This is a little extra episode of
"The Higgs Boson discovery explained".
Let's call it episode three and a half.
And in this short video I'll answer 
some of the questions that you had in the comments
and I'll expand on some of the points 
made in the other videos.
So if you haven't seen the first three episodes
it probably makes sense to watch them first
you can find the link in the description below.
That said, let's go
I'll start with a question that came up
quite a few times,
and that kind of picks up where the series left off
So how do we know that we found the Higgs boson?
Well, we have to study the properties of the
particle that we've discovered
and check if they match 
what's expected for the Higgs.
So the first step is finding something.
If we see a peak in the invariant mass spectrum
of two photons
we already learn that there's a particle there
and we learn the mass of this particle
and we learn that it decays
into two photons.
And in the first approximation 
it would seem that that's it
but actually, using certain rules 
that govern the particle world
we can extract some more information 
from just this one peak.
For example, we can learn 
the electrical charge of this particle.
Because if the particle decays into two photons
and a photon has zero electrical charge
this particle has also to have zero electrical
charge
otherwise this decay 
would break charge conservation.
The next thing is a property called spin.
A particle can either have integer spin, 
making it a boson
or half-integer spin, making it a fermion.
And in the Standard Model of particle physics
we have elementary fermions
the quarks and  the leptons that make up all matter
and they have spin 1/2
and we have elementary bosons that are responsible
for the interactions
and they have a spin of 1.
So the mathematics of spin is such
that if a particle decays into two bosons
it also has to be a boson.
But actually there's an extra law saying that
if a particle decays into two photons
two massless bosons
its spin cannot be 1
so in practice this leaves us with 
either zero or two.
Less than a year after discovery, 
using the extra data collected
and a complex analysis of the angular correlations
between the directions of the decay products
we were able to essentially rule out spin 2
establishing this new particle 
as a particle with no spin
what we call a "scalar boson"
which is what the Higgs is supposed to be
but it's actually quite a profound result in itself
because this is the first elementary particle
with no spin that we have seen.
We know other particles that have no spin,
for example the pi meson
but a meson is not elementary
it's a quark-antiquark pair.
But the real test of whether this new particle
is the Higgs boson or not
is checking how strongly it interacts 
with other particles
because for the Higgs boson 
there's a very specific pattern here:
the Higgs interaction strength depends on
mass.
The higher the mass, the stronger the interaction.
So how do we test this experimentally?
Well, let's look at the life of the Higgs boson,
it has a beginning and an end.
At the beginning the Higgs is produced from
some particles
and then at the end it decays into some particles.
And in both cases the probabilities 
of these processes happening
are influenced by the interaction strength.
But these are things that we can experimentally
measure.
We can look at the probabilities of the different
Higgs decays
measure them
compare them with predictions from theory
and check if everything agrees.
And so far within the precision that we have
and for the decays that we're able to measure
everything agrees very well.
How many Higgs boson decays to two photons
does the diphoton discovery plot show?
Well let's start with this:
how many photon pairs does it show in total?
So the plot covers a range of masses
between 100 and 160 GeV
and it has 60 points.
Which means that each point is telling us
how many photon pairs we found
in a range that's 1 GeV wide.
For example, the first point in the top left
tells us that we have about 4.5 thousand photon pairs
with invariant mass between 100 and 101 GeV.
So you can add all of these up 
and you'll get the total number
which is of the order of
150-160 thousand photon pairs.
So how many of these are Higgs boson decays?
Well you can read it off this plot.
At first you might be tempted to say
ok, to that's the height of the peak
so 2700
but that's not the height of the peak
because if there was no Higgs boson
you would still have about 2500 photon pairs
at that mass.
So the height of the peak is the difference
between that and what we're seeing
so about 200
But 200 is also not the right answer
because the peak is not just this one point
but also the ones next to it.
And that's because
we calculate the invariant mass
from measured energies and directions of photons
and these measurements have some uncertainty
and this uncertainty washes out, spreads out
the results a little bit.
So the total number 
after adding all of this together
is of the order of 500.
So this plot contains 150 thousand photon pairs
and only 500 of these are Higgs boson decays
but we can see that they're there
because of this peak that they're forming.
A few of the questions that came in
revolved around the Higgs mechanism itself
and things like:
"if the lifetime of the Higgs boson is so short
how can it give mass?"
Well, I have a short answer and a medium answer.
So the short answer is where to find 
the long answer.
We have several videos on the topic 
on our channel already
so we'll put in the video description down below
links to these.
Now the medium answer
I'll try to, well maybe not explain it
but I'll try to, very briefly, 
clear up a few things.
So, very quickly: 
how does the Higgs boson give mass
if it's so short lived?
Well, it doesn't.
That's a misconception that somehow appeared
but it's not the Higgs boson that gives mass
it's the Higgs field.
The Higgs field is something that 
fills up all the Universe
it's literally everywhere.
And, indeed, particles as they move through it
they gain mass by interacting with this field.
So what's the Higgs boson then?
Well the Higgs boson is a little excitation
like a wave in the Higgs field
and we need it to prove that the field exists
because we have no sensors capable of probing
of detecting the Higgs field directly.
But if we're able to make a wave
well if there's a wave
it means that something must be... "waving"
you cannot have a wave all by itself.
So finding the Higgs boson proves 
that the Higgs field exists
The Higgs boson doesn't give mass
But it's a way of detecting something that does.
Another thing that came up a lot in the questions
is how do accelerators work
and where do the protons come from.
Well, the protons come from a bottle of hydrogen
because the hydrogen atom
is just a proton and an electron.
If you take the electron away, 
you're left with a proton
But we actually talked about this in detail
in a recent livestream from the LINAC4 accelerator
we have another livestream planned for later
this year, from the Large Hadron Collider
and possibly some more videos on the topic.
So we'll keep updating the video description
with links to whatever's available,
meanwhile you can of course subscribe to this
youtube channel to be notified straight away
and I'll see you soon.
