticity from galaxies
not from galaxy clusters. And there was only one galaxy for
which the ellipticity had been measured. And not only that, but when you measure
ellipticity, if you think about
it, it's good to easiest to measure it
in the outer regions or more or
less outer regions. Whereas the inner
regions of the dense regions where the
interactions are more like they to occur.
So just putting that effect in alone -
even if you trusted their goal of
calculating velocity anisotropy -
made things really different.
Because if you just looked at the - if you
actually looked - given the errors of the
range of where the interactions are
versus where they can measure
ellipticity, you find that there's just a
really really weak constraint. So this
was our result - basically - the
light orange line of what parameter
space is allowed and sort of the
interaction coupling mass space -
those are various constraints
I have talked about. But again
we don't even trust this because we
don't know if this is the right calculation.
This was just assuming that you were
looking for this washing out of velocity
the way they did it. And we just did
it, but we did it really carefully and we
saw that, even doing that, would allow
something that was like weak scale in
mass, and interacted with
electromagnetic strength and didn't over-
close the universe. So there's really a
large parameter space out there for just
having all the Dark Matter being charged,
under its own force, with a reasonable
coupling, which is fairly interesting, in
my opinion. And the other thing is
that all those things - although as I said
the results are unreliable - ultimately
all of those will be ways that you can't
look for this model. But you just have to
do it a lot more carefully. For example
if you look at evaporation, they also did
that wrong, because it turns out that
it's multiple soft scatterings.
And the soft scatterings within the
object, matter more than the soft scatterings
within the exterior halo, because those
are lower velocities and we're looking
at a photon, so it's a one over B to the
fourth interaction. There are all sorts
of details that really matter, and it
makes it much harder to put constraints.
so our conclusion was that darkly
charged dark matter is really viable. And
the constraints were a lot weaker than
were stated. And like I said, we don't
even know what the real constraints are
in the end of the day. So there really is
this exciting possibility that dark
matter has its own world of interactions.
And I should say - you know - I'm
considering the pursuit of the most
dangerous kind you could also have just
short-range interactions - some heavy
particle exchange, or some strong
intertractions, in which case is just local.
This is what you get when you allow
something as dangerous-seeming as
long-range interactions with a dark
photon. And one thing I'll just mention
for those who are theoretically inclined
was there is also something really
interesting we discovered that I
promised myself I would follow up but
still haven't. Which is sort of like a
duality. You might think as you make the
interaction stronger and stronger that
you're gonna get more and more ruled out.
And because we allowed this new
parameter space, we thought - oh we've
might actually gone to the range where
we rule ourselves out because it would
just affect the core of the
galaxy so much, the interaction would
change things from spiky to flat, but
over the whole distribution. So it really
changed the density profile. But it turns
out there's something called Knudsen
number, which has to do with the mean
free path versus the size of the object.
And once those two cross - once you're
- once you start interacting -
on less the size of the object - then it's
basically saying that you can't really
transfer heat very efficiently. And it turns out there's sort of a
duality, at least at leading order. Where
having something to be really strongly
interacting - it might as well have been
very weakly interacting. So what you find
is that you get more and more effect, and
then it peaks, and then it goes down.
So it would be interesting to follow this
up and see how well you can take this
and if you can explain things on
different scales.
So, there I assumed that all of the dark
matter is charged. But actually the
original work that was done was with
Gigi Fan, Andrei Katz and Matt Reis that
was a question of whether only a
fraction of dark matter interacts.
Because we were interested, for various
reasons, in having something that
actually had a fairly strong interaction,
so much so that it
could actually dissipate. At the time there was some
experiment - or there was some
observation - that has since gone away but
it led to this very interesting class of
models even though the observation
did go away. And again I think that's
kind of interesting because a lot of the
time, even when we get these spurious
results, they sort of forced you to think
about things you might not have thought
about before, and sometimes lead to
interesting ideas. Sometimes you're just
chasing ambulances but sometimes you
have something qualitatively new that
you think about. So here, rather than
assume all of the dark matter is charged,
we're going to assume it's only a
fraction. And as you might expect, the
constraints become a lot weaker if it's
only a fraction. So I'm going to go
through that - it seems obvious. But
that could be really important. So we're
going to have what we call partially-
interacting dark matter. So dark matter
is charged, but it's not all the dark
matter. There's more than one type of
dark matter.
Just like there's more than one type of
standard model particles. We have quarks and
leptons. We have different flavors of quarks
and leptons - lots of different particles.
And we're assuming that there are at least
two different types in in the dark
matter sector. Now you might say "Well,
we haven't found the dark matter, so why
do we care about something that's
only a fraction of the dark matter?"
But if you think about it, you could have
asked the same question for ordinary
matter. After all, ordinary matter is only
1/6 of the energy at the universe,
and we care quite a lot about it. And the
reason for that is precisely because it
has interactions. Which means that it
does a lot more, and makes it interact
in ways that we can observe, and does all
sorts of interesting things.
So maybe the same is true for a
component of dark matter. Maybe it has
interactions. So even before we discover
what the bulk of the dark matter is,
maybe we can learn something about this
interacting component.
And that's what we were hoping. And in
particular we're going to show that
there could be a dissipative mechanism,
which could lead to either discs or even
point-like sources in some work I did with Pratik. But we're not going to talk about that.
Okay. So if it's really true that
it changes the structure, it's really
interesting, because it does make you go
back and look at a lot of measurements
that we've done and think of them quite
differently. And there's just one general
point that's going to come up repeatedly,
or would come up repeatedly if I had a
lot longer to talk, which is that it really
does help to have models in mind when
you're doing these messy experiments . I
mean you'd like to be able to just look
generically and say "Is there something
new?" So astronomers do really detailed
measurements. They're really impressive. I
have to say it's really impressive. But
a lot of the time they're just saying, 
"Does the model we have work and how can
we measure the different components?" But if you want to ask the kind of question
particle physicists ask, we want to ask,
"Is there something beyond? Is there
something new?" That's not good enough,
because we don't - you know - usually it's
true that you can pretty much explain
what you've seen if you're not
looking in a very detailed way by
ordinary stuff. But if you have
in mind a model, you usually have in mind
something distinctive that you'd want to
look for. So you can really pull it
out. So when people were measuring
different abundances in the galaxy,
it's sort of - maybe as an afterthought -
say, "Well do we need a Dark
Matter component?" They say, "No."
So then the fact is, we just want to
know what's allowed to start with.
Could you even have a dark matter component,
and if so how much? And if you think
about it, you can't ever rule out the
idea entirely, because you could always
just say, "Well we just didn't have that
much of it." So the question is, "What
is the amount that is allowed?" So
first just to explain the general idea,
we're going to assume that we have this
component of interacting dark matter
that allows you to cool into a disc. So
just to remind you, the reason we have
the Milky Way disc is because electrons
radiate, protons radiate too - but they're
much heavier. So really the energy is
mostly lost because the electrons can
radiate but then
the electrons and protons combine into
atoms. So we have the Milky Way disk
because we have this radiation of a
light species. And it turns out that here
too we're going to need both a heavy and a
light particle to get the necessary
dissipation. So the model is really
simple. It's just a U(1), which is
essentially a dark photon with an
associated dark coupling constant alpha
D. There are two matter fields - the heavy
fermion X, which is really it's just a
heavier particle and then it's a light
fermion C, which allows for it to
radiate. And there's probably some
asymmetric Dark Matter idea that allows
this to be formed. So X is gonna freeze
out. It could have half the temperature
of SM particles so you have both thermal and
non-thermal components in general. But
the upshot is, at the end of the day, what
we're proposing is that it radiates and
gives you a thin disc inside the Milky Way.
And one reason this is interesting
is because if there were say annihilations,
it's a much much denser disc of dark
matter. And also because, frankly it just
changes the structure of the milky way.
So if we could really measure everything
about the milky way we could know a lot
more. And - you know - it was really amusing
when we did this because, well,
that would be really nice if they can
measure - sort of - more about the density
distribution and the velocity
distribution near the galaxy because
then you could determine the
gravitational potential. And - you know -
we're all particle physicists, so we're used
to - you know - an idea gets proposed, and
maybe, if you're lucky, within a couple of
decades they test it. But when we first
proposed this something called the
Gaia satellite was set to launch. Which -
you know - none of us had even heard of at
that time. It hasn't launched yet, but
it was doing exactly that: it was
proposed to measure very accurately, a
billion stars: the velocity and
density distribution. So that would be
the best way in principle to test the
Dark Matter idea. But as I'll see, it
turns out, like many things, there are
caveats. Okay. This is just to say that we
worked out the parameter space for which
you would get the necessary
dissipation. mC is the mass the light
particle. alpha-D is the interaction
strength of the dark photon. And not too
surprisingly, you find that these are
roughly in the range that they are for
the electron mass and alpha QED. And the
reason it's not surprising, as we know,
that's what you need to form the Milky
Way galaxy. And I could go into more
detail if you have questions later.
The other really interesting thing that
we hadn't anticipated, or at least I hadn't,
was that something really interesting
happens. Which is that if that is really
true - that those parameters are similar -
what you would find is that the density
of the dark disk is is less than the
density of the ordinary disk. In fact, it
scales like one over the mass. And, I
mean, part of that is explained by the
fact that if you have roughly the same
temperature, and it's alpha M squared
because M is bigger, then you
have the density - sorry - you have the
thickness there. So the thickness is also
because it's actually a surface
density. That's one reason. And the other
reason is that mV squared is related to
T. So if M is bigger, the velocity is
smaller, and if the velocity is smaller, you
have a thinner disc. So in principle you
can have - even if it's a very small
component - you could have a very dense
disk. Now, of course, there are all sorts
of instabilities that can happen. This is
a very simple picture. But it does give
rise to the possibility that there is a
dense dark disk inside the ordinary disk.
Okay.
So the summary of the model is: there was
a heavy component. It was originally
motivated Fermi signal, But since then
it's gone away. But for the disc to form,
we need a light component. And there's
radiation, so that we have a much denser
region of dark matter than we would have had otherwise. That is what the idea is.
Like I said, you could hope to see it
just because of these distributions of
density and velocity.
So with Eric Kramer who was a student
here, we reworked some of the bounds
that had been done, Because the
previous balance hadn't taken into
account the fact that the thickness of
the disc is actually a parameter.
And also, it hadn't taken into account
the fact that if you have the dark disk,
it changes the distribution of other
components of the disk. So the basic idea
is that kinematically - you know - you can
pin down density distribution of
velocities. Then you have to measure the
variance separately. Once you know the
baryon components in the disk, what's
left over might be the dark disk. So you
have to measure all of those things
really carefully. Actually, knowing the
baryon components is quite a messy bit
in the literature. And Erik did a quite heroic
job of figuring out what all the gas
components were. But we also noticed
something really peculiar - which is - you
know - basically you can only relate the
density and the velocity to the
potential, simply, if you have some
equilibrium distribution. But there were
signs that it wasn't in equilibrium - that
the tracer population was actually
moving. So we studied this distribution of stars,
and found that it didn't look quite
centered. And it also it looked like it
was moving. So there are a lot of details
here. I think I'm running low on time so
I'm going to skip through them quickly. But
please ask me if you're interested.
Basically the idea is that if you looked
at these, if you had no surface density,
that's what the data looks like versus
the curve. And if you have some surface
density where you have this dark disk,
basically both of those go through those
points at the level of error that they
had. And so we just made this a lot more
careful. And it turned out it really
did matter if you were in equilibrium
or not. Because then you even have
different conditions for whether or not
this is permitted. Like I said this was
with our parco stat satellite. Since then
there's been GAIA data. And actually a
couple of groups have
reanalyzed. And it looks like they get
somewhat significant constraints.
Except for the fact that there really is
at least one very strong
indication that the tracer stars are not in
equilibrium.  Which is that, if you try to
figure out what the height of the Sun is
for each of the different populations, so
there there's a chart with A, F and G. If
you look at the last column,
you see that those solar heights are all
over the place. And if you're at
equilibrium you'd expect them all but to
be in the same place. And the other
analysis that was done by Schultz and
Lin has it in a completely different
place. So I would say that until we pin
that down it would be very hard to
believe that you really are constraining
the dark matter based on that. But if you
do trust it, it says that you probably do
have somewhat less dark matter than we
might have hoped for, for various reasons
in terms of the surface density. But I
would say that we really don't know at
this point. The dark disk is still in
play, even with fairly significant
surface density. So I'm running out of
time, but I just want to say that there
really are several different
implications and there's really a lot of
work left to do that would be really
interesting to do more carefully. One
thing that I did with Linda was
asking the question of what are the
shapes of dwarf galaxies. Dwarf galaxies
can be elliptical, but they could be oblate or prolate. And of course we only
measure a two-dimensional distribution.
But you can look at the correlation with
surface brightness and velocity and look
for a discrepancy. And actually, it turns
out that if you compare it to what's
predicted, or what's actually simulated,
that when you have large mass-to-light
ratio, that is to say you have dim
galaxies, it doesn't seem to agree
with what's been
measured, which is quite interesting. I
don't know if this will hold up, but it's
one way to test. And so basically when
they did the simulations they looked
prolate. If you had something like a dark
disk it would be oblate. And it looks
like the data supports oblate more
than than you would have thought.
Another thing I did with Jakob Schultz
was looking at the satellite to the
Andromeda galaxy. It turns out, in the
Andromeda galaxy, if you look at these
dwarf galaxies I mentioned earlier,
there are about 30 of them. And about half
of them are not distributed in a
spherical manner. They're distributed in
sort of a vast plain. And so the proposed
explanation was maybe they're formed
by which galaxies are merging. 
And then there's a tidal force that
pulls out matter. But the problem with
that is that it also looks like they
contain dark matter, which could be true
if it was just pulling out the disk
material which would just be ordinary
matter. And furthermore it even has
significant amounts of that dark matter
which you think maybe even we would have
trouble explaining. Because we have a smaller
fraction of dark matter than ordinary
matter. But it's really important that
our dark matter is at low velocity and
it's more likely to be trapped in those
satellites. And that's what we showed. And
I'm going through this very quickly. And
the final thing which is just sort of
probably got the most press, which is the
craziest, is if you really have this
dark disk, and this is something that
actually Paul Davies
told me about . Some people had worked out, that if you look at the crater record,
you find there is some evidence of
periodicity. Actually I say that but it's
really controversial. Some people said
there was evidence of periodicity for big
craters; some said there wasn't. It's
actually just cool that you can see
a record of craters - at all - from stuff
hitting the earth in the last in last
say 250 million years. This says 250 years
but that should be 250 million years.
There's evidence for something like a 30
to 35 year periodicities. And the
question is"What causes that?" So the
suggestion was - maybe - as our galaxy goes
around the Milky Way, it turns out it's
like horses on a carousel. It goes up and
down a little bit as it goes around so
maybe if every time it went through the
Milky Way disk you'd have a little bit
of an extra push, or a tidal force that
can pull out stuff that's really far
away. Which is in the Oort cloud, which is
thousands of times farther away
from the Sun than the earth, and it's
very weakly bound. The problem is, it
didn't work. There's not enough stuff in
the disk. It's not enough if you just had
ordinary matter. And the periodicity is
wrong. But if you have this thin dark
disc it works perfectly or it works
as well as you could hope, given
the existing data. Does that make it right?
We don't know. But it does give you a
prediction for what you expect the
surface density to be. You can see
there is a peak somewhere between 10 and
15 solar masses per parsec
squared. I just pointed in a way that you
obviously cannot see. But I was pointing
to the upper left hand plot there.
So is it right? We don't know. But it's
certainly worth looking for, this dark
disk, which is what those people are
doing. And the problem is - it's not clear
that the GAIA data will ever be
definitive because it's very sensitive
to these measurements of
velocities. But just in general, there's
clearly this whole new area opened up
of interacting Dark Matter. There are
lots of interesting questions that are
still out there, some of which I
mentioned, some of which I didn't have
time to get to. It's clearly a big
program.
Dark Matter charge is clearly a
possibility. But it can be more elusive
or subtle than anticipated. But it's a nice
time to be thinking about it, because there is this convergence of large datasets, and
numerical methods. But I hope I've
convinced you that it's important to
have targets, because you would never
find this if you're just randomly
looking. You really have to know what to
look for and how to simulate it. So it
could be the dawn of new era. And I
wouldn't ordinarily close a colloquium
with this but since this is just a silly
stay-at-home colloquium, I will just close with
something that I like to show, because I
think it shows why we care about model
building, which is that - I don't know
if you can see, but this is - I was once
asked - I had some friends for writing for
the Big Bang Theory. And so I was just
going to visit them one day on the set. 
And they said "Why don't you just be an
extra?" And apparently I'm a very good
actor because I was supposed to sit in
the lunchroom and be inconspicuous. And I
was so inconspicuous, that no one even
knew I was there. Even though, as you can
see, I'm right there - like - I'm right
behind the lead characters. And so this
is just - I like this as an analogy for
why we like to build models. Which is
that unless you know to look for
something, you just sometimes won't find
it. So once you have it in mind, then it's
obvious. So there are lots of signals
like that, that we just don't see unless
we look in the right place. And so that's
what we're trying to do with dark matter.
Thank you.
Are there questions?
Sachdev: Hi Lisa, This is Subir Sachdev. Sorry I wasn't here at the beginning.
So, aplogies for not introducing you.
I recently introduced you. Please are there any questions? We can hit the
"raise hand" tool.
Yang:
Hi. I wanted to ask if you could get
a dark disk in the Milky Way if you had
interacting dark matter along - if you
had interactions between all your dark
matter particles.
Randall: Say it again please?
Yang: Between all of your dark matter
particles. Does it need to be partially interacting?
Randall: Oh right. So the problem is -
that if you have - so we
had - in the first place - we had all of the
dark matter charged. But the dark matter
particle was fairly heavy, like weak
scale for example. Once you
have a charged particle that's too light,
then it will maintain thermal
equilibrium with ordinary stuff. And then
it becomes very dangerous. And it's ruled
out by the CMB etc. So you really
need to thermally decouple, early enough
on, say at the weak scale, in which
case it would have half the temperature
and you'd be fine. But if it's still in
thermal equilibrium, then it'd be ruled
out for many reasons. Even just as
basic as the number of degrees of
freedom that you would have that are in
thermal equilibrium. So in this
case, if it's a light particle, yes we do
need it to be separated.
Yang: Thank you.
Randall: Anybody else?
Halperin: I have a question.
Sachdev: Go ahead Bert.
Halperin: Yes, this goes back to an earlier part. You went through it - I thought - a little quickly.
Where did the antiprotons
come from? And what would
they be exactly be showing us?  ... the anti-deuteron. Sorry.
Randall: All right. So anti-deuterons would be
a sign essentially that there were anti-
protons. So, the same way antiprotons
could in principle be evidence of Dark
Matter annihilation - that dark matter
annihilated to produce matter and it's
anti particle - anti-deuterons could do
the same thing. Now you'd say, "Well, that's
crazy. Why look for anti-deuterons when
there are many more anti-protons?" But the
point is that if you look at low kinetic
energy,  if you just look at astrophysical
processes, because you need to get
together a couple of nucleons, and then
if you're making both anti-deuterons and their anti-particle, you need FOUR nucleons, you find
that there's very little that you have -
just by working out simple kinematic
equations - there's very little at low
kinetic energy. So if you were to find
anything at low kinetic energy, it's
a sign that it wasn't made from these
astrophysical processes. It was made
directly - more or less directly - from this
dark matter annihilation.
So you need the dark matter to
annihilate at - basically at - very low
velocities. So you needed to be pretty
much on shell, and you need to be able to
have things be close enough together.
So if you annihilate into stuff that's - like -
you know - shooting off, then it's not
going to happen. It has to be stuff
that's moving slowly enough, generally,
so that it can, sort of, combine together, so
that you can form these more complex
molecules or atoms.
Halperin: So are you saying
what you need is a  dark particle and
an antiparticle? Their masses should be
lower than the mass of a deuteron and
an anti-deuteron, but they have
some kinetic energy. That means that when
you're all done, they disappear. And
you produce something with the same
total energy,  but now it's all rest mass
energy, and you have just very low
velocity. Is that what's going on?
Randall: Yes, you want the low
velocities to be - sort of - of the particles
that you started with. So suppose I
have a dark matter and an anti-dark
matter and maybe they annihilate to some
heavy quark, or some other quark. Then
that could decay to - say - an up quark, but
if it was a really heavy particle, that
up quark might have a lot of velocity.
So it's usually going to be better if it's -
so - you saw that what I presented was
something where things were -
so you generally - so it's -
There's enough of it - it depends on,
obviously all the parameters in
the problem. But you pretty much want
things to be formed with as low a
velocity as possible, so that it's most
likely that you can have this
coalescence process, where you would form
these nucleons. But essentially, from the
particle physics point of view, you're
just producing  a quark and an
anti-quark.That then eventually will lead
into into a proton and antiproton. Then
you hope that there's some other thing
that's produced, and then that would
there would be some coalescence process.
And generally the way it's done inis
some model where you say - sort of - there's
some relative momenta that are allowed if
the relative momentum
between those two quarks is less than
something, then you have a chance of
coalescence. And otherwise it won't
coalesce. So - you know - it's
not the most precise prediction, and
there are some measurements from
the Z factories about the rate of anti-
deuteron production, which are used to -
sort of - normalize things. But what IS
known is that the background rate is
really low. So the prediction is somewhat
uncertain, but it does seem
that there's a reasonable chance that a
reasonably interesting parameter space
could be detected. But the predictions -
the detailed predictions - have a fair
degree of uncertainty, both in the
production and also even just getting to
us  - just traveling through the galaxy.
But the fact is that the signal - if there
is any signal at all - as long as it's at
low enough kinetic energy, it's a sign of
dark matter. That's the idea.
Halperin: Thank you.
Sachdev: Any other questions? Okay. Well then let
me take a minute. This is very unusual to have an
introduction at the very end the
colloquium. Apologies again. Put it down
to these strange times that I missed the
beginning of Lisa's colloquium. So as I'm
sure you all know, she is someone who really
needs no introduction. She is the Frank
Baird Professor of Science at Harvard.
She contributed to the Randall-Sundrum model, and many other things in particle physics.
She's won many awards including the Sakurai prize
of theoretical particle physics of the
American Physical Society. So thank you
very much for giving this colloquium.
Randall: I feel like I went through this too quickly.
It's weird to get to give a talk when you can't see people. Usually there are a lot of
questions, so if there's any more
questions I'm happy to answer.
You can ask online or offline.
It's very nice that you've
tried to arrange these things, so we get
to hear about - I should say that I
really enjoyed the colloquia by
our colleagues to find out what what
people are doing in the department. It
was a really nice idea. That's why I
thought I would accept your invitation,
because I think it is a really nice thing to do.
Sachdev: Thank you very much, Lisa, again.
Next week will be the last colloquium of the
semester, and it will be given by John Huth,
on celestial navigation.
See you all next week.
Randall: Bye, guys. Do be in touch if
you have questions.
