MARKUS KLUTE: Welcome back to 8.701.
So in this lecture and also the next one,
we'll look at some of the experimental findings
of neutrinos.
Given the sheer number of experiments
and the long history in which we are
trying to understand neutrinos and neutrinos' behavior,
this can be rather confusing.
So I'm trying to condense this a little bit
and just give you the highlights, or the basic pieces
of information.
So this one here shows a summary of what we
know from neutrino oscillation.
So if we look at atmospheric neutrinos,
we find that mirror neutrinos and anti-mirror neutrinos
disappear, and they're most likely
converting into tau neutrinos and anti-tau neutrinos.
We look at accelerating neutrinos-- here
we are using mirror neutrinos and anti-mirror
ones-- we can show that they disappear over distances
of 200 to 800 kilometers.
From accelerators, we also know that they appear or reappear
as electron or anti-electron neutrinos
over those same distances.
From the solar neutrinos, we know
that electron neutrinos convert into mirror neutrinos
and/or tau neutrinos.
There is more detail to this story
than I'm giving you here, where we
would have to discuss the interaction of the matter
effects of neutrinos.
That is for a different lecture.
That goes beyond the scope of what I want to discuss here.
From reactor neutrinos, we also know
that anti-electron neutrinos disappear as well.
So the name of the game now is to take
all of those pieces of information
and extract information about the neutrinos' property.
And in order to do that, one has to make assumption
about the number of available neutrino generations,
and in some part of the interpretation,
also about the nature of the neutrinos.
As you can simply figure out of the exercise we had before,
it matters to the neutrino oscillation probabilities
whether one assumes two or three or four neutrinos in the mix.
But if you just focus here on three neutrinos,
you still have the problem that we have
degeneracies in the discussion.
And they can be boiled down to two major kind of trends.
One is where the spectrum of the neutrino mass
follows a normal ordering, meaning
that the mass of the first is smaller
than the mass of the second is smaller
than the mass of the third, or that the spectrum is inverted,
meaning that the mass of the third might be smaller
than the mass of the second and the mass of--
the first and the second.
Data suggests that the difference squared
in mass splittings between those states
is such that delta m12 squared is
much smaller than delta m31 squared, which
is approximately the same size as delta m32 squared.
So if you look now at the numbers
for the normal hierarchy spectrum,
we find that the mass of the first is much, much smaller
than the mass of the second, which is a little bit smaller
than the mass of the third.
Numerically, we find the mass of the second
is in the order of 8 times 10 to the minus 3 electron-volt,
and the mass of the third in the order of 0.05 electron-volts,
so really, really small masses.
The inverted spectrum-- here the story is slightly different.
Here we find that m1 is about 0.05 election-volts, which
is similar to the square root of the mass splitting between 3
and 2, which is also 0.05 electron-volts.
The information of the neutrino oscillation experiment,
and then how to map into the individual parameters
of our neutrino CKM matrix is summarized here, and also
in the mass information.
And I don't want to read the entire table.
I'll just leave this here for you.
So in order to understand this, one
has to go back to the first slide
and understand what kind of information
we extract from various neutrino experiments-- for example,
the solar neutrino experiments-- and then think about,
is this sensitive to oscillations
between the first and the second generation,
or the first and the third generation?
So that's kind of the mapping you have to do in order
to understand this table fully.
There are some experiment where the information just
dominates the position of a certain measurement.
In others, there is combinations of results coming out.
The other reason why I put this table here in this lecture
is to just illustrate how diverse the landscape
of experiments is and why that's needed.
In order to get a full picture of neutrinos
and their properties, one has to identify
the individual properties in the experiments
and then put the picture back together in a global fit
or in a general analysis of the data.