Questions arising from neutrino oscillations
Dr Tim
Hi!
I have read the explanation of neutrino oscillation: every flavour is
a different superposition of two (or is it three?) "underlying"
neutrino types with slightly different masses. In fact, neutrino
flavour is determined by the (continually changing) phase angle
between the wave forms of the two underneutrino masses.
Does this mean that all observed neutrino flavours have the same mass?
As I understand it, neutrino oscillation is a genuine oscillation
rather than a random fluctuation. Has anyone measured its frequency?
Is the neutrino actually a pair of underneutrinos bound together by an
unseen force? Is this the colour force?
A strange quark can decay into a normal quark: is this essentially the
same phenomenon as neutrino oscillation?
Squark
> As I understand it, neutrino oscillation is a genuine oscillation
> rather than a random fluctuation. Has anyone measured its frequency?
In fact, I believe they _are_ random fluctuations. They may be thought
as "decay" processes, charactarized by rate. The later, I'm sure, has
been measured / theoretically estimated, someone else here must know
the details.
Btw, anyone knows what's the current status of integrating neutrino
mass into the Standard Model?
Best regards,
Squark
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Write to me using the following e-mail:
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Squark
timro...@paradise.net.nz (Dr Tim) wrote in message news:<7fed4c14.0302...@posting.google.com>...
> I have read the explanation of neutrino oscillation: every flavour is
> a different superposition of two (or is it three?) "underlying"
> neutrino types with slightly different masses.
Probabely three, as there are three flavours.
> Does this mean that all observed neutrino flavours have the same mass?
No, it means a neutrino with definite flavour has undefinite mass,
much in the same way a particle with a definite position has
undefinite momentum: those are non-commuting observables.
John Baez
Squark <fii...@yahoo.com> wrote:
>timro...@paradise.net.nz (Dr Tim) wrote in message
>news:<7fed4c14.0302...@posting.google.com>...
>> As I understand it, neutrino oscillation is a genuine oscillation
>> rather than a random fluctuation. Has anyone measured its frequency?
Yes, lots of people are busy doing just that. Since there
are 3 flavors of neutrinos, there are presumably various kinds
of oscillations and various frequencies. I don't know enough
about this to summarize the state of the art, but you can get
to webpages of all the major experimental groups here:
http://www.hep.anl.gov/NDK/hypertext/nu_industry.html
Most of the data is expressed in terms of Delta(m) (mass difference)
rather than frequency, but you can convert to frequency by using
E = mc^2 and then E = hbar nu, where nu is the frequency.
>In fact, I believe they _are_ random fluctuations. They may be thought
>as "decay" processes, characterized by rate.
Eh? When people speak of neutrino oscillations, they really
do mean oscillations rather than "decays": in the usual model,
the flavor eigenstates are different than the mass eigenstates,
so if we start with a neutrino in a given flavor eigenstate -
e.g. an electron neutrino - it will slosh back and forth
between all 3 different flavors: electron, mu and tau.
Ignoring subtleties, the math is basically just
d psi/dt = -iH psi
where H is a 3x3 matrix. And what's "oscillating" is really the
neutrino's quantum state psi. So, if you *check* to see what flavor
the neutrino is in at a given moment, the result will be random,
with probabilities determined by this oscillating psi.
>Btw, anyone knows what's the current status of integrating neutrino
>mass into the Standard Model?
These days when people talk about the "Standard Model", they usually
mean the new version where neutrinos are Dirac spinors which gain mass
by coupling to the Higgs via the so-called Maki-Nakagawa-Sakata matrix,
which is a 3x3 matrix very much like the more familiar Cabibbo-Kobayashi-
Maskawa matrix for quarks. However, there are other less standard options,
such as treating the neutrinos as Majorana spinors, and "Mikheyev-Smirnov-
Wolfenstein (MSW) matter enhanced conversion" - don't ask me how that's
supposed to work! There is also a lot of wrangling over different models
of the sun.
This is a great website for learning about this stuff:
http://dept.physics.upenn.edu/neutrino/jhu/jhu.html
I append a somewhat outdated summary of what I once knew
about neutrinos. At the end I say how the experiments seem
to give conflicting results and maybe we can only wriggle out if
we assume a 4th kind of neutrino. I think fewer people believe
this now. Probably some of the experimental data was wrong...
I'll crosspost to sci.astro.research so maybe someone can tell
us the state of the art!
.....................................................................
Also available at http://math.ucr.edu/home/baez/week130.html
February 27, 1999
This Week's Finds in Mathematical Physics (Week 130)
John Baez
All sorts of cool stuff is happening in physics - and I don't mean
mathematical physics, I mean real live experimental physics! I feel
slightly guilty for not mentioning it on This Week's Finds. Let me
atone.
Here's the big news in a nutshell: we may have been wrong about four
fundamental constants of nature. We thought they were zero, but maybe
they're not! I'm talking about the masses of the neutrinos and the
cosmological constant.
Let's start with neutrinos.
There are three kinds of neutrinos: electron, muon, and tau neutrinos.
They are closely akin to the charged particles whose names they borrow -
the electron, muon and tau - but unlike those particles they are
electrically neutral and very light. They are rather elusive, since
they interact only via the weak force and gravity. I'm sure you've all
heard how a neutrino can easily make it through hundreds of light years
of lead without being absorbed.
But despite their ghostly nature, neutrinos play a very real role in
physics, since radioactive decay often involves a neutron turning into a
proton while releasing an electron and an electron antineutrino. (In
fact, Pauli proposed the existence of neutrinos in 1930 to account for a
little energy that went missing in this process. They were only
directly observed in 1956.) Similarly, in nuclear fusion, a proton may
become a neutron while releasing a positron and an electron neutrino.
For example, when a type II supernova goes off, it emits so many
neutrinos that if you're anywhere nearby, they'll kill you before
anything else gets to you! Indeed, in 1987 a supernova in the Large
Magellanic Cloud, about 100,000 light years away, was detected by four
separate neutrino detectors.
I said neutrinos were "very light", but just how light? So far most
work has only given upper bounds. In the 1980s, the Russian ITEP group
claimed to have found a nonzero mass for the electron neutrino, but this
was subsequently blamed on problems with their apparatus. As of now,
laboratory experiments give upper bounds of 4.4 eV for the electron
neutrino mass, .17 MeV for the muon neutrino, and 18 MeV for the tau
neutrino. By contrast, the electron's mass is .511 MeV, the muon's is
106 MeV, and the tau's is a whopping 1771 MeV.
For this reason, the conventional wisdom used to be that neutrinos were
massless. After all, the electron neutrino is definitely far lighter
than any known particle except the photon - which is massless. The
larger upper bounds on the other neutrino's masses are mainly due to
the greater difficulty in doing the experiments.
Having neutrinos be massless would also nicely explain their most
stunning characteristic, namely that they're only found in a left-handed
form. What I mean by this is that they spin counterclockwise when
viewed head-on as they come towards you. It turns out that this
violation of left-right symmetry comes fairly easily to massless
particles, but only with more difficulty to massive ones. The reason is
simple: massless particles move at the speed of light, so you can't
outrun them. Thus everyone, regardless of their velocity, agrees on
what it means for such a particle to be spinning one way or another as
it comes towards them. This is not the case for a massive particle!
There was, however, a fly in the ointment. Since the sun is powered by
fusion, it should emit lots of neutrinos. In fact, the standard solar
model predicts that here on earth we are bombarded by 60 billion solar
neutrinos per square centimeter per second! So in the late 1960s, a
team led by Ray Davis set out to detect these neutrinos by putting a
tank of 100,000 gallons of perchloroethylene down into a gold mine in
Homestake, South Dakota. Lots of different nuclear reactions are going
on in the sun, producing neutrinos of different energies. The Homestake
experiment can only detect the most energetic ones - those produced when
boron-8 decays into beryllium-8. These neutrinos have enough energy to
turn chlorine-37 in the tank into argon-37. Being a noble gas, the
argon can be separated out and measured. This is not easy - one only
expects about 4 atoms of argon a day! So the experiment required
extreme care and went on for decades.
They only saw about a quarter as many neutrinos as expected.
Of course, with an experiment as delicate as this, there are always many
possibilities for error, including errors in the standard solar model.
So a Japanese group decided to use a tank of 2,000 tons of water in a
mine in Kamioka to look for solar neutrinos. This "Kamiokande"
experiment used photomultiplier tubes to detect the Cherenkov radiation
formed by electrons that happen to be hit by neutrinos. Again it was
sensitive only to high-energy neutrinos.
After 5 years, they started seeing signs of a correlation between
sunspot activity and their neutrino count. Interesting. But more
interesting still, they didn't see as many neutrinos as expected.
Only about half as many, in fact.
Starting in the 1990s, various people began to build detectors that
could detect lower-energy neutrinos - including those produced in the
dominant fusion reactions powering the sun. For this it's good to use
gallium-71, which turns to germanium-71 when bombarded by neutrinos.
The GALLEX detector in Italy uses 30 tons of gallium in the form of
gallium chloride dissolved in water. The SAGE detector, located in a
tunnel in the Caucasus mountains, uses 60 tons of molten metallic
gallium. This isn't quite as scary as it sounds, because gallium has a
very low melting point - it melts in your hand! But still, of course,
these experiments are very difficult.
Again, these experiments didn't see as many neutrinos as expected.
By this point, the theorists had worked themselves into a full head of
steam trying to account for the missing neutrinos. Currently the most
popular theory is that some of the electron neutrinos have turned into
muon and tau neutrinos by the time they reach earth. These other
neutrinos would be not be registered by our detectors.
Folks call this hypothetical process "neutrino oscillation". For it
to happen, the neutrinos need to have a nonzero mass. After all,
a massless particle moves at the speed of light, so it doesn't experience
any passage of time - thanks to relativistic time dilation. Only particles
with mass can become something else while they are whizzing along minding
their own business.
If in fact you posit a small mass for the neutrinos, oscillations happen
automatically as long as the "mass eigenstates" are different from the
"flavor eigenstates". By "flavor" we mean whether the neutrino is an
electron, muon or tau neutrino. For simplicity, imagine that the state
of a neutrino at rest is given by a vector whose 3 components are the
amplitudes for it to be these three different flavors. If all but one
of these components are zero we have a neutrino with a definite
flavor - a "flavor eigenstate". On the other hand, the energy of a
particle at rest is basically just its mass. Thus in the present
context the energy of the neutrino is described by a 3 x 3 self-adjoint
matrix H, the "Hamiltonian", whose eigenvectors are called "mass
eigenstates". These may or may not be the same as the flavor
eigenstates! Schroedinger's equation says that any state psi of the
neutrino evolves as follows:
d psi/dt = -iH psi
Thus if psi starts out being a mass eigenstate it stays a mass eigenstate.
But if it starts out being a flavor eigenstate, it won't stay a flavor
eigenstate - unless the mass and flavor eigenstates coincide! Instead, it
will oscillate.
I bet you were wondering when the math would start. Don't worry, there
won't be much this time.
Anyway, for other particles, like quarks, it's well-known that the mass
and flavor eigenstates *don't* coincide. So we shouldn't be surprised
at neutrino oscillations, at least if neutrinos actually have nonzero
mass.
Actually things are more complicated than I'm letting on. In addition
to oscillating in empty space, it's possible that neutrinos oscillate
*more* as they are passing through the sun itself, thanks to something
called the MSW effect - named after Mikheyev, Smirnov and Wolfenstein.
And there are two different ways for neutrinos to have mass, depending
on whether they are Dirac spinors or Majorana spinors (see "week93").
But I don't want to get caught up in theoretical nuances here! I want
to talk about experiments, and I haven't even gotten to the new stuff
yet - the stuff that's getting everybody *really* confused!
First of all, there's now some laboratory evidence for neutrino
oscillations coming from the Liquid Scintillator Neutrino Detector at
Los Alamos. What these folks do is let positively charged pions decay
into antimuons and muon neutrinos. Then they check to see if any muon
neutrinos become electron neutrinos. They claim that they do! They
also claim to see evidence of muon antineutrinos becoming electron
antineutrinos.
Secondly, and more intriguing still, there are a bunch of experiments
involving atmospheric neutrinos: Super-Kamiokande, Soudan 2, IMB, and
MACRO. You see, when cosmic rays smack into the upper atmosphere, they
produce all sorts of particles, including electron and muon neutrinos
and their corresponding antineutrinos. Cosmic ray experts think they
know how many of each sort of neutrino should be produced. But the
experimenters down on the ground are seeing different numbers!
Again, this could be due to neutrino oscillations. But what's REALLY
cool is that the numbers seem to depend on where the neutrinos are
coming from: from the sky right above the detector, from right below the
detector - in which case they must have come all the way through the
earth - or whatever. Neutrinos coming from different directions take
different amounts of time to get from the upper atmosphere to the
detector. Thus an obvious explanation for the experimental results is
that we're actually seeing the oscillation process AS IT TAKES PLACE.
If this is true, we can try to get detailed information about the
neutrino mass matrix from the numbers these experiments are measuring!
And this is exactly what people have been doing. But they're finding
something very strange. If all the experiments are right, and nobody is
making any mistakes, it seems that NO choice of neutrino mass matrix
really fits all the data! To fit all the data, folks need to do
something drastic - like posit a 4th kind of neutrino!
Jonathan Silverlight
writes
Massive (pun intended) snip.
One to keep - and bookmark. Are people still measuring the mass-squared
rather than the mass of neutrinos - and finding it is negative ?!
--
mail to jsilverlight AT merseia.fsnet.co.uk is welcome
John Baez
Dr Tim <timro...@paradise.net.nz> wrote:
>I have read the explanation of neutrino oscillation: every flavour is
>a different superposition of two (or is it three?) "underlying"
>neutrino types with slightly different masses.
Here's how the standard theory goes. It takes a bit of linear
algebra and quantum mechanics to understand it, and if you
don't know that, you'll have to fake it.
There's a 3d vector space describing different states of a
neutrino. This vector space has operators on it called
"flavor" and "mass".
The 3 eigenvectors of the flavor operator correspond to
three types of neutrinos with definite flavor. These
are called the "electron neutrino", the "mu neutrino"
and the "tau neutrino".
The 3 eigenvectors of the mass operator correspond to
three types of neutrinos with definite masses. These
don't have names that I know of.
If you start out with a neutrino having a definite mass,
it will just sit there. Actually, its phase will keep
circling around at a rate depending on (among other things)
the neutrino's mass. But you can't directly observe the
phase, so nothing much is really happening.
If you start out with a neutrino having a definite flavor,
to see what happens you need to realize that it's a linear
combination of neutrinos with different definite masses.
As time passes, the phases of these keep drifting in and
out of synch, since they circle around at different rates.
As a result, the neutrino oscillates between having different
flavors.
Well... it may not sound convincing until you do the math!
But the underlying mechanism is the same as that for many
other phenomena in nature, so it's not nearly as exotic or
strange as it might sound. Many things about neutrinos are
still controversial, but this oscillation theory is the most
conservative explanation for the funny things we see happening.
>In fact, neutrino
>flavour is determined by the (continually changing) phase angle
>between the wave forms of the two underneutrino masses.
I've never heard of "underneutrinos". I bet you just made that up.
If instead you had said "eigenvectors of the mass operator" or
"neutrinos with definite masses", I would have agreed with this statement.
>Does this mean that all observed neutrino flavours have the same mass?
No! They have somewhat indefinite masses, but in different
ways: they are different superpositions of the 3 kinds of neutrinos
with definite masses.
>As I understand it, neutrino oscillation is a genuine oscillation
>rather than a random fluctuation. Has anyone measured its frequency?
There's not just one frequency, because there are 3 kinds of
neutrinos, which oscillate into each other in rather complicated
ways. It takes a total of 7 numbers to completely describe what's
going on here - if the theory I'm describing is true.
People are busily trying to measure these numbers in different ways.
Some people are looking at neutrinos coming from the sun:
http://www.hep.anl.gov/ndk/hypertext/solar_experiments.html
Some people are looking at neutrinos coming from cosmic
rays colliding with air in the upper atmosphere:
http://www.hep.anl.gov/ndk/hypertext/gatmospheric_cev.html
Some people are looking at neutrinos they make themselves:
http://www.hep.anl.gov/ndk/hypertext/long_baseline.html
Other people are doing other things.
To give you a tiny feel for what's going on: in 1998 people
in Japan found evidence that muon neutrinos produced when
cosmic rays in the upper atmosphere have turned into tau
neutrinos by the time they get down here. The strength
of this effect gives us some information about how rapidly
muon neutrinos oscillate into tau neutrinos. Don't ask me
for numbers - I'm not an expert on this stuff! But I do
know that more recently, people in Japan are trying to
replicate this result by making their own neutrinos in
a particle accelerator and then detecting them in a town 250
kilometers away. They have succeded in detecting them -
that's already a feat! - but as far as I know, they haven't
yet seen the oscillation effect.
>Is the neutrino actually a pair of underneutrinos bound together by an
>unseen force?
No - not unless you know something I don't!
Again, I've never even heard of an "underneutrino".
I should emphasize that when I say a neutrino with definite
flavor is a "linear combination" of neutrinos with definite mass,
I don't mean it's a bunch of neutrinos with definite mass bound
together by some force. I mean that if you were to measure
the mass of this neutrino, you would suddenly see that it was
a single neutrino with a definite mass Weird, but quite
normal in quantum mechanics.
> Is this the colour force?
It appears neutrinos don't feel the color force at all, so
it's highly unlikely they there are made of constituents that
do. In our current theories, neutrinos don't have any constituents.
>A strange quark can decay into a normal quark: is this essentially the
>same phenomenon as neutrino oscillation?
No: when a strange quark decays into a down quark it emits a Z boson.
This is called a "flavor-changing weak interaction". There is
something quarks can do that's related to neutrino oscillations, but
it's not this.
Lucius Chiaraviglio
the different flavors of neutrino have different rest masses, how are they
supposed to interconvert without violating conservation of energy and/or
momentum?
--
Lucius Chiaraviglio
Approximate E-mail address: luci...@chapter.net
To get the exact address: ^^^ ^replace this with 'r'
|||
replace this with single digit meaning the same thing
(Spambots of Doom, take that!).
Ralph Hartley
> Are people still measuring the mass-squared
> rather than the mass of neutrinos - and finding it is negative ?!
In other words does experiment rule out tachionic neutrinos (with small
imaginary masses)? I don't know! Would the Standard Model care?
Would neutrinos still oscillate if they were tachions? The difference
between an oscillation and an exponential decay is just a factor of i, so
it wouldn't surprise me too much if tachions decayed after all. I haven't
tried hard to figure it out yet.
I don't even remember which way tachions "red shift". My guess is to lower
energy (higher speed), until they get to 0 energy (instantaious) after
which they would be going the other way, so they would start to be "blue
shifted".
Neutrinos at any energy we could detect would all be *very* close to the
speed of light. How big an imaginary mass would be needed to have a
cosmological effect? My guess would be about the same as for positive mass,
but maybe with some signs different.
Ralph Hartley
John Baez
Lucius Chiaraviglio <luci...@chapter.net> wrote:
> Let me add another question arising from neutrino oscillations: if
>the different flavors of neutrino have different rest masses, how are they
>supposed to interconvert without violating conservation of energy and/or
>momentum?
It's not right to say "the different flavors of neutrinos have different
rest masses", as if they had definite rest masses.
The key is that "the flavor eigenstates are not the mass eigenstates".
If you don't know what this means, consult your local quantum mechanic.
Here are some things one can say without any math:
Neutrinos have a property called mass and a property called flavor. But
the uncertainty principle says that if you know the flavor of a neutrino
for sure, you can't know its mass for sure. Conversely, if you know the
mass of a neutrino for sure, you can't know its flavor for sure. Energy
is conserved, so if you start out with a neutrino having a definite mass
it will never change to one of a different mass. But flavor is not
conserved, and if you start out with a neutrino having a definite flavor
it will oscillate to having other flavors (with a certain nonzero
probability). This happens whenever a neutrino is created in a fission
or fusion reaction.
Needless to say, all this is just a summary of our current best
theory of neutrino oscillations. Lots of experiments are underway
to test these theories.
Squark
news:<b323bp$209$1...@glue.ucr.edu>...
> In article <939044f.03021...@posting.google.com>,
> Squark <fii...@yahoo.com> wrote:
> >In fact, I believe they _are_ random fluctuations. They may be thought
> >as "decay" processes, characterized by rate.
> Eh? When people speak of neutrino oscillations, they really
> do mean oscillations rather than "decays": in the usual model,
> the flavor eigenstates are different than the mass eigenstates,
> so if we start with a neutrino in a given flavor eigenstate -
> e.g. an electron neutrino - it will slosh back and forth
> between all 3 different flavors: electron, mu and tau.
>
> Ignoring subtleties, the math is basically just
>
> d psi/dt = -iH psi
>
> where H is a 3x3 matrix. And what's "oscillating" is really the
> neutrino's quantum state psi. So, if you *check* to see what flavor
> the neutrino is in at a given moment, the result will be random,
> with probabilities determined by this oscillating psi.
Yeah, indeed I was grossly mistaken. I thought about the possibility
you describe here, but couldn't see how the situation can be
different from ordinary decays, say, where there is a certain rate,
rather than anything deterministic (like the period we have here).
I.e., I was thinking about it as a "decay into one particle". The
difference is apparently just that. When we got decay into several
particles, they "fly apart", while here it cannot happen. Therefore
there the situation can be roughly described as an exponentially
decaying probability of still being in the original state, while
here the probability oscillates in a squared sine form.
John Baez
Ralph Hartley <har...@aic.nrl.navy.mil> wrote:
>In other words does experiment rule out tachyonic neutrinos (with small
>imaginary masses)? I don't know! Would the Standard Model care?
The Standard Model would probably shrivel up and die if there
were tachyonic neutrinos.
By definition tachyons have imaginary mass, hence negative mass
squared, and they can have have positive or negative energy.
If there are tachyons in an interacting quantum field theory,
the conventional wisdom is that the vacuum becomes unstable.
In other words, it explodes in a burst of positive-energy particles
while simultaneously emitting negative-energy tachyons to conserve
energy.
This is a BAD THING.
So, what do the current experiments say? The only sort of
neutrino where we can accurately measure the mass (as opposed to
mass *differences*) is the electron neutrino, and people
usuallly do this by letting tritium decay. The tritium
nucleus has one proton and two neutrons; one of the neutrons
decays into a proton, an electron, and an electron antineutrino.
Thus one sees the tritium nucleus decay into helium-3 and an electron;
the hard-to-see antineutrino carries off some extra energy, and we can
use what we see to estimate the antineutrino's mass.
Paul Langacker's excellent page on the implications of neutrino
mass
http://dept.physics.upenn.edu/neutrino/jhu/jhu.html
dates back to around 1995, and he writes:
One disturbing feature is that the tritium decay
experiments all yield negative m^2 values, with a weighted average
(electron neutrino mass)^2 = -96 +- 21 ev^2
suggesting a common systematic or theoretical uncertainty in the
experiments.
A more recent webpage
http://cupp.oulu.fi/neutrino/nd-mass.html
shows that this outrageous discrepancy is gradually shrinking:
To be exact, the experiments measure the neutrino mass squared.
Curiously, when taken at the face value, all results point to
a negative mass squared, particularly the oldest experiment.
This is probably due to a systematic error, and actually two
running experiments, Mainz and Troitsk, have been able to measure
physically acceptable values.
Experiment measured mass squared formal limit C.L. Year
Mainz -1.6 +- 2.5 +- 2.1 2.2 95% 2000
Troitsk -1.0 +- 3.0 +- 2.1 2.5 95% 2000
Zurich -24 +- 48 +- 61 11.7 95% 1992
Tokyo INS -65 +- 85 +- 65 13.1 95% 1991
Los Alamos -147 +- 68 +- 41 9.3 95% 1991
Livermore -130 +- 20 +- 15 7.0 95% 1995
China - 31 +- 75 +- 48 12.4 95% 1995
Average of PDG -27 +- 20 15 95% 1998
(Here the mass squared is in units of eV^2, the "formal limit" is an
upper limit on the mass, "C.L." means confidence level, and "Average
of PDG" is an average taken from the 1998 Particle Data Group handbook.)
But, it's quite curious.
Jon Bell
> Let me add another question arising from neutrino oscillations: if
>the different flavors of neutrino have different rest masses, how are they
>supposed to interconvert without violating conservation of energy and/or
>momentum?
The oscillations occur only when you don't know enough about the
neutrino's energy and momentum to be able to assign it definitely to a
particular mass eigenstate. If you could measure all the other particles
in the interaction that produces the neutrino, with sufficient precision
to determine (by energy and momentum conservation) which mass state the
neutrino is in, then you will not observe any oscillations.
The neutrino can still be "converted" into a different flavor, but the
probability of conversion will remain constant regardless of how far the
neutrino travels.
And if you could measure all of the other particles in the interaction
that absorbs the neutrino, with sufficient precision to determine the mass
of the neutrino, you would get the same mass that you found in the
production interaction, regardless of whether the flavors at production
and absorption are the same or different.
--
Jon Bell <jtbe...@presby.edu> Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA
Lucius Chiaraviglio
>[. . .]
>So, what do the current experiments say? The only sort of
>neutrino where we can accurately measure the mass (as opposed to
>mass *differences*) is the electron neutrino, and people
One of the links you gave earlier eventually points to
http://www.hep.umn.edu/numass/, where it sounds like someone is gearing
up to get a direct measurement of the mass of muon neutrinos by measuring
the upper tail of the muon energy distribution from pion decay.
Steve Willner
ba...@galaxy.ucr.edu (John Baez) writes:
> There's not just one frequency, because there are 3 kinds of
> neutrinos, which oscillate into each other in rather complicated
> ways. It takes a total of 7 numbers to completely describe what's
> going on here - if the theory I'm describing is true.
Hi, John. Could you expand on this a bit more? I see the three
masses and three mixing angles, which have something to do with how
fast the flavors oscillate. (Maybe you have a better qualitative
explanation?) But what's the seventh number? Or am I on the wrong
track entirely?
--
Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)
Dave Hilbert
>If you could measure all the other particles in
>the interaction that produces the neutrino, with
>sufficient precision to determine (by energy and
>momentum conservation) which mass state the
>neutrino is in, then you will not observe any
>oscillations.
Is this really true? The only way I know to
produce a neutrino is using the weak
interaction. The weak interaction, by definition,
produces weak eigenstates that are superpostions
of the mass eigenstates.
Dave (?)
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Dave Hilbert
*** Friday, John Baez allegedly wrote ***
>>A strange quark can decay into a normal quark:
>>is this essentially the same phenomenon as
>>neutrino oscillation?
>
>No: when a strange quark decays into a down quark
>it emits a Z boson. This is called a
>"flavor-changing weak interaction". There is
>something quarks can do that's related to
>neutrino oscillations, but it's not this.
Flavor-changing neutral currents (FCNC) is the
jargon I've heard for a strange->down quark
transition. And I think FCNC only happens in
"penguin diagrams"[*]. Emitting a Z boson doesn't
change a quarks flavor - sort of like a photon. If
you followed LEP or SLC, you never heard of
Z->up+strange.
When a strange quark decays to an up quark,
it just emits a W- boson. However, when
a bottom quark decays to and up or a strange
quark, a similar effect occurs as in the neutrino
oscillations. The bottom quark decays into a W-
boson and a superposition of up & charm quarks (&
top, but it's not kinematically allowable).
The reason we never hear about "quark mixing" is
that you'll never see a free quark on it's own, so
the masses of quarks are not well defined. But
mixing does occur with groups of quarks that do
have well defined masses.
It is interesting to note the convention for which
member of the SU(2) doublet gets the "mass
eigenstate=weak eigenstate" property. The nature
of the physics allows us to pick any 3 quarks to
have this property, and the physics community uses
the 3 *up-type* quarks.
Because neutrinos have mass, we have to make a
similar convention for the leptons. In this case,
the 3 *down-type* leptons (the electron, muon, tau)
are chosen.
Dave(?)
[*] Penguin is a spurious and unfortunate name for
this process and has no direct link to what is
happening. Rumor has it that the penguin diagrams
were named this way because of a bet between two
physicists.
An example of a penguin diagram is when the
strange quark emits a W- boson, becoming a virtual
up-type quark (either a top, charm, or up) for a
short time before it reabsorbs the W- boson to
become a down quark. During it's time as a
virtual up-type quark, the quark can emit a gluon
to carry away the excess energy. There are other
examples, as well.
Jon Bell
Dave Hilbert <wannado...@yahoo.com> wrote:
>*** Yesterday, Jon Bell allegedly wrote ***
>>
>>If you could measure all the other particles in the interaction that
>>produces the neutrino, with sufficient precision to determine (by energy
>>and momentum conservation) which mass state the neutrino is in, then you
>>will not observe any oscillations.
>
>Is this really true? The only way I know to produce a neutrino is using
>the weak interaction. The weak interaction, by definition, produces weak
>eigenstates that are superpostions of the mass eigenstates.
You cannot make the measurements necessary to determine the mass of the
neutrino until *after* the production interaction has taken place. You
need to know the energies and momenta of the other outgoing particles in
order to apply energy and momentum conservation. So you're not fixing the
neutrino state to be in a mass eigenstate at the instant of production,
but a short time later, instead.
John Baez
Dave Hilbert <wannado...@yahoo.com> wrote:
>*** Friday, John Baez allegedly wrote ***
It wasn't really me, honest!
>>>A strange quark can decay into a normal quark:
>>>is this essentially the same phenomenon as
>>>neutrino oscillation?
>>No: when a strange quark decays into a down quark
>>it emits a Z boson.
See, that couldn't have been me.
Would I have written something so stupid???
YES.
Ugh!!!
>Emitting a Z boson doesn't change a quark's flavor -
>sort of like a photon.
Right. Sorry. I spent the morning at the Macquarie
University cafeteria reviewing this stuff, sipping a
coffee, and occasionally smashing my forehead against
the table to punish my brain for making such an idiotic
error. I think the buzzphrase "flavor-changing neutral
current" is what scrambled my thinking.
Repeat after me, brain:
A strange quark can decay into an up quark by emitting a W-.
It cannot decay into a down quark by emitting a Z.
Quarks can change flavor by their coupling to the W+ and W-
since these correspond to matrices that are not diagonal
in the flavor basis.
Quarks cannot change flavor by their coupling to the Z and photon
since these correspond to matrices are diagonal
in the flavor basis.
>If you followed LEP or SLC, you never heard of Z->up+strange.
I'm not such a practical down-to-earth person as to closely
follow what's going on at actual particle accelerators, alas.
Dave Hilbert
>In article <b3groq$40p$1...@lfa222122.richmond.edu>,
>determine the mass of the neutrino until *after*
>the production interaction has taken place. You
>need to know the energies and momenta of the
>other outgoing particles in order to apply energy
>and momentum conservation. So you're not fixing
>the neutrino state to be in a mass eigenstate at
>the instant of production, but a short time
>later, instead.
Are you saying that if X -> Y Z nu_weak, then the
moment I finish accurately measuring the momenta and
masses of X & Y & Z I will collapese nu_weak into a
mass eigenstate? Does this mean my mass measurement
can produce any of the 3 neutrino masses,
with the probability of measuring a particular
mass determined by the fraction that mass
eigenstate participates in nu_weak?
Mike Mowbray
>> [...] when a strange quark decays into a
>> down quark it emits a Z boson.
> See, that couldn't have been me.
> Would I have written something so stupid???
>
> YES.
>
> Ugh!!!
Oh, you're forgiven! I suspect a number of s.p.r.
readers besides me even feel slightly better about
themselves after seeing you make a mistake. :-)
>> Emitting a Z boson doesn't change a quark's flavor
>> - sort of like a photon.
> Right. Sorry. I spent the morning at the Macquarie
> University cafeteria reviewing this stuff,
My main reason for posting this reply is to ask you
which books/papers you find most useful for doing such
revision? (I'm feeling the need to do a bit myself.)
> [...] and occasionally smashing my forehead
> against the table to punish my brain for
> making such an idiotic error.
It doesn't work (speaking from much experience).
But I guess none of us will forget this little fact
in a hurry. I just hope it wasn't caused by the
Sydney environment or else I'm in deep trouble. :-)
- MikeM.
Jon Bell
Dave Hilbert <wannado...@yahoo.com> wrote:
>
>Are you saying that if X -> Y Z nu_weak, then the
>moment I finish accurately measuring the momenta and
>masses of X & Y & Z I will collapese nu_weak into a
>mass eigenstate?
Right, assuming you accept the "collapse of the wave function"
interpretation of quantum mechanics, in general.
>Does this mean my mass measurement
>can produce any of the 3 neutrino masses,
>with the probability of measuring a particular
>mass determined by the fraction that mass
>eigenstate participates in nu_weak?
That's how I figure it, based on my understanding of the way that
measurements on superposed states in general work in QM. In practice,
it's probably extremely unlikely that we'll ever be able to observe this
behavior directly in neutrinos.
John Baez
Mike Mowbray <mi...@despammed.com> wrote:
>John Baez wrote:
> > Ugh!!!
>Oh, you're forgiven! I suspect a number of s.p.r.
>readers besides me even feel slightly better about
>themselves after seeing you make a mistake. :-)
I'm sure - and all those good feelings, totalled up, probably
equal just about how bad I felt. Conservation of happiness
strikes again.
> >> Emitting a Z boson doesn't change a quark's flavor
> >> - sort of like a photon.
> > Right. Sorry. I spent the morning at the Macquarie
> > University cafeteria reviewing this stuff,
>My main reason for posting this reply is to ask you
>which books/papers you find most useful for doing such
>revision? (I'm feeling the need to do a bit myself.)
If I'd been able to get ahold of them, I would have used
one of these:
Kerson Huang, Quarks, Leptons & Gauge Fields, World Scientific, 1982.
L. B. Okun, Leptons and Quarks, translated from Russian by V. I.
Kisin, North-Holland, 1982.
K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear,
Particle, and Astrophysics, Hilger, Bristol, 1990.
Huang's book is a great way to learn about the Standard Model.
Okun's book is better on the experimental side of things.
Grotz is great for the weak force and neutrinos. Unfortunately
all three books are too old to cover the latest discoveries about
neutrino oscillations.
But, I wasn't able to find any of these books at Macquarie U.,
so I used two books I like a lot less.
Aaron Bergman
In article <b469li$m3h$1...@glue.ucr.edu>, John Baez wrote:
>
> If I'd been able to get ahold of them, I would have used
> one of these:
I like Chris Quigg's book, myself. Huang is pretty good, too
Aaron
John Baez
Steve Willner <wil...@cfa.harvard.edu> wrote:
>In article <b34jbu$4l2$1...@glue.ucr.edu>,
> ba...@galaxy.ucr.edu (John Baez) writes:
>> There's not just one frequency, because there are 3 kinds of
>> neutrinos, which oscillate into each other in rather complicated
>> ways. It takes a total of 7 numbers to completely describe what's
>> going on here - if the theory I'm describing is true.
>Hi, John. Could you expand on this a bit more? I see the three
>masses and three mixing angles, which have something to do with how
>fast the flavors oscillate. (Maybe you have a better qualitative
>explanation?) But what's the seventh number? Or am I on the wrong
>track entirely?
Sorry for taking so long to reply... I'm afraid you're on a bit
of a wrong track. I wanted to give you a really good explanation,
but it's not so easy! So, I kept putting it off. But here goes:
There are 3 kinds of neutrino:
electron neutrino
mu neutrino
tau neutrino
It takes 3 numbers to describe their masses. But, the neutrino
states having a definite mass are not the same as the states
have a definite flavor! Mathematically, we have a 3-dimensional
complex vector space with two orthonormal bases: the "mass
eigenstate basis"
e_1, e_2, e_3
and the "flavor eigenstate basis"
f_1, f_2, f_3
They are related by a 3x3 unitary matrix U:
Ue_i = f_i
This matrix is called the Maki-Nakagawa-Sakata matrix - if you want
to show off to your friends, say *that* three times fast! Besides
the masses of the neutrinos, it's the numbers in this matrix that
describe the phenomenon of neutrino oscillations in the new Standard
Model.
Now, to describe the unitary 3x3 matrix U involves a total of 9 real
parameters. But, without changing the physics we can redefine the
mass eigenstate basis by multiplying each basis element by a
phase - for a total of 3 phases. Similarly, without changing the
physics we can redefine the flavor eigenstate by multiplying each
basis element by a phase - for a total of 3 more phases. These
phases corresponds to ways of changing the matrix U without changing
the physics. But if we multiply *all* the basis elements by the
*same* phase, the matrix U doesn't change at all. So, while it takes
9 parameters to describe the matrix U, only 9 - 3 - 3 + 1 = 4 of these
parameters actually affect the physics.
That's where the number 4 comes from!
For extra fun, we can see how this would work for N generations
of neutrinos. There would then be N masses. The NxN unitary matrix
U would take N^2 real parameters to describe, but there would be only
N^2 - N - N + 1 = (N - 1)^2
parameters that actually affect the physics. So, N masses and
(N - 1)^2 extra numbers describing oscillations.
All this stuff works for quarks as well as leptons, but then the
matrix U is called the Cabibbo-Kobayashi-Maskawa matrix.
A neat thing about these matrices is that if their entries can all
be made real (after multiplying by suitable phases as described
above), there is no violation of time reversal symmetry in the
Standard Model. But if we can't get all their entries to be real,
time reversal symmetry is violated! Particles know the difference
between past and future!
If there were only 2 generations of quarks and leptons, we could
always get the entries to be real. Thus, there would be no violation
of time reversal symmetry. But, time reversal symmetry is observed
to occur in the physics of kaons!
This led Kobayashi and Maskawa to predict in 1973 that there were
3 generations of quarks and leptons. In 1975 they were proven
correct when Perl and collaborators discovered the tau. By now
we have seen all the particles in the 3rd generation: tau and tau
neutrino, top and bottom quark.
Interestingly, however, the Cabibbo-Kobayashi-Maskawa matrix is *very*
close to being real... so close that we're still not 100% sure that
this matrix is truly the explanation of the difference between future
and past in the standard model. The
If you want to actually see the numbers in the Cabibbo-Kobayashi-Maskawa
matrix, look at this:
http://www-pdg.lbl.gov/1999/kmmixrpp.pdf
You'll see they look like real numbers to within current experimental
limits. For the complete state of the art on this matrix as of 2000,
see:
http://arxiv.org/abs/hep-ph/0001293
The Maki-Nakagawa-Sakata matrix is much less well known, since
our only source of information about it is neutrino oscillation
experiments, which are very hard to do.