 
The Higgs boson has been
discovered at the LHC,
and the work of professors
Englert and Higgs
has now been awarded
with the Nobel Prize.
So, are we finished
with Higgs physics?
Well, the answer to that is no.
While the particle at
the LHC looks a lot
like we expected the
Higgs boson to behave,
it could be that, in
detail, it behaves
in a quite different way.
For example, in
the standard model,
we've seen that these are
the most important decays
of the Higgs boson.
We need to go ahead and check
to see if the Higgs actually
does decay like this.
The standard model gives
detailed numerical predictions
for precisely how important
each of these decays is,
so there's a lot
of detailed work
to do to see if the
Higgs boson really
is behaving as
physicists expect.
Discovering the Higgs boson
has been a triumph for particle
physics, but there is much
more going on in the universe
that we don't understand.
Cosmological observations
have taught us
that the universe is filled with
a kind of dark matter, that is,
a stable, feebly
interacting particle, which
we don't understand.
In addition, we don't understand
why the universe around us
is made mostly of matter.
There doesn't seem to be
any appreciable amounts
of antimatter in the universe.
We don't understand
the details of this.
Since there is so much going
on that we don't understand,
it makes sense for us to think
of more refined descriptions
of physics, which would
supersede the standard model.
That will the topic
of today's talk.
In the standard model,
electroweak symmetry
is broken because
the Higgs field takes
on a vacuum expectation value
which is different from 0.
One possibility for physics
beyond the standard model
is that, instead of
just one Higgs field
breaking electroweak
symmetry, there
are two Higgs
fields, each of which
breaks electroweak
symmetry This model, known
as the two-Higgs-doublet model,
has two Higgs fields, which
we call H1 and H2.
H1 takes on a vacuum
expectation value V1,
and H2 takes on a vacuum
expectation value V2.
Let's take a moment to look at
the number of particle states
in this two-Higgs-doublet model.
Before electroweak
symmetry breaking,
many things are just
like we saw before.
The massless W plus,
W minus, and W3
contribute a total of 3
times 2, which is 6, states.
The massless B just
contributes two states.
Now there are two Higgs
fields, each of which
contributes four states.
So there's a total of
16 states in this model
before electroweak
symmetry breaking.
After electroweak symmetry
breaking, of course,
there must still be 16 states.
These are made up, as before,
of a massive W plus and W minus,
contributing six states, a
massive Z boson contributing
three states, the massless
photon, which contributes two.
So the remaining number of
states are Higgs particles.
In this two-Higgs-doublet
model, there
are a total of five Higgs
particles in nature.
So in the
two-Higgs-doublet model,
we've only just scratched
the surface of Higgs physics.
There are four more Higgs
particles to be discovered.
One interesting thing about
two-Higgs-doublet models
is that they are required by one
of the most exciting theories
for beyond the standard
model physics, which
is known as supersymmetry.
In the standard model, there are
two basic classes of particles.
These are the bosons
and the fermions.
Examples of bosons are
photons, and, of course,
the Higgs boson and the Z boson.
Simple examples of fermions
include the electrons
and the quarks.
The basic idea of
supersymmetry is
that there's a new
symmetry in nature,
which is the symmetry
between bosons and fermions.
Now, since there
are no fermions that
behave, for example,
like the photon,
and there are no bosons
that behave, for example,
like the electron, to
implement supersymmetry,
we introduce new
classes of particles.
So for each boson in
the standard model,
we introduce a
fermionic superpartner.
For example, the photon has
a supersymmetric partner,
which we call the photino
in supersymmetric theories.
Similarly, for each fermion,
we introduce a bosonic partner.
So for the electron,
for example,
we introduce a
superpartner called
the selectron, which is a boson.
For the quarks,
there's a superpartner,
which we call the squarks.
So in supersymmetry,
since there's
a Higgs boson in nature, we have
to find some Higgs fermions.
So there's a whole new
kind of Higgs particle
to be discovered in
supersymmetric theories.
 
Supersymmetry is a symmetry, so
there are many different ways
we can implement it
in physical theories.
Most of our interest has
been on a theory called
the minimally supersymmetric
standard model, or the MSSM,
for short.
In the MSSM, there is
a new kind of charge,
called the R-charge, which
is exactly conserved.
This exact conservation
means that, just
like the electric
charge, in any process
the R-charge before is
equal to the R-charge after.
Let's see how this works in
a simple process involving
just the electric charge.
For example, we could
consider a process
where an up quark
splits into a down quark
and a W. Before the
process, the charge is
the charge of the up
quark, which is 2/3.
 
After the process, the
charge is the charge
of the down quark,
which is minus 1/3
plus the charge of the W.
So to balance these
charges, I better
say that the W is
positively charged,
so it contributes plus 1.
The charge before is 2/3.
The charge after is 2/3.
So the electric charge
has been conserved.
R-charge behaves in
much the same way.
One difference is that, to
compute the electric charge
of a composite state involving
a bunch of different particles,
you just go and add
the electric charges
of the separate particles.
To compute the R-charge
of a composite system,
you multiply the R-charges
of the individual particles.
R-charge is assigned to
particles in the MSSM
in a very simple way.
The R-charge of all standard
model particles is plus 1,
and R-charge of all the new
superpartners is minus 1.
So let's see R-charge working.
Here's an example of a process.
It's a familiar process
involving a Higgs decaying
to two quarks.
R-charge of the Higgs is plus 1.
After the process,
we have to compute
R-charge of the two quarks.
Since each quark
has R-charge plus 1,
the total R-charge
after the process
is plus 1 times plus 1,
which is, again, plus 1.
So the R-charge
before the process
is equal to the R-charge after.
Here's another example
of a process in the MSSM.
In this case, the
process involves
an h tilde, the
Higgsino, decaying
to q tilde, which is
a squark and a quark.
 
The R-charge before the
process is the R-charge
of the Higgsino, which is minus
1 since it's a superpartner.
After the process,
the total R-charge
is the R-charge of the
squark, which is minus 1,
times the R-charge of a
quark, which is plus 1.
So the total R-charge after
the process is minus 1,
which, again,
balances the process.
Conservation of R-charge has an
extremely important consequence
in the MSSM.
One superpartner must be
the lightest superpartner.
We call this lightest
superpartner the LSP.
Since the LSP is the
lightest superpartner,
the only way it can decay would
be to standard model particles.
They are the only things
that are sufficiently
light to allow the LSP
to decay into them.
However, let's consider the
conservation of R-charge.
Before the process occurs,
R-charge is minus 1
for the LSP.
After the process, no matter how
many standard model particles
the LSP decays to,
R-charge would be plus 1.
This is because each standard
model particle contributes
a plus 1 to the final R-charge.
Now, since R-charge
must be conserved,
the R-charge after the
process must be minus 1
in any physical process.
Since it's not, this process
simply isn't allowed.
That means that the
LSP is exactly stable.
 
So we've learned
that in the MSSM
the lightest supersymmetric
partner, the LSP, is stable.
In fact, you could arrange
parameters in the MSSM
so that the LSP
has the properties
you'd expect of dark matter.
This is one of the reasons why
supersymmetric theories are
so exciting.
They automatically predict
dark matter particles.
So now we've considered two
possibilities for physics
beyond the standard model.
First thing we talked about was
the two-Higgs-doublet model,
where there are entirely new
fundamental Higgs particles
to be discovered.
We also talked about
supersymmetry, in which there
are new fundamental Higgs
fermions to be discovered.
But another
possibility for physics
beyond the standard model
is that, in fact, there
are no fundamental Higgs
particles in nature.
These theories are called
composite Higgs models.
The basic idea is that the
Higgs, like the proton,
is made up of some more
fundamental particles.
The motivation for
this is quite simple.
We've never discovered a
fundamental scalar particle
before.
So scalar particles
are something
that are really new in nature.
That's not to say
that we've never
seen any scalar particle before.
It's just that we've never seen
fundamental scalar particles
before.
In fact, there have been plenty
of scalar particles discovered.
For example, in
1947, in Bristol,
a trio of scalar particles
called pions were discovered.
Pions, like protons,
are made up of quarks.
An example is the pi
plus, which is made up
of an up quark and
an antidown quark.
Holding the pion together
is a bunch of gluons.
It could be that the Higgs
boson is quite similar.
It's a scalar particle,
which is made up
of some more
fundamental components.
A specific example of this is
a theory called technicolour.
Technicolour is modelled
on quantum chromodynamics,
our theory of how the
proton is made up.
In technicolor, the
Higgs is made up
in a pretty similar
way to the pions.
Inside it are techniquarks.
 
One techniquark and
one antitechniquark
so that the net charge
of this whole thing is 0.
Now if technicolour
is realised in nature,
we expect that we can discover
a whole slew of new particles
if we collide protons with
sufficiently large energy.
Again, this is just
like what would
happen in nuclear physics.
When we take photons and smash
them together at low energies,
at first not much happens.
But then we start to release
pions and more complicated
particles, which are
made up of quarks.
In technicolour, if we smash
particles together with
sufficiently large energies,
we could make more and more
complicated systems made up of
technigluons and techniquarks.
 
