We closed the previous episode by seeing that
if a particle with a given mass decays into a pair of photons we can reconstruct this mass
if we measure the properties of the photons. This is actually true for decays into any
particles that we can precisely measure. For example, if the Higgs boson
decays into two Z bosons one Z boson decays into two muons,
the other into two electrons you'll have two muons and two electrons
in the final state and it will again be possible
to reconstruct the mass of the Higgs from the energies and the momenta
of these four particles But let's stay with our example of photon pairs
and let's ask the following question what if the two photons are not coming
from the decay of the Higgs boson? In fact what if they're not coming
from the decay of anything at all? They're just two completely unrelated photons produced somewhere during the particle collision. When we detect them we cannot see their past,
so we won't know that. So what will be the meaning
of the mass that we calculate? Well for such two unrelated photons
it's going to essentially be a random number with no clear physical meaning. So our situation is basically this We see two photons, we calculate
the invariant mass of the system and now there are essentially two possibilities either the photons are coming from the decay
of some particle (for example the Higgs boson) and then the mass that we've calculated is
the mass of that particle. Or they're not coming from any decay
and the mass is a random number. Now, if we only ever see one pair of photons,
it's impossible to tell the difference between these two cases. But if we do the experiment many times then the difference between the random number
and the fixed number is going to eventually show up. Now let's illustrate this with a short story. For this we need to travel to the heart of the Swiss Alps where deep inside the lush Alpine forest you can find the home of a remarkable creature. Let's take a look. What looks like an ordinary hole under a tree is actually the entrance to a network of tunnels inhabited by a rabbit. Not an ordinary rabbit but a white rabbit that once lived in a casino but had to move out
when the casino was torn down to build a supermarket. Ok, at this point you're probably wondering:
what has just happened? You were watching a video about particle physics
and suddenly - this? Magical gambling rabbits in the forest? Well I'm here to reassure you -
this is still the video about particle physics. This story is just an analogy
illustrating an important point. So stay with me. The story is that back in the casino,
the rabbit would love watching people play dice and what made him especially happy was when the result on the dice was "four". And to this day,
whenever he comes across a die he always turns it
such that the number four is facing upwards. Now, the rabbit is said to be very, very shy to the point where nobody has ever seen it and the only way to know if it's there is by throwing dice into the hole coming back in a few hours or the next day and checking what the result is. If the rabbit was passing by,
it will surely be his favorite number. Let's give it a try. Okay, let's see what we got. Yeah, it's a four. But actually, maybe I just rolled a four
by accident. So let's try it again. Ah, it's a three. So maybe this time he just didn't come. Let's try again. It's a two. Two. Ah, there's a four! One. One. Five. Three. Six. Two. Two. Ok so what are we learning here exactly? We have a sequence of numbers,
some of them are four but not all of them so if anything, the rabbit doesn't always
come out and interfere. So to better understand what's happening,
let's make a histogram. One, two, three, four, five, six. So, I'll draw a plot and I'll mark the results. So the first number we got was four then we got three then we got two then we got another two. Ok, this is gonna be easier on a computer We got: four, three, two, two, four, one, one, five,
three, six, two, two, four, five, three, four, six, three, two, three, two, three, two, three
(that's what we got) five, six, four, one, six, three This is the result that we got after 30 tries. So a month, if we did this once per day. Okay, so the number four
didn't come up that many times actually we got the number three more often. So, okay. What happens if we run this experiment longer,
for a year, we do 300 tries? Ok, this is getting weird,
what is happening here? Well okay, what do YOU think is happening? Go ahead, hit pause
and think about it for a second. Ok, we're back. I won't tell you the answer,
but instead I'll run the experiment for 10 years. So now we have rolled the dice 3000 times. What are we seeing? Well we can draw two conclusions: One, the story about the rabbit is most likely true and two, looks like his favorite number
is not "four" like we thought but "three". The plot shows us how many times
we got each possible result after 3000 dice rolls and if the rabbit didn't exist at all you'd expect all numbers to be just as likely
to show up But we have a clear excess at "three" so looks like not all results were random some have been altered,
replaced with the number "three". So we have in a way observed the rabbit,
without ever seeing it directly. We have learned what it's favorite number is:
"three". Oh, and you can also deduce the fact
that the rabbit shows up on average once in 10 dice rolls. Ok, so now back to the Higgs. With the Higgs it's a similar situation
but instead of throwing dice we're colliding particles
and looking at what's produced in the collision. Specifically, we're looking at invariant masses
of photon pairs. If we didn't produce a Higgs in the collision,
that invariant mass is going to be a random number just like the result of the dice roll
was a random number when the rabbit didn't come. But if we do produce a Higgs,
and that Higgs decays into a pair of photons, the invariant mass of that photon pair is
going to be the mass of the Higgs just like the favorite number of the rabbit. Now with the rabbit we ended up learning
that his favorite number was different than what we expected with the Higgs we didn't have an expectation because we didn't know its mass
before we found it. We just had a broad range. So we had to look if a peak would appear
somewhere in that range. To see how this works let's make another plot. Previously for every dice roll we were plotting
the result on the dice. Now for collisions in which we find two photons
we're gonna be plotting their invariant masses. And we'll animate this plot
to see how it was filling up as we were taking data
throughout the years 2011 and 2012. Alright, let's pause for a second. One thing that you can see already see
is that the plot is not flat. Why is that? Well, for dice rolls
the probabilities of all outcomes were equal so the result was flat. Here that's not the case.
The probabilities are different. It's easier to produce photons with low energy and it's harder to produce
photons with higher energy. So these are still random numbers,
but some are more likely than others. We call that a non-flat probability distribution. Alright, let's continue with the animation. And there you have it. At around 125 you see a peak telling us that there's a particle there with that mass, decaying into pairs of photons. Remember the rabbit again if there was no rabbit all of the dice rolls would have been just
normal, random dice rolls and the result would have been a flat plot. But the plot had a peak, created by the rabbit inserting the number "three" into the results. Now, if there was no Higgs boson this plot would have been
just a smooth falling curve of random masses. But clearly they're not all random something inserted the number 125 into the results a particle with that mass decaying into two photons. Which is what we were expecting
for the Higgs boson. Okay, I want to stress one more point and for that let's go back to what the plots look like early on both the photons and the dice. You see that it's not obvious where the peak is or whether there's actually any peak at all. In the beginning the plots are so random you can barely tell what's going on. Only with enough data the picture smoothes out the randomness,
the statistical fluctuations become smaller and the effect starts coming through. So you might wonder - at which point
can we actually be sure that our peak is not
just another statistical fluctuation. Well we can never be 100% sure but for a given peak,
we can calculate the probability. And the commonly accepted threshold for discovery is the point at which the probability that there's nothing there and that the peak we're seeing is just
the result of pure chance the probability of that
is about one in 3.5 million. Still not 100%, but pretty close. So for the Higgs boson discovery in 2012 this level was not reached by a single peak but by a combination of peaks found by looking
at different Higgs boson decays so in addition to the two photon decay
this was the decay into two Z bosons giving four leptons in the final state and the decay into two W bosons giving two leptons and two neutrinos. Ok, we made it to the end and I hope that you'll agree with me
that conceptually finding new particles is not that complicated. Let's summarize the steps. First we have to produce the particle so we accumulate energy in particles
in a particle accelerator collide them,
and then this energy can transform into the mass of this new particle. That particle will then immediately
decay into other particles and we can measure them in our particle detectors and calculate the invariant mass. If we do this many times we can make a plot of these invariant masses and the particle we're looking for
will show up as a peak in that plot, just like the Higgs boson did. Now, this was of course a bird's-eye view
of the analysis in reality this analysis was
much more detailed and complex but the general principle is what we just
said. This is really how we do it. Just remember that
to actually find the Higgs boson it took us two years of accumulating and analysing
the data from the LHC, two experiments, ATLAS and CMS,
with several thousand of people involved in each one of them. And that's not counting the many, many more
years and people involved in the design, construction and operation
of the LHC and the experiments. On the other hand this story was about finding the Higgs boson decaying into two photons. But the Higgs boson was really just used as
an example here. The story was really about seeing and detecting, or discovering particles. Many other particles have been discovered
using a similar approach in the past and we hope to find more in the future. So, I hope it was clear, and thanks for watching. If you have questions
or things you'd like us to cover in future videos please type them in the comments below and I'll see you soon.
