Some of these. Okay.
Thanks, Dave. Um, yeah. It's a great pleasure and indeed an honour to be here.
So celebrate, uh, Don's career. And it's lovely to see so many, uh, old friends here in the audience.
Um. Special thanks.
Go to Bill Scott, of course, both for the the collaboration over many years and for specific recollections, um, that he passed on to me for this talk.
So, um. Uh, Don retired, I think, in 1992.
And from 1994 to 2002, Don and I and Bill Scott collaborated on five phenomenal phenomenology papers, uh, which, uh,
we we attempted to understand the the large array of, um, uh,
neutrino oscillation data that was started to come in and put, know, impose some sort of order in it.
So of course, the only people to do to attempt to do that, but I think we had some success and,
um, I hope to convey some of the interest of that and also,
um, some of the impact that that had in terms of perhaps the feedback that we've received and whatever.
So, um, I don't firstly, I'm Mark prepared the ground very well for me.
Um, I didn't meet Don until 1994 when he was already retired.
Um, and so, uh, I've enjoyed very much hearing about what he did before I was born and when I was still in short trousers.
And so, uh, I was asked to cover a little bit of what happened at the beginning.
And as Mark said, he worked on these proton decay experiments to don one to shoot on to.
And he really championed the importance of the atmospheric neutrinos, um, as the background, uh, in proton decay.
And so as part of that, he pioneered and helped helped, uh, push the calculations of atmospheric neutrino fluxes,
which became very important, as Marcus alluded to, for other reasons.
Um, a quote here from this, uh, proton decay experiments, um, review, which Mark already mentioned from 1984.
Um, the dominant background of proton decay experiments is due to atmospheric neutrinos,
which the ultimate limiting factor determining the sensitivity to proton lifetimes.
It's become abundantly clear that a proper understanding of this background is at least 90% of the battle to discover a proton decay signal.
You can kind of imagine him saying that over coffee to to mark at some point.
Um, so the context before, just before I met Don, uh, towards the end of 1993, say was we'd had, uh, something like 25 years of the Homestake, uh,
solar neutrino, uh, experiment,
which I remember as an undergraduate being told there's only a third as many neutrinos coming from the sun as expected.
And that was, uh, that was in the late, uh, that was in the early 80s.
Um, so it was already known then. And, um, uh, these, these experiments went on and on, of course, and proved to be perfectly correct.
And they've, of course, took a major part in proving that they were correct.
Uh, but, uh, later in the early 90s, the gallium experiment started, uh, producing results sage and galaxies and, uh, candy.
Candy, of course, the, uh, the water tank off detector and they all or they also saw deficits,
although they rather than seeing about a third, they saw some something around point six of the expected flux.
The generally accepted theoretical solution, uh, for this was the small so-called small angle MSW effect, a very,
uh, subtle and intricate effect to do with the the interactions of neutrinos in the sun as they're coming out.
Um, so the first signs of issues with the atmospheric neutrinos.
Uh, there's this paper from 1988 here. And you can see that the, um, this is as a function of momentum, the, the the, uh,
block histogram is the, the prediction from Monte Carlo, and the data points are clear.
The electron seems to be propagating perfectly fine and uh, on suppressed.
But the mean once again you sort of thinking about 0.6, although the errors are very large.
So Don of course was involved in this. He did some calculations and he wrote this paper, uh, the atmospheric neutrino problem, a critique.
And from the abstract he said interpretations in terms of neutrino oscillations are correspondingly dubious.
So what happened to turn that situation around in Dong's mind?
Uh, so really, this was when I started getting involved in the business, summer 1994, the turning point.
Um, so Bill Scott and I had been discussing, uh, actually, uh, mixing, um, theories about mixing for, for donkey's years, actually.
And in 1994, we published our first paper, phenomenology paper proposing, uh, quite uh uh, it was,
it was quite out there, really try maximum mixing of the corks and I'll explain what tri maximum mixing is in a minute.
Um, but the idea was, would be that the all the mix angles were equal, essentially, and that the low energy mixing that we see today is to do with,
uh, with radiative corrections and running, essentially running coupling constants with driving the small mixing angles down.
Anyway. Um, so that was where I came into business.
And then at the end of June. There was the neutrino 94 conference in a lot, and they were updated solar neutrino results from several experiments.
And these firmed up these measurements that seem to imply that the suppression was down to about point six of expectation.
And so shortly after that conference, really, uh, Bill and I realised that, uh,
tri Maxwell mixing could actually rather be applied to the neutrinos rather than the quarks.
And that that would be a much more sensible thing to do, because at least there was some sign of large mixing angles,
potentially both in the solar neutrinos and in the atmospheric neutrinos.
We weren't the first people to suggest that about 4 or 5 authors in the previous 20 years had suggested that perhaps,
uh, neutrinos or leptons could have large rectangles, maximum mixing angles.
But we were the people, I think, at the time who picked that up and ran with it.
When the when the data started saying something exciting was happening.
Uh, so then we came to the conference here in the UK, Glasgow, and Don was there, I was there, Bill was there.
And of course we actually got talking. Uh, I'd never met Don before bill introduced me and uh, we got talking of course, about the neutrino results.
There were new atmospheric neutrino results. And, um, there was this fantastic result, which, you know, I still remember, just like it was yesterday.
This.
So this what this is it's the ratio of the muon to the electron, uh, rates, um, in data divided by the expectation of that ratio from Monte Carlo.
So of course this should be unity everywhere. And it's plotted as a function of cos theta.
So one is the downward going neutrinos. They just travelled about ten kilometres from the upper atmosphere.
Minus one is the upward going neutrinos. They've travelled through the Earth.
They've gone about 10 or 15,000km whatever.
And of course, the ones that are travelling a long way are suppressed away down with, with pretty good errors.
So no longer was there any kind of, uh, there wasn't a serious, uh, dependence on normalisation.
This is a self normalising curve because the one is fixed by the right hand end of the curve.
Okay. So Don said, and I remember him saying, I've become more convinced maybe there's neutrino oscillations.
So this was the first part of the turning point. Um, Kyoto relaxed conference.
So many talks. He gave the latest results from Sage and Calix.
Um, we've been saying to Don, well, you know, I'll try maximal mixing scenario.
The suppression of the, uh, CO2 emission should be five nights.
They should be suppressed to 5/9 of the original. Right. And Don said he looked at the this table.
And there are two possible it's data over expectation.
There are two models, the expectation. So there's a little bit of difference between the middle column on the right hand column.
But basically Don said yep, the Gary Max fronts are really shouting five nights.
And you can hear him saying that I think anyone who's, uh, spent much time with Don.
So we go back to the, the the timeline, if you like, of 1994.
So we realise the opportunity uh, the of the Glasgow conference and we agree.
We talked a lot. It was very exciting. We agreed to form this collaboration, uh, after Donald retired.
So he, he remains a busy physicist. Certainly. Um, the collaboration was to try and show or demonstrate that they were actually large rectangles.
In fact, the try match more mixing might be the right answer. And we have, of course, a vested interest in that try.
Maximal mixing is a very symmetric, uh, maximal anything uh is a sign of a symmetry in principle in physics.
So the rest of the year we work together on this, uh, on, on a paper and on brought to that, uh,
a deep knowledge of atmospheric neutrino fluxes and his healthy scepticism having only just been converted to the cause.
So, um, what are our goals? Uh, well, of course, to fully embrace three flavours of neutrinos, most of the early work have been done.
A lot of work has been done with two flavours of neutrinos in the solar effect, and two flavours of neutrinos in the atmospheric situation.
Some people, of course, Roger Phillips included, had worked on three flavours neutrinos.
But this was the way to go. Of course, they were three families of neutrinos.
We wanted to understand all the essentially all the data on neutrino oscillations in a single unified framework.
Keep it as simple as possible, but not simpler. So what did that mean?
Of course, a three by three neutrino mixing matrix and two independent mass squared differences,
the third difference obviously being just the sum of the other two effectively.
And so we wanted to work within this theoretical framework.
We wanted to interpret the the theory visually.
And I'll discuss that in a few minutes. And also to be aware of the possibilities of new symmetries.
Everything in physics today has been governed by symmetries. Perhaps there were new symmetries in particular.
Try maximal mixing would need new symmetries.
So what is trying Maxwell mixing? The basic idea here is you have this uh, p m and s matrix.
The columns are labelled by the neutrino mass eigenstates one, two, three.
The rows are labelled by the flavour, the flavours E, mu and tau, and the omegas.
Here are just the complex cube roots of one. So of course you've got the one itself, Omega one and the number three.
Uh uh, distributed around the circle 120 degrees to each other.
All of them are of magnitude one. They simply have different phases.
And so the matrix, every element has got a magnitude one over root three and modulus one over root three.
And they all have different phases in such a way as to keep the rows and columns mutually orthogonal as they must be.
So that was the idea. What were the predictions of that? Well, essentially that there are universal survival probabilities for all flavours.
So the probability of each new we going to new E, which will become a function of L over years,
will seed minute should be the same as the probability of uh mew mew mew mew.
That's to say, the ones which don't oscillate uh, are equal.
And you know, the probability for new targets, new, tough, eminently testable.
So what is this? This is just a cosine squared off on a little bit of a pedestal.
That's the prediction from um try match mixing threes.
All right. So mixing as we call it in those things. And it's not very helpful.
And it looks pretty horrible. And the one of the problems is we're going from not 50,000 in kilometres per GV.
And that doesn't cover all the possibilities for all the experiments.
So you put it on a log scale, log scale. You can go as far as you like to infinity, but of course your solutions get bunched up on the right hand end.
We were the first people to do this, so this is quite well known in the literature from the early 80s,
is full of plots like this from Roger Phillips and others. Um, what thing we think that I think was, was very important.
Here is all the experiments have a resolution that the blue curve is just the theory.
Experiments have a resolution I put on here three Gaussians.
They look asymmetric because the log plot, they're all 30% width.
But the point is when you measure the energy, your error is in a is a percentage.
So the width on the log scale is constant. Okay.
So you can see that the nice yellow one that doesn't even enclose the whole oscillation,
um, a whole oscillation cycle, the red one on the other hand is enclosing dozens.
Okay. So the oscillations are completely washed out by the resolution at the right hand end, but not at the left hand.
And so what does that do? What it means.
And I've expanded the yellow scale here a little bit.
You've got a threshold here, uh, a single uh, reduction to a new to a plateau in try maximum mixing with plateau 5/9 height.
Um. So the top bar of this is, I don't know.
Yeah. The top that measures the mixing angles in some function of the mixing angles and the position along here.
It's reciprocal. Is the delta m squared for the neutrino mass squared difference.
So these are the observables potentially that can be a second threshold for the second squared difference.
Going to a new plateau level.
And that second plateau level also measures a function of the the mass square differences I mean try by Maxwell is five minus methods.
So that's what I've drawn. Okay. So here's the data confronting the theory.
And on this plot, essentially all the neutrino oscillation data in 1994 are shown.
Um, you start off with the accelerators. Yeah. So this is also a function of l overy so small.
E goes to the right and largely goes to the left. So your accelerators at the right, the subtle ones.
Sorry. Yeah. Accelerator neutrinos are on the left. So the neutrinos are on the right.
Partly because they're low energy, but partly also because they have very low. The sun's a very long way away.
Then you have the reactor. So the accelerator mostly will be muon neutrinos, the reactors.
Electromagnetic neutrinos. Atmospheric. Well, there's it's actually the double ratio that's plotted here with some corrections.
Um, so that's mu over three. So muon and electron neutrinos essentially.
And so of course the solar neutrinos, electron neutrinos and they all fit except this one point, this triangular point here.
That's the the third from the home state, the longest standing one.
Um, so we took the view here.
That is, a lot of physicists took the view that this might actually be be not right.
It would have been going for 25, 30 years.
And we essentially took a gamble, I suppose, that there would be no energy dependence here, that this would be a long plateau.
Eventually that would be another threshold going down to a third. But that the data didn't.
Once you go down to a third here, at least in vacuum oscillations, you can't go back to five nights.
So that's why we discounted this point essentially. And the chi squared excluding that point was a very good fit.
20.5 over 28 for all the points.
So. Well it worked. Uh, that was our first fit of the neutrino.
A massive difference in difference. And delta and prime delta m prime squared was unresolved.
And as I promised, I wanted to, uh, illustrate some of the impact we had.
Um, Luciano Mariani at the. It's, uh, we contractions of neutrinos conference in 1997 dubbed this this wonderful plot.
So, of course, we don't usually hear what people think of your work,
but if you happen to be in the audience, you sometimes, you know, that's nice to hear.
Okay, we got some more nice feedback now. This was one was interesting, joked Harrison.
This was, uh, I didn't know John Bacall. John Bacall was the father of the standard Solow model, essentially,
and he spent many years of his career calculating the rate of solid neutrinos, which form the denominator for all the solar neutrino experiments.
And he said, I think you must have just addressed it to me, because mine was the first name on the paper and he knew Don.
He's like me, and I didn't know if you wrote me your preprint with Perkins.
Scott is extremely interesting to me. It's a very nice idea, well argued and presented.
I don't think he really liked it because he liked the Mass Effect.
And of course we said there's no Mass Effect, but he was being very polite and very, very proper.
Um, so we wrote back and in fact, we had quite a correspondence with him, and Don wrote to him.
Um, and that was all very nice. So just as a sort of interlude.
So a little bit about working with Don, I don't remember getting emails from Don.
Maybe I got some I haven't looked because I've moved universes.
I can't get his email accounts. I do have an archive somewhere, but I got letters from Don.
Loads of letters, letters and faxes. Okay, we have mobile phones in those days.
So, um, gentleman to Paul and go gentleman his his, uh, my offering on the paragraph on atmospheric neutrino oscillations in his inimitable hand.
And this one, this is my favourite one over here. I'll. You stand an extra chance of being sued.
Was with was his reaction to one of our drafts.
He felt that we hadn't given due credit to one of the experiments.
Well, I'm sure he was right. And Don was very good at holding our feet to the fire and, uh, keep us focussed while keeping us on the ground, actually,
because Bill and I have a tendency to to go off into more, uh, more theoretical directions, which perhaps weren't warranted.
So I learned. Of course, I learned a vast amount from Donna.
It was a great thing. Um, so our second paper was this no mystery.
So no matter of fact, in Maxwell mixing, actually, specifically in two fold.
Maxwell mixing, uh, in the sun.
So we were saying that if, uh, Tri Maxwell mixing was correct, there would be no matter, in fact, in the sun and there would be no dip.
And the one on the right looks a bit like the one you've seen already,
but it's actually plotted as delta m prime squared every, not all over it, because the distance the sun is fixed.
We know that. So you just put L fixed and then you can make the plot.
So what we did we did a computer program and we uh, we simulated essentially we we integrated the propagation equations,
including the matter of fact and um, starting off with actually in vacuum with no much effect.
And the physics here is that because the mixing angles, theta 12.79 is, uh, one over three value for the mixing angle.
And uh, this one is a smaller angle and this one is a bigger angle.
And you see that three of those, you get less suppression. So Maxwell mixing had the most suppression.
But if you have a small angle, if you're coming out of the sun and the density is changing slowly as you propagate out of the sun,
then essentially the, um, the mixing angles change with time.
You get this dramatic, uh, change of electron neutrinos into into muon neutrinos, and you get a deficit here.
And this deficit can actually go to essentially as close to zero as you like the smaller mixing angle,
the lower down this gets and there's an inverse deficit, uh, an increase if the angles get bigger than actually, uh, sine one over root three.
So for bigger mixing angles you get this anti MSW suppression.
And we said look in the vacuum in the story in the three fold Maxwell mixing case alone.
The third is completely unaltered.
There is no match effect uniquely in Maxwell mixing actually two full much mixing and to some extent in the for Max Maxwell mixing as seen here.
Um. So I didn't leave the conclusion.
We also put in the paper little explanation of this as an analogy with the diabetic flip of a, um, a spin half magnetic moment and jump call.
This time you send us an email.
Uh, I was very surprised by the result, initially wondering if your computer program could possibly have been in error.
No, it wasn't in error, but the analogy with the spin off dipole in the magnetic field is very convincing.
Quite a remarkable result. So again we bank this. This was a nice thing to be told.
Um, and you know, he liked the analogy, made it very clear.
Um, that's just a picture of the analogy.
So, um, we also made this prediction that, um, that there could be a five like one third, five months faster.
We didn't say it applied to the data at the time. Probably we should have done it.
Uh, it wouldn't have helped. Actually.
It wouldn't have helped because we were still selling three fold, much more mixing, which turned out to be wrong as it happened.
But I think all this, you know, the paper generated a lot of excitement, a lot of interest, and got people thinking about this and that.
That's part of the legacy, I think. So, um, as I've said, I've just put on this these point data points weren't put on at the time.
These are the, the modern, uh, the the modern points, the, the error bars are roughly comparable to the size of the points.
I didn't it's just a sketch really, but it shows, um, that you've walked, uh, snow, uh,
discovery essentially that we're in the large mixing mystery thing which which we kind of said,
well, this is what the bathtub will look like in the bath. We didn't like the name Bath tub.
I don't know who made who made the name bathtub, I have no idea. But anyway, um, we predicted at least a five nights, two bath tub.
Um, so I'm not going to talk very much about these two papers.
Uh, three and four. Um, the only thing to say is these are the four possibilities for what's happening at the solar scale,
at the far right and end of the US, which is three for maximum mixing.
Nothing interesting happening. These are the data points. Um, this is the small angle.
As I said, it could go to zero and then come back up. This is the large angle of view.
The five minutes to five nights bathtub.
And this is the so-called, uh, this is blackouts just so oscillations that even he said was fine tuned when he published it.
Um, but anyway, we felt these were fine tuned and say they were disfavoured.
Don't have an anecdote. He was in the US some years before I met him, and he was giving a talk, apparently explaining the MSW effect.
And Chandrasekhar was in the audience and Chandrasekhar says, yeah, leave that to you.
So, um, I don't know if that influenced on, but we we, you know, the fine tuning seemed to be an issue at least.
Oops. Coincidences do happen, but they don't happen so often.
Um, and our prediction here of this third paper was spectacular.
Effects will be expected. Long baseline reaction centre experiments choose Palo Verde, Minos, etc.
Uh, no spectacular effect. So this is the two reactor results.
It's um, uh, one kilometre three MeV energy.
No spectacular effect. So this trial, Maxwell mixing is wrong.
We were excluded from this point. Um, E3 squared has to be small.
Could be zero. Might be just. Just a small number. So that was the end of try.
Max might say that they've worked. Sno collaboration came out with this again,
a third confirming the Homestake third and putting the final nail in the coffin of Tiber Tri Maxwell mixing.
So I mean Maxwell mixing excluded. Long live tri by Maxwell mixing.
So the fifth and final paper I'm going to talk about today HP, S5.
Um, so data is king. We made a virtue of necessity and put out a new mass matrix.
Um, the the 5/9 to bath bathtub was in fact, uh, confirmed beautifully by snow.
And, um, uh, so I'm going to just mark the data point speak for themselves.
We originally had up to scratch the third. We still had u e2 square root of a third.
The super K atmospheric neutrino was strongly pointing to larger values.
Umu three and Utah three. I'll show you these on a actually on a on a matrix in a minute.
And so we accepted the half here. We accepted the third here.
And we accepted the previous zero, the very small number.
And that of course dictates the form of the matrix. So we had here the reactor max angle the show limit.
So this was either small or zero. If you got a number small in physics that could be anything.
It's probably zero. Or you've got a symmetry. Make it zero or maybe have a slightly broken symmetry.
The atmospheric new moon Utah maximal mixing here.
This is the two three scale for the atmospheric neutrinos.
The universal survival probability was no longer valid.
Uh, we had a solar mixing angle here that we still was saying should be one over three on aesthetic grounds
and a solar mass scale trials from one to square the five parameters of neutrino oscillations.
And we put in a little, uh, a little legal clause here, smaller non-zero values of E3 and somewhat different values.
If you if you use things that are more or less equally acceptable experimentally.
So we're pinning all colours to this masked world, allowing the possibility that we might be wrong.
It's a very sensible. Of course. Um.
I promised you. This is the only really mathematical slide, I hope.
Um, symmetries of tribal mixing,
as we know that the mixing matrix exists because the mass matrices of the two charge states in the doublets of the weak interaction.
Here the charged leptons and the nutrients have different forms.
They can't be diagonalised at the same time. And that then gives you a mixing.
And so what the way to build tri by Maxwell mixing here is you have what we call um a circulant matrix.
So this is simply invariant under the discrete transformation.
Generation one and two two goes to three and three goes to one cyclically doesn't change.
Okay. And if you do uh if you flip a pair it's complex conjugates.
This one it's invariant under one free interchange okay.
If you want to diagonalise that you use the original tri Maxwell matrix.
If you want to diagnose that, use A13 by Maxwell.
And you know, find together. This is what how you build the mixing matrix from a modal and you get a mixing matrix out.
Today's setting is a colloquium at CERN.
You can find the video of this bill. Scots very fond of showing people the idea of this because he says it's a tremendous achievement.
Um, I'm quite an exaggeration, I think, but, uh, although some, some, you know, we, we got we got people's attention at least.
So the future. Um.
This is, uh, the Juno experiment, which is another reactor experiment in China.
It's about to start taking data this year, any time now.
They are, amazingly, claiming that they're going to be sensitive to the atmospheric mass scale,
these short wavelength oscillations, while at the same time being sensitive to the solar scale, this long wavelength oscillation.
This is the survival probability of the electrons and neutrinos.
This is the appearance probability, the sort of complement of that.
And this I think the blue and the redder than normal in the inverted hierarchy, which is something that just the way the, the uh,
the mass uh eigenstates are ordered in the um for the neutrinos and they claim a 1% resolution Eui to del 21 squared and delta m three squared.
And, uh, they could resolve the question of the neutrino mass ordering of three sigma.
Uh, the Holy Grail for CP violation. Mark Thompson touched on this.
As you know, E3 is non-zero. Um, and all the other angles and non-zero.
That means you can have CP violation if the phase in the p, m and S matrix is non-zero and not equal to pi.
And these two experiments hyper k, I don't. My apologies to anyone who works on these because I don't know anything about them.
Um, but um, hyper K claim a five sigma level of sensitivity to CP violation over 57% of the range of the CP phase delta by after ten years of running.
And this is a truly an almost. It's like Minos that Mike was talking about bigger and much more powerful beam in Japan.
Mark. Mark mentioned June, of course, you guys involved in both these explosions, more in June and amazing.
They also have a five sigma sensitivity over 57% of the possible range.
Oh, for ten years. So this is a completely different experiment.
Different beam lines, different, uh, path lengths.
So they just happened to both come to exactly the same sensitivity.
Um, uh, coincidence? No doubt. So, um, my time is nearly up.
I just did want to say something about what I considered the legacy of this work.
Um, that Don, um, Bill and I did.
He decided to leave the collaboration on a high, um, making HB five his last publication with us.
Um, TBM was finally executed ten years later.
Um, so, um. Because as with the loud, the little pause for you is not to be zero.
It was executed by Daya, by Reno and to take um.
This single paper, Pierce five, has been cited by over 1500 phenomenology papers.
This is the citation count inspires or inspire hope, as they call it.
Now this is the paper. Yeah, this is about where we got excluded.
I was so [INAUDIBLE] up a few dozen citations a year, nearly all from Phenomenologist.
Why? Because they like the symmetric forms of mass matrices.
They suggest deeper symmetries and they can build, uh, they can build models whose end result is matrices with these symmetries that we discussed.
So I think that's that's an impact, as the politicians like to tell us, uh, it's purely an academic impact, but a very valuable one, I believe.
Um. 120 experimental publications cited five, including several of the proposals for the experiments that I've mentioned.
And um, I would say, uh, reflecting exactly what Mark said, I think when, when we when we started this in 1994,
the UK, uh, experimental neutrino community had shrunk over the years, and they came and joined us and other people.
And I think this work, many people have done a vast amount to build that up again.
But I think this work had a little bit to do with encouraging that from the start.
Um, this I love plot that we showed and variance of it, I think had a significant impact, as I think I've demonstrated.
And, uh, Bill and I have published 25 further papers on topics very closely related to this work.
And because you three square is non-zero, it does allow the possibility of CP violation in the future.
So, um, uh, all I'm done, all apart from uh, saying, you know, I'm extremely grateful to have had the opportunity to do this work with Don and Bill.
It was one of the most exciting parts of my career.
Thank you very much.