So, welcome to today's colloquium.
Tom LeCompte is a physicist from Argonne.
He did his undergraduate at MIT.
He did his Ph.D. at Northwestern, which is actually where I met him.
We were students together.
You have to guess which of us is older.
And then he went to Illinois to work on CDF
and then to Argonne as a staff scientist where he worked on CDF,
STAR, as well as ATLAS.
And, he was a physics coordinator for STAR
as well as the ATLAS experiment at LHC.
And, I don't know if you realize this, but being a physics coordinator
at ATLAS at LCH where there's 3000 collaborators to manage all
of the physics output is actually on of the great challenges in
the physics world, I believe.
So, for the last couple of years he's been helping DOE
manage the LHC program and he's going to talk to us about...
what happens when you build the world's largest microscope
and point it at nothing?
Thank you Rick.
So, just to get started.
Large Hardon Collider, if you're not familiar with it.
It's proton-proton, proton-ion, ion-ion collider.
Designed center of mass is 14 TeV, so 1000 times the CEBAF energy.
It's located at CERN near Geneva, Switzerland.
Our radius is 4.2 kilometers.
The magnetic field is 8.5 Tesla.
1100 Amps to do that.
First collisions were almost 10 year ago and they're at four points.
And, the RF cavities are normal and the magnets are superconducting.
The exact opposite of the way CEBAF runs, so one of us is backwards.
So, why would you want such a thing?
And, the answer it to answer a question that goes back to the 19th century.
How old is the earth?
And, after the invention of thermodynamics in the middle
of the 19th century people were running into this crisis
a few years later about how old the earth could be.
And, you had, on one hand, the Helmholtzs of the world,
and they argued that there's no way the sun could
possibly shine for more than 10, 20 million years, tops.
So, the earth had to be about that old.
And, on the other, you had people looking down,
the Darwins, Charles and George,
and they argued that there are features in the earth
that are several hundred million years old
and the earth could be no younger than its oldest feature.
So, there was a tension here.
How's it going to be resolved?
And, here's where Helmholtz made a mistake.
So, what Helmholtz said is, let me relate the
gravitational potential energy of the sun to its luminosity.
And, if you do this, you get numbers on the order of 10 million years.
You can try and tweak this by having meteorites fall in or,
in one case, having the aether fall in, but it doesn't actually help you.
You still get numbers that are this order of magnitude.
And, we know today that's not where the sun gets its energy.
It comes from fusion.
Turns out, though, this doesn't solve the problem.
Right, if I add more energy to the system,
it doesn't make the sun burn longer,
it makes the sun burn brighter.
If I throw a stick of dynamite in my fireplace
it doesn't make the fire burn longer.
You could argue that, yes, now the fire will last as long as I own my house,
but this is an issue of compressing duration, not anything else.
So, the sun powered by this reaction.
Four protons go to a helium nucleus and to two leptons.
And this requires two protons to turn into two neutrons.
That's the weak interaction which is carried by the W boson.
The strength of the interaction has a suppression of E over M to the 4th power.
And, for the sun, this is 10 to the minus 32.
So, this throttles the nuclear fusion rate so the sun lasts for billions of years.
Now you don't have this tension between looking up and looking down.
So, the reason the sun shines for billions of years is the W boson is heavy.
Simple as that.
If I change the W mass by 5%,
it changes the sun's luminosity by a factor of 2.
So, it's a very strong function of this mass.
But all this does is it, you know.
If anyone has a four year old going through "Why, why, why?"
This pushes the question one level of "Why?" back.
If this happens because the W is heavy, why is the W heavy?
And that's what the LHC is trying to find out.
So, let's step back to quantum mechanics.
And quantum mechanics, the probability
is given by the square of the wave function.
And, if I change this to...
The wave function to minus the wave function,
there's no physical effects.
A week later in the class they tell you that you can actually
write this as having a phase on top of the wave function.
If a change the phase, it doesn't make any real difference
because when I change this phi, add this phase,
when I add phi-star as the opposite phase.
Now, if I can't actually observe this phase,
how do I know it's the same over here as it is over there?
How do I know it's the same today as it was yesterday?
How do I - you know - why is it have to be constant?
And the answer is "Well, it doesn't."
The phase could be a function of space and time.
This looks completely harmless, but it turns out
this is a very, very powerful constraint on the
kinds of theories you can write down.
And here's the problem.
It's one little derivative.
The Shrodinger equation, and its descendents like
the Dirac equation and so on,
they have this derivative in there.
And, the two terms, the derivative of a product, has two pieces to it.
And that gives me leftover phi's.
And, at the end of the day, I can't have any.
By construction, they're suppose to be unobservable.
So, if I want to write down a Lagrangian
or a Hamiltonian to describe electrically charged particles,
I need to add a new piece to it,
and that new piece is a massless photon.
Massless. A massive particle has three spin states.
Massive spin-1 particle.
This way, this way or this way.
However, if it's massless, it only has two.
And, a hand-wavy way to think about this is,
if it's massless, it's moving at the speed of light,
so there's no way to overtake it
so the spin is pointing in another direction.
So that's - it's sort of hand-waving.
To cancel the phi's I need to add two,
and only two, degrees of freedom.
So, this one and that one.
If I add the middle state, that overdoes the
cancellation and I'm right back where I started.
I have these unobservable phi's sitting everywhere.
So the photon that I add must be massless.
If you're a theorist, you'll want to think more technically,
I need a parameter that has dimensions of mass
in the theory somewhere, so the W can be
proportional to it, but there's no place I can put
the mass in the Lagrangian that spoils the symmetry.
Now, a good theory is predictive.
Or, at least, retrodictive.
So, if I start with Coulomb's Law
and I want to make it work out
with relativity and quantum mechanics, what pops out?
Magnetism pops out.
Electromagnetic waves pops out.
A quantum mechanical photon of zero mass pops out.
And, experimentally, the photon is massless.
We know its mass is less than 10 to the minus 22 of an electron.
That's 10 molecules of ethanol in a glass of water.
We call that lite beer.
It's roughly the radius of my head to the radius of the galaxy.
And that third one, I used to put a probability,
and I'd have the name of a particular celebrity of politician there,
won't do anything shameless or stupid in the next 12 months.
That turns out to be less funny than it was in the past.
So, let's do this again.
So, if I describe electrically charged particles
by a Hamiltonian, out pops a massless photon.
I try to do the same thing with color charge
and out pops, not just a massless gluon,
but 8 massless gluons. The right number.
And, if I do this with the weak charge,
I get massless W-plus, W-minus and Z-zero bosons.
But, experimentally, they're heavy.
So, we're trying to figure out what breaks here.
What makes the weak force different than all the other forces.
What makes it weak.
To do that, we need to understand spontaneous symmetry breaking.
This is the audience participation part.
I want - if I've got four cities at the corners of a square
and I want to put train track between them
so that you can get from any city to any other city.
And I want to do that with the least track.
So, one option is to do this with four units of track.
Alright, that cost me four.
I can do this with three as well.
I can get from that guy to that guy by going through the other two.
If you think this is optimal, put up your hand.
Alright, option three.
This requires 2 root 2.
If you think this is optimal, put up your hand.
Alright, I have two half-hands.
How many of you know the right answer
and how many of you just suspect a trap?
Suspect a trap - right! Exactly!
There's a trap.
This is the real optimal solution.
This actually only takes 1 plus root 3.
There are 120 degree angles and I can
get from any one to any other one.
So, notice that the symmetry of the solution
is lower than the symmetry of the problem.
I had a problem with four-fold symmetry,
but the solution has only two-fold symmetry.
And, if you're wondering how is this possible,
there's another solution that goes the other way,
and the sum of those two solutions
still has the symmetry of the problem.
This is spontaneous symmetry breaking.
So, you might have guessed the answer
by looking at soap bubbles.
Soap bubbles try to minimize their surface area
and they tend to go into this 120 degree -
Same thing happens in a ferromagnet.
The Hamiltonian is spatially symmetric,
but one direction gets pulled out of that
and everything aligns along that direction
to get to the lowest energy state.
If you're more mathematically inclined,
if I have a quartic potential it can look like,
on the left hand, just have a lobe at the bottom.
Or, it can have this wine bottle punt in the middle.
And that is driven by this sign right there.
This one has a solution right at the middle here,
where the symmetry is preserved.
This one has a minimum over here, not at zero.
The symmetry is spontaneously broken.
This distance here, a, is called the v.e.v.,
the vacuum expectation value.
That just means the value that minimizes it.
Which, in this case, is not zero.
So, what's the Higgs mechanism?
I can write down a theory of weak - of massless weak bosons.
There is nothing whatsoever wrong with this theory,
except that it doesn't describe the world we live in.
I then add a doublet of spin-zero particles.
And, by doublet, I mean four.
This is again, bad terminology.
It adds the particles and their anti-particles.
And I can write down the interaction between
the new doublet and itself, and the new doublet
and the weak bosons in just the right way to do two things.
First one is it spontaneously breaks the symmetry,
just like a ferromagnet, and it allows something
really cute to happen.
The really cute thing is the massless W-plus
and phi-plus that I just added mix.
So, instead of having two particles, I have one
particle that has three spin states.
That's a massive particle.
So the W has gained a mass.
The same thing happens for the W-minus.
The neutral case, it happens for one
of the two combinations.
That gives us the Z.
And, the other one doesn't couple to the Higgs field at all
and it gives the massless photon.
So, that gives you one degree of freedom left.
And, because of the non-zero v.e.v. of the Higgs field,
produces a massive Higgs.
Now, how cute is it?
It's pretty cute.
That's my nephew.
He can't help being this cute. It's genetic.
So, you really have very little choice
in how you write down these theories.
There's one free parameter,
and that determines the Higgs boson's mass.
There's one sign which determines
whether the symmetry breaks or not.
We saw that happen before.
Other than that, it leaves the Standard Model
pretty much untouched, except for adding a new
Higgs boson which we can then go out and look for.
It also adds a new piece to the W-W scattering cross-section.
Otherwise, that would be infinite,
which is another sign that a Higgs-less theory is sick.
And, the new piece interfers destructively
with the piece that was going to infinity
and makes the whole thing nice and finite.
In this model, the v.e.v. of the Higgs field
is the Fermi constant, give or take a square root
and factors of two, and it shows a very deep
connection between the weak interaction and the Higgs.
Our story so far.
Unlike the photon and the gluon,
the W and Z are massive, in apparent
violation of local gauge invariance
in quantum mechanics.
This is the thing that throttles nuclear fusion
in the sun and lets it shine for 5 billion years.
A fix to this is a Higgs mechanism which is a
spontaneous broken symmetry that allows the
Higgs field to develop a non-zero vacuum
expectation value that has dimensions of mass.
This allows the originally massless W
to absorb a degree of freedom and become massive.
Now, if this idea is right,
and the vacuum really behaves this way,
there will be a Higgs boson with predicted properties.
And, can we look at these things?
So, let's talk about how we look at these things
and experiment design.
The basic design of all of our experiments is the same
and this should look very familiar to most of you.
We have a tracking chamber followed by
electromagnetic and hardon calorimeters
which would stop the particles and
measure their energy.
And, finally, a muon chamber to look
at muons as they go through.
Tracking, calorimetry and muons.
And this is driven by the physics
of the interaction of the particle with matter.
Because the physics of the detection is the same,
experiments all look more or less similar.
For example, in a fixed target experiment,
the beam comes, hits a target, and you
have trackers, calorimeters and muons.
And, again, different particles have different responses.
This is an example of one such device.
This is CLAS.
It stops at the red because of the physics
of what they're looking at.
Makes no sense to build the green
and the blue on top of that.
If you do a collider, you start with the same idea.
Instead of having the beam come in,
it's now - you're having a collision.
Beam comes in the page.
But you start with the fixed-target detector,
like I had before.
You replicate it.
And then you keep replicating it
until you've covered all of four pi.
This is an example of what one of these detectors looks like.
You have tracking...
Tracking, calorimeters and, finally, a muon system.
And each one of these basically, you can think of
as chopping an area pointing to see what's happening
at the interaction point.
ATLAS, the other experiment,
has a very similar design,
but it uses different technologies.
And, for good reason.
If you have a discovery at one of the experiments,
you'd like to see it confirmed or refuted
by another experiment that has very different technologies
so that you don't know that you're doing something
wrong with how you built the experiment.
So, what can these detectors do?
There's a plethorasaurous of Standard Model measurements
that cross over twelve orders of magnitude.
We call these dinosaur plots because of their shape.
And we have searches after searches after searches.
And, as of last month, each experiment had
published about 350 search papers.
In most cases, about 10 times the sensitivity
of pre-LHC experiments.
Some cases more, some cases less.
I've decided that a death march
through all 700 papers is probably
not the right way to do this talk.
So, I'm not going to go into this in any detail.
Instead, I'm going to talk about the Higgs boson discovery in 2012.
The Higgs boson branching tracks - it decays many, many different ways.
And, depending on its mass, the decays are different.
It wants to do, if it can, it want to decay to heavy gauge bosons.
That's its job.
And, if it can't, it wants to decay to fermions.
The heaviest ones.
That's its other job.
Modes like gamma-gamma, which we look at,
are suppressed by a factor of about 1000.
So, why would be want to do that?
Well, although the signal's very small
the background is also very small and easy to understand.
So, while it looks like a crappy way to be looking at it,
your background is much better than, say, glue-glue.
Which, although you're having 100 times the signal,
you have 100,000 times as much background.
So, the best channels for the early searches
are gamma-gamma and Z-Z.
This is a typical two-photon event.
And, by 'typical' we had graduate students
staying up nights looking for events
that look exactly this typical.
It's hard to find an event that's quite this typical.
You have tracks that are produced from the
interaction point and two photons.
One here, one there.
You see their energies in the calorimeter.
You see plenty of tracks but none that are
exactly pointing at that,
particularly in three dimensions.
It needs to hit within a millimeter
or a few millimeters of the calorimeter
to be considered a track.
And, one of the nice things about this particular detector
is that the photons point back to the primary vertex.
We have several collisions going on at any given time,
so it's nice to be able to say that
these two photons point at the same vertex.
Here's the data.
You can see a bump there.
That's the Higgs.
But it's more fun - well...
At the time of the discovery, the two experiments said:
We each see a particle, with the same mass.
In two decay channels.
About the same production rate.
Same two decay channels.
Same rate as the Standard Model Higgs.
Combined statistical significance above 6 sigma.
Less than one in a billion possibility of it being a fluctuation.
And there was some minor supporting evidence.
So, with more data, how does it look?
This is the two photon signature.
To remind you, the Higgs bump is at 125.
And you can watch as it kind of comes out of the background.
That's when we switched energy.
Luminosity went up, so it's going up faster.
And now you can see the Higgs particle coming up.
So not only does it persist in the new data,
and we've now collected much more data than this,
it's coming at the right rates.
So, roughly for every collision,
you have a certain probability of producing a Higgs.
And there you go, so, that's pretty clear.
In the other channel, Z-Z, again 125 is the number you want to look at.
So, it's around there.
This is a much, much lower rate of study,
so each event had a name as it came in
and people were looking at it.
And, the background looks particularly peculiar.
These are two-Z events and this is one Z decaying into 4 muons -
4 leptons, and there's our Higgs over there.
It helps when it comes in in blue.
So, what is our story so far?
The vacuum is not perfectly symmetric.
The Higgs field symmetry is broken.
The vacuum expectation value is not zero.
It's 246 GeV which is the Fermi constant.
And the weak decays are weak because of the vacuum
more so than the weak force, per se.
You're actually seeing vacuum properties that make it weak.
We know this because we can see the Higgs boson,
that the theory predicted, pop out.
So, in some ways, the vacuum is like a ferromagnet.
There's a non-zero magnetization in the
ground state of a ferromagnet.
There's a non-zero vacuum expectation value
of the Higgs in the vacuum.
Unlike a ferromagnet, this 246 GeV doesn't point anywhere.
It's a scalar. It's just a number.
But they're other examples in condensed matter where you do get a scalar.
I've listed them there.
Things like niobium-selenium charge density wave superconductors.
Things I'm not very familiar with, but condensed matter
physicist see this happening all the time and they say
"Yes, this is exactly the same thing that's going on."
Now, after we've seen the vacuum has
one non-trivial property, does it have more?
And Nima Arkani-Hamed always said, well, the Higgs
is not telling us, you know, the vacuum is not a crappy metal.
Although, I think I've just show you that the vacuum
is kind of a crappy metal.
But it's also a crappy dielectric.
Okay, trigger warning time.
Those of you who have taken Jackson probably
still live in fear of the Maxwell equations.
The important thing about them is they are linear in the fields.
And that means that light waves don't interact with each other.
Which is good.
If they did, vision would be impossible because the
light going here would screw-up the light going there.
In quantum mechanics it's different.
In quantum mechanics, this happens.
The vacuum becomes polarized because I have a loop of particles,
in this case electrons, running around in them,
and that gives me an effective four-photon interaction.
So, if I write down what the D and B fields look like,
and I allow - this is what QED says they should be -
so there's a linear piece you know and then there's
these non-linear pieces.
The thing that matters for this is these last two here
with the 7's in front of them because they link
field components in different directions.
That's what will allow light-by-light scattering.
If you think of it classically,
I've got light waves coming in, so the fields
are pointing in a particular direction.
When they scatter, they're now pointing in different directions.
Well, how different could it be?
You can write down the most general way
of writing the D and B fields.
And, this is it.
So, you've got the piece that you remember from taking Jackson,
and then you've got two other pieces here.
This piece has the even Lorentz invariance times the same parity field.
This one has the odd times the opposite parity field.
And then they've got coefficients kappa and lambda in front of them.
I just made up kappa and lambda.
This is a post-Maxwellian parameterization formula for theories of E&M.
It's just empirical.
But it's the most general expression you could write down
that is Lorentz invariant, parity conserving
and the weakest new scale in field strength, which is cubic.
Classical E&M has these two coefficients as zero.
QED has kappa of two and lambda of seven.
Light-by-light scattering has sensitivity to lambda.
Now, that was a toy model, a real model -
this is a model of Born and Infeld.
They had the problem of why does the electron have the
mass that it does and not infinite because, if the
electron is pointless, its field becomes infin-
field density becomes infinite.
It's mass becomes infinite.
This is a problem.
So, they said perhaps this is the Lagrangian.
And beta here is a free parameter
with dimensions of mass squared.
If it's infinity, you get the Standard Model.
And, what they're trying to do is they're saying
well, maybe there's an upper field strength limit.
Once I get above 10 to the 20 or so volts per meter,
perhaps fields no longer add linearly,
and that keeps the electron mass finite.
That's what they're trying to do.
The same thing happens in string theories for the same reason.
You're trying not to have infinities, so you impose these kinds of cut-offs.
So, how do you explore these high electric fields?
It turns out, lead is what you want.
Lead-208, which is what they run at the accelerator.
Lead-208 is more expensive than the gold they run at RHIC
because it's isotopically pure.
It has a radius of about 7 fermi, so it has
a surface field of about 2 times 10 to the 21 volts per meter.
If I accelerate it to 5 TeV, it Lorentz contracts.
It gets an aspect ratio about the same as a sheet of paper.
And, more importantly, the electric field around it
also Lorentz transforms, so it becomes stronger
by a factor of gamma.
So I have fields of about 3 times 10 to the 25 volts per meter present.
There are similar measurements of people who are
trying to explore non-linear QED this way.
Nobody, including this measurement,
has seen it in its purest form.
Two photons in, two photons out.
We're all looking at it somewhat indirectly.
What this measurement is, is we look at these lead collisions
where I've got field strengths greater than 10 to the 25th.
The fields from the nuclei can be approximated as virtual photons.
This is the Weizsaker-Williams approximation,
and the way to think about it is,
if I'm watching the beam come by,
if it's on this side, as it get close to me,
its field gets large and points in this direction.
As it passes me, the field points in that direction,
so what the field is doing is this
and that looks a lot like a photon.
So, the signal is two real photos
in an otherwise empty event.
The lead nucleus, in fact, usually survives this.
It goes through intact.
There's that little energy taken out of it.
And we expect about a dozen events.
So, the signal is two back-to-back photons,
and nothing else in the event.
Photon one. Photon two.
Empty event.
This is perspective.
So, they're actually back-to-back in phi,
but they're pointing in that direction in theta,
that is, in forwards.
So it's, it's a boosted system.
This is what the background looks like.
So, it's simply a question of pulling this out of that.
Now, not every event is a signal.
ATLAS sees 13 events over a background of a little less than 3.
I have the backgrounds all listed here
for those of you who are interested in them.
This is the one that's the killer.
The central exclusive gamma-gamma.
These are cases where I have two photons
and nothing else in the event
that had nothing to do with light-by-light scattering.
Now, the good news is, this is down an order of magnitude
from the signal that we want, but, you know,
to be honest, how many of you are convinced
by the background calculation?
You'd like to see some evidence that this is signal.
And, the thing that does that is the back-to-back cut.
To require that the two photons be within
1.8 degrees of each other. Back-to-back.
The reason this works is the signal source
I told you was the electric field from the ion.
The background is caused by gluons that are
sitting inside a nucleon inside the nucleus interacts.
Those gluons have motion inside the nucleon.
The nucleon has Fermi motion inside of the ion.
So it's moving around in all sorts of directions.
So only in the rare case is it back-to-back.
And you can see this on this plot.
So, my signal in the red is almost all
on this side of the selection requirement.
My background, in grey, is pretty much flat
and goes on everywhere.
So the fact that we see out here a big signal
in exactly the right angular distribution
gives us confidence that we really are
seeing light-by-light scattering.
If you look at the diphoton mass,
it's more or less what you'd expect.
So, I have many event displays of this.
I've looked at all 13 of them.
I've shown you the top event before.
The bottom, also looks back-to-back.
I could show you 11 other events that look exactly like this.
Now, to get to a cross-section, you have a number
of systematic uncertainties which add up to about 25%.
If you have 13 events, you're talking about a
statistical uncertainty between 1/3 and 1/4.
Again, about 25%.
We can go through all of this.
We get a number of 70 nanobarns with that sort of uncertainty.
The theoretical prediction is 50.
Again, well within that uncertainty.
So, what have we learned through this detour
about looking at light-by-light scattering?
Well, the vacuum is polarizable, just like a crappy dielectric,
but it takes enormous fields to do this.
More than 10 to the 25th volts per meter.
The degree of non-linearity matches QED's prediction.
If you go through the math, there's 9 plus or minus 3
is the measurement of lambda, QED predicts 7.
Born-Infield type models are excluded for beta less than
about 10 to the 4 GeV squared.
It also tells us that the particle with the
largest charge to mass ratio is the electron.
We didn't actually know that before.
There are no megacharged particles with very high mass.
There's no particle of 1 GeV mass with 10 to the 12th charge.
We know that now from experiment.
I have no idea why anybody would propose such a thing,
but the point now is that it's moot.
There aren't anything out there like that.
But, this is different than most searches.
Most searches are sensitive to mass.
This is sensitive to charge over mass.
So, they're different things that you could see.
Finally, in high school physics lab,
I measured e over m for the electron to about 15%.
Now, many year later, a third of a century,
10 billion dollars later, I measure e over m
for the electron to about 15%.
So, I'm sure there's a lesson in that somewhere.
Alright, back to the Higgs.
What have we learned?
One thing that we have learned is that
there are exactly three fermion generations.
There's the one that makes up
the matter that we all know and love.
There's the charm, strange and muon and its neutrino.
Top, bottom, tau and its neutrino.
And that's it.
There's nothing else at all the way up to the -
you know, up to the Plank scale, that replicates this.
Second thing, nature has provided us a fundamental scalar.
And, as far as we can tell, it's property matches the Higgs.
Its mass makes no sense, and I'll explain why in a minute.
And, finally, the Higgs mass is suggesting
that there's new physics at the TeV scale.
And, flavor, however, is telling us that,
if it's there at all, it's at least 10 times heavier.
So, let's go with the argument for three generations.
This is also a statement about the vacuum.
The way the you produce 90% of the Higgses is through this diagram.
Two photons come in, they interact with a virtual
top loop in the vacuum, and pop out a Higgs.
So, they excite the vacuum through its t-t-bar properties
and out comes a real Higgs.
As, in most times, when you write down
this kind of diagram, these kinds of loops,
right, the heavier the mass of the particle
in the loop, the more suppressed the diagram is
and the rarer the process.
It doesn't happen in this case.
This case is special.
Because the Higgs couples to mass,
the heavier the particle is,
the stronger that coupling.
And, it turns out, those two exactly cancel.
So, if there's a b-prime and a t-prime,
I would have three times as many loops
and, thus, I would have 9 times the cross-section.
Because it's a constant.
So we are asked to determine whether our data
fits this model or that model.
That's three. That's four.
So, this is not a tiny effect.
This is enormous.
One silly way to look at this is
the number of generations is
three point zero zero plus or minus point zero four.
Four is excluded at very high confidence.
Another is that we are actually more confident
that there are three families that the Higgs exists.
Because we are sure -
We are more confident that the data
excludes this point than excludes that point.
So we are absolutely sure there are three,
and only three, generations modulo loopholes!
So, there are loopholes.
I'm talking about a truly sequential
fourth generation that gets its mass
from the same Higgs that gives mass
to the W's and Z's.
If I have a more complicated theory,
where, for example, the quarks are vector-like,
they're multiple Higgs bosons, whatever.
This is, things could be different.
You could also have, always,
the miraculous cancellation.
There are two pieces of new physics,
one that turns it on
and one that makes it look like it's not there.
So, there are loopholes.
But, in so far as you
don't go through these loopholes,
we know there are exactly three generations.
You also might ask,
"Well, how do you really know this is the Higgs?
You found a scalar, but maybe it's something else."
Well, this particle couple very strongly to Z-Z,
despite being 25 partial widths away from the pole.
So, the Higgs decays to two Z.
One can be on-shell, but the other
is stuck to being 40 GeV or less.
That's a huge degree from the pole.
It also couples very strongly to W-W-star.
The equivalent figure is just unreadable.
So, no matter what, you can't write down
a theory of electroweak symmetry breaking
that doen not include this new particle
that has any hope of being right.
So, it looks exactly like a Higgs
and it definitely plays some role.
Now, I mentioned, as far as we can tell,
the Higgs couplings match what the
Standard Model expects.
And, this is a clever way of putting
different particles on the same curve.
This is what you expect relative
to the Higgs coupling so that this line is at one.
And you think this is good news.
And the answer is, "Well, maybe."
The experimental sensitivity of the LHC
is given by the red curve.
And you can see, everything is
just above that sensitivity.
So, if things were well below the Higgs coupling,
we wouldn't have seen the particles at all,
and they wouldn't be on the plot.
And, if it was well above that,
it would have been discovered much earlier at the Tevatron.
So, it's... Yes, it tells us something
of the couplings appears to be right,
but perhaps not everything that you might want.
This is everything that we know about the Higgs
and the first two generations.
It all fits on one slide.
What about another Higgs?
Nature gave us one.
Why not two? Or 10? Or 100?
One useful framework is to think about this is
what's called the two Higgs doublet model.
I added one doublet to give mass to the W's and Z's.
Well, maybe that's not what happens.
Maybe there's two.
And, maybe there's ten,
but let's think about just the first two.
If I add just one more complex doublet,
there's four degrees of freedom.
That gives me five physical particles.
A Higgs, another Higgs that looks
more or less like it, A C-P odd Higgs
and two charged Higgs.
And you can put these models together
in many different ways.
You can say one Higgs deals with the up-type quarks
and the other the down-type.
You can say one deals with the fermions,
one deals with the bosons.
You can say one operates on leptons,
one on quarks, and so on.
In type-two, which is SUSY-like,
and I'll explain supersymmetry in a bit,
there are two parameters.
One is called alpha, that's mixing
of how much one Higgs is in the other.
And beta, which is the ratio of u-type v.e.v.
to the d-type v.e.v.
People explain this with words that I don't understand,
like superpotential and holomorphic.
This is just how it works.
There's two ways you can see this.
One is direct observation.
You just look and you discover a new particle.
The other is by saying "Ahhh. The Higgs
that we found at 125 has properties
that are different from the Standard Model Higgs
and these two are coupled."
If my other guy looks a lot like
a Standard Model Higgs, it's easy to spot.
If it looks very different, it might be hard.
Alright, some random facts.
Starting with humans share 50% of their DNA with bananas.
Under supersymmetry, and I'll get to that in a second,
the Higgs mass is less than the Z mass all the time,
which implies, right, because there's a cosine there.
It could be that radiative corrections are large.
Or it could be we found the wrong Higgs
and we found a heavier guy
and I'll show you why this is not likely in a moment.
The direct searches are just repeats
of the original searches.
At this moment we have 15 times the data,
which gives us about 4 times the sensitivity.
But it only gives us 4 times the sensitivity.
It doesn't give us 1000 times the sensitivity.
And that's for a second Higgs
that looks exactly like the first Higgs.
If I'm mixing two different Higgses,
the more one looks like the Standard Model,
the less the other one does.
And we're looking for the guy that doesn't
look very much like the Standard Model.
And, experiments can really only measure a few things.
One is topology.
Was this produced with a W or extra jets?
I can measure cross-sections.
I can measure rates.
And I can look at kinematics - energies and angles.
And, in general, these are easier to measure.
Harder to measure.
And they become less constraining
as you go on down.
In a two Higgs doublet model,
the region in white is allowed.
The Standard Model is dead center in these four plots.
And you can see, okay, these are excluded regions.
These are allowed regions.
And we've excluded maybe half of the region.
There's a lot left to go.
So, it does say we have certainly found
the more Standard Model-like
of the Higgs bosons,
if there is more than one,
but not a whole lot else.
It says that, you know,
we can measure that it agrees
to the 10 or 30 percent-ish levels
with what we expect, but not
the 1 or 2 percent measure.
If you're thinking about this in terms of mixing,
you're trying to find the cosine
of a small mixing angle
and see that it deviates from 1.
That's a hard thing to do.
I don't believe we've ever discovered
anything by looking at that kind of deviation.
We find it the other way.
We find that the sine of the mixing angle
deviates from zero.
But, this is what we have,
and this is what we measure.
So, another way of doing this is to have
a Higgs that couples only to bosons.
And then, one only couples to leptons.
Maybe we found the bosonic one.
Well, what happens?
Well, the branching fractions to W's, Z's and gammas
goes up by an order of magnitude,
but the production mechanism shuts off
and the cross-section goes down
by an order of magnitude
and the rate is almost unchanged.
So, you can run yourself into periods of
theory-space that appear to give you
more or less the same answer.
Now, this turns out not to be as hard as it looks.
We again have rates, kinematics and so on.
In this particular case, what would happen,
if this were true, is that every Higgs
would be accompanied by two more jets.
And we don't see that.
So we know that's not the case.
I mentioned that the Higgs mass is crazy.
It's too light to be heavy,
and it's too heavy to be light.
The problem is, the physical Higgs mass
is what it is, is the bare mass
plus the radiative corrections.
The radiative corrections are of order
the weak coupling constant times
the scale of new physics.
And, there's potentially a lot
of new physics there.
Eventually, we're going to run into gravity.
There's probably unification somewhere in between.
We know that electrons and protons
have the same charge.
There's some reason for that.
So this is a number we think
should be very, very high.
Michael Dine said "It's like saying
that the Higgs mass is this number
minus this other number
and they cancel to 30 digits."
And this looks absurd because it is.
Those two pieces that are circled
don't have anything whatsoever
to do with each other.
It's just - in this case,
would just be a random coincidence
that two numbers from two different places,
neither of which we understand,
agree to that level of accuracy.
So, if you want to fix this problem,
what do you have to do?
You have to figure out why
the bare mass and the corrections
are about the same size.
And, there are three ideas that are going on.
Idea one is, this is just an accident.
I don't particularly care for that answer,
but it's a possibility.
The second one is, the Standard Model is incomplete.
There's new physics at the electroweak scale
and, this idea of a cut-off at some high energy,
that really doesn't happen because something
new and ususal happens to make that model,
that framework, invalid.
And then the third idea is, there's a cancellation
that makes this be small.
And, the usual trick is to involve supersymmetry,
which makes it zero.
This has some nice features,
like it gives us a dark matter candiate.
And, again, the minimum number of
of Higgs bosons is 5.
Alright, I've mentioned supersymmetry three times
and I have not yet explained what it is.
It is usually described as a doubling of particles.
For every fermion, there's a boson.
For every boson, there's a fermion.
In my thesis qualifying exam, the oral,
I was asked "So, tell me about supersymmetry."
And I said "Well, for every fermion, there's a boson.
And for every boson there's a..."
And the word 'fermion' left my brain
at that moment, never to return.
And all that could come out of my mouth was
"For every boson, there's bosun's mate."
In any event, this is the effect, not the cause.
The cause is a new symmetry in the Lagrangian,
it's a space-time symmetry,
like rotation or translation.
And, it actually didn't come about
trying to explain this, it came about
trying to explain why we have baryons and mesons.
That's what the symmetry was originally induced for.
The symmetry is inexact because the superparticles,
if they exist, have to be much heavier
than ordinary particles, and that's good.
Because, if the supersymmetric electron
had the same mass as the electron,
we wouldn't have molecules.
Because, it's a boson, so it would
all collect in the ground state
and atoms would never combine with each other.
So, this is good.
That would, as I say, put a real damper on the talk.
It has some nice features, like a dark matter candiate.
This is actually a convenient side effect
for putting a band-aid on the theory.
If you just write down the simplest thing,
you discover that the proton lifetime
is under a second.
And you'd like to fix that.
And, when you fix this,
it gives you a dark matter candiate.
And, as I said before,
you need 5 Higgs bosons as a minimum.
There are three families that I'm going to talk about.
What we talk about conventional supersymmetry
people say the spectrum looks like this.
Where all of my squarks,
my quark partners, are degenerates.
And the gluino, the gluon partner, is heavier.
Natural SUSY, which has only the stop squark
light and the other squarks up here.
And electroweak, where the gluino is
so heavy you could never produce it,
so you're only producing things
through the electric or weak charge.
These guys in the left have large cross-sections
and are thus easy to produce.
Those guys on the right have small cross-sections
and are hard to produce.
So, is supersymmetry the answer?
Well, it gives you the cancellation that you'd like.
Maybe a little too much, but it's there.
It's broken in the right way.
Might give you Higgs at the right mass.
It favors a light top squark.
And how light depends on, you know,
how light is light depends on how natural is natural.
It's someting that we can all discuss.
And it gives you a dark metter candiate.
These are the search - limits of various
searches that have been done.
And this is on a two-dimensional plot.
We call these limit plots.
There is no sign of it anywhere
and the limits are starting to
put these ideas into tension.
Now, I've flashed the limit plots
without explaining it because I think
these limit plots have limitations
that are more important to understand.
Every plot has some model dependence moved in.
So, when we say "Ah, we're excluding SUSY
below this number or that number or this other number."
What we're really saying is "We've picked one
particular model and, if that model is right,
we've excluded it for those parameters."
Typically, they assume that the only particles
that you have to worry about are the ones
being searched for, and their daughters,
and they all decay with 100% branching fractions
into the mode that's easiest to look for.
This is almost certainly not the case.
But, there's really not a whole lot else you can do.
Right, if I say "I'm going to change that 10% number
to 50% or 20% or 10%," those are equally arbitrary.
So, many of these plots seem to exclude
supersymmetry below about a Tev,
but this is absolutely not ironclad.
A different way to look at this is, you say
"I'm going to look at an n-dimensional parameterization
of all of the models out there and I'm going to
pick a model and I'm going to look at all of
it's predictions. Not just in collider world,
but in precision electroweak or cosmology
or whatever. And, if this model is viable,
I make a mark on my plot on where it is.
And, if it's not viable, I don't."
And then you plot the points that aren't excluded.
And, in this case, what you find, for example,
this is the mass of the lightest supersymmetric particle,
you're actually only excluding down to 30.
There are models that are perfectly viable
where it would be substantially less.
And you can plot many different variables here.
So, you might say "Well, what do 10,000 wrong
theories tell you about the one right theory?"
And the answer is nothing, other than where you have
or have not excluded all possible theories.
So, I would say our SUSY story has come to a middle.
The LHC has not discovered it.
Nor has it eliminated it.
As you saw in the last plot, there are
literally thousands of models that are still good,
but it's constrained it.
The easy to spot models have all been excluded.
And, over a beer, we can argue whether it's
likely or not that nature has arranged things this way.
And whether it even makes sense to ask that question.
But, the typical characteristics of the surviving model
is much of the spectrum is very heavy.
Only a fraction of it is accessible at the LHC.
And, to stabilize the Higgs mass, you really only need
the top squark to be light.
The other guys are allowed to be heavy.
The lighter particles can also cluster in mass
and that makes any individual one hard to see.
I'm going to talk a little bit about flavor
before I open this up for questions.
The decay B sub s to mu-mu in the Standard Model
occurs only by the top diagrams.
And, these are suppressed very,
very strongly though loops.
The partial lifetimes of B mesons,
if this were all that occurred,
would be measured in seconds.
You could practically make
a box of them and ship them.
If you had a B factory,
they'd be raining these experiments.
They'd be on the floor of the detector, just rolling around.
In fact, the actual lifetime is 1.5 picoseconds.
If I have, beyond the Standard Model amplitudes,
it competes with the Standard Model
and the amplitudes can be enhanced.
And, in SUSY, it's enhanced by a lot.
I mentioned there's these alpha and beta parameters,
right, they're enhanced by tangent of beta to the 6th power.
So, if the tangent of beta is 10,
there's a million-fold enhancement on the bottom.
So, what's the data show?
The signal is very weak.
There are three decays per billion,
so the first observations took two
LCH experiments to combine them.
That's the signal they're looking for.
That's its lighter partner,
which was considered anomalously high
at the time, that since went away.
And, now that there's more data,
individual experiments are able
to see it on its own.
So, what does this mean?
The data, as you see,
is right on the Standard Model prediction.
That means, if there's new physics,
the amplitude has to be less than
30 to 50 percent of the Standard Model.
So, this sort of enhancement is, you know -
has to be acting on something that was
already microscopically small,
or this just doesn't happen.
So, this is just a taste of flavor physics.
There are other B decays explored at the
LHC and electron machines.
There are K and D experiments explored elsewhere.
There are rare muon decays.
Or, actually, there aren't.
But, people look for them.
There are precision measurements
like G-minus-two of the electron,
which got the Noble Prize,
and the muon running at Fermi Lab now.
And the emerging picture is that flavor
measurements are matching the
Standard Model exceptionally well.
How high? Well, if you express it as
a scale of new physics, it's 10 to 30 TeV.
So, the Higgs mass is trying to tell us
that some new physics that's canceling it
has to be happening at the scale of a TeV,
or maybe even a little less.
Flavor is telling us "No, no.
It's ten to thirty times higher than that."
Alternatively, there has to be some reason
that this new physics at the TeV scale
somehow leaves flavor alone.
So, the next big step for us
is the high luminosity LHC.
Stands for the High Luminosity
Large Hadron Collider.
It would collect 300 times the discovery
dataset that I showed you.
About 20 times what we have today in the can.
The Higgs mass is determined by the
self-coupling parameter, which is
about an eighth in the Standard Model.
Is that what we will see?
We don't know.
We have to look at an extremely rare
process to see that.
And that is double Higgs production.
And that probes this tri-linear coupling.
So, to see a rare process, you need a lot of data.
We'd like to see does the Higgs have anything
to do with the second generation at all?
Higgs to mu-mu is a decay that we might be able to see.
That's what you'd... That's the signal.
And, way up here, many of orders of
magnitude higher, is the background.
And, as you know, the background
uncertainty goes as root n.
So we need to get millions of times the -
the signal that we see before we can see it
statistically significantly come out of the background.
If we had 20 times the integrated luminosity,
we will - let us push all of our searches
out in sensitivity by a factor of a few.
But we're starting to hit the fact -
starting to hit diminishing returns.
We're at the point where doubling the data
gets you another 10 or 15 percent.
Not at the point where doubling the data
gives you a substantial increase.
And, the challenge that we're facing there is
if we want 20 times the data in our lifetime,
we have to run at 3 to 5 times our luminosity,
which means we'll have, on average,
200 collisions for every crossing
and we will have to pick out
which is the one that we like
and which is the 199 that we don't.
That is a simulated event that is -
has only 102 vertices in it.
So, our problem is 50 to 100 percent
times bigger than that.
This event here is taken recently.
It's an event that has two Z's in it.
One that was produced from that vertex
and one that was produced from that vertex.
So, there will be so many events out here that we -
actually we'll have multiple interesting events
in the same collision.
So, let me summarise and leave some time for questions.
The vacuum is more interesting than one might think.
Certainly more interesting than I thought.
Elvis Costello once said "I love Rock and Roll,
but I hate Rock. A rock just sits there."
The vacuum doesn't just sit there.
The vacuum is an active participant
in the physics that we see.
If it were different, we wouldn't be here discussing it.
If the Higgs symmetry were exact, we would -
we wouldn't - there wouldn't be atoms.
We wouldn't be here.
The Higgs boson's mass is telling us
there's new physics somewhere near its energy scale.
246 GeV. I wrote 1 TeV here.
Flavor physics, on the other hand,
is telling us that there's not.
So, it's the job of the next generation of experiments,
as well as the next generation of experimenters,
to take these two facts and somehow reconcile them.
And that's that. And, I believe, that's all.
And, the quiz is, is this from
a Looney Tune or a Merrie Melody.
If anyone knows, raise your hand.
So, thank you very much.
Thank you, Tom. Questions?
So, does anybody actually still believe in SUSY,
or do they just use it to...
make predictions that are kind of
variations from the Standard Model?
There are true believers.
I - I will tell you what I think.
That's probably safer than telling you
what other people think.
I think the real utility of SUSY is a class
of theories that might explain various things.
They guide us on what we should be looking for
and the sort of signatures that are common.
I think if you look at where SUSY runs into trouble,
a lot of other theories that do similar things
also run into trouble.
So, as a prototype of a beyond the Standard Model
theory that we don't really know yet,
it's probably as good as any.
Do I think it's telling us something
about physics at the electroweak scale?
I - I have bets with people that it is not.
And, since I joined DOE, I have not been
able to collect on any of those bets.
In some kind of a fantasy world,
if you could build a bigger machine,
like, larger energies, what would you select?
What range would be important?
Well, if I could select a machine of any energy,
it would be as much as possible because
I could always tune it down.
So, I think it's important that we have
two thrusts going on at any given time
because we see a tension between
what's going on in the electroweak scale
and what that's telling us and what's
going on in the flavor sector and what
that's telling us.
So, I've been a strong proponent that
we need to have both of those going forward
because I don't know which string I'm tugging at
is going to show the discrepancy first.
So, I think it's important to be looking -
particularly at things like rare muon decays,
rare B decays, in addition to the "Let's just
crank the energy and do the search as best we can."
So, I didn't answer your question, but I thought
it's a good non-answer.
So that - so, you know, the balance
between the precision measurements and
direct searches - I mean, obviously,
the direct searches become more and more
difficult now, right?
And so do the precision measurements.
Well, yeah, it does, but it's a lot cheaper
in some sense, depending on where you do it, I guess.
I'm not so sure. Mu to e is 275 million dollars.
It's not 10 billion.
It's not 10 billion, but it's - the U.S. piece
is on a comparable scale.
I think one of the - one of the advantages
of collider physics is that there's, you know,
the 750 papers the two experiments have come out.
There's a lot of physics that comes out
that's filling in the gaps so we have a
clearer picture of what the Standard Model is,
even if the searches are coming up dry.
I also think the fact that the searches
are coming up dry is forcing us to start
thinking about things like "What is SUSY
really telling us?"
I mean, we used to think that SUZY was
saying every particle had to be within
reach of the experiments.
And now we're saying, "Well, really,
when you think about it, I only really
need one or, perhaps, a few, to do
the cancellation right."
I mean, the problem we have with the Higgs mass
without SUSY is every single cancellation
is pulling in the same direction.
Once I allow them to go 50-50,
if one of them happens to be doing most of the work,
well that's, you know, it's just how nature is.
So, I think it's forcing us to examine what
our assumptions are in a way that if we
didn't have this data, we would still be even blinder.
But, I'm not a theorist. I'm an experimentalist.
I go out and I measure stuff.
Can you tells us what the - remind us
what the schedule is for the high luminosity LHC?
So, now the beam is - it's shut down.
Right. So, the beam is shut down.
They're going to have another run
for two years, perhaps three years.
It's scheduled for three but
the first year is kind of commissioning.
At a little bit more luminosity
than we see now, but more or less the same.
Then, there'll be another multi-year shutdown.
At about 2026 they will start the high luminosity LHC.
So, I think most people have come to the conclusion that
the next run, which we call run 3,
is probably not going to give us a major discovery
because it's going to double our datasets and,
if you had a major discovery then, you'd have
a minor discovery now. But, what it does do
is it starts getting us used to the idea of the
sort of luminosity and data handling that we're
going to have to deal with when we get to the [HL]-LCH.
It's a very important dress rehearsal for that.
Okay, any other questions or comments?
Thank you. So, about vacuum.
It's not just, like, what we do when
evacuate or pump down all the molecules
in our electron gun to make the electrons.
It seems to be way more complicated than that.
If we eliminate - even if ideally I could get
all of the molecules out of this can,
there's still fields which doesn't make a vacuum.
But, where can we find, you know, like -
it really looks like a very philosophical question.
Imagine a volume in the universe and, if we could get,
not only molecules out of this volume,
all the fields and everything out of it,
what I understood from what you were saying
is that there is a non-symmetry - something in that
volume is going to make something.
That's right.
Okay, so what can we find something
if there is [unclear] about this.
It's - you're right - it's very philosophical.
I would have guessed the vacuum is the most
symmetric state of the universe where
absolutely everything is zero.
And, guess what?
That's not the universe we live in.
The low energy state actually has
stuff happening in it.
And, we're also not just able to probe
particles we know exist in the vacuum,
but hypothetical particles also would
make an impact in the vacuum.
So, the vacuum is the stage and the
scenery that the play goes on in.
And, the play would be a very different play
if it had a different stage and scenery behind it.
So, maybe I'm answering philosophy with poetry,
but that's what's going on.
Okay, anything else?
Alright, let's thank Tom again.
